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
↳ QTRS Reverse
↳ QTRS Reverse
↳ 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.
We have reversed the following QTRS:
The set of rules R is
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)
The set Q is empty.
We have obtained the following QTRS:
b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
The set Q is empty.
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
Q restricted rewrite system:
The TRS R consists of the following rules:
b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
Q is empty.
We have reversed the following QTRS:
The set of rules R is
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)
The set Q is empty.
We have obtained the following QTRS:
b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
The set Q is empty.
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS
↳ DependencyPairsProof
Q restricted rewrite system:
The TRS R consists of the following rules:
b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(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:
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
↳ QTRS Reverse
↳ QTRS Reverse
↳ 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
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ Narrowing
↳ 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.
By narrowing [15] the rule B(a(b(a(a(a(a(b(x1)))))))) → B(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))) at position [0,0] we obtained the following new rules:
B(a(b(a(a(a(a(b(a(a(b(b(x0)))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(x0))))))))))))))))))
B(a(b(a(a(a(a(b(a(b(a(a(a(a(b(x0))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))))))))
B(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))
B(a(b(a(a(a(a(b(a(b(b(x0))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(b(x0)))))))))))))
B(a(b(a(a(a(a(b(x0)))))))) → B(a(b(x0)))
B(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(x0)))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
B(a(b(a(a(a(a(b(a(b(b(x0))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(b(x0)))))))))))))
B(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))
B(a(b(a(a(a(a(b(x0)))))))) → B(a(b(x0)))
B(a(b(a(a(a(a(b(a(a(b(b(x0)))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(x0))))))))))))))))))
B(a(b(a(a(a(a(b(a(b(a(a(a(a(b(x0))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))))))))
B(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(x0)))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))
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 finiteness of this DP problem is implied by strong termination of a SRS due to [12].
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QDP
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)
B(a(b(a(a(a(a(b(a(b(b(x0))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(b(x0)))))))))))))
B(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))
B(a(b(a(a(a(a(b(x0)))))))) → B(a(b(x0)))
B(a(b(a(a(a(a(b(a(a(b(b(x0)))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(x0))))))))))))))))))
B(a(b(a(a(a(a(b(a(b(a(a(a(a(b(x0))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))))))))
B(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(x0)))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))
Q is empty.
We have reversed the following QTRS:
The set of rules R is
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)
B(a(b(a(a(a(a(b(a(b(b(x0))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(b(x0)))))))))))))
B(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))
B(a(b(a(a(a(a(b(x0)))))))) → B(a(b(x0)))
B(a(b(a(a(a(a(b(a(a(b(b(x0)))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(x0))))))))))))))))))
B(a(b(a(a(a(a(b(a(b(a(a(a(a(b(x0))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))))))))
B(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(x0)))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))
The set Q is empty.
We have obtained the following QTRS:
b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
b(b(a(b(a(a(a(a(b(a(B(x))))))))))) → b(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
b(a(a(a(a(b(a(B(x)))))))) → b(a(B(x)))
b(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))
The set Q is empty.
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
Q restricted rewrite system:
The TRS R consists of the following rules:
b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
b(b(a(b(a(a(a(a(b(a(B(x))))))))))) → b(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
b(a(a(a(a(b(a(B(x)))))))) → b(a(B(x)))
b(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))
Q is empty.
We have reversed the following QTRS:
The set of rules R is
b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
b(b(a(b(a(a(a(a(b(a(B(x))))))))))) → b(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
b(a(a(a(a(b(a(B(x)))))))) → b(a(B(x)))
b(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))
The set Q is empty.
We have obtained the following QTRS:
b(a(a(b(b(x))))) → b(a(a(a(a(b(b(x)))))))
b(a(b(b(x)))) → b(b(x))
b(a(b(a(a(a(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(b(a(a(a(a(b(x))))))))) → b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x)))))))))))))))
b(a(a(a(b(a(a(a(a(b(x)))))))))) → b(x)
B(a(b(a(a(a(a(b(a(b(b(x))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(b(x)))))))))))))
B(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))
B(a(b(a(a(a(a(b(x)))))))) → B(a(b(x)))
B(a(b(a(a(a(a(b(a(a(b(b(x)))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(x))))))))))))))))))
B(a(b(a(a(a(a(b(a(b(a(a(a(a(b(x))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x)))))))))))))))))))))))))))))))))
B(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(x)))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))))))
The set Q is empty.
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
Q restricted rewrite system:
The TRS R consists of the following rules:
b(a(a(b(b(x))))) → b(a(a(a(a(b(b(x)))))))
b(a(b(b(x)))) → b(b(x))
b(a(b(a(a(a(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(b(a(a(a(a(b(x))))))))) → b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x)))))))))))))))
b(a(a(a(b(a(a(a(a(b(x)))))))))) → b(x)
B(a(b(a(a(a(a(b(a(b(b(x))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(b(x)))))))))))))
B(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))
B(a(b(a(a(a(a(b(x)))))))) → B(a(b(x)))
B(a(b(a(a(a(a(b(a(a(b(b(x)))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(x))))))))))))))))))
B(a(b(a(a(a(a(b(a(b(a(a(a(a(b(x))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x)))))))))))))))))))))))))))))))))
B(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(x)))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))))))
Q is empty.
We have reversed the following QTRS:
The set of rules R is
b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
b(b(a(b(a(a(a(a(b(a(B(x))))))))))) → b(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
b(a(a(a(a(b(a(B(x)))))))) → b(a(B(x)))
b(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))
The set Q is empty.
We have obtained the following QTRS:
b(a(a(b(b(x))))) → b(a(a(a(a(b(b(x)))))))
b(a(b(b(x)))) → b(b(x))
b(a(b(a(a(a(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(b(a(a(a(a(b(x))))))))) → b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x)))))))))))))))
b(a(a(a(b(a(a(a(a(b(x)))))))))) → b(x)
B(a(b(a(a(a(a(b(a(b(b(x))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(b(x)))))))))))))
B(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))
B(a(b(a(a(a(a(b(x)))))))) → B(a(b(x)))
B(a(b(a(a(a(a(b(a(a(b(b(x)))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(x))))))))))))))))))
B(a(b(a(a(a(a(b(a(b(a(a(a(a(b(x))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x)))))))))))))))))))))))))))))))))
B(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(x)))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))))))
The set Q is empty.
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS
↳ DependencyPairsProof
↳ QDP
Q restricted rewrite system:
The TRS R consists of the following rules:
b(a(a(b(b(x))))) → b(a(a(a(a(b(b(x)))))))
b(a(b(b(x)))) → b(b(x))
b(a(b(a(a(a(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(b(a(a(a(a(b(x))))))))) → b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x)))))))))))))))
b(a(a(a(b(a(a(a(a(b(x)))))))))) → b(x)
B(a(b(a(a(a(a(b(a(b(b(x))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(b(x)))))))))))))
B(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))
B(a(b(a(a(a(a(b(x)))))))) → B(a(b(x)))
B(a(b(a(a(a(a(b(a(a(b(b(x)))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(x))))))))))))))))))
B(a(b(a(a(a(a(b(a(b(a(a(a(a(b(x))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x)))))))))))))))))))))))))))))))))
B(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(x)))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(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:
B1(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → B1(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))
B1(a(a(a(a(b(a(a(b(x))))))))) → B1(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
B1(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → B1(a(a(a(b(a(B(x)))))))
B1(a(a(a(a(b(a(a(b(x))))))))) → B1(a(a(b(a(b(x))))))
B1(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → B1(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))
B1(b(a(b(a(a(a(a(b(a(B(x))))))))))) → B1(a(a(a(b(a(B(x)))))))
B1(a(a(a(a(b(a(b(x)))))))) → B1(a(b(a(a(a(a(b(a(a(a(a(b(x)))))))))))))
B1(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → B1(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
B1(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B1(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))
B1(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B1(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))
B1(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → B1(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
B1(a(a(a(a(b(a(a(b(x))))))))) → B1(a(a(a(b(a(a(b(a(b(x))))))))))
B1(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B1(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))))
B1(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B1(a(a(a(b(a(B(x)))))))
B1(a(a(a(a(b(a(b(x)))))))) → B1(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
B1(b(a(b(x)))) → B1(b(x))
B1(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → B1(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))
B1(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → B1(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
B1(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B1(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
B1(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → B1(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
B1(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B1(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
B1(b(a(b(a(a(a(a(b(a(B(x))))))))))) → B1(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
B1(b(a(b(a(a(a(a(b(a(B(x))))))))))) → B1(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
B1(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → B1(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))
B1(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → B1(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))
B1(a(a(a(a(b(a(b(x)))))))) → B1(a(a(a(a(b(a(a(a(a(b(x)))))))))))
B1(b(a(a(b(x))))) → B1(a(a(a(a(b(x))))))
B1(a(a(a(a(b(a(b(x)))))))) → B1(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x)))))))))))))))))
B1(a(a(a(a(b(a(b(x)))))))) → B1(a(a(a(a(b(x))))))
B1(a(a(a(a(b(a(a(b(x))))))))) → B1(a(b(x)))
B1(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → B1(a(a(a(b(a(B(x)))))))
B1(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → B1(a(a(a(b(a(B(x)))))))
B1(b(a(a(b(x))))) → B1(b(a(a(a(a(b(x)))))))
B1(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B1(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))
The TRS R consists of the following rules:
b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
b(b(a(b(a(a(a(a(b(a(B(x))))))))))) → b(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
b(a(a(a(a(b(a(B(x)))))))) → b(a(B(x)))
b(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
B1(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → B1(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))
B1(a(a(a(a(b(a(a(b(x))))))))) → B1(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
B1(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → B1(a(a(a(b(a(B(x)))))))
B1(a(a(a(a(b(a(a(b(x))))))))) → B1(a(a(b(a(b(x))))))
B1(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → B1(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))
B1(b(a(b(a(a(a(a(b(a(B(x))))))))))) → B1(a(a(a(b(a(B(x)))))))
B1(a(a(a(a(b(a(b(x)))))))) → B1(a(b(a(a(a(a(b(a(a(a(a(b(x)))))))))))))
B1(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → B1(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
B1(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B1(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))
B1(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B1(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))
B1(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → B1(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
B1(a(a(a(a(b(a(a(b(x))))))))) → B1(a(a(a(b(a(a(b(a(b(x))))))))))
B1(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B1(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))))
B1(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B1(a(a(a(b(a(B(x)))))))
B1(a(a(a(a(b(a(b(x)))))))) → B1(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
B1(b(a(b(x)))) → B1(b(x))
B1(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → B1(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))
B1(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → B1(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
B1(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B1(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
B1(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → B1(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
B1(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B1(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
B1(b(a(b(a(a(a(a(b(a(B(x))))))))))) → B1(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
B1(b(a(b(a(a(a(a(b(a(B(x))))))))))) → B1(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
B1(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → B1(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))
B1(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → B1(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))
B1(a(a(a(a(b(a(b(x)))))))) → B1(a(a(a(a(b(a(a(a(a(b(x)))))))))))
B1(b(a(a(b(x))))) → B1(a(a(a(a(b(x))))))
B1(a(a(a(a(b(a(b(x)))))))) → B1(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x)))))))))))))))))
B1(a(a(a(a(b(a(b(x)))))))) → B1(a(a(a(a(b(x))))))
B1(a(a(a(a(b(a(a(b(x))))))))) → B1(a(b(x)))
B1(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → B1(a(a(a(b(a(B(x)))))))
B1(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → B1(a(a(a(b(a(B(x)))))))
B1(b(a(a(b(x))))) → B1(b(a(a(a(a(b(x)))))))
B1(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B1(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))
The TRS R consists of the following rules:
b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
b(b(a(b(a(a(a(a(b(a(B(x))))))))))) → b(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
b(a(a(a(a(b(a(B(x)))))))) → b(a(B(x)))
b(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))
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 22 less nodes.
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ Narrowing
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
B1(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → B1(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))
B1(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B1(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))
B1(a(a(a(a(b(a(b(x)))))))) → B1(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
B1(a(a(a(a(b(a(a(b(x))))))))) → B1(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
B1(a(a(a(a(b(a(b(x)))))))) → B1(a(a(a(a(b(a(a(a(a(b(x)))))))))))
B1(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B1(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
B1(a(a(a(a(b(a(b(x)))))))) → B1(a(a(a(a(b(x))))))
B1(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B1(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))
The TRS R consists of the following rules:
b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
b(b(a(b(a(a(a(a(b(a(B(x))))))))))) → b(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
b(a(a(a(a(b(a(B(x)))))))) → b(a(B(x)))
b(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B1(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B1(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))) at position [0,0,0,0,0] we obtained the following new rules:
B1(a(a(a(a(b(a(b(a(a(a(a(b(a(B(y0))))))))))))))) → B1(a(a(a(a(b(a(B(y0))))))))
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
B1(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → B1(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))
B1(a(a(a(a(b