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