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:
f(x, f(a, f(f(a, a), a))) → f(f(a, x), x)
Q is empty.
↳ QTRS
↳ Overlay + Local Confluence
Q restricted rewrite system:
The TRS R consists of the following rules:
f(x, f(a, f(f(a, a), a))) → f(f(a, x), x)
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:
f(x, f(a, f(f(a, a), a))) → f(f(a, x), x)
The set Q consists of the following terms:
f(x0, f(a, f(f(a, a), a)))
Using Dependency Pairs [1,13] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:
F(x, f(a, f(f(a, a), a))) → F(f(a, x), x)
F(x, f(a, f(f(a, a), a))) → F(a, x)
The TRS R consists of the following rules:
f(x, f(a, f(f(a, a), a))) → f(f(a, x), x)
The set Q consists of the following terms:
f(x0, f(a, f(f(a, a), a)))
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:
F(x, f(a, f(f(a, a), a))) → F(f(a, x), x)
F(x, f(a, f(f(a, a), a))) → F(a, x)
The TRS R consists of the following rules:
f(x, f(a, f(f(a, a), a))) → f(f(a, x), x)
The set Q consists of the following terms:
f(x0, f(a, f(f(a, a), a)))
We have to consider all minimal (P,Q,R)-chains.