Termination w.r.t. Q of the following Term Rewriting System could not be shown:
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.
↳ QTRS
↳ DependencyPairsProof
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.
Using Dependency Pairs [1,15] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:
G(f(x, y)) → G(g(y))
G(f(x, y)) → G(g(x))
G(f(x, y)) → G(x)
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))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
↳ QTRS
↳ DependencyPairsProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
G(f(x, y)) → G(g(y))
G(f(x, y)) → G(g(x))
G(f(x, y)) → G(x)
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))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.