(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(g(f(a), h(a, f(a)))) → f(h(g(f(a), a), g(f(a), f(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(g(f(a), h(a, f(a)))) → f(h(g(f(a), a), g(f(a), f(a))))
The set Q consists of the following terms:
f(g(f(a), h(a, f(a))))
(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(g(f(a), h(a, f(a)))) → F(h(g(f(a), a), g(f(a), f(a))))
The TRS R consists of the following rules:
f(g(f(a), h(a, f(a)))) → f(h(g(f(a), a), g(f(a), f(a))))
The set Q consists of the following terms:
f(g(f(a), h(a, f(a))))
We have to consider all minimal (P,Q,R)-chains.
(5) DependencyGraphProof (EQUIVALENT transformation)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.
(6) TRUE