We consider the system h41.

  Alphabet:

    0 : [] --> A 
    active : [] --> A -> A 
    afterNth : [] --> A -> A -> A 
    app : [] --> (A -> A) -> A -> A 
    cons : [] --> A -> A -> A 
    fst : [] --> A -> A 
    head : [] --> A -> A 
    map : [] --> (A -> A) -> A -> A 
    mark : [] --> A -> A 
    natsFrom : [] --> A -> A 
    nil : [] --> A 
    pair : [] --> A -> A -> A 
    s : [] --> A -> A 
    sel : [] --> A -> A -> A 
    snd : [] --> A -> A 
    splitAt : [] --> A -> A -> A 
    tail : [] --> A -> A 
    take : [] --> A -> A -> A 
    tt : [] --> A 
    u11 : [] --> A -> A -> A -> A 
    u12 : [] --> A -> A -> A -> A 
    u21 : [] --> A -> A -> A 
    u22 : [] --> A -> A -> A 
    u31 : [] --> A -> A -> A 
    u32 : [] --> A -> A -> A 
    u41 : [] --> A -> A -> A -> A 
    u42 : [] --> A -> A -> A -> A 
    u51 : [] --> A -> A -> A 
    u52 : [] --> A -> A -> A 
    u61 : [] --> A -> A -> A -> A -> A 
    u62 : [] --> A -> A -> A -> A -> A 
    u63 : [] --> A -> A -> A -> A -> A 
    u64 : [] --> A -> A -> A 
    u71 : [] --> A -> A -> A 
    u72 : [] --> A -> A -> A 
    u81 : [] --> A -> A -> A -> A 
    u82 : [] --> A -> A -> A -> A 

  Rules:

    active (u11 tt x y) => mark (u12 tt x y) 
    active (u12 tt x y) => mark (snd (splitAt x y)) 
    active (u21 tt x) => mark (u22 tt x) 
    active (u22 tt x) => mark x 
    active (u31 tt x) => mark (u32 tt x) 
    active (u32 tt x) => mark x 
    active (u41 tt x y) => mark (u42 tt x y) 
    active (u42 tt x y) => mark (head (afterNth x y)) 
    active (u51 tt x) => mark (u52 tt x) 
    active (u52 tt x) => mark x 
    active (u61 tt x y z) => mark (u62 tt x y z) 
    active (u62 tt x y z) => mark (u63 tt x y z) 
    active (u63 tt x y z) => mark (u64 (splitAt x z) y) 
    active (u64 (pair x y) z) => mark (pair (cons z x) y) 
    active (u71 tt x) => mark (u72 tt x) 
    active (u72 tt x) => mark x 
    active (u81 tt x y) => mark (u82 tt x y) 
    active (u82 tt x y) => mark (fst (splitAt x y)) 
    active (afterNth x y) => mark (u11 tt x y) 
    active (fst (pair x y)) => mark (u21 tt x) 
    active (head (cons x y)) => mark (u31 tt x) 
    active (natsFrom x) => mark (cons x (natsFrom (s x))) 
    active (sel x y) => mark (u41 tt x y) 
    active (snd (pair x y)) => mark (u51 tt y) 
    active (splitAt 0 x) => mark (pair nil x) 
    active (splitAt (s x) (cons y z)) => mark (u61 tt x y z) 
    active (tail (cons x y)) => mark (u71 tt y) 
    active (take x y) => mark (u81 tt x y) 
    mark (u11 x y z) => active (u11 (mark x) y z) 
    mark tt => active tt 
    mark (u12 x y z) => active (u12 (mark x) y z) 
    mark (snd x) => active (snd (mark x)) 
    mark (splitAt x y) => active (splitAt (mark x) (mark y)) 
    mark (u21 x y) => active (u21 (mark x) y) 
    mark (u22 x y) => active (u22 (mark x) y) 
    mark (u31 x y) => active (u31 (mark x) y) 
    mark (u32 x y) => active (u32 (mark x) y) 
    mark (u41 x y z) => active (u41 (mark x) y z) 
    mark (u42 x y z) => active (u42 (mark x) y z) 
    mark (head x) => active (head (mark x)) 
    mark (afterNth x y) => active (afterNth (mark x) (mark y)) 
    mark (u51 x y) => active (u51 (mark x) y) 
    mark (u52 x y) => active (u52 (mark x) y) 
    mark (u61 x y z u) => active (u61 (mark x) y z u) 
    mark (u62 x y z u) => active (u62 (mark x) y z u) 
    mark (u63 x y z u) => active (u63 (mark x) y z u) 
    mark (u64 x y) => active (u64 (mark x) y) 
    mark (pair x y) => active (pair (mark x) (mark y)) 
    mark (cons x y) => active (cons (mark x) y) 
    mark (u71 x y) => active (u71 (mark x) y) 
    mark (u72 x y) => active (u72 (mark x) y) 
    mark (u81 x y z) => active (u81 (mark x) y z) 
    mark (u82 x y z) => active (u82 (mark x) y z) 
    mark (fst x) => active (fst (mark x)) 
    mark (natsFrom x) => active (natsFrom (mark x)) 
    mark (s x) => active (s (mark x)) 
    mark (sel x y) => active (sel (mark x) (mark y)) 
    mark 0 => active 0 
    mark nil => active nil 
    mark (tail x) => active (tail (mark x)) 
    mark (take x y) => active (take (mark x) (mark y)) 
    u11 (mark x) y z => u11 x y z 
    u11 x (mark y) z => u11 x y z 
    u11 x y (mark z) => u11 x y z 
    u11 (active x) y z => u11 x y z 
    u11 x (active y) z => u11 x y z 
    u11 x y (active z) => u11 x y z 
    u12 (mark x) y z => u12 x y z 
    u12 x (mark y) z => u12 x y z 
    u12 x y (mark z) => u12 x y z 
    u12 (active x) y z => u12 x y z 
    u12 x (active y) z => u12 x y z 
    u12 x y (active z) => u12 x y z 
    snd (mark x) => snd x 
    snd (active x) => snd x 
    splitAt (mark x) y => splitAt x y 
    splitAt x (mark y) => splitAt x y 
    splitAt (active x) y => splitAt x y 
    splitAt x (active y) => splitAt x y 
    u21 (mark x) y => u21 x y 
    u21 x (mark y) => u21 x y 
    u21 (active x) y => u21 x y 
    u21 x (active y) => u21 x y 
    u22 (mark x) y => u22 x y 
    u22 x (mark y) => u22 x y 
    u22 (active x) y => u22 x y 
    u22 x (active y) => u22 x y 
    u31 (mark x) y => u31 x y 
    u31 x (mark y) => u31 x y 
    u31 (active x) y => u31 x y 
    u31 x (active y) => u31 x y 
    u32 (mark x) y => u32 x y 
    u32 x (mark y) => u32 x y 
    u32 (active x) y => u32 x y 
    u32 x (active y) => u32 x y 
    u41 (mark x) y z => u41 x y z 
    u41 x (mark y) z => u41 x y z 
    u41 x y (mark z) => u41 x y z 
    u41 (active x) y z => u41 x y z 
    u41 x (active y) z => u41 x y z 
    u41 x y (active z) => u41 x y z 
    u42 (mark x) y z => u42 x y z 
    u42 x (mark y) z => u42 x y z 
    u42 x y (mark z) => u42 x y z 
    u42 (active x) y z => u42 x y z 
    u42 x (active y) z => u42 x y z 
    u42 x y (active z) => u42 x y z 
    head (mark x) => head x 
    head (active x) => head x 
    afterNth (mark x) y => afterNth x y 
    afterNth x (mark y) => afterNth x y 
    afterNth (active x) y => afterNth x y 
    afterNth x (active y) => afterNth x y 
    u51 (mark x) y => u51 x y 
    u51 x (mark y) => u51 x y 
    u51 (active x) y => u51 x y 
    u51 x (active y) => u51 x y 
    u52 (mark x) y => u52 x y 
    u52 x (mark y) => u52 x y 
    u52 (active x) y => u52 x y 
    u52 x (active y) => u52 x y 
    u61 (mark x) y z u => u61 x y z u 
    u61 x (mark y) z u => u61 x y z u 
    u61 x y (mark z) u => u61 x y z u 
    u61 x y z (mark u) => u61 x y z u 
    u61 (active x) y z u => u61 x y z u 
    u61 x (active y) z u => u61 x y z u 
    u61 x y (active z) u => u61 x y z u 
    u61 x y z (active u) => u61 x y z u 
    u62 (mark x) y z u => u62 x y z u 
    u62 x (mark y) z u => u62 x y z u 
    u62 x y (mark z) u => u62 x y z u 
    u62 x y z (mark u) => u62 x y z u 
    u62 (active x) y z u => u62 x y z u 
    u62 x (active y) z u => u62 x y z u 
    u62 x y (active z) u => u62 x y z u 
    u62 x y z (active u) => u62 x y z u 
    u63 (mark x) y z u => u63 x y z u 
    u63 x (mark y) z u => u63 x y z u 
    u63 x y (mark z) u => u63 x y z u 
    u63 x y z (mark u) => u63 x y z u 
    u63 (active x) y z u => u63 x y z u 
    u63 x (active y) z u => u63 x y z u 
    u63 x y (active z) u => u63 x y z u 
    u63 x y z (active u) => u63 x y z u 
    u64 (mark x) y => u64 x y 
    u64 x (mark y) => u64 x y 
    u64 (active x) y => u64 x y 
    u64 x (active y) => u64 x y 
    pair (mark x) y => pair x y 
    pair x (mark y) => pair x y 
    pair (active x) y => pair x y 
    pair x (active y) => pair x y 
    cons (mark x) y => cons x y 
    cons x (mark y) => cons x y 
    cons (active x) y => cons x y 
    cons x (active y) => cons x y 
    u71 (mark x) y => u71 x y 
    u71 x (mark y) => u71 x y 
    u71 (active x) y => u71 x y 
    u71 x (active y) => u71 x y 
    u72 (mark x) y => u72 x y 
    u72 x (mark y) => u72 x y 
    u72 (active x) y => u72 x y 
    u72 x (active y) => u72 x y 
    u81 (mark x) y z => u81 x y z 
    u81 x (mark y) z => u81 x y z 
    u81 x y (mark z) => u81 x y z 
    u81 (active x) y z => u81 x y z 
    u81 x (active y) z => u81 x y z 
    u81 x y (active z) => u81 x y z 
    u82 (mark x) y z => u82 x y z 
    u82 x (mark y) z => u82 x y z 
    u82 x y (mark z) => u82 x y z 
    u82 (active x) y z => u82 x y z 
    u82 x (active y) z => u82 x y z 
    u82 x y (active z) => u82 x y z 
    fst (mark x) => fst x 
    fst (active x) => fst x 
    natsFrom (mark x) => natsFrom x 
    natsFrom (active x) => natsFrom x 
    s (mark x) => s x 
    s (active x) => s x 
    sel (mark x) y => sel x y 
    sel x (mark y) => sel x y 
    sel (active x) y => sel x y 
    sel x (active y) => sel x y 
    tail (mark x) => tail x 
    tail (active x) => tail x 
    take (mark x) y => take x y 
    take x (mark y) => take x y 
    take (active x) y => take x y 
    take x (active y) => take x y 
    map (/\x.f x) nil => nil 
    map (/\x.f x) (cons y z) => cons (f y) (map (/\u.f u) z) 
    app (/\x.f x) y => f y 

Using the transformations described in [Kop11], this system can be brought in a form without leading free variables in the left-hand side, and where the left-hand side of a variable is always a functional term or application headed by a functional term.

We now transform the resulting AFS into an AFSM by replacing all free variables by meta-variables (with arity 0).  This leads to the following AFSM:

  Alphabet:

    0 : [] --> A 
    active : [A] --> A 
    afterNth : [A * A] --> A 
    app : [A -> A * A] --> A 
    cons : [A * A] --> A 
    fst : [A] --> A 
    head : [A] --> A 
    map : [A -> A * A] --> A 
    mark : [A] --> A 
    natsFrom : [A] --> A 
    nil : [] --> A 
    pair : [A * A] --> A 
    s : [A] --> A 
    sel : [A * A] --> A 
    snd : [A] --> A 
    splitAt : [A * A] --> A 
    tail : [A] --> A 
    take : [A * A] --> A 
    tt : [] --> A 
    u11 : [A * A * A] --> A 
    u12 : [A * A * A] --> A 
    u21 : [A * A] --> A 
    u22 : [A * A] --> A 
    u31 : [A * A] --> A 
    u32 : [A * A] --> A 
    u41 : [A * A * A] --> A 
    u42 : [A * A * A] --> A 
    u51 : [A * A] --> A 
    u52 : [A * A] --> A 
    u61 : [A * A * A * A] --> A 
    u62 : [A * A * A * A] --> A 
    u63 : [A * A * A * A] --> A 
    u64 : [A * A] --> A 
    u71 : [A * A] --> A 
    u72 : [A * A] --> A 
    u81 : [A * A * A] --> A 
    u82 : [A * A * A] --> A 
    ~AP1 : [A -> A * A] --> A 

  Rules:

    active(u11(tt, X, Y)) => mark(u12(tt, X, Y)) 
    active(u12(tt, X, Y)) => mark(snd(splitAt(X, Y))) 
    active(u21(tt, X)) => mark(u22(tt, X)) 
    active(u22(tt, X)) => mark(X) 
    active(u31(tt, X)) => mark(u32(tt, X)) 
    active(u32(tt, X)) => mark(X) 
    active(u41(tt, X, Y)) => mark(u42(tt, X, Y)) 
    active(u42(tt, X, Y)) => mark(head(afterNth(X, Y))) 
    active(u51(tt, X)) => mark(u52(tt, X)) 
    active(u52(tt, X)) => mark(X) 
    active(u61(tt, X, Y, Z)) => mark(u62(tt, X, Y, Z)) 
    active(u62(tt, X, Y, Z)) => mark(u63(tt, X, Y, Z)) 
    active(u63(tt, X, Y, Z)) => mark(u64(splitAt(X, Z), Y)) 
    active(u64(pair(X, Y), Z)) => mark(pair(cons(Z, X), Y)) 
    active(u71(tt, X)) => mark(u72(tt, X)) 
    active(u72(tt, X)) => mark(X) 
    active(u81(tt, X, Y)) => mark(u82(tt, X, Y)) 
    active(u82(tt, X, Y)) => mark(fst(splitAt(X, Y))) 
    active(afterNth(X, Y)) => mark(u11(tt, X, Y)) 
    active(fst(pair(X, Y))) => mark(u21(tt, X)) 
    active(head(cons(X, Y))) => mark(u31(tt, X)) 
    active(natsFrom(X)) => mark(cons(X, natsFrom(s(X)))) 
    active(sel(X, Y)) => mark(u41(tt, X, Y)) 
    active(snd(pair(X, Y))) => mark(u51(tt, Y)) 
    active(splitAt(0, X)) => mark(pair(nil, X)) 
    active(splitAt(s(X), cons(Y, Z))) => mark(u61(tt, X, Y, Z)) 
    active(tail(cons(X, Y))) => mark(u71(tt, Y)) 
    active(take(X, Y)) => mark(u81(tt, X, Y)) 
    mark(u11(X, Y, Z)) => active(u11(mark(X), Y, Z)) 
    mark(tt) => active(tt) 
    mark(u12(X, Y, Z)) => active(u12(mark(X), Y, Z)) 
    mark(snd(X)) => active(snd(mark(X))) 
    mark(splitAt(X, Y)) => active(splitAt(mark(X), mark(Y))) 
    mark(u21(X, Y)) => active(u21(mark(X), Y)) 
    mark(u22(X, Y)) => active(u22(mark(X), Y)) 
    mark(u31(X, Y)) => active(u31(mark(X), Y)) 
    mark(u32(X, Y)) => active(u32(mark(X), Y)) 
    mark(u41(X, Y, Z)) => active(u41(mark(X), Y, Z)) 
    mark(u42(X, Y, Z)) => active(u42(mark(X), Y, Z)) 
    mark(head(X)) => active(head(mark(X))) 
    mark(afterNth(X, Y)) => active(afterNth(mark(X), mark(Y))) 
    mark(u51(X, Y)) => active(u51(mark(X), Y)) 
    mark(u52(X, Y)) => active(u52(mark(X), Y)) 
    mark(u61(X, Y, Z, U)) => active(u61(mark(X), Y, Z, U)) 
    mark(u62(X, Y, Z, U)) => active(u62(mark(X), Y, Z, U)) 
    mark(u63(X, Y, Z, U)) => active(u63(mark(X), Y, Z, U)) 
    mark(u64(X, Y)) => active(u64(mark(X), Y)) 
    mark(pair(X, Y)) => active(pair(mark(X), mark(Y))) 
    mark(cons(X, Y)) => active(cons(mark(X), Y)) 
    mark(u71(X, Y)) => active(u71(mark(X), Y)) 
    mark(u72(X, Y)) => active(u72(mark(X), Y)) 
    mark(u81(X, Y, Z)) => active(u81(mark(X), Y, Z)) 
    mark(u82(X, Y, Z)) => active(u82(mark(X), Y, Z)) 
    mark(fst(X)) => active(fst(mark(X))) 
    mark(natsFrom(X)) => active(natsFrom(mark(X))) 
    mark(s(X)) => active(s(mark(X))) 
    mark(sel(X, Y)) => active(sel(mark(X), mark(Y))) 
    mark(0) => active(0) 
    mark(nil) => active(nil) 
    mark(tail(X)) => active(tail(mark(X))) 
    mark(take(X, Y)) => active(take(mark(X), mark(Y))) 
    u11(mark(X), Y, Z) => u11(X, Y, Z) 
    u11(X, mark(Y), Z) => u11(X, Y, Z) 
    u11(X, Y, mark(Z)) => u11(X, Y, Z) 
    u11(active(X), Y, Z) => u11(X, Y, Z) 
    u11(X, active(Y), Z) => u11(X, Y, Z) 
    u11(X, Y, active(Z)) => u11(X, Y, Z) 
    u12(mark(X), Y, Z) => u12(X, Y, Z) 
    u12(X, mark(Y), Z) => u12(X, Y, Z) 
    u12(X, Y, mark(Z)) => u12(X, Y, Z) 
    u12(active(X), Y, Z) => u12(X, Y, Z) 
    u12(X, active(Y), Z) => u12(X, Y, Z) 
    u12(X, Y, active(Z)) => u12(X, Y, Z) 
    snd(mark(X)) => snd(X) 
    snd(active(X)) => snd(X) 
    splitAt(mark(X), Y) => splitAt(X, Y) 
    splitAt(X, mark(Y)) => splitAt(X, Y) 
    splitAt(active(X), Y) => splitAt(X, Y) 
    splitAt(X, active(Y)) => splitAt(X, Y) 
    u21(mark(X), Y) => u21(X, Y) 
    u21(X, mark(Y)) => u21(X, Y) 
    u21(active(X), Y) => u21(X, Y) 
    u21(X, active(Y)) => u21(X, Y) 
    u22(mark(X), Y) => u22(X, Y) 
    u22(X, mark(Y)) => u22(X, Y) 
    u22(active(X), Y) => u22(X, Y) 
    u22(X, active(Y)) => u22(X, Y) 
    u31(mark(X), Y) => u31(X, Y) 
    u31(X, mark(Y)) => u31(X, Y) 
    u31(active(X), Y) => u31(X, Y) 
    u31(X, active(Y)) => u31(X, Y) 
    u32(mark(X), Y) => u32(X, Y) 
    u32(X, mark(Y)) => u32(X, Y) 
    u32(active(X), Y) => u32(X, Y) 
    u32(X, active(Y)) => u32(X, Y) 
    u41(mark(X), Y, Z) => u41(X, Y, Z) 
    u41(X, mark(Y), Z) => u41(X, Y, Z) 
    u41(X, Y, mark(Z)) => u41(X, Y, Z) 
    u41(active(X), Y, Z) => u41(X, Y, Z) 
    u41(X, active(Y), Z) => u41(X, Y, Z) 
    u41(X, Y, active(Z)) => u41(X, Y, Z) 
    u42(mark(X), Y, Z) => u42(X, Y, Z) 
    u42(X, mark(Y), Z) => u42(X, Y, Z) 
    u42(X, Y, mark(Z)) => u42(X, Y, Z) 
    u42(active(X), Y, Z) => u42(X, Y, Z) 
    u42(X, active(Y), Z) => u42(X, Y, Z) 
    u42(X, Y, active(Z)) => u42(X, Y, Z) 
    head(mark(X)) => head(X) 
    head(active(X)) => head(X) 
    afterNth(mark(X), Y) => afterNth(X, Y) 
    afterNth(X, mark(Y)) => afterNth(X, Y) 
    afterNth(active(X), Y) => afterNth(X, Y) 
    afterNth(X, active(Y)) => afterNth(X, Y) 
    u51(mark(X), Y) => u51(X, Y) 
    u51(X, mark(Y)) => u51(X, Y) 
    u51(active(X), Y) => u51(X, Y) 
    u51(X, active(Y)) => u51(X, Y) 
    u52(mark(X), Y) => u52(X, Y) 
    u52(X, mark(Y)) => u52(X, Y) 
    u52(active(X), Y) => u52(X, Y) 
    u52(X, active(Y)) => u52(X, Y) 
    u61(mark(X), Y, Z, U) => u61(X, Y, Z, U) 
    u61(X, mark(Y), Z, U) => u61(X, Y, Z, U) 
    u61(X, Y, mark(Z), U) => u61(X, Y, Z, U) 
    u61(X, Y, Z, mark(U)) => u61(X, Y, Z, U) 
    u61(active(X), Y, Z, U) => u61(X, Y, Z, U) 
    u61(X, active(Y), Z, U) => u61(X, Y, Z, U) 
    u61(X, Y, active(Z), U) => u61(X, Y, Z, U) 
    u61(X, Y, Z, active(U)) => u61(X, Y, Z, U) 
    u62(mark(X), Y, Z, U) => u62(X, Y, Z, U) 
    u62(X, mark(Y), Z, U) => u62(X, Y, Z, U) 
    u62(X, Y, mark(Z), U) => u62(X, Y, Z, U) 
    u62(X, Y, Z, mark(U)) => u62(X, Y, Z, U) 
    u62(active(X), Y, Z, U) => u62(X, Y, Z, U) 
    u62(X, active(Y), Z, U) => u62(X, Y, Z, U) 
    u62(X, Y, active(Z), U) => u62(X, Y, Z, U) 
    u62(X, Y, Z, active(U)) => u62(X, Y, Z, U) 
    u63(mark(X), Y, Z, U) => u63(X, Y, Z, U) 
    u63(X, mark(Y), Z, U) => u63(X, Y, Z, U) 
    u63(X, Y, mark(Z), U) => u63(X, Y, Z, U) 
    u63(X, Y, Z, mark(U)) => u63(X, Y, Z, U) 
    u63(active(X), Y, Z, U) => u63(X, Y, Z, U) 
    u63(X, active(Y), Z, U) => u63(X, Y, Z, U) 
    u63(X, Y, active(Z), U) => u63(X, Y, Z, U) 
    u63(X, Y, Z, active(U)) => u63(X, Y, Z, U) 
    u64(mark(X), Y) => u64(X, Y) 
    u64(X, mark(Y)) => u64(X, Y) 
    u64(active(X), Y) => u64(X, Y) 
    u64(X, active(Y)) => u64(X, Y) 
    pair(mark(X), Y) => pair(X, Y) 
    pair(X, mark(Y)) => pair(X, Y) 
    pair(active(X), Y) => pair(X, Y) 
    pair(X, active(Y)) => pair(X, Y) 
    cons(mark(X), Y) => cons(X, Y) 
    cons(X, mark(Y)) => cons(X, Y) 
    cons(active(X), Y) => cons(X, Y) 
    cons(X, active(Y)) => cons(X, Y) 
    u71(mark(X), Y) => u71(X, Y) 
    u71(X, mark(Y)) => u71(X, Y) 
    u71(active(X), Y) => u71(X, Y) 
    u71(X, active(Y)) => u71(X, Y) 
    u72(mark(X), Y) => u72(X, Y) 
    u72(X, mark(Y)) => u72(X, Y) 
    u72(active(X), Y) => u72(X, Y) 
    u72(X, active(Y)) => u72(X, Y) 
    u81(mark(X), Y, Z) => u81(X, Y, Z) 
    u81(X, mark(Y), Z) => u81(X, Y, Z) 
    u81(X, Y, mark(Z)) => u81(X, Y, Z) 
    u81(active(X), Y, Z) => u81(X, Y, Z) 
    u81(X, active(Y), Z) => u81(X, Y, Z) 
    u81(X, Y, active(Z)) => u81(X, Y, Z) 
    u82(mark(X), Y, Z) => u82(X, Y, Z) 
    u82(X, mark(Y), Z) => u82(X, Y, Z) 
    u82(X, Y, mark(Z)) => u82(X, Y, Z) 
    u82(active(X), Y, Z) => u82(X, Y, Z) 
    u82(X, active(Y), Z) => u82(X, Y, Z) 
    u82(X, Y, active(Z)) => u82(X, Y, Z) 
    fst(mark(X)) => fst(X) 
    fst(active(X)) => fst(X) 
    natsFrom(mark(X)) => natsFrom(X) 
    natsFrom(active(X)) => natsFrom(X) 
    s(mark(X)) => s(X) 
    s(active(X)) => s(X) 
    sel(mark(X), Y) => sel(X, Y) 
    sel(X, mark(Y)) => sel(X, Y) 
    sel(active(X), Y) => sel(X, Y) 
    sel(X, active(Y)) => sel(X, Y) 
    tail(mark(X)) => tail(X) 
    tail(active(X)) => tail(X) 
    take(mark(X), Y) => take(X, Y) 
    take(X, mark(Y)) => take(X, Y) 
    take(active(X), Y) => take(X, Y) 
    take(X, active(Y)) => take(X, Y) 
    map(/\x.~AP1(F, x), nil) => nil 
    map(/\x.~AP1(F, x), cons(X, Y)) => cons(~AP1(F, X), map(/\y.~AP1(F, y), Y)) 
    app(/\x.~AP1(F, x), X) => ~AP1(F, X) 
    map(/\x.active(x), nil) => nil 
    map(/\x.afterNth(X, x), nil) => nil 
    map(/\x.app(F, x), nil) => nil 
    map(/\x.cons(X, x), nil) => nil 
    map(/\x.fst(x), nil) => nil 
    map(/\x.head(x), nil) => nil 
    map(/\x.map(F, x), nil) => nil 
    map(/\x.mark(x), nil) => nil 
    map(/\x.natsFrom(x), nil) => nil 
    map(/\x.pair(X, x), nil) => nil 
    map(/\x.s(x), nil) => nil 
    map(/\x.sel(X, x), nil) => nil 
    map(/\x.snd(x), nil) => nil 
    map(/\x.splitAt(X, x), nil) => nil 
    map(/\x.tail(x), nil) => nil 
    map(/\x.take(X, x), nil) => nil 
    map(/\x.u11(X, Y, x), nil) => nil 
    map(/\x.u12(X, Y, x), nil) => nil 
    map(/\x.u21(X, x), nil) => nil 
    map(/\x.u22(X, x), nil) => nil 
    map(/\x.u31(X, x), nil) => nil 
    map(/\x.u32(X, x), nil) => nil 
    map(/\x.u41(X, Y, x), nil) => nil 
    map(/\x.u42(X, Y, x), nil) => nil 
    map(/\x.u51(X, x), nil) => nil 
    map(/\x.u52(X, x), nil) => nil 
    map(/\x.u61(X, Y, Z, x), nil) => nil 
    map(/\x.u62(X, Y, Z, x), nil) => nil 
    map(/\x.u63(X, Y, Z, x), nil) => nil 
    map(/\x.u64(X, x), nil) => nil 
    map(/\x.u71(X, x), nil) => nil 
    map(/\x.u72(X, x), nil) => nil 
    map(/\x.u81(X, Y, x), nil) => nil 
    map(/\x.u82(X, Y, x), nil) => nil 
    map(/\x.active(x), cons(X, Y)) => cons(active(X), map(/\y.active(y), Y)) 
    map(/\x.afterNth(X, x), cons(Y, Z)) => cons(afterNth(X, Y), map(/\y.afterNth(X, y), Z)) 
    map(/\x.app(F, x), cons(X, Y)) => cons(app(F, X), map(/\y.app(F, y), Y)) 
    map(/\x.cons(X, x), cons(Y, Z)) => cons(cons(X, Y), map(/\y.cons(X, y), Z)) 
    map(/\x.fst(x), cons(X, Y)) => cons(fst(X), map(/\y.fst(y), Y)) 
    map(/\x.head(x), cons(X, Y)) => cons(head(X), map(/\y.head(y), Y)) 
    map(/\x.map(F, x), cons(X, Y)) => cons(map(F, X), map(/\y.map(F, y), Y)) 
    map(/\x.mark(x), cons(X, Y)) => cons(mark(X), map(/\y.mark(y), Y)) 
    map(/\x.natsFrom(x), cons(X, Y)) => cons(natsFrom(X), map(/\y.natsFrom(y), Y)) 
    map(/\x.pair(X, x), cons(Y, Z)) => cons(pair(X, Y), map(/\y.pair(X, y), Z)) 
    map(/\x.s(x), cons(X, Y)) => cons(s(X), map(/\y.s(y), Y)) 
    map(/\x.sel(X, x), cons(Y, Z)) => cons(sel(X, Y), map(/\y.sel(X, y), Z)) 
    map(/\x.snd(x), cons(X, Y)) => cons(snd(X), map(/\y.snd(y), Y)) 
    map(/\x.splitAt(X, x), cons(Y, Z)) => cons(splitAt(X, Y), map(/\y.splitAt(X, y), Z)) 
    map(/\x.tail(x), cons(X, Y)) => cons(tail(X), map(/\y.tail(y), Y)) 
    map(/\x.take(X, x), cons(Y, Z)) => cons(take(X, Y), map(/\y.take(X, y), Z)) 
    map(/\x.u11(X, Y, x), cons(Z, U)) => cons(u11(X, Y, Z), map(/\y.u11(X, Y, y), U)) 
    map(/\x.u12(X, Y, x), cons(Z, U)) => cons(u12(X, Y, Z), map(/\y.u12(X, Y, y), U)) 
    map(/\x.u21(X, x), cons(Y, Z)) => cons(u21(X, Y), map(/\y.u21(X, y), Z)) 
    map(/\x.u22(X, x), cons(Y, Z)) => cons(u22(X, Y), map(/\y.u22(X, y), Z)) 
    map(/\x.u31(X, x), cons(Y, Z)) => cons(u31(X, Y), map(/\y.u31(X, y), Z)) 
    map(/\x.u32(X, x), cons(Y, Z)) => cons(u32(X, Y), map(/\y.u32(X, y), Z)) 
    map(/\x.u41(X, Y, x), cons(Z, U)) => cons(u41(X, Y, Z), map(/\y.u41(X, Y, y), U)) 
    map(/\x.u42(X, Y, x), cons(Z, U)) => cons(u42(X, Y, Z), map(/\y.u42(X, Y, y), U)) 
    map(/\x.u51(X, x), cons(Y, Z)) => cons(u51(X, Y), map(/\y.u51(X, y), Z)) 
    map(/\x.u52(X, x), cons(Y, Z)) => cons(u52(X, Y), map(/\y.u52(X, y), Z)) 
    map(/\x.u61(X, Y, Z, x), cons(U, V)) => cons(u61(X, Y, Z, U), map(/\y.u61(X, Y, Z, y), V)) 
    map(/\x.u62(X, Y, Z, x), cons(U, V)) => cons(u62(X, Y, Z, U), map(/\y.u62(X, Y, Z, y), V)) 
    map(/\x.u63(X, Y, Z, x), cons(U, V)) => cons(u63(X, Y, Z, U), map(/\y.u63(X, Y, Z, y), V)) 
    map(/\x.u64(X, x), cons(Y, Z)) => cons(u64(X, Y), map(/\y.u64(X, y), Z)) 
    map(/\x.u71(X, x), cons(Y, Z)) => cons(u71(X, Y), map(/\y.u71(X, y), Z)) 
    map(/\x.u72(X, x), cons(Y, Z)) => cons(u72(X, Y), map(/\y.u72(X, y), Z)) 
    map(/\x.u81(X, Y, x), cons(Z, U)) => cons(u81(X, Y, Z), map(/\y.u81(X, Y, y), U)) 
    map(/\x.u82(X, Y, x), cons(Z, U)) => cons(u82(X, Y, Z), map(/\y.u82(X, Y, y), U)) 
    app(/\x.active(x), X) => active(X) 
    app(/\x.afterNth(X, x), Y) => afterNth(X, Y) 
    app(/\x.app(F, x), X) => app(F, X) 
    app(/\x.cons(X, x), Y) => cons(X, Y) 
    app(/\x.fst(x), X) => fst(X) 
    app(/\x.head(x), X) => head(X) 
    app(/\x.map(F, x), X) => map(F, X) 
    app(/\x.mark(x), X) => mark(X) 
    app(/\x.natsFrom(x), X) => natsFrom(X) 
    app(/\x.pair(X, x), Y) => pair(X, Y) 
    app(/\x.s(x), X) => s(X) 
    app(/\x.sel(X, x), Y) => sel(X, Y) 
    app(/\x.snd(x), X) => snd(X) 
    app(/\x.splitAt(X, x), Y) => splitAt(X, Y) 
    app(/\x.tail(x), X) => tail(X) 
    app(/\x.take(X, x), Y) => take(X, Y) 
    app(/\x.u11(X, Y, x), Z) => u11(X, Y, Z) 
    app(/\x.u12(X, Y, x), Z) => u12(X, Y, Z) 
    app(/\x.u21(X, x), Y) => u21(X, Y) 
    app(/\x.u22(X, x), Y) => u22(X, Y) 
    app(/\x.u31(X, x), Y) => u31(X, Y) 
    app(/\x.u32(X, x), Y) => u32(X, Y) 
    app(/\x.u41(X, Y, x), Z) => u41(X, Y, Z) 
    app(/\x.u42(X, Y, x), Z) => u42(X, Y, Z) 
    app(/\x.u51(X, x), Y) => u51(X, Y) 
    app(/\x.u52(X, x), Y) => u52(X, Y) 
    app(/\x.u61(X, Y, Z, x), U) => u61(X, Y, Z, U) 
    app(/\x.u62(X, Y, Z, x), U) => u62(X, Y, Z, U) 
    app(/\x.u63(X, Y, Z, x), U) => u63(X, Y, Z, U) 
    app(/\x.u64(X, x), Y) => u64(X, Y) 
    app(/\x.u71(X, x), Y) => u71(X, Y) 
    app(/\x.u72(X, x), Y) => u72(X, Y) 
    app(/\x.u81(X, Y, x), Z) => u81(X, Y, Z) 
    app(/\x.u82(X, Y, x), Z) => u82(X, Y, Z) 
    ~AP1(F, X) => F X 

Symbol ~AP1 is an encoding for application that is only used in innocuous ways.  We can simplify the program (without losing non-termination) by removing it.  Additionally, we can remove some (now-)redundant rules.  This gives:

  Alphabet:

    0 : [] --> A 
    active : [A] --> A 
    afterNth : [A * A] --> A 
    app : [A -> A * A] --> A 
    cons : [A * A] --> A 
    fst : [A] --> A 
    head : [A] --> A 
    map : [A -> A * A] --> A 
    mark : [A] --> A 
    natsFrom : [A] --> A 
    nil : [] --> A 
    pair : [A * A] --> A 
    s : [A] --> A 
    sel : [A * A] --> A 
    snd : [A] --> A 
    splitAt : [A * A] --> A 
    tail : [A] --> A 
    take : [A * A] --> A 
    tt : [] --> A 
    u11 : [A * A * A] --> A 
    u12 : [A * A * A] --> A 
    u21 : [A * A] --> A 
    u22 : [A * A] --> A 
    u31 : [A * A] --> A 
    u32 : [A * A] --> A 
    u41 : [A * A * A] --> A 
    u42 : [A * A * A] --> A 
    u51 : [A * A] --> A 
    u52 : [A * A] --> A 
    u61 : [A * A * A * A] --> A 
    u62 : [A * A * A * A] --> A 
    u63 : [A * A * A * A] --> A 
    u64 : [A * A] --> A 
    u71 : [A * A] --> A 
    u72 : [A * A] --> A 
    u81 : [A * A * A] --> A 
    u82 : [A * A * A] --> A 

  Rules:

    active(u11(tt, X, Y)) => mark(u12(tt, X, Y)) 
    active(u12(tt, X, Y)) => mark(snd(splitAt(X, Y))) 
    active(u21(tt, X)) => mark(u22(tt, X)) 
    active(u22(tt, X)) => mark(X) 
    active(u31(tt, X)) => mark(u32(tt, X)) 
    active(u32(tt, X)) => mark(X) 
    active(u41(tt, X, Y)) => mark(u42(tt, X, Y)) 
    active(u42(tt, X, Y)) => mark(head(afterNth(X, Y))) 
    active(u51(tt, X)) => mark(u52(tt, X)) 
    active(u52(tt, X)) => mark(X) 
    active(u61(tt, X, Y, Z)) => mark(u62(tt, X, Y, Z)) 
    active(u62(tt, X, Y, Z)) => mark(u63(tt, X, Y, Z)) 
    active(u63(tt, X, Y, Z)) => mark(u64(splitAt(X, Z), Y)) 
    active(u64(pair(X, Y), Z)) => mark(pair(cons(Z, X), Y)) 
    active(u71(tt, X)) => mark(u72(tt, X)) 
    active(u72(tt, X)) => mark(X) 
    active(u81(tt, X, Y)) => mark(u82(tt, X, Y)) 
    active(u82(tt, X, Y)) => mark(fst(splitAt(X, Y))) 
    active(afterNth(X, Y)) => mark(u11(tt, X, Y)) 
    active(fst(pair(X, Y))) => mark(u21(tt, X)) 
    active(head(cons(X, Y))) => mark(u31(tt, X)) 
    active(natsFrom(X)) => mark(cons(X, natsFrom(s(X)))) 
    active(sel(X, Y)) => mark(u41(tt, X, Y)) 
    active(snd(pair(X, Y))) => mark(u51(tt, Y)) 
    active(splitAt(0, X)) => mark(pair(nil, X)) 
    active(splitAt(s(X), cons(Y, Z))) => mark(u61(tt, X, Y, Z)) 
    active(tail(cons(X, Y))) => mark(u71(tt, Y)) 
    active(take(X, Y)) => mark(u81(tt, X, Y)) 
    mark(u11(X, Y, Z)) => active(u11(mark(X), Y, Z)) 
    mark(tt) => active(tt) 
    mark(u12(X, Y, Z)) => active(u12(mark(X), Y, Z)) 
    mark(snd(X)) => active(snd(mark(X))) 
    mark(splitAt(X, Y)) => active(splitAt(mark(X), mark(Y))) 
    mark(u21(X, Y)) => active(u21(mark(X), Y)) 
    mark(u22(X, Y)) => active(u22(mark(X), Y)) 
    mark(u31(X, Y)) => active(u31(mark(X), Y)) 
    mark(u32(X, Y)) => active(u32(mark(X), Y)) 
    mark(u41(X, Y, Z)) => active(u41(mark(X), Y, Z)) 
    mark(u42(X, Y, Z)) => active(u42(mark(X), Y, Z)) 
    mark(head(X)) => active(head(mark(X))) 
    mark(afterNth(X, Y)) => active(afterNth(mark(X), mark(Y))) 
    mark(u51(X, Y)) => active(u51(mark(X), Y)) 
    mark(u52(X, Y)) => active(u52(mark(X), Y)) 
    mark(u61(X, Y, Z, U)) => active(u61(mark(X), Y, Z, U)) 
    mark(u62(X, Y, Z, U)) => active(u62(mark(X), Y, Z, U)) 
    mark(u63(X, Y, Z, U)) => active(u63(mark(X), Y, Z, U)) 
    mark(u64(X, Y)) => active(u64(mark(X), Y)) 
    mark(pair(X, Y)) => active(pair(mark(X), mark(Y))) 
    mark(cons(X, Y)) => active(cons(mark(X), Y)) 
    mark(u71(X, Y)) => active(u71(mark(X), Y)) 
    mark(u72(X, Y)) => active(u72(mark(X), Y)) 
    mark(u81(X, Y, Z)) => active(u81(mark(X), Y, Z)) 
    mark(u82(X, Y, Z)) => active(u82(mark(X), Y, Z)) 
    mark(fst(X)) => active(fst(mark(X))) 
    mark(natsFrom(X)) => active(natsFrom(mark(X))) 
    mark(s(X)) => active(s(mark(X))) 
    mark(sel(X, Y)) => active(sel(mark(X), mark(Y))) 
    mark(0) => active(0) 
    mark(nil) => active(nil) 
    mark(tail(X)) => active(tail(mark(X))) 
    mark(take(X, Y)) => active(take(mark(X), mark(Y))) 
    u11(mark(X), Y, Z) => u11(X, Y, Z) 
    u11(X, mark(Y), Z) => u11(X, Y, Z) 
    u11(X, Y, mark(Z)) => u11(X, Y, Z) 
    u11(active(X), Y, Z) => u11(X, Y, Z) 
    u11(X, active(Y), Z) => u11(X, Y, Z) 
    u11(X, Y, active(Z)) => u11(X, Y, Z) 
    u12(mark(X), Y, Z) => u12(X, Y, Z) 
    u12(X, mark(Y), Z) => u12(X, Y, Z) 
    u12(X, Y, mark(Z)) => u12(X, Y, Z) 
    u12(active(X), Y, Z) => u12(X, Y, Z) 
    u12(X, active(Y), Z) => u12(X, Y, Z) 
    u12(X, Y, active(Z)) => u12(X, Y, Z) 
    snd(mark(X)) => snd(X) 
    snd(active(X)) => snd(X) 
    splitAt(mark(X), Y) => splitAt(X, Y) 
    splitAt(X, mark(Y)) => splitAt(X, Y) 
    splitAt(active(X), Y) => splitAt(X, Y) 
    splitAt(X, active(Y)) => splitAt(X, Y) 
    u21(mark(X), Y) => u21(X, Y) 
    u21(X, mark(Y)) => u21(X, Y) 
    u21(active(X), Y) => u21(X, Y) 
    u21(X, active(Y)) => u21(X, Y) 
    u22(mark(X), Y) => u22(X, Y) 
    u22(X, mark(Y)) => u22(X, Y) 
    u22(active(X), Y) => u22(X, Y) 
    u22(X, active(Y)) => u22(X, Y) 
    u31(mark(X), Y) => u31(X, Y) 
    u31(X, mark(Y)) => u31(X, Y) 
    u31(active(X), Y) => u31(X, Y) 
    u31(X, active(Y)) => u31(X, Y) 
    u32(mark(X), Y) => u32(X, Y) 
    u32(X, mark(Y)) => u32(X, Y) 
    u32(active(X), Y) => u32(X, Y) 
    u32(X, active(Y)) => u32(X, Y) 
    u41(mark(X), Y, Z) => u41(X, Y, Z) 
    u41(X, mark(Y), Z) => u41(X, Y, Z) 
    u41(X, Y, mark(Z)) => u41(X, Y, Z) 
    u41(active(X), Y, Z) => u41(X, Y, Z) 
    u41(X, active(Y), Z) => u41(X, Y, Z) 
    u41(X, Y, active(Z)) => u41(X, Y, Z) 
    u42(mark(X), Y, Z) => u42(X, Y, Z) 
    u42(X, mark(Y), Z) => u42(X, Y, Z) 
    u42(X, Y, mark(Z)) => u42(X, Y, Z) 
    u42(active(X), Y, Z) => u42(X, Y, Z) 
    u42(X, active(Y), Z) => u42(X, Y, Z) 
    u42(X, Y, active(Z)) => u42(X, Y, Z) 
    head(mark(X)) => head(X) 
    head(active(X)) => head(X) 
    afterNth(mark(X), Y) => afterNth(X, Y) 
    afterNth(X, mark(Y)) => afterNth(X, Y) 
    afterNth(active(X), Y) => afterNth(X, Y) 
    afterNth(X, active(Y)) => afterNth(X, Y) 
    u51(mark(X), Y) => u51(X, Y) 
    u51(X, mark(Y)) => u51(X, Y) 
    u51(active(X), Y) => u51(X, Y) 
    u51(X, active(Y)) => u51(X, Y) 
    u52(mark(X), Y) => u52(X, Y) 
    u52(X, mark(Y)) => u52(X, Y) 
    u52(active(X), Y) => u52(X, Y) 
    u52(X, active(Y)) => u52(X, Y) 
    u61(mark(X), Y, Z, U) => u61(X, Y, Z, U) 
    u61(X, mark(Y), Z, U) => u61(X, Y, Z, U) 
    u61(X, Y, mark(Z), U) => u61(X, Y, Z, U) 
    u61(X, Y, Z, mark(U)) => u61(X, Y, Z, U) 
    u61(active(X), Y, Z, U) => u61(X, Y, Z, U) 
    u61(X, active(Y), Z, U) => u61(X, Y, Z, U) 
    u61(X, Y, active(Z), U) => u61(X, Y, Z, U) 
    u61(X, Y, Z, active(U)) => u61(X, Y, Z, U) 
    u62(mark(X), Y, Z, U) => u62(X, Y, Z, U) 
    u62(X, mark(Y), Z, U) => u62(X, Y, Z, U) 
    u62(X, Y, mark(Z), U) => u62(X, Y, Z, U) 
    u62(X, Y, Z, mark(U)) => u62(X, Y, Z, U) 
    u62(active(X), Y, Z, U) => u62(X, Y, Z, U) 
    u62(X, active(Y), Z, U) => u62(X, Y, Z, U) 
    u62(X, Y, active(Z), U) => u62(X, Y, Z, U) 
    u62(X, Y, Z, active(U)) => u62(X, Y, Z, U) 
    u63(mark(X), Y, Z, U) => u63(X, Y, Z, U) 
    u63(X, mark(Y), Z, U) => u63(X, Y, Z, U) 
    u63(X, Y, mark(Z), U) => u63(X, Y, Z, U) 
    u63(X, Y, Z, mark(U)) => u63(X, Y, Z, U) 
    u63(active(X), Y, Z, U) => u63(X, Y, Z, U) 
    u63(X, active(Y), Z, U) => u63(X, Y, Z, U) 
    u63(X, Y, active(Z), U) => u63(X, Y, Z, U) 
    u63(X, Y, Z, active(U)) => u63(X, Y, Z, U) 
    u64(mark(X), Y) => u64(X, Y) 
    u64(X, mark(Y)) => u64(X, Y) 
    u64(active(X), Y) => u64(X, Y) 
    u64(X, active(Y)) => u64(X, Y) 
    pair(mark(X), Y) => pair(X, Y) 
    pair(X, mark(Y)) => pair(X, Y) 
    pair(active(X), Y) => pair(X, Y) 
    pair(X, active(Y)) => pair(X, Y) 
    cons(mark(X), Y) => cons(X, Y) 
    cons(X, mark(Y)) => cons(X, Y) 
    cons(active(X), Y) => cons(X, Y) 
    cons(X, active(Y)) => cons(X, Y) 
    u71(mark(X), Y) => u71(X, Y) 
    u71(X, mark(Y)) => u71(X, Y) 
    u71(active(X), Y) => u71(X, Y) 
    u71(X, active(Y)) => u71(X, Y) 
    u72(mark(X), Y) => u72(X, Y) 
    u72(X, mark(Y)) => u72(X, Y) 
    u72(active(X), Y) => u72(X, Y) 
    u72(X, active(Y)) => u72(X, Y) 
    u81(mark(X), Y, Z) => u81(X, Y, Z) 
    u81(X, mark(Y), Z) => u81(X, Y, Z) 
    u81(X, Y, mark(Z)) => u81(X, Y, Z) 
    u81(active(X), Y, Z) => u81(X, Y, Z) 
    u81(X, active(Y), Z) => u81(X, Y, Z) 
    u81(X, Y, active(Z)) => u81(X, Y, Z) 
    u82(mark(X), Y, Z) => u82(X, Y, Z) 
    u82(X, mark(Y), Z) => u82(X, Y, Z) 
    u82(X, Y, mark(Z)) => u82(X, Y, Z) 
    u82(active(X), Y, Z) => u82(X, Y, Z) 
    u82(X, active(Y), Z) => u82(X, Y, Z) 
    u82(X, Y, active(Z)) => u82(X, Y, Z) 
    fst(mark(X)) => fst(X) 
    fst(active(X)) => fst(X) 
    natsFrom(mark(X)) => natsFrom(X) 
    natsFrom(active(X)) => natsFrom(X) 
    s(mark(X)) => s(X) 
    s(active(X)) => s(X) 
    sel(mark(X), Y) => sel(X, Y) 
    sel(X, mark(Y)) => sel(X, Y) 
    sel(active(X), Y) => sel(X, Y) 
    sel(X, active(Y)) => sel(X, Y) 
    tail(mark(X)) => tail(X) 
    tail(active(X)) => tail(X) 
    take(mark(X), Y) => take(X, Y) 
    take(X, mark(Y)) => take(X, Y) 
    take(active(X), Y) => take(X, Y) 
    take(X, active(Y)) => take(X, Y) 
    map(/\x.X(x), nil) => nil 
    map(/\x.X(x), cons(Y, Z)) => cons(X(Y), map(/\y.X(y), Z)) 
    app(/\x.X(x), Y) => X(Y) 

We observe that the rules contain a first-order subset:

  active(u11(tt, X, Y)) => mark(u12(tt, X, Y)) 
  active(u12(tt, X, Y)) => mark(snd(splitAt(X, Y))) 
  active(u21(tt, X)) => mark(u22(tt, X)) 
  active(u22(tt, X)) => mark(X) 
  active(u31(tt, X)) => mark(u32(tt, X)) 
  active(u32(tt, X)) => mark(X) 
  active(u41(tt, X, Y)) => mark(u42(tt, X, Y)) 
  active(u42(tt, X, Y)) => mark(head(afterNth(X, Y))) 
  active(u51(tt, X)) => mark(u52(tt, X)) 
  active(u52(tt, X)) => mark(X) 
  active(u61(tt, X, Y, Z)) => mark(u62(tt, X, Y, Z)) 
  active(u62(tt, X, Y, Z)) => mark(u63(tt, X, Y, Z)) 
  active(u63(tt, X, Y, Z)) => mark(u64(splitAt(X, Z), Y)) 
  active(u64(pair(X, Y), Z)) => mark(pair(cons(Z, X), Y)) 
  active(u71(tt, X)) => mark(u72(tt, X)) 
  active(u72(tt, X)) => mark(X) 
  active(u81(tt, X, Y)) => mark(u82(tt, X, Y)) 
  active(u82(tt, X, Y)) => mark(fst(splitAt(X, Y))) 
  active(afterNth(X, Y)) => mark(u11(tt, X, Y)) 
  active(fst(pair(X, Y))) => mark(u21(tt, X)) 
  active(head(cons(X, Y))) => mark(u31(tt, X)) 
  active(natsFrom(X)) => mark(cons(X, natsFrom(s(X)))) 
  active(sel(X, Y)) => mark(u41(tt, X, Y)) 
  active(snd(pair(X, Y))) => mark(u51(tt, Y)) 
  active(splitAt(0, X)) => mark(pair(nil, X)) 
  active(splitAt(s(X), cons(Y, Z))) => mark(u61(tt, X, Y, Z)) 
  active(tail(cons(X, Y))) => mark(u71(tt, Y)) 
  active(take(X, Y)) => mark(u81(tt, X, Y)) 
  mark(u11(X, Y, Z)) => active(u11(mark(X), Y, Z)) 
  mark(tt) => active(tt) 
  mark(u12(X, Y, Z)) => active(u12(mark(X), Y, Z)) 
  mark(snd(X)) => active(snd(mark(X))) 
  mark(splitAt(X, Y)) => active(splitAt(mark(X), mark(Y))) 
  mark(u21(X, Y)) => active(u21(mark(X), Y)) 
  mark(u22(X, Y)) => active(u22(mark(X), Y)) 
  mark(u31(X, Y)) => active(u31(mark(X), Y)) 
  mark(u32(X, Y)) => active(u32(mark(X), Y)) 
  mark(u41(X, Y, Z)) => active(u41(mark(X), Y, Z)) 
  mark(u42(X, Y, Z)) => active(u42(mark(X), Y, Z)) 
  mark(head(X)) => active(head(mark(X))) 
  mark(afterNth(X, Y)) => active(afterNth(mark(X), mark(Y))) 
  mark(u51(X, Y)) => active(u51(mark(X), Y)) 
  mark(u52(X, Y)) => active(u52(mark(X), Y)) 
  mark(u61(X, Y, Z, U)) => active(u61(mark(X), Y, Z, U)) 
  mark(u62(X, Y, Z, U)) => active(u62(mark(X), Y, Z, U)) 
  mark(u63(X, Y, Z, U)) => active(u63(mark(X), Y, Z, U)) 
  mark(u64(X, Y)) => active(u64(mark(X), Y)) 
  mark(pair(X, Y)) => active(pair(mark(X), mark(Y))) 
  mark(cons(X, Y)) => active(cons(mark(X), Y)) 
  mark(u71(X, Y)) => active(u71(mark(X), Y)) 
  mark(u72(X, Y)) => active(u72(mark(X), Y)) 
  mark(u81(X, Y, Z)) => active(u81(mark(X), Y, Z)) 
  mark(u82(X, Y, Z)) => active(u82(mark(X), Y, Z)) 
  mark(fst(X)) => active(fst(mark(X))) 
  mark(natsFrom(X)) => active(natsFrom(mark(X))) 
  mark(s(X)) => active(s(mark(X))) 
  mark(sel(X, Y)) => active(sel(mark(X), mark(Y))) 
  mark(0) => active(0) 
  mark(nil) => active(nil) 
  mark(tail(X)) => active(tail(mark(X))) 
  mark(take(X, Y)) => active(take(mark(X), mark(Y))) 
  u11(mark(X), Y, Z) => u11(X, Y, Z) 
  u11(X, mark(Y), Z) => u11(X, Y, Z) 
  u11(X, Y, mark(Z)) => u11(X, Y, Z) 
  u11(active(X), Y, Z) => u11(X, Y, Z) 
  u11(X, active(Y), Z) => u11(X, Y, Z) 
  u11(X, Y, active(Z)) => u11(X, Y, Z) 
  u12(mark(X), Y, Z) => u12(X, Y, Z) 
  u12(X, mark(Y), Z) => u12(X, Y, Z) 
  u12(X, Y, mark(Z)) => u12(X, Y, Z) 
  u12(active(X), Y, Z) => u12(X, Y, Z) 
  u12(X, active(Y), Z) => u12(X, Y, Z) 
  u12(X, Y, active(Z)) => u12(X, Y, Z) 
  snd(mark(X)) => snd(X) 
  snd(active(X)) => snd(X) 
  splitAt(mark(X), Y) => splitAt(X, Y) 
  splitAt(X, mark(Y)) => splitAt(X, Y) 
  splitAt(active(X), Y) => splitAt(X, Y) 
  splitAt(X, active(Y)) => splitAt(X, Y) 
  u21(mark(X), Y) => u21(X, Y) 
  u21(X, mark(Y)) => u21(X, Y) 
  u21(active(X), Y) => u21(X, Y) 
  u21(X, active(Y)) => u21(X, Y) 
  u22(mark(X), Y) => u22(X, Y) 
  u22(X, mark(Y)) => u22(X, Y) 
  u22(active(X), Y) => u22(X, Y) 
  u22(X, active(Y)) => u22(X, Y) 
  u31(mark(X), Y) => u31(X, Y) 
  u31(X, mark(Y)) => u31(X, Y) 
  u31(active(X), Y) => u31(X, Y) 
  u31(X, active(Y)) => u31(X, Y) 
  u32(mark(X), Y) => u32(X, Y) 
  u32(X, mark(Y)) => u32(X, Y) 
  u32(active(X), Y) => u32(X, Y) 
  u32(X, active(Y)) => u32(X, Y) 
  u41(mark(X), Y, Z) => u41(X, Y, Z) 
  u41(X, mark(Y), Z) => u41(X, Y, Z) 
  u41(X, Y, mark(Z)) => u41(X, Y, Z) 
  u41(active(X), Y, Z) => u41(X, Y, Z) 
  u41(X, active(Y), Z) => u41(X, Y, Z) 
  u41(X, Y, active(Z)) => u41(X, Y, Z) 
  u42(mark(X), Y, Z) => u42(X, Y, Z) 
  u42(X, mark(Y), Z) => u42(X, Y, Z) 
  u42(X, Y, mark(Z)) => u42(X, Y, Z) 
  u42(active(X), Y, Z) => u42(X, Y, Z) 
  u42(X, active(Y), Z) => u42(X, Y, Z) 
  u42(X, Y, active(Z)) => u42(X, Y, Z) 
  head(mark(X)) => head(X) 
  head(active(X)) => head(X) 
  afterNth(mark(X), Y) => afterNth(X, Y) 
  afterNth(X, mark(Y)) => afterNth(X, Y) 
  afterNth(active(X), Y) => afterNth(X, Y) 
  afterNth(X, active(Y)) => afterNth(X, Y) 
  u51(mark(X), Y) => u51(X, Y) 
  u51(X, mark(Y)) => u51(X, Y) 
  u51(active(X), Y) => u51(X, Y) 
  u51(X, active(Y)) => u51(X, Y) 
  u52(mark(X), Y) => u52(X, Y) 
  u52(X, mark(Y)) => u52(X, Y) 
  u52(active(X), Y) => u52(X, Y) 
  u52(X, active(Y)) => u52(X, Y) 
  u61(mark(X), Y, Z, U) => u61(X, Y, Z, U) 
  u61(X, mark(Y), Z, U) => u61(X, Y, Z, U) 
  u61(X, Y, mark(Z), U) => u61(X, Y, Z, U) 
  u61(X, Y, Z, mark(U)) => u61(X, Y, Z, U) 
  u61(active(X), Y, Z, U) => u61(X, Y, Z, U) 
  u61(X, active(Y), Z, U) => u61(X, Y, Z, U) 
  u61(X, Y, active(Z), U) => u61(X, Y, Z, U) 
  u61(X, Y, Z, active(U)) => u61(X, Y, Z, U) 
  u62(mark(X), Y, Z, U) => u62(X, Y, Z, U) 
  u62(X, mark(Y), Z, U) => u62(X, Y, Z, U) 
  u62(X, Y, mark(Z), U) => u62(X, Y, Z, U) 
  u62(X, Y, Z, mark(U)) => u62(X, Y, Z, U) 
  u62(active(X), Y, Z, U) => u62(X, Y, Z, U) 
  u62(X, active(Y), Z, U) => u62(X, Y, Z, U) 
  u62(X, Y, active(Z), U) => u62(X, Y, Z, U) 
  u62(X, Y, Z, active(U)) => u62(X, Y, Z, U) 
  u63(mark(X), Y, Z, U) => u63(X, Y, Z, U) 
  u63(X, mark(Y), Z, U) => u63(X, Y, Z, U) 
  u63(X, Y, mark(Z), U) => u63(X, Y, Z, U) 
  u63(X, Y, Z, mark(U)) => u63(X, Y, Z, U) 
  u63(active(X), Y, Z, U) => u63(X, Y, Z, U) 
  u63(X, active(Y), Z, U) => u63(X, Y, Z, U) 
  u63(X, Y, active(Z), U) => u63(X, Y, Z, U) 
  u63(X, Y, Z, active(U)) => u63(X, Y, Z, U) 
  u64(mark(X), Y) => u64(X, Y) 
  u64(X, mark(Y)) => u64(X, Y) 
  u64(active(X), Y) => u64(X, Y) 
  u64(X, active(Y)) => u64(X, Y) 
  pair(mark(X), Y) => pair(X, Y) 
  pair(X, mark(Y)) => pair(X, Y) 
  pair(active(X), Y) => pair(X, Y) 
  pair(X, active(Y)) => pair(X, Y) 
  cons(mark(X), Y) => cons(X, Y) 
  cons(X, mark(Y)) => cons(X, Y) 
  cons(active(X), Y) => cons(X, Y) 
  cons(X, active(Y)) => cons(X, Y) 
  u71(mark(X), Y) => u71(X, Y) 
  u71(X, mark(Y)) => u71(X, Y) 
  u71(active(X), Y) => u71(X, Y) 
  u71(X, active(Y)) => u71(X, Y) 
  u72(mark(X), Y) => u72(X, Y) 
  u72(X, mark(Y)) => u72(X, Y) 
  u72(active(X), Y) => u72(X, Y) 
  u72(X, active(Y)) => u72(X, Y) 
  u81(mark(X), Y, Z) => u81(X, Y, Z) 
  u81(X, mark(Y), Z) => u81(X, Y, Z) 
  u81(X, Y, mark(Z)) => u81(X, Y, Z) 
  u81(active(X), Y, Z) => u81(X, Y, Z) 
  u81(X, active(Y), Z) => u81(X, Y, Z) 
  u81(X, Y, active(Z)) => u81(X, Y, Z) 
  u82(mark(X), Y, Z) => u82(X, Y, Z) 
  u82(X, mark(Y), Z) => u82(X, Y, Z) 
  u82(X, Y, mark(Z)) => u82(X, Y, Z) 
  u82(active(X), Y, Z) => u82(X, Y, Z) 
  u82(X, active(Y), Z) => u82(X, Y, Z) 
  u82(X, Y, active(Z)) => u82(X, Y, Z) 
  fst(mark(X)) => fst(X) 
  fst(active(X)) => fst(X) 
  natsFrom(mark(X)) => natsFrom(X) 
  natsFrom(active(X)) => natsFrom(X) 
  s(mark(X)) => s(X) 
  s(active(X)) => s(X) 
  sel(mark(X), Y) => sel(X, Y) 
  sel(X, mark(Y)) => sel(X, Y) 
  sel(active(X), Y) => sel(X, Y) 
  sel(X, active(Y)) => sel(X, Y) 
  tail(mark(X)) => tail(X) 
  tail(active(X)) => tail(X) 
  take(mark(X), Y) => take(X, Y) 
  take(X, mark(Y)) => take(X, Y) 
  take(active(X), Y) => take(X, Y) 
  take(X, active(Y)) => take(X, Y) 

Moreover, the system is finitely branching.  Thus, by [Kop12, Thm. 7.55], we may omit all first-order dependency pairs from the dependency pair problem (DP(R), R) if this first-order part is Ce-terminating when seen as a many-sorted first-order TRS.

According to nattprover, this system is indeed Ce-terminating:

 || Input TRS:
 ||     1: active(u11(tt(),PeRCenTX,PeRCenTY)) -> mark(u12(tt(),PeRCenTX,PeRCenTY))
 ||     2: active(u12(tt(),PeRCenTX,PeRCenTY)) -> mark(snd(splitAt(PeRCenTX,PeRCenTY)))
 ||     3: active(u21(tt(),PeRCenTX)) -> mark(u22(tt(),PeRCenTX))
 ||     4: active(u22(tt(),PeRCenTX)) -> mark(PeRCenTX)
 ||     5: active(u31(tt(),PeRCenTX)) -> mark(u32(tt(),PeRCenTX))
 ||     6: active(u32(tt(),PeRCenTX)) -> mark(PeRCenTX)
 ||     7: active(u41(tt(),PeRCenTX,PeRCenTY)) -> mark(u42(tt(),PeRCenTX,PeRCenTY))
 ||     8: active(u42(tt(),PeRCenTX,PeRCenTY)) -> mark(head(afterNth(PeRCenTX,PeRCenTY)))
 ||     9: active(u51(tt(),PeRCenTX)) -> mark(u52(tt(),PeRCenTX))
 ||     10: active(u52(tt(),PeRCenTX)) -> mark(PeRCenTX)
 ||     11: active(u61(tt(),PeRCenTX,PeRCenTY,PeRCenTZ)) -> mark(u62(tt(),PeRCenTX,PeRCenTY,PeRCenTZ))
 ||     12: active(u62(tt(),PeRCenTX,PeRCenTY,PeRCenTZ)) -> mark(u63(tt(),PeRCenTX,PeRCenTY,PeRCenTZ))
 ||     13: active(u63(tt(),PeRCenTX,PeRCenTY,PeRCenTZ)) -> mark(u64(splitAt(PeRCenTX,PeRCenTZ),PeRCenTY))
 ||     14: active(u64(pair(PeRCenTX,PeRCenTY),PeRCenTZ)) -> mark(pair(cons(PeRCenTZ,PeRCenTX),PeRCenTY))
 ||     15: active(u71(tt(),PeRCenTX)) -> mark(u72(tt(),PeRCenTX))
 ||     16: active(u72(tt(),PeRCenTX)) -> mark(PeRCenTX)
 ||     17: active(u81(tt(),PeRCenTX,PeRCenTY)) -> mark(u82(tt(),PeRCenTX,PeRCenTY))
 ||     18: active(u82(tt(),PeRCenTX,PeRCenTY)) -> mark(fst(splitAt(PeRCenTX,PeRCenTY)))
 ||     19: active(afterNth(PeRCenTX,PeRCenTY)) -> mark(u11(tt(),PeRCenTX,PeRCenTY))
 ||     20: active(fst(pair(PeRCenTX,PeRCenTY))) -> mark(u21(tt(),PeRCenTX))
 ||     21: active(head(cons(PeRCenTX,PeRCenTY))) -> mark(u31(tt(),PeRCenTX))
 ||     22: active(natsFrom(PeRCenTX)) -> mark(cons(PeRCenTX,natsFrom(s(PeRCenTX))))
 ||     23: active(sel(PeRCenTX,PeRCenTY)) -> mark(u41(tt(),PeRCenTX,PeRCenTY))
 ||     24: active(snd(pair(PeRCenTX,PeRCenTY))) -> mark(u51(tt(),PeRCenTY))
 ||     25: active(splitAt(0(),PeRCenTX)) -> mark(pair(nil(),PeRCenTX))
 ||     26: active(splitAt(s(PeRCenTX),cons(PeRCenTY,PeRCenTZ))) -> mark(u61(tt(),PeRCenTX,PeRCenTY,PeRCenTZ))
 ||     27: active(tail(cons(PeRCenTX,PeRCenTY))) -> mark(u71(tt(),PeRCenTY))
 ||     28: active(take(PeRCenTX,PeRCenTY)) -> mark(u81(tt(),PeRCenTX,PeRCenTY))
 ||     29: mark(u11(PeRCenTX,PeRCenTY,PeRCenTZ)) -> active(u11(mark(PeRCenTX),PeRCenTY,PeRCenTZ))
 ||     30: mark(tt()) -> active(tt())
 ||     31: mark(u12(PeRCenTX,PeRCenTY,PeRCenTZ)) -> active(u12(mark(PeRCenTX),PeRCenTY,PeRCenTZ))
 ||     32: mark(snd(PeRCenTX)) -> active(snd(mark(PeRCenTX)))
 ||     33: mark(splitAt(PeRCenTX,PeRCenTY)) -> active(splitAt(mark(PeRCenTX),mark(PeRCenTY)))
 ||     34: mark(u21(PeRCenTX,PeRCenTY)) -> active(u21(mark(PeRCenTX),PeRCenTY))
 ||     35: mark(u22(PeRCenTX,PeRCenTY)) -> active(u22(mark(PeRCenTX),PeRCenTY))
 ||     36: mark(u31(PeRCenTX,PeRCenTY)) -> active(u31(mark(PeRCenTX),PeRCenTY))
 ||     37: mark(u32(PeRCenTX,PeRCenTY)) -> active(u32(mark(PeRCenTX),PeRCenTY))
 ||     38: mark(u41(PeRCenTX,PeRCenTY,PeRCenTZ)) -> active(u41(mark(PeRCenTX),PeRCenTY,PeRCenTZ))
 ||     39: mark(u42(PeRCenTX,PeRCenTY,PeRCenTZ)) -> active(u42(mark(PeRCenTX),PeRCenTY,PeRCenTZ))
 ||     40: mark(head(PeRCenTX)) -> active(head(mark(PeRCenTX)))
 ||     41: mark(afterNth(PeRCenTX,PeRCenTY)) -> active(afterNth(mark(PeRCenTX),mark(PeRCenTY)))
 ||     42: mark(u51(PeRCenTX,PeRCenTY)) -> active(u51(mark(PeRCenTX),PeRCenTY))
 ||     43: mark(u52(PeRCenTX,PeRCenTY)) -> active(u52(mark(PeRCenTX),PeRCenTY))
 ||     44: mark(u61(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)) -> active(u61(mark(PeRCenTX),PeRCenTY,PeRCenTZ,PeRCenTU))
 ||     45: mark(u62(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)) -> active(u62(mark(PeRCenTX),PeRCenTY,PeRCenTZ,PeRCenTU))
 ||     46: mark(u63(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)) -> active(u63(mark(PeRCenTX),PeRCenTY,PeRCenTZ,PeRCenTU))
 ||     47: mark(u64(PeRCenTX,PeRCenTY)) -> active(u64(mark(PeRCenTX),PeRCenTY))
 ||     48: mark(pair(PeRCenTX,PeRCenTY)) -> active(pair(mark(PeRCenTX),mark(PeRCenTY)))
 ||     49: mark(cons(PeRCenTX,PeRCenTY)) -> active(cons(mark(PeRCenTX),PeRCenTY))
 ||     50: mark(u71(PeRCenTX,PeRCenTY)) -> active(u71(mark(PeRCenTX),PeRCenTY))
 ||     51: mark(u72(PeRCenTX,PeRCenTY)) -> active(u72(mark(PeRCenTX),PeRCenTY))
 ||     52: mark(u81(PeRCenTX,PeRCenTY,PeRCenTZ)) -> active(u81(mark(PeRCenTX),PeRCenTY,PeRCenTZ))
 ||     53: mark(u82(PeRCenTX,PeRCenTY,PeRCenTZ)) -> active(u82(mark(PeRCenTX),PeRCenTY,PeRCenTZ))
 ||     54: mark(fst(PeRCenTX)) -> active(fst(mark(PeRCenTX)))
 ||     55: mark(natsFrom(PeRCenTX)) -> active(natsFrom(mark(PeRCenTX)))
 ||     56: mark(s(PeRCenTX)) -> active(s(mark(PeRCenTX)))
 ||     57: mark(sel(PeRCenTX,PeRCenTY)) -> active(sel(mark(PeRCenTX),mark(PeRCenTY)))
 ||     58: mark(0()) -> active(0())
 ||     59: mark(nil()) -> active(nil())
 ||     60: mark(tail(PeRCenTX)) -> active(tail(mark(PeRCenTX)))
 ||     61: mark(take(PeRCenTX,PeRCenTY)) -> active(take(mark(PeRCenTX),mark(PeRCenTY)))
 ||     62: u11(mark(PeRCenTX),PeRCenTY,PeRCenTZ) -> u11(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     63: u11(PeRCenTX,mark(PeRCenTY),PeRCenTZ) -> u11(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     64: u11(PeRCenTX,PeRCenTY,mark(PeRCenTZ)) -> u11(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     65: u11(active(PeRCenTX),PeRCenTY,PeRCenTZ) -> u11(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     66: u11(PeRCenTX,active(PeRCenTY),PeRCenTZ) -> u11(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     67: u11(PeRCenTX,PeRCenTY,active(PeRCenTZ)) -> u11(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     68: u12(mark(PeRCenTX),PeRCenTY,PeRCenTZ) -> u12(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     69: u12(PeRCenTX,mark(PeRCenTY),PeRCenTZ) -> u12(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     70: u12(PeRCenTX,PeRCenTY,mark(PeRCenTZ)) -> u12(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     71: u12(active(PeRCenTX),PeRCenTY,PeRCenTZ) -> u12(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     72: u12(PeRCenTX,active(PeRCenTY),PeRCenTZ) -> u12(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     73: u12(PeRCenTX,PeRCenTY,active(PeRCenTZ)) -> u12(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     74: snd(mark(PeRCenTX)) -> snd(PeRCenTX)
 ||     75: snd(active(PeRCenTX)) -> snd(PeRCenTX)
 ||     76: splitAt(mark(PeRCenTX),PeRCenTY) -> splitAt(PeRCenTX,PeRCenTY)
 ||     77: splitAt(PeRCenTX,mark(PeRCenTY)) -> splitAt(PeRCenTX,PeRCenTY)
 ||     78: splitAt(active(PeRCenTX),PeRCenTY) -> splitAt(PeRCenTX,PeRCenTY)
 ||     79: splitAt(PeRCenTX,active(PeRCenTY)) -> splitAt(PeRCenTX,PeRCenTY)
 ||     80: u21(mark(PeRCenTX),PeRCenTY) -> u21(PeRCenTX,PeRCenTY)
 ||     81: u21(PeRCenTX,mark(PeRCenTY)) -> u21(PeRCenTX,PeRCenTY)
 ||     82: u21(active(PeRCenTX),PeRCenTY) -> u21(PeRCenTX,PeRCenTY)
 ||     83: u21(PeRCenTX,active(PeRCenTY)) -> u21(PeRCenTX,PeRCenTY)
 ||     84: u22(mark(PeRCenTX),PeRCenTY) -> u22(PeRCenTX,PeRCenTY)
 ||     85: u22(PeRCenTX,mark(PeRCenTY)) -> u22(PeRCenTX,PeRCenTY)
 ||     86: u22(active(PeRCenTX),PeRCenTY) -> u22(PeRCenTX,PeRCenTY)
 ||     87: u22(PeRCenTX,active(PeRCenTY)) -> u22(PeRCenTX,PeRCenTY)
 ||     88: u31(mark(PeRCenTX),PeRCenTY) -> u31(PeRCenTX,PeRCenTY)
 ||     89: u31(PeRCenTX,mark(PeRCenTY)) -> u31(PeRCenTX,PeRCenTY)
 ||     90: u31(active(PeRCenTX),PeRCenTY) -> u31(PeRCenTX,PeRCenTY)
 ||     91: u31(PeRCenTX,active(PeRCenTY)) -> u31(PeRCenTX,PeRCenTY)
 ||     92: u32(mark(PeRCenTX),PeRCenTY) -> u32(PeRCenTX,PeRCenTY)
 ||     93: u32(PeRCenTX,mark(PeRCenTY)) -> u32(PeRCenTX,PeRCenTY)
 ||     94: u32(active(PeRCenTX),PeRCenTY) -> u32(PeRCenTX,PeRCenTY)
 ||     95: u32(PeRCenTX,active(PeRCenTY)) -> u32(PeRCenTX,PeRCenTY)
 ||     96: u41(mark(PeRCenTX),PeRCenTY,PeRCenTZ) -> u41(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     97: u41(PeRCenTX,mark(PeRCenTY),PeRCenTZ) -> u41(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     98: u41(PeRCenTX,PeRCenTY,mark(PeRCenTZ)) -> u41(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     99: u41(active(PeRCenTX),PeRCenTY,PeRCenTZ) -> u41(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     100: u41(PeRCenTX,active(PeRCenTY),PeRCenTZ) -> u41(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     101: u41(PeRCenTX,PeRCenTY,active(PeRCenTZ)) -> u41(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     102: u42(mark(PeRCenTX),PeRCenTY,PeRCenTZ) -> u42(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     103: u42(PeRCenTX,mark(PeRCenTY),PeRCenTZ) -> u42(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     104: u42(PeRCenTX,PeRCenTY,mark(PeRCenTZ)) -> u42(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     105: u42(active(PeRCenTX),PeRCenTY,PeRCenTZ) -> u42(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     106: u42(PeRCenTX,active(PeRCenTY),PeRCenTZ) -> u42(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     107: u42(PeRCenTX,PeRCenTY,active(PeRCenTZ)) -> u42(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     108: head(mark(PeRCenTX)) -> head(PeRCenTX)
 ||     109: head(active(PeRCenTX)) -> head(PeRCenTX)
 ||     110: afterNth(mark(PeRCenTX),PeRCenTY) -> afterNth(PeRCenTX,PeRCenTY)
 ||     111: afterNth(PeRCenTX,mark(PeRCenTY)) -> afterNth(PeRCenTX,PeRCenTY)
 ||     112: afterNth(active(PeRCenTX),PeRCenTY) -> afterNth(PeRCenTX,PeRCenTY)
 ||     113: afterNth(PeRCenTX,active(PeRCenTY)) -> afterNth(PeRCenTX,PeRCenTY)
 ||     114: u51(mark(PeRCenTX),PeRCenTY) -> u51(PeRCenTX,PeRCenTY)
 ||     115: u51(PeRCenTX,mark(PeRCenTY)) -> u51(PeRCenTX,PeRCenTY)
 ||     116: u51(active(PeRCenTX),PeRCenTY) -> u51(PeRCenTX,PeRCenTY)
 ||     117: u51(PeRCenTX,active(PeRCenTY)) -> u51(PeRCenTX,PeRCenTY)
 ||     118: u52(mark(PeRCenTX),PeRCenTY) -> u52(PeRCenTX,PeRCenTY)
 ||     119: u52(PeRCenTX,mark(PeRCenTY)) -> u52(PeRCenTX,PeRCenTY)
 ||     120: u52(active(PeRCenTX),PeRCenTY) -> u52(PeRCenTX,PeRCenTY)
 ||     121: u52(PeRCenTX,active(PeRCenTY)) -> u52(PeRCenTX,PeRCenTY)
 ||     122: u61(mark(PeRCenTX),PeRCenTY,PeRCenTZ,PeRCenTU) -> u61(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||     123: u61(PeRCenTX,mark(PeRCenTY),PeRCenTZ,PeRCenTU) -> u61(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||     124: u61(PeRCenTX,PeRCenTY,mark(PeRCenTZ),PeRCenTU) -> u61(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||     125: u61(PeRCenTX,PeRCenTY,PeRCenTZ,mark(PeRCenTU)) -> u61(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||     126: u61(active(PeRCenTX),PeRCenTY,PeRCenTZ,PeRCenTU) -> u61(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||     127: u61(PeRCenTX,active(PeRCenTY),PeRCenTZ,PeRCenTU) -> u61(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||     128: u61(PeRCenTX,PeRCenTY,active(PeRCenTZ),PeRCenTU) -> u61(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||     129: u61(PeRCenTX,PeRCenTY,PeRCenTZ,active(PeRCenTU)) -> u61(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||     130: u62(mark(PeRCenTX),PeRCenTY,PeRCenTZ,PeRCenTU) -> u62(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||     131: u62(PeRCenTX,mark(PeRCenTY),PeRCenTZ,PeRCenTU) -> u62(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||     132: u62(PeRCenTX,PeRCenTY,mark(PeRCenTZ),PeRCenTU) -> u62(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||     133: u62(PeRCenTX,PeRCenTY,PeRCenTZ,mark(PeRCenTU)) -> u62(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||     134: u62(active(PeRCenTX),PeRCenTY,PeRCenTZ,PeRCenTU) -> u62(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||     135: u62(PeRCenTX,active(PeRCenTY),PeRCenTZ,PeRCenTU) -> u62(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||     136: u62(PeRCenTX,PeRCenTY,active(PeRCenTZ),PeRCenTU) -> u62(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||     137: u62(PeRCenTX,PeRCenTY,PeRCenTZ,active(PeRCenTU)) -> u62(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||     138: u63(mark(PeRCenTX),PeRCenTY,PeRCenTZ,PeRCenTU) -> u63(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||     139: u63(PeRCenTX,mark(PeRCenTY),PeRCenTZ,PeRCenTU) -> u63(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||     140: u63(PeRCenTX,PeRCenTY,mark(PeRCenTZ),PeRCenTU) -> u63(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||     141: u63(PeRCenTX,PeRCenTY,PeRCenTZ,mark(PeRCenTU)) -> u63(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||     142: u63(active(PeRCenTX),PeRCenTY,PeRCenTZ,PeRCenTU) -> u63(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||     143: u63(PeRCenTX,active(PeRCenTY),PeRCenTZ,PeRCenTU) -> u63(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||     144: u63(PeRCenTX,PeRCenTY,active(PeRCenTZ),PeRCenTU) -> u63(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||     145: u63(PeRCenTX,PeRCenTY,PeRCenTZ,active(PeRCenTU)) -> u63(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||     146: u64(mark(PeRCenTX),PeRCenTY) -> u64(PeRCenTX,PeRCenTY)
 ||     147: u64(PeRCenTX,mark(PeRCenTY)) -> u64(PeRCenTX,PeRCenTY)
 ||     148: u64(active(PeRCenTX),PeRCenTY) -> u64(PeRCenTX,PeRCenTY)
 ||     149: u64(PeRCenTX,active(PeRCenTY)) -> u64(PeRCenTX,PeRCenTY)
 ||     150: pair(mark(PeRCenTX),PeRCenTY) -> pair(PeRCenTX,PeRCenTY)
 ||     151: pair(PeRCenTX,mark(PeRCenTY)) -> pair(PeRCenTX,PeRCenTY)
 ||     152: pair(active(PeRCenTX),PeRCenTY) -> pair(PeRCenTX,PeRCenTY)
 ||     153: pair(PeRCenTX,active(PeRCenTY)) -> pair(PeRCenTX,PeRCenTY)
 ||     154: cons(mark(PeRCenTX),PeRCenTY) -> cons(PeRCenTX,PeRCenTY)
 ||     155: cons(PeRCenTX,mark(PeRCenTY)) -> cons(PeRCenTX,PeRCenTY)
 ||     156: cons(active(PeRCenTX),PeRCenTY) -> cons(PeRCenTX,PeRCenTY)
 ||     157: cons(PeRCenTX,active(PeRCenTY)) -> cons(PeRCenTX,PeRCenTY)
 ||     158: u71(mark(PeRCenTX),PeRCenTY) -> u71(PeRCenTX,PeRCenTY)
 ||     159: u71(PeRCenTX,mark(PeRCenTY)) -> u71(PeRCenTX,PeRCenTY)
 ||     160: u71(active(PeRCenTX),PeRCenTY) -> u71(PeRCenTX,PeRCenTY)
 ||     161: u71(PeRCenTX,active(PeRCenTY)) -> u71(PeRCenTX,PeRCenTY)
 ||     162: u72(mark(PeRCenTX),PeRCenTY) -> u72(PeRCenTX,PeRCenTY)
 ||     163: u72(PeRCenTX,mark(PeRCenTY)) -> u72(PeRCenTX,PeRCenTY)
 ||     164: u72(active(PeRCenTX),PeRCenTY) -> u72(PeRCenTX,PeRCenTY)
 ||     165: u72(PeRCenTX,active(PeRCenTY)) -> u72(PeRCenTX,PeRCenTY)
 ||     166: u81(mark(PeRCenTX),PeRCenTY,PeRCenTZ) -> u81(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     167: u81(PeRCenTX,mark(PeRCenTY),PeRCenTZ) -> u81(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     168: u81(PeRCenTX,PeRCenTY,mark(PeRCenTZ)) -> u81(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     169: u81(active(PeRCenTX),PeRCenTY,PeRCenTZ) -> u81(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     170: u81(PeRCenTX,active(PeRCenTY),PeRCenTZ) -> u81(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     171: u81(PeRCenTX,PeRCenTY,active(PeRCenTZ)) -> u81(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     172: u82(mark(PeRCenTX),PeRCenTY,PeRCenTZ) -> u82(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     173: u82(PeRCenTX,mark(PeRCenTY),PeRCenTZ) -> u82(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     174: u82(PeRCenTX,PeRCenTY,mark(PeRCenTZ)) -> u82(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     175: u82(active(PeRCenTX),PeRCenTY,PeRCenTZ) -> u82(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     176: u82(PeRCenTX,active(PeRCenTY),PeRCenTZ) -> u82(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     177: u82(PeRCenTX,PeRCenTY,active(PeRCenTZ)) -> u82(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||     178: fst(mark(PeRCenTX)) -> fst(PeRCenTX)
 ||     179: fst(active(PeRCenTX)) -> fst(PeRCenTX)
 ||     180: natsFrom(mark(PeRCenTX)) -> natsFrom(PeRCenTX)
 ||     181: natsFrom(active(PeRCenTX)) -> natsFrom(PeRCenTX)
 ||     182: s(mark(PeRCenTX)) -> s(PeRCenTX)
 ||     183: s(active(PeRCenTX)) -> s(PeRCenTX)
 ||     184: sel(mark(PeRCenTX),PeRCenTY) -> sel(PeRCenTX,PeRCenTY)
 ||     185: sel(PeRCenTX,mark(PeRCenTY)) -> sel(PeRCenTX,PeRCenTY)
 ||     186: sel(active(PeRCenTX),PeRCenTY) -> sel(PeRCenTX,PeRCenTY)
 ||     187: sel(PeRCenTX,active(PeRCenTY)) -> sel(PeRCenTX,PeRCenTY)
 ||     188: tail(mark(PeRCenTX)) -> tail(PeRCenTX)
 ||     189: tail(active(PeRCenTX)) -> tail(PeRCenTX)
 ||     190: take(mark(PeRCenTX),PeRCenTY) -> take(PeRCenTX,PeRCenTY)
 ||     191: take(PeRCenTX,mark(PeRCenTY)) -> take(PeRCenTX,PeRCenTY)
 ||     192: take(active(PeRCenTX),PeRCenTY) -> take(PeRCenTX,PeRCenTY)
 ||     193: take(PeRCenTX,active(PeRCenTY)) -> take(PeRCenTX,PeRCenTY)
 ||     194: TIlDePAIR(PeRCenTX,PeRCenTY) -> PeRCenTX
 ||     195: TIlDePAIR(PeRCenTX,PeRCenTY) -> PeRCenTY
 || Number of strict rules: 195
 || Direct POLO(bPol) ... failed.
 || Uncurrying ... failed.
 || Dependency Pairs:
 ||    #1: #active(u12(tt(),PeRCenTX,PeRCenTY)) -> #mark(snd(splitAt(PeRCenTX,PeRCenTY)))
 ||    #2: #active(u12(tt(),PeRCenTX,PeRCenTY)) -> #snd(splitAt(PeRCenTX,PeRCenTY))
 ||    #3: #active(u12(tt(),PeRCenTX,PeRCenTY)) -> #splitAt(PeRCenTX,PeRCenTY)
 ||    #4: #u22(active(PeRCenTX),PeRCenTY) -> #u22(PeRCenTX,PeRCenTY)
 ||    #5: #mark(u52(PeRCenTX,PeRCenTY)) -> #active(u52(mark(PeRCenTX),PeRCenTY))
 ||    #6: #mark(u52(PeRCenTX,PeRCenTY)) -> #u52(mark(PeRCenTX),PeRCenTY)
 ||    #7: #mark(u52(PeRCenTX,PeRCenTY)) -> #mark(PeRCenTX)
 ||    #8: #mark(u11(PeRCenTX,PeRCenTY,PeRCenTZ)) -> #active(u11(mark(PeRCenTX),PeRCenTY,PeRCenTZ))
 ||    #9: #mark(u11(PeRCenTX,PeRCenTY,PeRCenTZ)) -> #u11(mark(PeRCenTX),PeRCenTY,PeRCenTZ)
 ||    #10: #mark(u11(PeRCenTX,PeRCenTY,PeRCenTZ)) -> #mark(PeRCenTX)
 ||    #11: #mark(u22(PeRCenTX,PeRCenTY)) -> #active(u22(mark(PeRCenTX),PeRCenTY))
 ||    #12: #mark(u22(PeRCenTX,PeRCenTY)) -> #u22(mark(PeRCenTX),PeRCenTY)
 ||    #13: #mark(u22(PeRCenTX,PeRCenTY)) -> #mark(PeRCenTX)
 ||    #14: #u21(PeRCenTX,active(PeRCenTY)) -> #u21(PeRCenTX,PeRCenTY)
 ||    #15: #u11(PeRCenTX,active(PeRCenTY),PeRCenTZ) -> #u11(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #16: #u82(PeRCenTX,PeRCenTY,active(PeRCenTZ)) -> #u82(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #17: #mark(u63(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)) -> #active(u63(mark(PeRCenTX),PeRCenTY,PeRCenTZ,PeRCenTU))
 ||    #18: #mark(u63(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)) -> #u63(mark(PeRCenTX),PeRCenTY,PeRCenTZ,PeRCenTU)
 ||    #19: #mark(u63(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)) -> #mark(PeRCenTX)
 ||    #20: #mark(u51(PeRCenTX,PeRCenTY)) -> #active(u51(mark(PeRCenTX),PeRCenTY))
 ||    #21: #mark(u51(PeRCenTX,PeRCenTY)) -> #u51(mark(PeRCenTX),PeRCenTY)
 ||    #22: #mark(u51(PeRCenTX,PeRCenTY)) -> #mark(PeRCenTX)
 ||    #23: #u51(PeRCenTX,mark(PeRCenTY)) -> #u51(PeRCenTX,PeRCenTY)
 ||    #24: #u64(PeRCenTX,active(PeRCenTY)) -> #u64(PeRCenTX,PeRCenTY)
 ||    #25: #u32(PeRCenTX,active(PeRCenTY)) -> #u32(PeRCenTX,PeRCenTY)
 ||    #26: #mark(afterNth(PeRCenTX,PeRCenTY)) -> #active(afterNth(mark(PeRCenTX),mark(PeRCenTY)))
 ||    #27: #mark(afterNth(PeRCenTX,PeRCenTY)) -> #afterNth(mark(PeRCenTX),mark(PeRCenTY))
 ||    #28: #mark(afterNth(PeRCenTX,PeRCenTY)) -> #mark(PeRCenTX)
 ||    #29: #mark(afterNth(PeRCenTX,PeRCenTY)) -> #mark(PeRCenTY)
 ||    #30: #mark(u32(PeRCenTX,PeRCenTY)) -> #active(u32(mark(PeRCenTX),PeRCenTY))
 ||    #31: #mark(u32(PeRCenTX,PeRCenTY)) -> #u32(mark(PeRCenTX),PeRCenTY)
 ||    #32: #mark(u32(PeRCenTX,PeRCenTY)) -> #mark(PeRCenTX)
 ||    #33: #u51(mark(PeRCenTX),PeRCenTY) -> #u51(PeRCenTX,PeRCenTY)
 ||    #34: #u41(active(PeRCenTX),PeRCenTY,PeRCenTZ) -> #u41(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #35: #u72(PeRCenTX,mark(PeRCenTY)) -> #u72(PeRCenTX,PeRCenTY)
 ||    #36: #u41(PeRCenTX,mark(PeRCenTY),PeRCenTZ) -> #u41(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #37: #u31(PeRCenTX,active(PeRCenTY)) -> #u31(PeRCenTX,PeRCenTY)
 ||    #38: #u12(PeRCenTX,PeRCenTY,active(PeRCenTZ)) -> #u12(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #39: #mark(u64(PeRCenTX,PeRCenTY)) -> #active(u64(mark(PeRCenTX),PeRCenTY))
 ||    #40: #mark(u64(PeRCenTX,PeRCenTY)) -> #u64(mark(PeRCenTX),PeRCenTY)
 ||    #41: #mark(u64(PeRCenTX,PeRCenTY)) -> #mark(PeRCenTX)
 ||    #42: #take(PeRCenTX,mark(PeRCenTY)) -> #take(PeRCenTX,PeRCenTY)
 ||    #43: #mark(u82(PeRCenTX,PeRCenTY,PeRCenTZ)) -> #active(u82(mark(PeRCenTX),PeRCenTY,PeRCenTZ))
 ||    #44: #mark(u82(PeRCenTX,PeRCenTY,PeRCenTZ)) -> #u82(mark(PeRCenTX),PeRCenTY,PeRCenTZ)
 ||    #45: #mark(u82(PeRCenTX,PeRCenTY,PeRCenTZ)) -> #mark(PeRCenTX)
 ||    #46: #u82(PeRCenTX,mark(PeRCenTY),PeRCenTZ) -> #u82(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #47: #u12(active(PeRCenTX),PeRCenTY,PeRCenTZ) -> #u12(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #48: #u64(PeRCenTX,mark(PeRCenTY)) -> #u64(PeRCenTX,PeRCenTY)
 ||    #49: #u63(PeRCenTX,mark(PeRCenTY),PeRCenTZ,PeRCenTU) -> #u63(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||    #50: #mark(pair(PeRCenTX,PeRCenTY)) -> #active(pair(mark(PeRCenTX),mark(PeRCenTY)))
 ||    #51: #mark(pair(PeRCenTX,PeRCenTY)) -> #pair(mark(PeRCenTX),mark(PeRCenTY))
 ||    #52: #mark(pair(PeRCenTX,PeRCenTY)) -> #mark(PeRCenTX)
 ||    #53: #mark(pair(PeRCenTX,PeRCenTY)) -> #mark(PeRCenTY)
 ||    #54: #u61(PeRCenTX,mark(PeRCenTY),PeRCenTZ,PeRCenTU) -> #u61(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||    #55: #snd(active(PeRCenTX)) -> #snd(PeRCenTX)
 ||    #56: #fst(mark(PeRCenTX)) -> #fst(PeRCenTX)
 ||    #57: #afterNth(active(PeRCenTX),PeRCenTY) -> #afterNth(PeRCenTX,PeRCenTY)
 ||    #58: #snd(mark(PeRCenTX)) -> #snd(PeRCenTX)
 ||    #59: #u81(PeRCenTX,active(PeRCenTY),PeRCenTZ) -> #u81(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #60: #mark(0()) -> #active(0())
 ||    #61: #u63(mark(PeRCenTX),PeRCenTY,PeRCenTZ,PeRCenTU) -> #u63(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||    #62: #afterNth(PeRCenTX,active(PeRCenTY)) -> #afterNth(PeRCenTX,PeRCenTY)
 ||    #63: #u71(mark(PeRCenTX),PeRCenTY) -> #u71(PeRCenTX,PeRCenTY)
 ||    #64: #mark(take(PeRCenTX,PeRCenTY)) -> #active(take(mark(PeRCenTX),mark(PeRCenTY)))
 ||    #65: #mark(take(PeRCenTX,PeRCenTY)) -> #take(mark(PeRCenTX),mark(PeRCenTY))
 ||    #66: #mark(take(PeRCenTX,PeRCenTY)) -> #mark(PeRCenTX)
 ||    #67: #mark(take(PeRCenTX,PeRCenTY)) -> #mark(PeRCenTY)
 ||    #68: #mark(u41(PeRCenTX,PeRCenTY,PeRCenTZ)) -> #active(u41(mark(PeRCenTX),PeRCenTY,PeRCenTZ))
 ||    #69: #mark(u41(PeRCenTX,PeRCenTY,PeRCenTZ)) -> #u41(mark(PeRCenTX),PeRCenTY,PeRCenTZ)
 ||    #70: #mark(u41(PeRCenTX,PeRCenTY,PeRCenTZ)) -> #mark(PeRCenTX)
 ||    #71: #pair(PeRCenTX,mark(PeRCenTY)) -> #pair(PeRCenTX,PeRCenTY)
 ||    #72: #cons(mark(PeRCenTX),PeRCenTY) -> #cons(PeRCenTX,PeRCenTY)
 ||    #73: #u51(active(PeRCenTX),PeRCenTY) -> #u51(PeRCenTX,PeRCenTY)
 ||    #74: #cons(PeRCenTX,mark(PeRCenTY)) -> #cons(PeRCenTX,PeRCenTY)
 ||    #75: #active(u32(tt(),PeRCenTX)) -> #mark(PeRCenTX)
 ||    #76: #u72(PeRCenTX,active(PeRCenTY)) -> #u72(PeRCenTX,PeRCenTY)
 ||    #77: #mark(nil()) -> #active(nil())
 ||    #78: #take(PeRCenTX,active(PeRCenTY)) -> #take(PeRCenTX,PeRCenTY)
 ||    #79: #afterNth(mark(PeRCenTX),PeRCenTY) -> #afterNth(PeRCenTX,PeRCenTY)
 ||    #80: #u62(PeRCenTX,PeRCenTY,mark(PeRCenTZ),PeRCenTU) -> #u62(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||    #81: #mark(natsFrom(PeRCenTX)) -> #active(natsFrom(mark(PeRCenTX)))
 ||    #82: #mark(natsFrom(PeRCenTX)) -> #natsFrom(mark(PeRCenTX))
 ||    #83: #mark(natsFrom(PeRCenTX)) -> #mark(PeRCenTX)
 ||    #84: #u11(PeRCenTX,PeRCenTY,active(PeRCenTZ)) -> #u11(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #85: #mark(head(PeRCenTX)) -> #active(head(mark(PeRCenTX)))
 ||    #86: #mark(head(PeRCenTX)) -> #head(mark(PeRCenTX))
 ||    #87: #mark(head(PeRCenTX)) -> #mark(PeRCenTX)
 ||    #88: #u31(active(PeRCenTX),PeRCenTY) -> #u31(PeRCenTX,PeRCenTY)
 ||    #89: #u64(mark(PeRCenTX),PeRCenTY) -> #u64(PeRCenTX,PeRCenTY)
 ||    #90: #u42(PeRCenTX,PeRCenTY,active(PeRCenTZ)) -> #u42(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #91: #mark(u72(PeRCenTX,PeRCenTY)) -> #active(u72(mark(PeRCenTX),PeRCenTY))
 ||    #92: #mark(u72(PeRCenTX,PeRCenTY)) -> #u72(mark(PeRCenTX),PeRCenTY)
 ||    #93: #mark(u72(PeRCenTX,PeRCenTY)) -> #mark(PeRCenTX)
 ||    #94: #active(u63(tt(),PeRCenTX,PeRCenTY,PeRCenTZ)) -> #mark(u64(splitAt(PeRCenTX,PeRCenTZ),PeRCenTY))
 ||    #95: #active(u63(tt(),PeRCenTX,PeRCenTY,PeRCenTZ)) -> #u64(splitAt(PeRCenTX,PeRCenTZ),PeRCenTY)
 ||    #96: #active(u63(tt(),PeRCenTX,PeRCenTY,PeRCenTZ)) -> #splitAt(PeRCenTX,PeRCenTZ)
 ||    #97: #active(u51(tt(),PeRCenTX)) -> #mark(u52(tt(),PeRCenTX))
 ||    #98: #active(u51(tt(),PeRCenTX)) -> #u52(tt(),PeRCenTX)
 ||    #99: #active(u61(tt(),PeRCenTX,PeRCenTY,PeRCenTZ)) -> #mark(u62(tt(),PeRCenTX,PeRCenTY,PeRCenTZ))
 ||    #100: #active(u61(tt(),PeRCenTX,PeRCenTY,PeRCenTZ)) -> #u62(tt(),PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #101: #u41(PeRCenTX,PeRCenTY,mark(PeRCenTZ)) -> #u41(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #102: #cons(active(PeRCenTX),PeRCenTY) -> #cons(PeRCenTX,PeRCenTY)
 ||    #103: #mark(sel(PeRCenTX,PeRCenTY)) -> #active(sel(mark(PeRCenTX),mark(PeRCenTY)))
 ||    #104: #mark(sel(PeRCenTX,PeRCenTY)) -> #sel(mark(PeRCenTX),mark(PeRCenTY))
 ||    #105: #mark(sel(PeRCenTX,PeRCenTY)) -> #mark(PeRCenTX)
 ||    #106: #mark(sel(PeRCenTX,PeRCenTY)) -> #mark(PeRCenTY)
 ||    #107: #splitAt(mark(PeRCenTX),PeRCenTY) -> #splitAt(PeRCenTX,PeRCenTY)
 ||    #108: #u81(PeRCenTX,mark(PeRCenTY),PeRCenTZ) -> #u81(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #109: #take(mark(PeRCenTX),PeRCenTY) -> #take(PeRCenTX,PeRCenTY)
 ||    #110: #head(active(PeRCenTX)) -> #head(PeRCenTX)
 ||    #111: #u32(active(PeRCenTX),PeRCenTY) -> #u32(PeRCenTX,PeRCenTY)
 ||    #112: #active(snd(pair(PeRCenTX,PeRCenTY))) -> #mark(u51(tt(),PeRCenTY))
 ||    #113: #active(snd(pair(PeRCenTX,PeRCenTY))) -> #u51(tt(),PeRCenTY)
 ||    #114: #u62(active(PeRCenTX),PeRCenTY,PeRCenTZ,PeRCenTU) -> #u62(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||    #115: #u12(PeRCenTX,PeRCenTY,mark(PeRCenTZ)) -> #u12(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #116: #active(sel(PeRCenTX,PeRCenTY)) -> #mark(u41(tt(),PeRCenTX,PeRCenTY))
 ||    #117: #active(sel(PeRCenTX,PeRCenTY)) -> #u41(tt(),PeRCenTX,PeRCenTY)
 ||    #118: #u61(PeRCenTX,PeRCenTY,active(PeRCenTZ),PeRCenTU) -> #u61(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||    #119: #u21(PeRCenTX,mark(PeRCenTY)) -> #u21(PeRCenTX,PeRCenTY)
 ||    #120: #u52(mark(PeRCenTX),PeRCenTY) -> #u52(PeRCenTX,PeRCenTY)
 ||    #121: #splitAt(active(PeRCenTX),PeRCenTY) -> #splitAt(PeRCenTX,PeRCenTY)
 ||    #122: #mark(u62(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)) -> #active(u62(mark(PeRCenTX),PeRCenTY,PeRCenTZ,PeRCenTU))
 ||    #123: #mark(u62(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)) -> #u62(mark(PeRCenTX),PeRCenTY,PeRCenTZ,PeRCenTU)
 ||    #124: #mark(u62(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)) -> #mark(PeRCenTX)
 ||    #125: #u41(mark(PeRCenTX),PeRCenTY,PeRCenTZ) -> #u41(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #126: #u12(PeRCenTX,mark(PeRCenTY),PeRCenTZ) -> #u12(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #127: #u41(PeRCenTX,PeRCenTY,active(PeRCenTZ)) -> #u41(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #128: #active(u62(tt(),PeRCenTX,PeRCenTY,PeRCenTZ)) -> #mark(u63(tt(),PeRCenTX,PeRCenTY,PeRCenTZ))
 ||    #129: #active(u62(tt(),PeRCenTX,PeRCenTY,PeRCenTZ)) -> #u63(tt(),PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #130: #mark(u12(PeRCenTX,PeRCenTY,PeRCenTZ)) -> #active(u12(mark(PeRCenTX),PeRCenTY,PeRCenTZ))
 ||    #131: #mark(u12(PeRCenTX,PeRCenTY,PeRCenTZ)) -> #u12(mark(PeRCenTX),PeRCenTY,PeRCenTZ)
 ||    #132: #mark(u12(PeRCenTX,PeRCenTY,PeRCenTZ)) -> #mark(PeRCenTX)
 ||    #133: #u72(active(PeRCenTX),PeRCenTY) -> #u72(PeRCenTX,PeRCenTY)
 ||    #134: #splitAt(PeRCenTX,active(PeRCenTY)) -> #splitAt(PeRCenTX,PeRCenTY)
 ||    #135: #mark(s(PeRCenTX)) -> #active(s(mark(PeRCenTX)))
 ||    #136: #mark(s(PeRCenTX)) -> #s(mark(PeRCenTX))
 ||    #137: #mark(s(PeRCenTX)) -> #mark(PeRCenTX)
 ||    #138: #u31(PeRCenTX,mark(PeRCenTY)) -> #u31(PeRCenTX,PeRCenTY)
 ||    #139: #u62(PeRCenTX,PeRCenTY,PeRCenTZ,mark(PeRCenTU)) -> #u62(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||    #140: #u21(active(PeRCenTX),PeRCenTY) -> #u21(PeRCenTX,PeRCenTY)
 ||    #141: #afterNth(PeRCenTX,mark(PeRCenTY)) -> #afterNth(PeRCenTX,PeRCenTY)
 ||    #142: #active(u64(pair(PeRCenTX,PeRCenTY),PeRCenTZ)) -> #mark(pair(cons(PeRCenTZ,PeRCenTX),PeRCenTY))
 ||    #143: #active(u64(pair(PeRCenTX,PeRCenTY),PeRCenTZ)) -> #pair(cons(PeRCenTZ,PeRCenTX),PeRCenTY)
 ||    #144: #active(u64(pair(PeRCenTX,PeRCenTY),PeRCenTZ)) -> #cons(PeRCenTZ,PeRCenTX)
 ||    #145: #u42(PeRCenTX,active(PeRCenTY),PeRCenTZ) -> #u42(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #146: #sel(PeRCenTX,mark(PeRCenTY)) -> #sel(PeRCenTX,PeRCenTY)
 ||    #147: #u11(mark(PeRCenTX),PeRCenTY,PeRCenTZ) -> #u11(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #148: #mark(tt()) -> #active(tt())
 ||    #149: #mark(u81(PeRCenTX,PeRCenTY,PeRCenTZ)) -> #active(u81(mark(PeRCenTX),PeRCenTY,PeRCenTZ))
 ||    #150: #mark(u81(PeRCenTX,PeRCenTY,PeRCenTZ)) -> #u81(mark(PeRCenTX),PeRCenTY,PeRCenTZ)
 ||    #151: #mark(u81(PeRCenTX,PeRCenTY,PeRCenTZ)) -> #mark(PeRCenTX)
 ||    #152: #mark(cons(PeRCenTX,PeRCenTY)) -> #active(cons(mark(PeRCenTX),PeRCenTY))
 ||    #153: #mark(cons(PeRCenTX,PeRCenTY)) -> #cons(mark(PeRCenTX),PeRCenTY)
 ||    #154: #mark(cons(PeRCenTX,PeRCenTY)) -> #mark(PeRCenTX)
 ||    #155: #active(splitAt(0(),PeRCenTX)) -> #mark(pair(nil(),PeRCenTX))
 ||    #156: #active(splitAt(0(),PeRCenTX)) -> #pair(nil(),PeRCenTX)
 ||    #157: #u62(mark(PeRCenTX),PeRCenTY,PeRCenTZ,PeRCenTU) -> #u62(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||    #158: #u81(mark(PeRCenTX),PeRCenTY,PeRCenTZ) -> #u81(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #159: #head(mark(PeRCenTX)) -> #head(PeRCenTX)
 ||    #160: #u61(PeRCenTX,PeRCenTY,PeRCenTZ,active(PeRCenTU)) -> #u61(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||    #161: #active(fst(pair(PeRCenTX,PeRCenTY))) -> #mark(u21(tt(),PeRCenTX))
 ||    #162: #active(fst(pair(PeRCenTX,PeRCenTY))) -> #u21(tt(),PeRCenTX)
 ||    #163: #fst(active(PeRCenTX)) -> #fst(PeRCenTX)
 ||    #164: #u61(active(PeRCenTX),PeRCenTY,PeRCenTZ,PeRCenTU) -> #u61(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||    #165: #u82(PeRCenTX,PeRCenTY,mark(PeRCenTZ)) -> #u82(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #166: #u31(mark(PeRCenTX),PeRCenTY) -> #u31(PeRCenTX,PeRCenTY)
 ||    #167: #active(u41(tt(),PeRCenTX,PeRCenTY)) -> #mark(u42(tt(),PeRCenTX,PeRCenTY))
 ||    #168: #active(u41(tt(),PeRCenTX,PeRCenTY)) -> #u42(tt(),PeRCenTX,PeRCenTY)
 ||    #169: #mark(u42(PeRCenTX,PeRCenTY,PeRCenTZ)) -> #active(u42(mark(PeRCenTX),PeRCenTY,PeRCenTZ))
 ||    #170: #mark(u42(PeRCenTX,PeRCenTY,PeRCenTZ)) -> #u42(mark(PeRCenTX),PeRCenTY,PeRCenTZ)
 ||    #171: #mark(u42(PeRCenTX,PeRCenTY,PeRCenTZ)) -> #mark(PeRCenTX)
 ||    #172: #pair(PeRCenTX,active(PeRCenTY)) -> #pair(PeRCenTX,PeRCenTY)
 ||    #173: #u62(PeRCenTX,PeRCenTY,active(PeRCenTZ),PeRCenTU) -> #u62(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||    #174: #active(u52(tt(),PeRCenTX)) -> #mark(PeRCenTX)
 ||    #175: #u32(mark(PeRCenTX),PeRCenTY) -> #u32(PeRCenTX,PeRCenTY)
 ||    #176: #u82(active(PeRCenTX),PeRCenTY,PeRCenTZ) -> #u82(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #177: #u52(PeRCenTX,mark(PeRCenTY)) -> #u52(PeRCenTX,PeRCenTY)
 ||    #178: #u32(PeRCenTX,mark(PeRCenTY)) -> #u32(PeRCenTX,PeRCenTY)
 ||    #179: #u11(PeRCenTX,PeRCenTY,mark(PeRCenTZ)) -> #u11(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #180: #mark(splitAt(PeRCenTX,PeRCenTY)) -> #active(splitAt(mark(PeRCenTX),mark(PeRCenTY)))
 ||    #181: #mark(splitAt(PeRCenTX,PeRCenTY)) -> #splitAt(mark(PeRCenTX),mark(PeRCenTY))
 ||    #182: #mark(splitAt(PeRCenTX,PeRCenTY)) -> #mark(PeRCenTX)
 ||    #183: #mark(splitAt(PeRCenTX,PeRCenTY)) -> #mark(PeRCenTY)
 ||    #184: #u12(PeRCenTX,active(PeRCenTY),PeRCenTZ) -> #u12(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #185: #u72(mark(PeRCenTX),PeRCenTY) -> #u72(PeRCenTX,PeRCenTY)
 ||    #186: #sel(mark(PeRCenTX),PeRCenTY) -> #sel(PeRCenTX,PeRCenTY)
 ||    #187: #u52(active(PeRCenTX),PeRCenTY) -> #u52(PeRCenTX,PeRCenTY)
 ||    #188: #active(u31(tt(),PeRCenTX)) -> #mark(u32(tt(),PeRCenTX))
 ||    #189: #active(u31(tt(),PeRCenTX)) -> #u32(tt(),PeRCenTX)
 ||    #190: #mark(u61(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)) -> #active(u61(mark(PeRCenTX),PeRCenTY,PeRCenTZ,PeRCenTU))
 ||    #191: #mark(u61(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)) -> #u61(mark(PeRCenTX),PeRCenTY,PeRCenTZ,PeRCenTU)
 ||    #192: #mark(u61(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)) -> #mark(PeRCenTX)
 ||    #193: #u11(active(PeRCenTX),PeRCenTY,PeRCenTZ) -> #u11(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #194: #u64(active(PeRCenTX),PeRCenTY) -> #u64(PeRCenTX,PeRCenTY)
 ||    #195: #active(take(PeRCenTX,PeRCenTY)) -> #mark(u81(tt(),PeRCenTX,PeRCenTY))
 ||    #196: #active(take(PeRCenTX,PeRCenTY)) -> #u81(tt(),PeRCenTX,PeRCenTY)
 ||    #197: #active(natsFrom(PeRCenTX)) -> #mark(cons(PeRCenTX,natsFrom(s(PeRCenTX))))
 ||    #198: #active(natsFrom(PeRCenTX)) -> #cons(PeRCenTX,natsFrom(s(PeRCenTX)))
 ||    #199: #active(natsFrom(PeRCenTX)) -> #natsFrom(s(PeRCenTX))
 ||    #200: #active(natsFrom(PeRCenTX)) -> #s(PeRCenTX)
 ||    #201: #u61(PeRCenTX,active(PeRCenTY),PeRCenTZ,PeRCenTU) -> #u61(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||    #202: #u81(active(PeRCenTX),PeRCenTY,PeRCenTZ) -> #u81(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #203: #mark(u21(PeRCenTX,PeRCenTY)) -> #active(u21(mark(PeRCenTX),PeRCenTY))
 ||    #204: #mark(u21(PeRCenTX,PeRCenTY)) -> #u21(mark(PeRCenTX),PeRCenTY)
 ||    #205: #mark(u21(PeRCenTX,PeRCenTY)) -> #mark(PeRCenTX)
 ||    #206: #u81(PeRCenTX,PeRCenTY,active(PeRCenTZ)) -> #u81(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #207: #s(active(PeRCenTX)) -> #s(PeRCenTX)
 ||    #208: #u22(mark(PeRCenTX),PeRCenTY) -> #u22(PeRCenTX,PeRCenTY)
 ||    #209: #u22(PeRCenTX,active(PeRCenTY)) -> #u22(PeRCenTX,PeRCenTY)
 ||    #210: #cons(PeRCenTX,active(PeRCenTY)) -> #cons(PeRCenTX,PeRCenTY)
 ||    #211: #active(tail(cons(PeRCenTX,PeRCenTY))) -> #mark(u71(tt(),PeRCenTY))
 ||    #212: #active(tail(cons(PeRCenTX,PeRCenTY))) -> #u71(tt(),PeRCenTY)
 ||    #213: #u62(PeRCenTX,PeRCenTY,PeRCenTZ,active(PeRCenTU)) -> #u62(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||    #214: #u63(PeRCenTX,PeRCenTY,active(PeRCenTZ),PeRCenTU) -> #u63(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||    #215: #u63(active(PeRCenTX),PeRCenTY,PeRCenTZ,PeRCenTU) -> #u63(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||    #216: #u71(PeRCenTX,active(PeRCenTY)) -> #u71(PeRCenTX,PeRCenTY)
 ||    #217: #sel(PeRCenTX,active(PeRCenTY)) -> #sel(PeRCenTX,PeRCenTY)
 ||    #218: #pair(mark(PeRCenTX),PeRCenTY) -> #pair(PeRCenTX,PeRCenTY)
 ||    #219: #mark(tail(PeRCenTX)) -> #active(tail(mark(PeRCenTX)))
 ||    #220: #mark(tail(PeRCenTX)) -> #tail(mark(PeRCenTX))
 ||    #221: #mark(tail(PeRCenTX)) -> #mark(PeRCenTX)
 ||    #222: #u51(PeRCenTX,active(PeRCenTY)) -> #u51(PeRCenTX,PeRCenTY)
 ||    #223: #u82(mark(PeRCenTX),PeRCenTY,PeRCenTZ) -> #u82(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #224: #active(u81(tt(),PeRCenTX,PeRCenTY)) -> #mark(u82(tt(),PeRCenTX,PeRCenTY))
 ||    #225: #active(u81(tt(),PeRCenTX,PeRCenTY)) -> #u82(tt(),PeRCenTX,PeRCenTY)
 ||    #226: #mark(snd(PeRCenTX)) -> #active(snd(mark(PeRCenTX)))
 ||    #227: #mark(snd(PeRCenTX)) -> #snd(mark(PeRCenTX))
 ||    #228: #mark(snd(PeRCenTX)) -> #mark(PeRCenTX)
 ||    #229: #active(afterNth(PeRCenTX,PeRCenTY)) -> #mark(u11(tt(),PeRCenTX,PeRCenTY))
 ||    #230: #active(afterNth(PeRCenTX,PeRCenTY)) -> #u11(tt(),PeRCenTX,PeRCenTY)
 ||    #231: #u63(PeRCenTX,active(PeRCenTY),PeRCenTZ,PeRCenTU) -> #u63(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||    #232: #u61(PeRCenTX,PeRCenTY,PeRCenTZ,mark(PeRCenTU)) -> #u61(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||    #233: #take(active(PeRCenTX),PeRCenTY) -> #take(PeRCenTX,PeRCenTY)
 ||    #234: #sel(active(PeRCenTX),PeRCenTY) -> #sel(PeRCenTX,PeRCenTY)
 ||    #235: #u82(PeRCenTX,active(PeRCenTY),PeRCenTZ) -> #u82(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #236: #u11(PeRCenTX,mark(PeRCenTY),PeRCenTZ) -> #u11(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #237: #u62(PeRCenTX,active(PeRCenTY),PeRCenTZ,PeRCenTU) -> #u62(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||    #238: #u42(active(PeRCenTX),PeRCenTY,PeRCenTZ) -> #u42(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #239: #active(splitAt(s(PeRCenTX),cons(PeRCenTY,PeRCenTZ))) -> #mark(u61(tt(),PeRCenTX,PeRCenTY,PeRCenTZ))
 ||    #240: #active(splitAt(s(PeRCenTX),cons(PeRCenTY,PeRCenTZ))) -> #u61(tt(),PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #241: #u41(PeRCenTX,active(PeRCenTY),PeRCenTZ) -> #u41(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #242: #u22(PeRCenTX,mark(PeRCenTY)) -> #u22(PeRCenTX,PeRCenTY)
 ||    #243: #natsFrom(active(PeRCenTX)) -> #natsFrom(PeRCenTX)
 ||    #244: #u61(mark(PeRCenTX),PeRCenTY,PeRCenTZ,PeRCenTU) -> #u61(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||    #245: #u12(mark(PeRCenTX),PeRCenTY,PeRCenTZ) -> #u12(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #246: #u62(PeRCenTX,mark(PeRCenTY),PeRCenTZ,PeRCenTU) -> #u62(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||    #247: #mark(u31(PeRCenTX,PeRCenTY)) -> #active(u31(mark(PeRCenTX),PeRCenTY))
 ||    #248: #mark(u31(PeRCenTX,PeRCenTY)) -> #u31(mark(PeRCenTX),PeRCenTY)
 ||    #249: #mark(u31(PeRCenTX,PeRCenTY)) -> #mark(PeRCenTX)
 ||    #250: #active(head(cons(PeRCenTX,PeRCenTY))) -> #mark(u31(tt(),PeRCenTX))
 ||    #251: #active(head(cons(PeRCenTX,PeRCenTY))) -> #u31(tt(),PeRCenTX)
 ||    #252: #active(u72(tt(),PeRCenTX)) -> #mark(PeRCenTX)
 ||    #253: #active(u21(tt(),PeRCenTX)) -> #mark(u22(tt(),PeRCenTX))
 ||    #254: #active(u21(tt(),PeRCenTX)) -> #u22(tt(),PeRCenTX)
 ||    #255: #u71(PeRCenTX,mark(PeRCenTY)) -> #u71(PeRCenTX,PeRCenTY)
 ||    #256: #splitAt(PeRCenTX,mark(PeRCenTY)) -> #splitAt(PeRCenTX,PeRCenTY)
 ||    #257: #active(u11(tt(),PeRCenTX,PeRCenTY)) -> #mark(u12(tt(),PeRCenTX,PeRCenTY))
 ||    #258: #active(u11(tt(),PeRCenTX,PeRCenTY)) -> #u12(tt(),PeRCenTX,PeRCenTY)
 ||    #259: #u63(PeRCenTX,PeRCenTY,mark(PeRCenTZ),PeRCenTU) -> #u63(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||    #260: #u61(PeRCenTX,PeRCenTY,mark(PeRCenTZ),PeRCenTU) -> #u61(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||    #261: #mark(fst(PeRCenTX)) -> #active(fst(mark(PeRCenTX)))
 ||    #262: #mark(fst(PeRCenTX)) -> #fst(mark(PeRCenTX))
 ||    #263: #mark(fst(PeRCenTX)) -> #mark(PeRCenTX)
 ||    #264: #u71(active(PeRCenTX),PeRCenTY) -> #u71(PeRCenTX,PeRCenTY)
 ||    #265: #active(u42(tt(),PeRCenTX,PeRCenTY)) -> #mark(head(afterNth(PeRCenTX,PeRCenTY)))
 ||    #266: #active(u42(tt(),PeRCenTX,PeRCenTY)) -> #head(afterNth(PeRCenTX,PeRCenTY))
 ||    #267: #active(u42(tt(),PeRCenTX,PeRCenTY)) -> #afterNth(PeRCenTX,PeRCenTY)
 ||    #268: #pair(active(PeRCenTX),PeRCenTY) -> #pair(PeRCenTX,PeRCenTY)
 ||    #269: #u81(PeRCenTX,PeRCenTY,mark(PeRCenTZ)) -> #u81(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #270: #u63(PeRCenTX,PeRCenTY,PeRCenTZ,mark(PeRCenTU)) -> #u63(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||    #271: #u52(PeRCenTX,active(PeRCenTY)) -> #u52(PeRCenTX,PeRCenTY)
 ||    #272: #natsFrom(mark(PeRCenTX)) -> #natsFrom(PeRCenTX)
 ||    #273: #active(u71(tt(),PeRCenTX)) -> #mark(u72(tt(),PeRCenTX))
 ||    #274: #active(u71(tt(),PeRCenTX)) -> #u72(tt(),PeRCenTX)
 ||    #275: #u63(PeRCenTX,PeRCenTY,PeRCenTZ,active(PeRCenTU)) -> #u63(PeRCenTX,PeRCenTY,PeRCenTZ,PeRCenTU)
 ||    #276: #u42(mark(PeRCenTX),PeRCenTY,PeRCenTZ) -> #u42(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #277: #tail(active(PeRCenTX)) -> #tail(PeRCenTX)
 ||    #278: #u42(PeRCenTX,mark(PeRCenTY),PeRCenTZ) -> #u42(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #279: #active(u22(tt(),PeRCenTX)) -> #mark(PeRCenTX)
 ||    #280: #tail(mark(PeRCenTX)) -> #tail(PeRCenTX)
 ||    #281: #u42(PeRCenTX,PeRCenTY,mark(PeRCenTZ)) -> #u42(PeRCenTX,PeRCenTY,PeRCenTZ)
 ||    #282: #u21(mark(PeRCenTX),PeRCenTY) -> #u21(PeRCenTX,PeRCenTY)
 ||    #283: #mark(u71(PeRCenTX,PeRCenTY)) -> #active(u71(mark(PeRCenTX),PeRCenTY))
 ||    #284: #mark(u71(PeRCenTX,PeRCenTY)) -> #u71(mark(PeRCenTX),PeRCenTY)
 ||    #285: #mark(u71(PeRCenTX,PeRCenTY)) -> #mark(PeRCenTX)
 ||    #286: #active(u82(tt(),PeRCenTX,PeRCenTY)) -> #mark(fst(splitAt(PeRCenTX,PeRCenTY)))
 ||    #287: #active(u82(tt(),PeRCenTX,PeRCenTY)) -> #fst(splitAt(PeRCenTX,PeRCenTY))
 ||    #288: #active(u82(tt(),PeRCenTX,PeRCenTY)) -> #splitAt(PeRCenTX,PeRCenTY)
 ||    #289: #s(mark(PeRCenTX)) -> #s(PeRCenTX)
 || Number of SCCs: 31, DPs: 222
 ||   SCC { #243 #272 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: x1
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #243 #272
 || Number of SCCs: 30, DPs: 220
 ||   SCC { #110 #159 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: x1
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #110 #159
 || Number of SCCs: 29, DPs: 218
 ||   SCC { #207 #289 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: x1
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #207 #289
 || Number of SCCs: 28, DPs: 216
 ||   SCC { #277 #280 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: x1
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #277 #280
 || Number of SCCs: 27, DPs: 214
 ||   SCC { #55 #58 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: x1
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #55 #58
 || Number of SCCs: 26, DPs: 212
 ||   SCC { #56 #163 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: x1
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #56 #163
 || Number of SCCs: 25, DPs: 210
 ||   SCC { #120 #177 #187 #271 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: x1
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #120 #187
 || Number of SCCs: 25, DPs: 208
 ||   SCC { #177 #271 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: x2
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #177 #271
 || Number of SCCs: 24, DPs: 206
 ||   SCC { #24 #48 #89 #194 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: x1
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #89 #194
 || Number of SCCs: 24, DPs: 204
 ||   SCC { #24 #48 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: x2
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #24 #48
 || Number of SCCs: 23, DPs: 202
 ||   SCC { #42 #78 #109 #233 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: x1
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #109 #233
 || Number of SCCs: 23, DPs: 200
 ||   SCC { #42 #78 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: x2
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #42 #78
 || Number of SCCs: 22, DPs: 198
 ||   SCC { #146 #186 #217 #234 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: x2
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #146 #217
 || Number of SCCs: 22, DPs: 196
 ||   SCC { #186 #234 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: x1
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #186 #234
 || Number of SCCs: 21, DPs: 194
 ||   SCC { #72 #74 #102 #210 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: x1
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #72 #102
 || Number of SCCs: 21, DPs: 192
 ||   SCC { #74 #210 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: x2
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #74 #210
 || Number of SCCs: 20, DPs: 190
 ||   SCC { #57 #62 #79 #141 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: x2
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #62 #141
 || Number of SCCs: 20, DPs: 188
 ||   SCC { #57 #79 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: x1
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #57 #79
 || Number of SCCs: 19, DPs: 186
 ||   SCC { #71 #172 #218 #268 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: x2
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #71 #172
 || Number of SCCs: 19, DPs: 184
 ||   SCC { #218 #268 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: x1
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #218 #268
 || Number of SCCs: 18, DPs: 182
 ||   SCC { #4 #208 #209 #242 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: x1
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #4 #208
 || Number of SCCs: 18, DPs: 180
 ||   SCC { #209 #242 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: x2
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #209 #242
 || Number of SCCs: 17, DPs: 178
 ||   SCC { #23 #33 #73 #222 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: x2
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #23 #222
 || Number of SCCs: 17, DPs: 176
 ||   SCC { #33 #73 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: x1
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #33 #73
 || Number of SCCs: 16, DPs: 174
 ||   SCC { #25 #111 #175 #178 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: x1
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #111 #175
 || Number of SCCs: 16, DPs: 172
 ||   SCC { #25 #178 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: x2
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #25 #178
 || Number of SCCs: 15, DPs: 170
 ||   SCC { #37 #88 #138 #166 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: x1
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #88 #166
 || Number of SCCs: 15, DPs: 168
 ||   SCC { #37 #138 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: x2
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #37 #138
 || Number of SCCs: 14, DPs: 166
 ||   SCC { #14 #119 #140 #282 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: x2
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #14 #119
 || Number of SCCs: 14, DPs: 164
 ||   SCC { #140 #282 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: x1
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #140 #282
 || Number of SCCs: 13, DPs: 162
 ||   SCC { #35 #76 #133 #185 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: x1
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #133 #185
 || Number of SCCs: 13, DPs: 160
 ||   SCC { #35 #76 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: x2
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #35 #76
 || Number of SCCs: 12, DPs: 158
 ||   SCC { #63 #216 #255 #264 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: x1
 ||     USABLE RULES: { }
 ||     Removed DPs: #63 #264
 || Number of SCCs: 12, DPs: 156
 ||   SCC { #216 #255 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: x2
 ||     USABLE RULES: { }
 ||     Removed DPs: #216 #255
 || Number of SCCs: 11, DPs: 154
 ||   SCC { #107 #121 #134 #256 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: x1
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #107 #121
 || Number of SCCs: 11, DPs: 152
 ||   SCC { #134 #256 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: x2
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #134 #256
 || Number of SCCs: 10, DPs: 150
 ||   SCC { #15 #84 #147 #179 #193 #236 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: x2 + x3
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #15 #84 #179 #236
 || Number of SCCs: 10, DPs: 146
 ||   SCC { #147 #193 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: x1
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #147 #193
 || Number of SCCs: 9, DPs: 144
 ||   SCC { #34 #36 #101 #125 #127 #241 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: x1 + x2
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #34 #36 #125 #241
 || Number of SCCs: 9, DPs: 140
 ||   SCC { #101 #127 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: x3
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #101 #127
 || Number of SCCs: 8, DPs: 138
 ||   SCC { #38 #47 #115 #126 #184 #245 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: x1 + x2
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #47 #126 #184 #245
 || Number of SCCs: 8, DPs: 134
 ||   SCC { #38 #115 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: x3
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #38 #115
 || Number of SCCs: 7, DPs: 132
 ||   SCC { #16 #46 #165 #176 #223 #235 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: x1 + x3
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #16 #165 #176 #223
 || Number of SCCs: 7, DPs: 128
 ||   SCC { #46 #235 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: x2
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #46 #235
 || Number of SCCs: 6, DPs: 126
 ||   SCC { #59 #108 #158 #202 #206 #269 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: x2 + x3
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #59 #108 #206 #269
 || Number of SCCs: 6, DPs: 122
 ||   SCC { #158 #202 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: x1
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #158 #202
 || Number of SCCs: 5, DPs: 120
 ||   SCC { #90 #145 #238 #276 #278 #281 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: x2 + x3
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #90 #145 #278 #281
 || Number of SCCs: 5, DPs: 116
 ||   SCC { #238 #276 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: x1
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #238 #276
 || Number of SCCs: 4, DPs: 114
 ||   SCC { #49 #61 #214 #215 #231 #259 #270 #275 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: x2 + x3 + x4
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #49 #214 #231 #259 #270 #275
 || Number of SCCs: 4, DPs: 108
 ||   SCC { #61 #215 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: x1
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #61 #215
 || Number of SCCs: 3, DPs: 106
 ||   SCC { #80 #114 #139 #157 #173 #213 #237 #246 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: x2 + x3 + x4
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #80 #139 #173 #213 #237 #246
 || Number of SCCs: 3, DPs: 100
 ||   SCC { #114 #157 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
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 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
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 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: x1
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #114 #157
 || Number of SCCs: 2, DPs: 98
 ||   SCC { #54 #118 #160 #164 #201 #232 #244 #260 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: x1 + x2 + x3
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #54 #118 #164 #201 #244 #260
 || Number of SCCs: 2, DPs: 92
 ||   SCC { #160 #232 }
 || POLO(Sum)... succeeded.
 ||       u81	w: 0
 ||       #u22	w: 0
 ||       u62	w: 0
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: 0
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 0
 ||       #u21	w: 0
 ||       pair	w: 0
 ||       fst	w: 0
 ||       #u64	w: 0
 ||       natsFrom	w: 0
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: x4
 ||       splitAt	w: 0
 ||       u52	w: 0
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 0
 ||       #u81	w: 0
 ||       u41	w: 0
 ||       #u72	w: 0
 ||       u63	w: 0
 ||       u51	w: 0
 ||       tail	w: 0
 ||       #mark	w: 0
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: 0
 ||       sel	w: 0
 ||       u32	w: 0
 ||       #u63	w: 0
 ||       u64	w: 0
 ||       #s 	w: 0
 ||       afterNth	w: 0
 ||       nil	w: 0
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: 0
 ||       #afterNth	w: 0
 ||       u72	w: 0
 ||       u21	w: 0
 ||       #u41	w: 0
 ||       u82	w: 0
 ||       active	w: x1 + 1
 ||       head	w: 0
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: 0
 ||       #natsFrom	w: 0
 ||       #active	w: 0
 ||       #u31	w: 0
 ||       snd	w: 0
 ||       u22	w: 0
 ||       u42	w: 0
 ||       tt	w: 0
 ||       #pair	w: 0
 ||       u71	w: 0
 ||       #u32	w: 0
 ||       u31	w: 0
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { }
 ||     Removed DPs: #160 #232
 || Number of SCCs: 1, DPs: 90
 ||   SCC { #1 #5 #7 #8 #10 #11 #13 #17 #19 #20 #22 #26 #28..30 #32 #39 #41 #43 #45 #52 #53 #64 #66..68 #70 #75 #81 #83 #85 #87 #91 #93 #94 #97 #99 #103 #105 #106 #112 #116 #122 #124 #128 #130 #132 #137 #142 #149 #151 #154 #155 #161 #167 #169 #171 #174 #180 #182 #183 #188 #190 #192 #195 #197 #203 #205 #211 #219 #221 #224 #226 #228 #229 #239 #247 #249 #250 #252 #253 #257 #261 #263 #265 #273 #279 #283 #285 #286 }
 || POLO(Sum)... POLO(max)... succeeded.
 ||       u81	w: max(x1 + 26, x2 + 24, x3 + 23)
 ||       #u22	w: 0
 ||       u62	w: max(x1 + 12, x2 + 10, x3 + 9, x4 + 8)
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: x1
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: max(x1 + 29, x2 + 28)
 ||       #u21	w: 0
 ||       pair	w: max(x1 + 2, x2 + 1)
 ||       fst	w: x1 + 8
 ||       #u64	w: 0
 ||       natsFrom	w: x1 + 6
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: max(x1 + 10, x2 + 8)
 ||       u52	w: max(x1 + 2, x2 + 1)
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: max(x1 + 12, x2 + 10, x3 + 9, x4 + 8)
 ||       #u81	w: 0
 ||       u41	w: max(x1 + 45, x2 + 44, x3 + 43)
 ||       #u72	w: 0
 ||       u63	w: max(x1 + 12, x2 + 10, x3 + 7, x4 + 8)
 ||       u51	w: max(x1 + 5, x2 + 4)
 ||       tail	w: x1 + 9
 ||       #mark	w: x1
 ||       0 	w: 1
 ||       #sel	w: 0
 ||       u11	w: max(x1 + 26, x2 + 23, x3 + 25)
 ||       sel	w: max(x1 + 49, x2 + 48)
 ||       u32	w: max(x1 + 3, x2 + 1)
 ||       #u63	w: 0
 ||       u64	w: max(x1, x2 + 7)
 ||       #s 	w: 0
 ||       afterNth	w: max(x1 + 24, x2 + 28)
 ||       nil	w: 1
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1
 ||       u12	w: max(x1 + 21, x2 + 20, x3 + 19)
 ||       #afterNth	w: 0
 ||       u72	w: max(x1 + 2, x2 + 1)
 ||       u21	w: max(x1 + 6, x2 + 5)
 ||       #u41	w: 0
 ||       u82	w: max(x1 + 20, x2 + 19, x3 + 22)
 ||       active	w: x1
 ||       head	w: x1 + 7
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: max(x1 + 5, x2)
 ||       #natsFrom	w: 0
 ||       #active	w: x1
 ||       #u31	w: 0
 ||       snd	w: x1 + 8
 ||       u22	w: max(x1 + 2, x2 + 1)
 ||       u42	w: max(x1 + 40, x2 + 39, x3 + 38)
 ||       tt	w: 1
 ||       #pair	w: 0
 ||       u71	w: max(x1 + 5, x2 + 4)
 ||       #u32	w: 0
 ||       u31	w: max(x1 + 7, x2 + 5)
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { 1..193 }
 ||     Removed DPs: #1 #7 #10 #13 #19 #22 #28 #29 #32 #45 #52 #53 #66 #67 #70 #75 #83 #87 #93 #97 #105 #106 #112 #116 #124 #132 #151 #154 #155 #161 #167 #171 #174 #182 #183 #188 #192 #195 #205 #211 #221 #224 #228 #229 #249 #250 #252 #253 #257 #263 #265 #273 #279 #285 #286
 || Number of SCCs: 1, DPs: 10
 ||   SCC { #17 #41 #94 #99 #122 #128 #137 #180 #190 #239 }
 || POLO(Sum)... succeeded.
 ||       u81	w: x2 + 3
 ||       #u22	w: 0
 ||       u62	w: 7
 ||       TIlDePAIR	w: 0
 ||       #u82	w: 0
 ||       #cons	w: 0
 ||       s 	w: x1 + 1
 ||       #u52	w: 0
 ||       #take	w: 0
 ||       #u51	w: 0
 ||       take	w: 1
 ||       #u21	w: 0
 ||       pair	w: x1 + x2 + 1
 ||       fst	w: x1
 ||       #u64	w: 0
 ||       natsFrom	w: 1
 ||       #u12	w: 0
 ||       #head	w: 0
 ||       #u61	w: 0
 ||       splitAt	w: 7
 ||       u52	w: x2 + 3
 ||       #fst	w: 0
 ||       #u11	w: 0
 ||       u61	w: 7
 ||       #u81	w: 0
 ||       u41	w: x1 + x2 + x3
 ||       #u72	w: 0
 ||       u63	w: 7
 ||       u51	w: x2 + 1
 ||       tail	w: 4
 ||       #mark	w: x1 + 1
 ||       0 	w: 0
 ||       #sel	w: 0
 ||       u11	w: x2 + x3 + 4
 ||       sel	w: x1 + x2 + 3
 ||       u32	w: x1 + x2
 ||       #u63	w: 0
 ||       u64	w: x1
 ||       #s 	w: 0
 ||       afterNth	w: 1
 ||       nil	w: 8
 ||       #TIlDePAIR	w: 0
 ||       #tail	w: 0
 ||       #splitAt	w: 0
 ||       mark	w: x1 + 1
 ||       u12	w: x1 + x2 + x3
 ||       #afterNth	w: 0
 ||       u72	w: 1
 ||       u21	w: x1 + x2
 ||       #u41	w: 0
 ||       u82	w: x1 + x2 + x3
 ||       active	w: x1 + 2
 ||       head	w: x1
 ||       #u42	w: 0
 ||       #snd	w: 0
 ||       cons	w: x1 + 4
 ||       #natsFrom	w: 0
 ||       #active	w: 8
 ||       #u31	w: 0
 ||       snd	w: 1
 ||       u22	w: x1 + x2
 ||       u42	w: x2
 ||       tt	w: 5
 ||       #pair	w: 0
 ||       u71	w: x1
 ||       #u32	w: 0
 ||       u31	w: x1
 ||       #u62	w: 0
 ||       #u71	w: 0
 ||     USABLE RULES: { 62..107 110..177 180..183 190..193 }
 ||     Removed DPs: #137
 || Number of SCCs: 1, DPs: 9
 ||   SCC { #17 #41 #94 #99 #122 #128 #180 #190 #239 }
 || POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
 ||       u81	s: [2]	p: 0	w: x1 + x2 + x3 + 41
 ||       #u22	s: [1]	p: 0	w: x1
 ||       u62	s: [2,1]	p: 5	w: max(x1 + 38, x2 + 47, x3 + 41, x4 + 34)
 ||       TIlDePAIR	s: [1,2]	p: 0	w: x1 + x2 + 1
 ||       #u82	s: [1,3]	p: 0	w: x1 + x3
 ||       #cons	s: []	p: 0	w: max(x2 + 1)
 ||       s 	s: [1]	p: 0	w: x1
 ||       #u52	s: []	p: 0	w: x2 + 1
 ||       #take	s: [1]	p: 0	w: x1 + 1
 ||       #u51	s: []	p: 0	w: x2
 ||       take	s: [2]	p: 1	w: x1 + x2 + 49
 ||       #u21	s: [1,2]	p: 0	w: x1 + x2 + 1
 ||       pair	s: []	p: 2	w: max(x1 + 10, x2 + 21)
 ||       fst	s: [1]	p: 2	w: x1
 ||       #u64	s: []	p: 0	w: max(x1 + 1)
 ||       natsFrom	s: [1]	p: 4	w: x1 + 46
 ||       #u12	s: [1,3]	p: 0	w: x1 + x3 + 1
 ||       #head	s: []	p: 0	w: 1
 ||       #u61	s: [2]	p: 0	w: max(x2)
 ||       splitAt	s: [1]	p: 5	w: max(x1 + 47, x2 + 34)
 ||       u52	s: [2]	p: 1	w: x2
 ||       #fst	s: []	p: 0	w: 0
 ||       #u11	s: [3,2,1]	p: 0	w: x1 + x2 + x3
 ||       u61	s: [2,1,3]	p: 5	w: max(x1 + 37, x2 + 47, x3 + 42, x4 + 34)
 ||       #u81	s: []	p: 0	w: 1
 ||       u41	s: []	p: 6	w: x2 + x3 + 51
 ||       #u72	s: []	p: 0	w: 0
 ||       u63	s: [2,1]	p: 5	w: max(x1 + 39, x2 + 47, x3 + 40, x4 + 34)
 ||       u51	s: [1]	p: 1	w: x1 + x2 + 4
 ||       tail	s: []	p: 4	w: x1 + 10
 ||       #mark	s: 1
 ||       0 	s: []	p: 2	w: 22
 ||       #sel	s: [2,1]	p: 0	w: x1 + x2
 ||       u11	s: []	p: 1	w: x2 + x3 + 48
 ||       sel	s: [2]	p: 1	w: x1 + x2 + 52
 ||       u32	s: []	p: 0	w: x1 + x2 + 1
 ||       #u63	s: [3,2,4,1]	p: 0	w: max(x1, x2, x3 + 1, x4)
 ||       u64	s: [2,1]	p: 2	w: max(x1, x2 + 20)
 ||       #s 	s: []	p: 0	w: 0
 ||       afterNth	s: []	p: 1	w: x1 + x2 + 49
 ||       nil	s: []	p: 6	w: 23
 ||       #TIlDePAIR	s: [2,1]	p: 0	w: x1 + x2 + 1
 ||       #tail	s: []	p: 0	w: 1
 ||       #splitAt	s: []	p: 0	w: max(x1)
 ||       mark	s: 1
 ||       u12	s: [2,1]	p: 6	w: x1 + x2 + x3 + 40
 ||       #afterNth	s: [1,2]	p: 0	w: x1 + x2 + 1
 ||       u72	s: [2]	p: 2	w: x1 + x2 + 1
 ||       u21	s: []	p: 2	w: x2 + 10
 ||       #u41	s: [2]	p: 0	w: x1 + x2 + 1
 ||       u82	s: [1,3]	p: 6	w: x1 + x2 + x3 + 40
 ||       active	s: 1
 ||       head	s: []	p: 1	w: x1 + 1
 ||       #u42	s: []	p: 0	w: x2 + 1
 ||       #snd	s: []	p: 0	w: 1
 ||       cons	s: []	p: 4	w: max(x1 + 9, x2)
 ||       #natsFrom	s: []	p: 0	w: 0
 ||       #active	s: 1
 ||       #u31	s: [1]	p: 0	w: x1 + 1
 ||       snd	s: 1
 ||       u22	s: [2]	p: 5	w: x2 + 1
 ||       u42	s: []	p: 2	w: x2 + x3 + 50
 ||       tt	s: []	p: 3	w: 7
 ||       #pair	s: []	p: 0	w: 0
 ||       u71	s: [2]	p: 3	w: x2 + 10
 ||       #u32	s: []	p: 0	w: x2
 ||       u31	s: []	p: 1	w: x2 + 8
 ||       #u62	s: [3,1]	p: 0	w: max(x1, x2 + 1, x3)
 ||       #u71	s: [1]	p: 0	w: x1
 ||     USABLE RULES: { 1..193 }
 ||     Removed DPs: #41 #94 #99 #239
 || Number of SCCs: 0, DPs: 0
 || 
We use the dependency pair framework as described in [Kop12, Ch. 6/7], with static dependency pairs (see [KusIsoSakBla09] and the adaptation for AFSMs and accessible arguments in [FuhKop19]).

We thus obtain the following dependency pair problem (P_0, R_0, computable, formative):

  Dependency Pairs P_0:

    0] map#(/\x.X(x), cons(Y, Z)) =#> cons#(X(Y), map(/\y.X(y), Z))   
    1] map#(/\x.X(x), cons(Y, Z)) =#> map#(/\y.X(y), Z)   

  Rules R_0:

    active(u11(tt, X, Y)) => mark(u12(tt, X, Y)) 
    active(u12(tt, X, Y)) => mark(snd(splitAt(X, Y))) 
    active(u21(tt, X)) => mark(u22(tt, X)) 
    active(u22(tt, X)) => mark(X) 
    active(u31(tt, X)) => mark(u32(tt, X)) 
    active(u32(tt, X)) => mark(X) 
    active(u41(tt, X, Y)) => mark(u42(tt, X, Y)) 
    active(u42(tt, X, Y)) => mark(head(afterNth(X, Y))) 
    active(u51(tt, X)) => mark(u52(tt, X)) 
    active(u52(tt, X)) => mark(X) 
    active(u61(tt, X, Y, Z)) => mark(u62(tt, X, Y, Z)) 
    active(u62(tt, X, Y, Z)) => mark(u63(tt, X, Y, Z)) 
    active(u63(tt, X, Y, Z)) => mark(u64(splitAt(X, Z), Y)) 
    active(u64(pair(X, Y), Z)) => mark(pair(cons(Z, X), Y)) 
    active(u71(tt, X)) => mark(u72(tt, X)) 
    active(u72(tt, X)) => mark(X) 
    active(u81(tt, X, Y)) => mark(u82(tt, X, Y)) 
    active(u82(tt, X, Y)) => mark(fst(splitAt(X, Y))) 
    active(afterNth(X, Y)) => mark(u11(tt, X, Y)) 
    active(fst(pair(X, Y))) => mark(u21(tt, X)) 
    active(head(cons(X, Y))) => mark(u31(tt, X)) 
    active(natsFrom(X)) => mark(cons(X, natsFrom(s(X)))) 
    active(sel(X, Y)) => mark(u41(tt, X, Y)) 
    active(snd(pair(X, Y))) => mark(u51(tt, Y)) 
    active(splitAt(0, X)) => mark(pair(nil, X)) 
    active(splitAt(s(X), cons(Y, Z))) => mark(u61(tt, X, Y, Z)) 
    active(tail(cons(X, Y))) => mark(u71(tt, Y)) 
    active(take(X, Y)) => mark(u81(tt, X, Y)) 
    mark(u11(X, Y, Z)) => active(u11(mark(X), Y, Z)) 
    mark(tt) => active(tt) 
    mark(u12(X, Y, Z)) => active(u12(mark(X), Y, Z)) 
    mark(snd(X)) => active(snd(mark(X))) 
    mark(splitAt(X, Y)) => active(splitAt(mark(X), mark(Y))) 
    mark(u21(X, Y)) => active(u21(mark(X), Y)) 
    mark(u22(X, Y)) => active(u22(mark(X), Y)) 
    mark(u31(X, Y)) => active(u31(mark(X), Y)) 
    mark(u32(X, Y)) => active(u32(mark(X), Y)) 
    mark(u41(X, Y, Z)) => active(u41(mark(X), Y, Z)) 
    mark(u42(X, Y, Z)) => active(u42(mark(X), Y, Z)) 
    mark(head(X)) => active(head(mark(X))) 
    mark(afterNth(X, Y)) => active(afterNth(mark(X), mark(Y))) 
    mark(u51(X, Y)) => active(u51(mark(X), Y)) 
    mark(u52(X, Y)) => active(u52(mark(X), Y)) 
    mark(u61(X, Y, Z, U)) => active(u61(mark(X), Y, Z, U)) 
    mark(u62(X, Y, Z, U)) => active(u62(mark(X), Y, Z, U)) 
    mark(u63(X, Y, Z, U)) => active(u63(mark(X), Y, Z, U)) 
    mark(u64(X, Y)) => active(u64(mark(X), Y)) 
    mark(pair(X, Y)) => active(pair(mark(X), mark(Y))) 
    mark(cons(X, Y)) => active(cons(mark(X), Y)) 
    mark(u71(X, Y)) => active(u71(mark(X), Y)) 
    mark(u72(X, Y)) => active(u72(mark(X), Y)) 
    mark(u81(X, Y, Z)) => active(u81(mark(X), Y, Z)) 
    mark(u82(X, Y, Z)) => active(u82(mark(X), Y, Z)) 
    mark(fst(X)) => active(fst(mark(X))) 
    mark(natsFrom(X)) => active(natsFrom(mark(X))) 
    mark(s(X)) => active(s(mark(X))) 
    mark(sel(X, Y)) => active(sel(mark(X), mark(Y))) 
    mark(0) => active(0) 
    mark(nil) => active(nil) 
    mark(tail(X)) => active(tail(mark(X))) 
    mark(take(X, Y)) => active(take(mark(X), mark(Y))) 
    u11(mark(X), Y, Z) => u11(X, Y, Z) 
    u11(X, mark(Y), Z) => u11(X, Y, Z) 
    u11(X, Y, mark(Z)) => u11(X, Y, Z) 
    u11(active(X), Y, Z) => u11(X, Y, Z) 
    u11(X, active(Y), Z) => u11(X, Y, Z) 
    u11(X, Y, active(Z)) => u11(X, Y, Z) 
    u12(mark(X), Y, Z) => u12(X, Y, Z) 
    u12(X, mark(Y), Z) => u12(X, Y, Z) 
    u12(X, Y, mark(Z)) => u12(X, Y, Z) 
    u12(active(X), Y, Z) => u12(X, Y, Z) 
    u12(X, active(Y), Z) => u12(X, Y, Z) 
    u12(X, Y, active(Z)) => u12(X, Y, Z) 
    snd(mark(X)) => snd(X) 
    snd(active(X)) => snd(X) 
    splitAt(mark(X), Y) => splitAt(X, Y) 
    splitAt(X, mark(Y)) => splitAt(X, Y) 
    splitAt(active(X), Y) => splitAt(X, Y) 
    splitAt(X, active(Y)) => splitAt(X, Y) 
    u21(mark(X), Y) => u21(X, Y) 
    u21(X, mark(Y)) => u21(X, Y) 
    u21(active(X), Y) => u21(X, Y) 
    u21(X, active(Y)) => u21(X, Y) 
    u22(mark(X), Y) => u22(X, Y) 
    u22(X, mark(Y)) => u22(X, Y) 
    u22(active(X), Y) => u22(X, Y) 
    u22(X, active(Y)) => u22(X, Y) 
    u31(mark(X), Y) => u31(X, Y) 
    u31(X, mark(Y)) => u31(X, Y) 
    u31(active(X), Y) => u31(X, Y) 
    u31(X, active(Y)) => u31(X, Y) 
    u32(mark(X), Y) => u32(X, Y) 
    u32(X, mark(Y)) => u32(X, Y) 
    u32(active(X), Y) => u32(X, Y) 
    u32(X, active(Y)) => u32(X, Y) 
    u41(mark(X), Y, Z) => u41(X, Y, Z) 
    u41(X, mark(Y), Z) => u41(X, Y, Z) 
    u41(X, Y, mark(Z)) => u41(X, Y, Z) 
    u41(active(X), Y, Z) => u41(X, Y, Z) 
    u41(X, active(Y), Z) => u41(X, Y, Z) 
    u41(X, Y, active(Z)) => u41(X, Y, Z) 
    u42(mark(X), Y, Z) => u42(X, Y, Z) 
    u42(X, mark(Y), Z) => u42(X, Y, Z) 
    u42(X, Y, mark(Z)) => u42(X, Y, Z) 
    u42(active(X), Y, Z) => u42(X, Y, Z) 
    u42(X, active(Y), Z) => u42(X, Y, Z) 
    u42(X, Y, active(Z)) => u42(X, Y, Z) 
    head(mark(X)) => head(X) 
    head(active(X)) => head(X) 
    afterNth(mark(X), Y) => afterNth(X, Y) 
    afterNth(X, mark(Y)) => afterNth(X, Y) 
    afterNth(active(X), Y) => afterNth(X, Y) 
    afterNth(X, active(Y)) => afterNth(X, Y) 
    u51(mark(X), Y) => u51(X, Y) 
    u51(X, mark(Y)) => u51(X, Y) 
    u51(active(X), Y) => u51(X, Y) 
    u51(X, active(Y)) => u51(X, Y) 
    u52(mark(X), Y) => u52(X, Y) 
    u52(X, mark(Y)) => u52(X, Y) 
    u52(active(X), Y) => u52(X, Y) 
    u52(X, active(Y)) => u52(X, Y) 
    u61(mark(X), Y, Z, U) => u61(X, Y, Z, U) 
    u61(X, mark(Y), Z, U) => u61(X, Y, Z, U) 
    u61(X, Y, mark(Z), U) => u61(X, Y, Z, U) 
    u61(X, Y, Z, mark(U)) => u61(X, Y, Z, U) 
    u61(active(X), Y, Z, U) => u61(X, Y, Z, U) 
    u61(X, active(Y), Z, U) => u61(X, Y, Z, U) 
    u61(X, Y, active(Z), U) => u61(X, Y, Z, U) 
    u61(X, Y, Z, active(U)) => u61(X, Y, Z, U) 
    u62(mark(X), Y, Z, U) => u62(X, Y, Z, U) 
    u62(X, mark(Y), Z, U) => u62(X, Y, Z, U) 
    u62(X, Y, mark(Z), U) => u62(X, Y, Z, U) 
    u62(X, Y, Z, mark(U)) => u62(X, Y, Z, U) 
    u62(active(X), Y, Z, U) => u62(X, Y, Z, U) 
    u62(X, active(Y), Z, U) => u62(X, Y, Z, U) 
    u62(X, Y, active(Z), U) => u62(X, Y, Z, U) 
    u62(X, Y, Z, active(U)) => u62(X, Y, Z, U) 
    u63(mark(X), Y, Z, U) => u63(X, Y, Z, U) 
    u63(X, mark(Y), Z, U) => u63(X, Y, Z, U) 
    u63(X, Y, mark(Z), U) => u63(X, Y, Z, U) 
    u63(X, Y, Z, mark(U)) => u63(X, Y, Z, U) 
    u63(active(X), Y, Z, U) => u63(X, Y, Z, U) 
    u63(X, active(Y), Z, U) => u63(X, Y, Z, U) 
    u63(X, Y, active(Z), U) => u63(X, Y, Z, U) 
    u63(X, Y, Z, active(U)) => u63(X, Y, Z, U) 
    u64(mark(X), Y) => u64(X, Y) 
    u64(X, mark(Y)) => u64(X, Y) 
    u64(active(X), Y) => u64(X, Y) 
    u64(X, active(Y)) => u64(X, Y) 
    pair(mark(X), Y) => pair(X, Y) 
    pair(X, mark(Y)) => pair(X, Y) 
    pair(active(X), Y) => pair(X, Y) 
    pair(X, active(Y)) => pair(X, Y) 
    cons(mark(X), Y) => cons(X, Y) 
    cons(X, mark(Y)) => cons(X, Y) 
    cons(active(X), Y) => cons(X, Y) 
    cons(X, active(Y)) => cons(X, Y) 
    u71(mark(X), Y) => u71(X, Y) 
    u71(X, mark(Y)) => u71(X, Y) 
    u71(active(X), Y) => u71(X, Y) 
    u71(X, active(Y)) => u71(X, Y) 
    u72(mark(X), Y) => u72(X, Y) 
    u72(X, mark(Y)) => u72(X, Y) 
    u72(active(X), Y) => u72(X, Y) 
    u72(X, active(Y)) => u72(X, Y) 
    u81(mark(X), Y, Z) => u81(X, Y, Z) 
    u81(X, mark(Y), Z) => u81(X, Y, Z) 
    u81(X, Y, mark(Z)) => u81(X, Y, Z) 
    u81(active(X), Y, Z) => u81(X, Y, Z) 
    u81(X, active(Y), Z) => u81(X, Y, Z) 
    u81(X, Y, active(Z)) => u81(X, Y, Z) 
    u82(mark(X), Y, Z) => u82(X, Y, Z) 
    u82(X, mark(Y), Z) => u82(X, Y, Z) 
    u82(X, Y, mark(Z)) => u82(X, Y, Z) 
    u82(active(X), Y, Z) => u82(X, Y, Z) 
    u82(X, active(Y), Z) => u82(X, Y, Z) 
    u82(X, Y, active(Z)) => u82(X, Y, Z) 
    fst(mark(X)) => fst(X) 
    fst(active(X)) => fst(X) 
    natsFrom(mark(X)) => natsFrom(X) 
    natsFrom(active(X)) => natsFrom(X) 
    s(mark(X)) => s(X) 
    s(active(X)) => s(X) 
    sel(mark(X), Y) => sel(X, Y) 
    sel(X, mark(Y)) => sel(X, Y) 
    sel(active(X), Y) => sel(X, Y) 
    sel(X, active(Y)) => sel(X, Y) 
    tail(mark(X)) => tail(X) 
    tail(active(X)) => tail(X) 
    take(mark(X), Y) => take(X, Y) 
    take(X, mark(Y)) => take(X, Y) 
    take(active(X), Y) => take(X, Y) 
    take(X, active(Y)) => take(X, Y) 
    map(/\x.X(x), nil) => nil 
    map(/\x.X(x), cons(Y, Z)) => cons(X(Y), map(/\y.X(y), Z)) 
    app(/\x.X(x), Y) => X(Y) 

Thus, the original system is terminating if (P_0, R_0, computable, formative) is finite.

We consider the dependency pair problem (P_0, R_0, computable, formative).

We place the elements of P in a dependency graph approximation G (see e.g. [Kop12, Thm. 7.27, 7.29], as follows:

    * 0 :  
    * 1 : 0, 1 

This graph has the following strongly connected components:

  P_1:

    map#(/\x.X(x), cons(Y, Z)) =#> map#(/\y.X(y), Z)   

By [Kop12, Thm. 7.31], we may replace any dependency pair problem (P_0, R_0, m, f) by (P_1, R_0, m, f).

Thus, the original system is terminating if (P_1, R_0, computable, formative) is finite.

We consider the dependency pair problem (P_1, R_0, computable, formative).

We apply the subterm criterion with the following projection function:

  nu(map#) = 2 

Thus, we can orient the dependency pairs as follows:

  nu(map#(/\x.X(x), cons(Y, Z))) = cons(Y, Z) |> Z = nu(map#(/\y.X(y), Z)) 

By [FuhKop19, Thm. 61], we may replace a dependency pair problem (P_1, R_0, computable, f) by ({}, R_0, computable, f).  By the empty set processor [Kop12, Thm. 7.15] this problem may be immediately removed.

As all dependency pair problems were succesfully simplified with sound (and complete) processors until nothing remained, we conclude termination.


+++ Citations +++

[FuhKop19]  C. Fuhs, and C. Kop.  A static higher-order dependency pair framework.  In Proceedings of ESOP 2019, 2019.
[Kop11]  C. Kop.  Simplifying Algebraic Functional Systems.  In Proceedings of CAI 2011, volume 6742 of LNCS.  201--215, Springer, 2011.
[Kop12]  C. Kop.  Higher Order Termination.  PhD Thesis, 2012.
[KusIsoSakBla09]  K. Kusakari, Y. Isogai, M. Sakai, and F. Blanqui.  Static Dependency Pair Method Based On Strong Computability for Higher-Order Rewrite Systems.  In volume 92(10) of IEICE Transactions on Information and Systems.  2007--2015, 2009.