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