(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(x, x) → f(g(x), x)
g(x) → s(x)
Q is empty.
(1) AAECC Innermost (EQUIVALENT transformation)
We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is
g(x) → s(x)
The TRS R 2 is
f(x, x) → f(g(x), x)
The signature Sigma is {
f}
(2) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(x, x) → f(g(x), x)
g(x) → s(x)
The set Q consists of the following terms:
f(x0, x0)
g(x0)
(3) DependencyPairsProof (EQUIVALENT transformation)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
(4) Obligation:
Q DP problem:
The TRS P consists of the following rules:
F(x, x) → F(g(x), x)
F(x, x) → G(x)
The TRS R consists of the following rules:
f(x, x) → f(g(x), x)
g(x) → s(x)
The set Q consists of the following terms:
f(x0, x0)
g(x0)
We have to consider all minimal (P,Q,R)-chains.
(5) DependencyGraphProof (EQUIVALENT transformation)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
(6) Obligation:
Q DP problem:
The TRS P consists of the following rules:
F(x, x) → F(g(x), x)
The TRS R consists of the following rules:
f(x, x) → f(g(x), x)
g(x) → s(x)
The set Q consists of the following terms:
f(x0, x0)
g(x0)
We have to consider all minimal (P,Q,R)-chains.