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