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(c(x1))
a(b(b(x1))) → b(b(a(a(x1))))
b(a(x1)) → x1
Q is empty.
↳ QTRS
↳ DependencyPairsProof
Q restricted rewrite system:
The TRS R consists of the following rules:
a(x1) → b(c(x1))
a(b(b(x1))) → b(b(a(a(x1))))
b(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:
A(x1) → B(c(x1))
A(b(b(x1))) → A(x1)
A(b(b(x1))) → B(a(a(x1)))
A(b(b(x1))) → A(a(x1))
A(b(b(x1))) → B(b(a(a(x1))))
The TRS R consists of the following rules:
a(x1) → b(c(x1))
a(b(b(x1))) → b(b(a(a(x1))))
b(a(x1)) → x1
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
Q DP problem:
The TRS P consists of the following rules:
A(x1) → B(c(x1))
A(b(b(x1))) → A(x1)
A(b(b(x1))) → B(a(a(x1)))
A(b(b(x1))) → A(a(x1))
A(b(b(x1))) → B(b(a(a(x1))))
The TRS R consists of the following rules:
a(x1) → b(c(x1))
a(b(b(x1))) → b(b(a(a(x1))))
b(a(x1)) → x1
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 3 less nodes.
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
A(b(b(x1))) → A(x1)
A(b(b(x1))) → A(a(x1))
The TRS R consists of the following rules:
a(x1) → b(c(x1))
a(b(b(x1))) → b(b(a(a(x1))))
b(a(x1)) → x1
Q is empty.
We have to consider all minimal (P,Q,R)-chains.