(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(h(x), y) → h(f(y, f(x, h(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:
f(h(x), y) → h(f(y, f(x, h(a))))
The set Q consists of the following terms:
f(h(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:
F(h(x), y) → F(y, f(x, h(a)))
F(h(x), y) → F(x, h(a))
The TRS R consists of the following rules:
f(h(x), y) → h(f(y, f(x, h(a))))
The set Q consists of the following terms:
f(h(x0), x1)
We have to consider all minimal (P,Q,R)-chains.