(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
g(f(x, y)) → f(f(g(g(x)), g(g(y))), f(g(g(x)), g(g(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:
g(f(x, y)) → f(f(g(g(x)), g(g(y))), f(g(g(x)), g(g(y))))
The set Q consists of the following terms:
g(f(x0, 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:
G(f(x, y)) → G(g(x))
G(f(x, y)) → G(x)
G(f(x, y)) → G(g(y))
G(f(x, y)) → G(y)
The TRS R consists of the following rules:
g(f(x, y)) → f(f(g(g(x)), g(g(y))), f(g(g(x)), g(g(y))))
The set Q consists of the following terms:
g(f(x0, x1))
We have to consider all minimal (P,Q,R)-chains.