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