We consider universal computability of the MSTRS with no additional rule schemes:

  Signature: a :: o
             b :: o
             f :: o -> o -> o
             h :: o -> o

  Rules: f(x, x) -> x
         f(a, y) -> f(y, b)

The system is accessible function passing by a sort ordering that equates all sorts.

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

  P1. (1) f#(a, y) => f#(y, b)

***** We apply the Usable Rules Processor on D1 = (P1, R UNION R_?, i, c).

We obtain 0 usable rules (out of 2 rules in the input problem).

Processor output: { D2 = (P1, {}, i, c) }.

***** We apply the Usable rules with respect to an argument wiltering [with HORPO] Processor on D2 = (P1, {}, i, c).

Constrained HORPO yields:

  f#2(a0, y) (>) f#2(y, b0)

We do this using the following settings:

* Monotonicity requirements: this is a strongly monotonic reduction pair (all arguments of function symbols were regarded).

* Precedence and permutation:

    a0   { }
  > b0   { }
  > f#2  { 1 2 }

* Well-founded theory orderings:

  [>]_{Bool} = {(true,false)}
  [>]_{Int}  = {(x,y) | x < 1000 /\ x < y }

Processor output: { }.