(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(g(x), x, y) → f(y, y, g(y))
g(g(x)) → g(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(g(x), x, y) → F(y, y, g(y))
F(g(x), x, y) → G(y)
The TRS R consists of the following rules:
f(g(x), x, y) → f(y, y, g(y))
g(g(x)) → g(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(g(x), x, y) → F(y, y, g(y))
The TRS R consists of the following rules:
f(g(x), x, y) → f(y, y, g(y))
g(g(x)) → g(x)
Q is empty.
We have to consider all minimal (P,Q,R)-chains.