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:
a(f, a(g, a(f, x))) → a(f, a(g, a(g, a(f, x))))
a(g, a(f, a(g, x))) → a(g, a(f, a(f, a(g, x))))
Q is empty.
↳ QTRS
↳ DependencyPairsProof
Q restricted rewrite system:
The TRS R consists of the following rules:
a(f, a(g, a(f, x))) → a(f, a(g, a(g, a(f, x))))
a(g, a(f, a(g, x))) → a(g, a(f, a(f, a(g, x))))
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:
A(g, a(f, a(g, x))) → A(g, a(f, a(f, a(g, x))))
A(f, a(g, a(f, x))) → A(f, a(g, a(g, a(f, x))))
A(f, a(g, a(f, x))) → A(g, a(g, a(f, x)))
A(g, a(f, a(g, x))) → A(f, a(f, a(g, x)))
The TRS R consists of the following rules:
a(f, a(g, a(f, x))) → a(f, a(g, a(g, a(f, x))))
a(g, a(f, a(g, x))) → a(g, a(f, a(f, a(g, x))))
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:
A(g, a(f, a(g, x))) → A(g, a(f, a(f, a(g, x))))
A(f, a(g, a(f, x))) → A(f, a(g, a(g, a(f, x))))
A(f, a(g, a(f, x))) → A(g, a(g, a(f, x)))
A(g, a(f, a(g, x))) → A(f, a(f, a(g, x)))
The TRS R consists of the following rules:
a(f, a(g, a(f, x))) → a(f, a(g, a(g, a(f, x))))
a(g, a(f, a(g, x))) → a(g, a(f, a(f, a(g, x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.