(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(a, f(a, x)) → f(x, f(a, f(f(a, a), a)))
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:
F(a, f(a, x)) → F(x, f(a, f(f(a, a), a)))
F(a, f(a, x)) → F(a, f(f(a, a), a))
F(a, f(a, x)) → F(f(a, a), a)
F(a, f(a, x)) → F(a, a)
The TRS R consists of the following rules:
f(a, f(a, x)) → f(x, f(a, f(f(a, a), a)))
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 3 less nodes.
(4) Obligation:
Q DP problem:
The TRS P consists of the following rules:
F(a, f(a, x)) → F(x, f(a, f(f(a, a), a)))
The TRS R consists of the following rules:
f(a, f(a, x)) → f(x, f(a, f(f(a, a), a)))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.