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:
b(a(a(b(b(x1))))) → b(a(a(a(a(b(b(x1)))))))
b(a(b(b(x1)))) → b(b(x1))
b(a(b(a(a(a(a(b(x1)))))))) → b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))))))))))
b(a(a(b(a(a(a(a(b(x1))))))))) → b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))
b(a(a(a(b(a(a(a(a(b(x1)))))))))) → b(x1)
Q is empty.
↳ QTRS
↳ DependencyPairsProof
Q restricted rewrite system:
The TRS R consists of the following rules:
b(a(a(b(b(x1))))) → b(a(a(a(a(b(b(x1)))))))
b(a(b(b(x1)))) → b(b(x1))
b(a(b(a(a(a(a(b(x1)))))))) → b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))))))))))
b(a(a(b(a(a(a(a(b(x1))))))))) → b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))
b(a(a(a(b(a(a(a(a(b(x1)))))))))) → b(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(a(b(a(a(a(a(b(x1)))))))) → B(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))))))))))
B(a(a(b(a(a(a(a(b(x1))))))))) → B(a(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))
B(a(b(a(a(a(a(b(x1)))))))) → B(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))
B(a(a(b(a(a(a(a(b(x1))))))))) → B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))
B(a(b(a(a(a(a(b(x1)))))))) → B(a(a(a(b(a(a(a(a(b(x1))))))))))
B(a(a(b(a(a(a(a(b(x1))))))))) → B(a(a(a(b(a(a(a(a(b(x1))))))))))
B(a(b(a(a(a(a(b(x1)))))))) → B(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))))
B(a(a(b(b(x1))))) → B(a(a(a(a(b(b(x1)))))))
The TRS R consists of the following rules:
b(a(a(b(b(x1))))) → b(a(a(a(a(b(b(x1)))))))
b(a(b(b(x1)))) → b(b(x1))
b(a(b(a(a(a(a(b(x1)))))))) → b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))))))))))
b(a(a(b(a(a(a(a(b(x1))))))))) → b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))
b(a(a(a(b(a(a(a(a(b(x1)))))))))) → b(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:
B(a(b(a(a(a(a(b(x1)))))))) → B(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))))))))))
B(a(a(b(a(a(a(a(b(x1))))))))) → B(a(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))
B(a(b(a(a(a(a(b(x1)))))))) → B(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))
B(a(a(b(a(a(a(a(b(x1))))))))) → B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))
B(a(b(a(a(a(a(b(x1)))))))) → B(a(a(a(b(a(a(a(a(b(x1))))))))))
B(a(a(b(a(a(a(a(b(x1))))))))) → B(a(a(a(b(a(a(a(a(b(x1))))))))))
B(a(b(a(a(a(a(b(x1)))))))) → B(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))))
B(a(a(b(b(x1))))) → B(a(a(a(a(b(b(x1)))))))
The TRS R consists of the following rules:
b(a(a(b(b(x1))))) → b(a(a(a(a(b(b(x1)))))))
b(a(b(b(x1)))) → b(b(x1))
b(a(b(a(a(a(a(b(x1)))))))) → b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))))))))))
b(a(a(b(a(a(a(a(b(x1))))))))) → b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))
b(a(a(a(b(a(a(a(a(b(x1)))))))))) → b(x1)
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 2 SCCs with 6 less nodes.
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
B(a(b(a(a(a(a(b(x1)))))))) → B(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))
The TRS R consists of the following rules:
b(a(a(b(b(x1))))) → b(a(a(a(a(b(b(x1)))))))
b(a(b(b(x1)))) → b(b(x1))
b(a(b(a(a(a(a(b(x1)))))))) → b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))))))))))
b(a(a(b(a(a(a(a(b(x1))))))))) → b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))
b(a(a(a(b(a(a(a(a(b(x1)))))))))) → b(x1)
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
B(a(a(b(a(a(a(a(b(x1))))))))) → B(a(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))
The TRS R consists of the following rules:
b(a(a(b(b(x1))))) → b(a(a(a(a(b(b(x1)))))))
b(a(b(b(x1)))) → b(b(x1))
b(a(b(a(a(a(a(b(x1)))))))) → b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))))))))))
b(a(a(b(a(a(a(a(b(x1))))))))) → b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))
b(a(a(a(b(a(a(a(a(b(x1)))))))))) → b(x1)
Q is empty.
We have to consider all minimal (P,Q,R)-chains.