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