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
↳ Overlay + Local Confluence
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.
The TRS is overlay and locally confluent. By [15] we can switch to innermost.
↳ QTRS
↳ Overlay + Local Confluence
↳ 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))))
The set Q consists of the following terms:
g(f(x0, x1))
Using Dependency Pairs [1,13] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:
G(f(x, y)) → G(x)
G(f(x, y)) → G(g(x))
G(f(x, y)) → G(y)
G(f(x, y)) → G(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.
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
G(f(x, y)) → G(x)
G(f(x, y)) → G(g(x))
G(f(x, y)) → G(y)
G(f(x, y)) → G(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.