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