(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(x, f(a, y)) → f(a, f(f(f(a, a), y), 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:
F(x, f(a, y)) → F(a, f(f(f(a, a), y), x))
F(x, f(a, y)) → F(f(f(a, a), y), x)
F(x, f(a, y)) → F(f(a, a), y)
F(x, f(a, y)) → F(a, a)
The TRS R consists of the following rules:
f(x, f(a, y)) → f(a, f(f(f(a, a), y), 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 1 less node.
(4) Obligation:
Q DP problem:
The TRS P consists of the following rules:
F(x, f(a, y)) → F(f(f(a, a), y), x)
F(x, f(a, y)) → F(a, f(f(f(a, a), y), x))
F(x, f(a, y)) → F(f(a, a), y)
The TRS R consists of the following rules:
f(x, f(a, y)) → f(a, f(f(f(a, a), y), x))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.