(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
h(f(x, y)) → f(y, f(h(h(x)), a))
Q is empty.
(1) Overlay + Local Confluence (EQUIVALENT transformation)
The TRS is overlay and locally confluent. By [NOC] we can switch to innermost.
(2) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
h(f(x, y)) → f(y, f(h(h(x)), a))
The set Q consists of the following terms:
h(f(x0, x1))
(3) DependencyPairsProof (EQUIVALENT transformation)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
(4) Obligation:
Q DP problem:
The TRS P consists of the following rules:
H(f(x, y)) → H(h(x))
H(f(x, y)) → H(x)
The TRS R consists of the following rules:
h(f(x, y)) → f(y, f(h(h(x)), a))
The set Q consists of the following terms:
h(f(x0, x1))
We have to consider all minimal (P,Q,R)-chains.