(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(s(x)) → f(g(x, x))
g(0, 1) → s(0)
0 → 1
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(s(x)) → F(g(x, x))
F(s(x)) → G(x, x)
The TRS R consists of the following rules:
f(s(x)) → f(g(x, x))
g(0, 1) → s(0)
0 → 1
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(s(x)) → F(g(x, x))
The TRS R consists of the following rules:
f(s(x)) → f(g(x, x))
g(0, 1) → s(0)
0 → 1
Q is empty.
We have to consider all minimal (P,Q,R)-chains.