We consider termination of the STRS with no additional rule schemes:

  Signature: cons     :: b -> c -> c
             leaf     :: a -> b
             mapt     :: (a -> a) -> b -> b
             maptlist :: (a -> a) -> c -> c
             nil      :: c
             node     :: c -> b

  Rules: mapt(F, leaf(Y)) -> leaf(F(Y))
         mapt(G, node(V)) -> node(maptlist(G, V))
         maptlist(I, nil) -> nil
         maptlist(J, cons(X1, Y1)) -> cons(mapt(J, X1), maptlist(J, Y1))

The system is accessible function passing by a sort ordering with b = c ≻ a.

We start by computing the initial DP problem D1 = (P1, R, i, c), where:

  P1. (1) mapt#(G, node(V)) => maptlist#(G, V)
      (2) maptlist#(J, cons(X1, Y1)) => mapt#(J, X1)
      (3) maptlist#(J, cons(X1, Y1)) => maptlist#(J, Y1)

***** We apply the Subterm Criterion Processor on D1 = (P1, R, i, c).

We use the following projection function:

  nu(mapt#)     = 2
  nu(maptlist#) = 2

We thus have:

  (1) node(V)      |>| V
  (2) cons(X1, Y1) |>| X1
  (3) cons(X1, Y1) |>| Y1

All DPs are strictly oriented, and may be removed.  Hence, this DP problem is finite.

Processor output: { }.