(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(x, a) → x
f(x, g(y)) → f(g(x), y)
Q is empty.
(1) Overlay + Local Confluence (EQUIVALENT transformation)
The TRS is overlay and locally confluent. By [NOC] we can switch to innermost.
(2) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(x, a) → x
f(x, g(y)) → f(g(x), y)
The set Q consists of the following terms:
f(x0, a)
f(x0, g(x1))
(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, g(y)) → F(g(x), y)
The TRS R consists of the following rules:
f(x, a) → x
f(x, g(y)) → f(g(x), y)
The set Q consists of the following terms:
f(x0, a)
f(x0, g(x1))
We have to consider all minimal (P,Q,R)-chains.