(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(a, x) → g(a, x)
g(a, x) → f(b, x)
f(a, x) → f(b, x)
Q is empty.
(1) AAECC Innermost (EQUIVALENT transformation)
We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is none
The TRS R 2 is
f(a, x) → g(a, x)
g(a, x) → f(b, x)
f(a, x) → f(b, x)
The signature Sigma is {
f,
g}
(2) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(a, x) → g(a, x)
g(a, x) → f(b, x)
f(a, x) → f(b, x)
The set Q consists of the following terms:
f(a, x0)
g(a, 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(a, x) → G(a, x)
G(a, x) → F(b, x)
F(a, x) → F(b, x)
The TRS R consists of the following rules:
f(a, x) → g(a, x)
g(a, x) → f(b, x)
f(a, x) → f(b, x)
The set Q consists of the following terms:
f(a, x0)
g(a, 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 0 SCCs with 3 less nodes.
(6) TRUE