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(a(a(x1))) → a(c(a(a(x1))))
c(c(c(x1))) → a(x1)
a(x1) → x1
Q is empty.
↳ QTRS
↳ DependencyPairsProof
Q restricted rewrite system:
The TRS R consists of the following rules:
a(a(a(x1))) → a(c(a(a(x1))))
c(c(c(x1))) → a(x1)
a(x1) → x1
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:
C(c(c(x1))) → A(x1)
A(a(a(x1))) → A(c(a(a(x1))))
A(a(a(x1))) → C(a(a(x1)))
The TRS R consists of the following rules:
a(a(a(x1))) → a(c(a(a(x1))))
c(c(c(x1))) → a(x1)
a(x1) → x1
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:
C(c(c(x1))) → A(x1)
A(a(a(x1))) → A(c(a(a(x1))))
A(a(a(x1))) → C(a(a(x1)))
The TRS R consists of the following rules:
a(a(a(x1))) → a(c(a(a(x1))))
c(c(c(x1))) → a(x1)
a(x1) → x1
Q is empty.
We have to consider all minimal (P,Q,R)-chains.