(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
h(f(f(x))) → h(f(g(f(x))))
f(g(f(x))) → f(f(x))
Q is empty.
(1) DependencyPairsProof (EQUIVALENT transformation)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
(2) Obligation:
Q DP problem:
The TRS P consists of the following rules:
H(f(f(x))) → H(f(g(f(x))))
H(f(f(x))) → F(g(f(x)))
F(g(f(x))) → F(f(x))
The TRS R consists of the following rules:
h(f(f(x))) → h(f(g(f(x))))
f(g(f(x))) → f(f(x))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
(3) DependencyGraphProof (EQUIVALENT transformation)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
(4) Obligation:
Q DP problem:
The TRS P consists of the following rules:
H(f(f(x))) → H(f(g(f(x))))
The TRS R consists of the following rules:
h(f(f(x))) → h(f(g(f(x))))
f(g(f(x))) → f(f(x))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.