(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(f(x)) → f(x)
g(0) → g(f(0))
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:
G(0) → G(f(0))
G(0) → F(0)
The TRS R consists of the following rules:
f(f(x)) → f(x)
g(0) → g(f(0))
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 0 SCCs with 2 less nodes.
(4) TRUE