MAYBE
Termination w.r.t. Q proof of ../tpdb/SRS/HofWald/4.srs
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(b(a(a(a(a(b(x1))))))) → b(a(a(a(a(b(b(a(a(a(a(b(a(x1)))))))))))))
Q is empty.
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
Q restricted rewrite system:
The TRS R consists of the following rules:
a(b(a(a(a(a(b(x1))))))) → b(a(a(a(a(b(b(a(a(a(a(b(a(x1)))))))))))))
Q is empty.
We have reversed the following QTRS:
The set of rules R is
a(b(a(a(a(a(b(x1))))))) → b(a(a(a(a(b(b(a(a(a(a(b(a(x1)))))))))))))
The set Q is empty.
We have obtained the following QTRS:
b(a(a(a(a(b(a(x))))))) → a(b(a(a(a(a(b(b(a(a(a(a(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(a(a(a(a(b(a(x))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(x)))))))))))))
Q is empty.
We have reversed the following QTRS:
The set of rules R is
a(b(a(a(a(a(b(x1))))))) → b(a(a(a(a(b(b(a(a(a(a(b(a(x1)))))))))))))
The set Q is empty.
We have obtained the following QTRS:
b(a(a(a(a(b(a(x))))))) → a(b(a(a(a(a(b(b(a(a(a(a(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(a(a(a(a(b(a(x))))))) → a(b(a(a(a(a(b(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:
A(b(a(a(a(a(b(x1))))))) → A(a(a(b(a(x1)))))
A(b(a(a(a(a(b(x1))))))) → A(a(b(b(a(a(a(a(b(a(x1))))))))))
A(b(a(a(a(a(b(x1))))))) → A(a(a(a(b(b(a(a(a(a(b(a(x1))))))))))))
A(b(a(a(a(a(b(x1))))))) → A(a(b(a(x1))))
A(b(a(a(a(a(b(x1))))))) → A(b(a(x1)))
A(b(a(a(a(a(b(x1))))))) → A(b(b(a(a(a(a(b(a(x1)))))))))
A(b(a(a(a(a(b(x1))))))) → A(x1)
A(b(a(a(a(a(b(x1))))))) → A(a(a(a(b(a(x1))))))
A(b(a(a(a(a(b(x1))))))) → A(a(a(b(b(a(a(a(a(b(a(x1)))))))))))
The TRS R consists of the following rules:
a(b(a(a(a(a(b(x1))))))) → b(a(a(a(a(b(b(a(a(a(a(b(a(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:
A(b(a(a(a(a(b(x1))))))) → A(a(a(b(a(x1)))))
A(b(a(a(a(a(b(x1))))))) → A(a(b(b(a(a(a(a(b(a(x1))))))))))
A(b(a(a(a(a(b(x1))))))) → A(a(a(a(b(b(a(a(a(a(b(a(x1))))))))))))
A(b(a(a(a(a(b(x1))))))) → A(a(b(a(x1))))
A(b(a(a(a(a(b(x1))))))) → A(b(a(x1)))
A(b(a(a(a(a(b(x1))))))) → A(b(b(a(a(a(a(b(a(x1)))))))))
A(b(a(a(a(a(b(x1))))))) → A(x1)
A(b(a(a(a(a(b(x1))))))) → A(a(a(a(b(a(x1))))))
A(b(a(a(a(a(b(x1))))))) → A(a(a(b(b(a(a(a(a(b(a(x1)))))))))))
The TRS R consists of the following rules:
a(b(a(a(a(a(b(x1))))))) → b(a(a(a(a(b(b(a(a(a(a(b(a(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 4 less nodes.
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
Q DP problem:
The TRS P consists of the following rules:
A(b(a(a(a(a(b(x1))))))) → A(a(a(b(a(x1)))))
A(b(a(a(a(a(b(x1))))))) → A(a(b(a(x1))))
A(b(a(a(a(a(b(x1))))))) → A(b(a(x1)))
A(b(a(a(a(a(b(x1))))))) → A(x1)
A(b(a(a(a(a(b(x1))))))) → A(a(a(a(b(a(x1))))))
The TRS R consists of the following rules:
a(b(a(a(a(a(b(x1))))))) → b(a(a(a(a(b(b(a(a(a(a(b(a(x1)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A(b(a(a(a(a(b(x1))))))) → A(a(a(b(a(x1))))) at position [0] we obtained the following new rules:
A(b(a(a(a(a(b(b(a(a(a(a(b(x0))))))))))))) → A(a(a(b(b(a(a(a(a(b(b(a(a(a(a(b(a(x0)))))))))))))))))
A(b(a(a(a(a(b(a(a(a(b(x0))))))))))) → A(a(b(a(a(a(a(b(b(a(a(a(a(b(a(x0)))))))))))))))
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
Q DP problem:
The TRS P consists of the following rules:
A(b(a(a(a(a(b(x1))))))) → A(a(b(a(x1))))
A(b(a(a(a(a(b(x1))))))) → A(b(a(x1)))
A(b(a(a(a(a(b(x1))))))) → A(x1)
A(b(a(a(a(a(b(x1))))))) → A(a(a(a(b(a(x1))))))
A(b(a(a(a(a(b(b(a(a(a(a(b(x0))))))))))))) → A(a(a(b(b(a(a(a(a(b(b(a(a(a(a(b(a(x0)))))))))))))))))
A(b(a(a(a(a(b(a(a(a(b(x0))))))))))) → A(a(b(a(a(a(a(b(b(a(a(a(a(b(a(x0)))))))))))))))
The TRS R consists of the following rules:
a(b(a(a(a(a(b(x1))))))) → b(a(a(a(a(b(b(a(a(a(a(b(a(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 1 less node.
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
Q DP problem:
The TRS P consists of the following rules:
A(b(a(a(a(a(b(x1))))))) → A(a(b(a(x1))))
A(b(a(a(a(a(b(x1))))))) → A(b(a(x1)))
A(b(a(a(a(a(b(x1))))))) → A(x1)
A(b(a(a(a(a(b(x1))))))) → A(a(a(a(b(a(x1))))))
A(b(a(a(a(a(b(a(a(a(b(x0))))))))))) → A(a(b(a(a(a(a(b(b(a(a(a(a(b(a(x0)))))))))))))))
The TRS R consists of the following rules:
a(b(a(a(a(a(b(x1))))))) → b(a(a(a(a(b(b(a(a(a(a(b(a(x1)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A(b(a(a(a(a(b(x1))))))) → A(a(b(a(x1)))) at position [0] we obtained the following new rules:
A(b(a(a(a(a(b(a(a(a(b(x0))))))))))) → A(b(a(a(a(a(b(b(a(a(a(a(b(a(x0))))))))))))))
A(b(a(a(a(a(b(b(a(a(a(a(b(x0))))))))))))) → A(a(b(b(a(a(a(a(b(b(a(a(a(a(b(a(x0))))))))))))))))
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
Q DP problem:
The TRS P consists of the following rules:
A(b(a(a(a(a(b(b(a(a(a(a(b(x0))))))))))))) → A(a(b(b(a(a(a(a(b(b(a(a(a(a(b(a(x0))))))))))))))))
A(b(a(a(a(a(b(x1))))))) → A(b(a(x1)))
A(b(a(a(a(a(b(x1))))))) → A(x1)
A(b(a(a(a(a(b(x1))))))) → A(a(a(a(b(a(x1))))))
A(b(a(a(a(a(b(a(a(a(b(x0))))))))))) → A(b(a(a(a(a(b(b(a(a(a(a(b(a(x0))))))))))))))
A(b(a(a(a(a(b(a(a(a(b(x0))))))))))) → A(a(b(a(a(a(a(b(b(a(a(a(a(b(a(x0)))))))))))))))
The TRS R consists of the following rules:
a(b(a(a(a(a(b(x1))))))) → b(a(a(a(a(b(b(a(a(a(a(b(a(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 1 less node.
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
Q DP problem:
The TRS P consists of the following rules:
A(b(a(a(a(a(b(x1))))))) → A(b(a(x1)))
A(b(a(a(a(a(b(x1))))))) → A(x1)
A(b(a(a(a(a(b(x1))))))) → A(a(a(a(b(a(x1))))))
A(b(a(a(a(a(b(a(a(a(b(x0))))))))))) → A(b(a(a(a(a(b(b(a(a(a(a(b(a(x0))))))))))))))
A(b(a(a(a(a(b(a(a(a(b(x0))))))))))) → A(a(b(a(a(a(a(b(b(a(a(a(a(b(a(x0)))))))))))))))
The TRS R consists of the following rules:
a(b(a(a(a(a(b(x1))))))) → b(a(a(a(a(b(b(a(a(a(a(b(a(x1)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A(b(a(a(a(a(b(x1))))))) → A(a(a(a(b(a(x1)))))) at position [0] we obtained the following new rules:
A(b(a(a(a(a(b(a(a(a(b(x0))))))))))) → A(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(x0))))))))))))))))
A(b(a(a(a(a(b(b(a(a(a(a(b(x0))))))))))))) → A(a(a(a(b(b(a(a(a(a(b(b(a(a(a(a(b(a(x0))))))))))))))))))
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
Q DP problem:
The TRS P consists of the following rules:
A(b(a(a(a(a(b(a(a(a(b(x0))))))))))) → A(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(x0))))))))))))))))
A(b(a(a(a(a(b(b(a(a(a(a(b(x0))))))))))))) → A(a(a(a(b(b(a(a(a(a(b(b(a(a(a(a(b(a(x0))))))))))))))))))
A(b(a(a(a(a(b(x1))))))) → A(b(a(x1)))
A(b(a(a(a(a(b(x1))))))) → A(x1)
A(b(a(a(a(a(b(a(a(a(b(x0))))))))))) → A(b(a(a(a(a(b(b(a(a(a(a(b(a(x0))))))))))))))
A(b(a(a(a(a(b(a(a(a(b(x0))))))))))) → A(a(b(a(a(a(a(b(b(a(a(a(a(b(a(x0)))))))))))))))
The TRS R consists of the following rules:
a(b(a(a(a(a(b(x1))))))) → b(a(a(a(a(b(b(a(a(a(a(b(a(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 1 less node.
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPToSRSProof
Q DP problem:
The TRS P consists of the following rules:
A(b(a(a(a(a(b(a(a(a(b(x0))))))))))) → A(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(x0))))))))))))))))
A(b(a(a(a(a(b(x1))))))) → A(b(a(x1)))
A(b(a(a(a(a(b(x1))))))) → A(x1)
A(b(a(a(a(a(b(a(a(a(b(x0))))))))))) → A(b(a(a(a(a(b(b(a(a(a(a(b(a(x0))))))))))))))
A(b(a(a(a(a(b(a(a(a(b(x0))))))))))) → A(a(b(a(a(a(a(b(b(a(a(a(a(b(a(x0)))))))))))))))
The TRS R consists of the following rules:
a(b(a(a(a(a(b(x1))))))) → b(a(a(a(a(b(b(a(a(a(a(b(a(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
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
Q restricted rewrite system:
The TRS R consists of the following rules:
a(b(a(a(a(a(b(x1))))))) → b(a(a(a(a(b(b(a(a(a(a(b(a(x1)))))))))))))
A(b(a(a(a(a(b(a(a(a(b(x0))))))))))) → A(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(x0))))))))))))))))
A(b(a(a(a(a(b(x1))))))) → A(b(a(x1)))
A(b(a(a(a(a(b(x1))))))) → A(x1)
A(b(a(a(a(a(b(a(a(a(b(x0))))))))))) → A(b(a(a(a(a(b(b(a(a(a(a(b(a(x0))))))))))))))
A(b(a(a(a(a(b(a(a(a(b(x0))))))))))) → A(a(b(a(a(a(a(b(b(a(a(a(a(b(a(x0)))))))))))))))
Q is empty.
We have reversed the following QTRS:
The set of rules R is
a(b(a(a(a(a(b(x1))))))) → b(a(a(a(a(b(b(a(a(a(a(b(a(x1)))))))))))))
A(b(a(a(a(a(b(a(a(a(b(x0))))))))))) → A(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(x0))))))))))))))))
A(b(a(a(a(a(b(x1))))))) → A(b(a(x1)))
A(b(a(a(a(a(b(x1))))))) → A(x1)
A(b(a(a(a(a(b(a(a(a(b(x0))))))))))) → A(b(a(a(a(a(b(b(a(a(a(a(b(a(x0))))))))))))))
A(b(a(a(a(a(b(a(a(a(b(x0))))))))))) → A(a(b(a(a(a(a(b(b(a(a(a(a(b(a(x0)))))))))))))))
The set Q is empty.
We have obtained the following QTRS:
b(a(a(a(a(b(a(x))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(x)))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(A(x))))))))))))))))
b(a(a(a(a(b(A(x))))))) → a(b(A(x)))
b(a(a(a(a(b(A(x))))))) → A(x)
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(A(x))))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(x)))))))))))))))
The set Q is empty.
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
Q restricted rewrite system:
The TRS R consists of the following rules:
b(a(a(a(a(b(a(x))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(x)))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(A(x))))))))))))))))
b(a(a(a(a(b(A(x))))))) → a(b(A(x)))
b(a(a(a(a(b(A(x))))))) → A(x)
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(A(x))))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(x)))))))))))))))
Q is empty.
We have reversed the following QTRS:
The set of rules R is
b(a(a(a(a(b(a(x))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(x)))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(A(x))))))))))))))))
b(a(a(a(a(b(A(x))))))) → a(b(A(x)))
b(a(a(a(a(b(A(x))))))) → A(x)
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(A(x))))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(x)))))))))))))))
The set Q is empty.
We have obtained the following QTRS:
a(b(a(a(a(a(b(x))))))) → b(a(a(a(a(b(b(a(a(a(a(b(a(x)))))))))))))
A(b(a(a(a(a(b(a(a(a(b(x))))))))))) → A(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(x))))))))))))))))
A(b(a(a(a(a(b(x))))))) → A(b(a(x)))
A(b(a(a(a(a(b(x))))))) → A(x)
A(b(a(a(a(a(b(a(a(a(b(x))))))))))) → A(b(a(a(a(a(b(b(a(a(a(a(b(a(x))))))))))))))
A(b(a(a(a(a(b(a(a(a(b(x))))))))))) → A(a(b(a(a(a(a(b(b(a(a(a(a(b(a(x)))))))))))))))
The set Q is empty.
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
Q restricted rewrite system:
The TRS R consists of the following rules:
a(b(a(a(a(a(b(x))))))) → b(a(a(a(a(b(b(a(a(a(a(b(a(x)))))))))))))
A(b(a(a(a(a(b(a(a(a(b(x))))))))))) → A(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(x))))))))))))))))
A(b(a(a(a(a(b(x))))))) → A(b(a(x)))
A(b(a(a(a(a(b(x))))))) → A(x)
A(b(a(a(a(a(b(a(a(a(b(x))))))))))) → A(b(a(a(a(a(b(b(a(a(a(a(b(a(x))))))))))))))
A(b(a(a(a(a(b(a(a(a(b(x))))))))))) → A(a(b(a(a(a(a(b(b(a(a(a(a(b(a(x)))))))))))))))
Q is empty.
We have reversed the following QTRS:
The set of rules R is
b(a(a(a(a(b(a(x))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(x)))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(A(x))))))))))))))))
b(a(a(a(a(b(A(x))))))) → a(b(A(x)))
b(a(a(a(a(b(A(x))))))) → A(x)
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(A(x))))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(x)))))))))))))))
The set Q is empty.
We have obtained the following QTRS:
a(b(a(a(a(a(b(x))))))) → b(a(a(a(a(b(b(a(a(a(a(b(a(x)))))))))))))
A(b(a(a(a(a(b(a(a(a(b(x))))))))))) → A(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(x))))))))))))))))
A(b(a(a(a(a(b(x))))))) → A(b(a(x)))
A(b(a(a(a(a(b(x))))))) → A(x)
A(b(a(a(a(a(b(a(a(a(b(x))))))))))) → A(b(a(a(a(a(b(b(a(a(a(a(b(a(x))))))))))))))
A(b(a(a(a(a(b(a(a(a(b(x))))))))))) → A(a(b(a(a(a(a(b(b(a(a(a(a(b(a(x)))))))))))))))
The set Q is empty.
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS
↳ DependencyPairsProof
Q restricted rewrite system:
The TRS R consists of the following rules:
a(b(a(a(a(a(b(x))))))) → b(a(a(a(a(b(b(a(a(a(a(b(a(x)))))))))))))
A(b(a(a(a(a(b(a(a(a(b(x))))))))))) → A(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(x))))))))))))))))
A(b(a(a(a(a(b(x))))))) → A(b(a(x)))
A(b(a(a(a(a(b(x))))))) → A(x)
A(b(a(a(a(a(b(a(a(a(b(x))))))))))) → A(b(a(a(a(a(b(b(a(a(a(a(b(a(x))))))))))))))
A(b(a(a(a(a(b(a(a(a(b(x))))))))))) → A(a(b(a(a(a(a(b(b(a(a(a(a(b(a(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(a(a(a(b(a(x))))))) → B(b(a(a(a(a(b(x)))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(b(a(a(a(a(b(a(a(A(x)))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(b(a(a(a(a(b(A(x)))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(a(A(x)))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(A(x)))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(a(a(A(x)))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(a(A(x))))))))
B(a(a(a(a(b(a(x))))))) → B(x)
B(a(a(a(a(b(a(x))))))) → B(a(a(a(a(b(b(a(a(a(a(b(x))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(b(a(a(a(a(b(a(A(x))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(a(a(A(x))))))))))
B(a(a(a(a(b(a(x))))))) → B(a(a(a(a(b(x))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(A(x))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(A(x))))))))
The TRS R consists of the following rules:
b(a(a(a(a(b(a(x))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(x)))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(A(x))))))))))))))))
b(a(a(a(a(b(A(x))))))) → a(b(A(x)))
b(a(a(a(a(b(A(x))))))) → A(x)
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(A(x))))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(x)))))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
Q DP problem:
The TRS P consists of the following rules:
B(a(a(a(a(b(a(x))))))) → B(b(a(a(a(a(b(x)))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(b(a(a(a(a(b(a(a(A(x)))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(b(a(a(a(a(b(A(x)))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(a(A(x)))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(A(x)))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(a(a(A(x)))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(a(A(x))))))))
B(a(a(a(a(b(a(x))))))) → B(x)
B(a(a(a(a(b(a(x))))))) → B(a(a(a(a(b(b(a(a(a(a(b(x))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(b(a(a(a(a(b(a(A(x))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(a(a(A(x))))))))))
B(a(a(a(a(b(a(x))))))) → B(a(a(a(a(b(x))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(A(x))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(A(x))))))))
The TRS R consists of the following rules:
b(a(a(a(a(b(a(x))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(x)))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(A(x))))))))))))))))
b(a(a(a(a(b(A(x))))))) → a(b(A(x)))
b(a(a(a(a(b(A(x))))))) → A(x)
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(A(x))))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(x)))))))))))))))
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 2 less nodes.
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
Q DP problem:
The TRS P consists of the following rules:
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(b(a(a(a(a(b(a(a(A(x)))))))))))))))
B(a(a(a(a(b(a(x))))))) → B(b(a(a(a(a(b(x)))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(a(a(A(x))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(a(A(x)))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(b(a(a(a(a(b(A(x)))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(a(a(A(x)))))))))
B(a(a(a(a(b(a(x))))))) → B(a(a(a(a(b(x))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(a(A(x))))))))
B(a(a(a(a(b(a(x))))))) → B(x)
B(a(a(a(a(b(a(x))))))) → B(a(a(a(a(b(b(a(a(a(a(b(x))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(b(a(a(a(a(b(a(A(x))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(A(x))))))))
The TRS R consists of the following rules:
b(a(a(a(a(b(a(x))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(x)))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(A(x))))))))))))))))
b(a(a(a(a(b(A(x))))))) → a(b(A(x)))
b(a(a(a(a(b(A(x))))))) → A(x)
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(A(x))))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(x)))))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B(a(a(a(a(b(a(x))))))) → B(b(a(a(a(a(b(x))))))) at position [0] we obtained the following new rules:
B(a(a(a(a(b(a(a(a(a(a(b(a(x0))))))))))))) → B(b(a(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(x0)))))))))))))))))))
B(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(A(x0))))))))))))))))) → B(b(a(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(A(x0))))))))))))))))))))
B(a(a(a(a(b(a(a(a(a(a(b(A(x0))))))))))))) → B(b(a(a(a(a(a(b(A(x0)))))))))
B(a(a(a(a(b(a(a(a(a(a(b(A(x0))))))))))))) → B(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(b(a(A(x0)))))))) → B(a(b(A(x0))))
B(a(a(a(a(b(a(A(x0)))))))) → B(A(x0))
B(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(A(x0))))))))))))))))) → B(b(a(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(A(x0))))))))))))))))))))))
B(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(A(x0))))))))))))))))) → B(b(a(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(x0)))))))))))))))))))))
B(a(a(a(a(b(a(a(x0)))))))) → B(a(b(a(a(a(a(b(b(a(a(a(a(b(x0))))))))))))))
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
Q DP problem:
The TRS P consists of the following rules:
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(b(a(a(a(a(b(a(a(A(x)))))))))))))))
B(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(A(x0))))))))))))))))) → B(b(a(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(A(x0))))))))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(b(a(a(a(a(b(A(x)))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(a(A(x)))))))))
B(a(a(a(a(b(a(a(a(a(a(b(A(x0))))))))))))) → B(b(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(a(a(A(x)))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(a(A(x))))))))
B(a(a(a(a(b(a(x))))))) → B(x)
B(a(a(a(a(b(a(x))))))) → B(a(a(a(a(b(b(a(a(a(a(b(x))))))))))))
B(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(A(x0))))))))))))))))) → B(b(a(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(A(x0))))))))))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(b(a(a(a(a(b(a(A(x))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(a(a(A(x))))))))))
B(a(a(a(a(b(a(a(a(a(a(b(a(x0))))))))))))) → B(b(a(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(x0)))))))))))))))))))
B(a(a(a(a(b(a(a(a(a(a(b(A(x0))))))))))))) → B(b(a(a(a(a(a(b(A(x0)))))))))
B(a(a(a(a(b(a(x))))))) → B(a(a(a(a(b(x))))))
B(a(a(a(a(b(a(A(x0)))))))) → B(a(b(A(x0))))
B(a(a(a(a(b(a(A(x0)))))))) → B(A(x0))
B(a(a(a(a(b(a(a(x0)))))))) → B(a(b(a(a(a(a(b(b(a(a(a(a(b(x0))))))))))))))
B(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(A(x0))))))))))))))))) → B(b(a(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(x0)))))))))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(A(x))))))))
The TRS R consists of the following rules:
b(a(a(a(a(b(a(x))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(x)))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(A(x))))))))))))))))
b(a(a(a(a(b(A(x))))))) → a(b(A(x)))
b(a(a(a(a(b(A(x))))))) → A(x)
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(A(x))))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(x)))))))))))))))
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 8 less nodes.
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
Q DP problem:
The TRS P consists of the following rules:
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(b(a(a(a(a(b(a(a(A(x)))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(a(a(A(x))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(a(A(x)))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(b(a(a(a(a(b(A(x)))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(a(a(A(x)))))))))
B(a(a(a(a(b(a(x))))))) → B(a(a(a(a(b(x))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(a(A(x))))))))
B(a(a(a(a(b(a(x))))))) → B(x)
B(a(a(a(a(b(a(x))))))) → B(a(a(a(a(b(b(a(a(a(a(b(x))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(b(a(a(a(a(b(a(A(x))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(A(x))))))))
B(a(a(a(a(b(a(a(x0)))))))) → B(a(b(a(a(a(a(b(b(a(a(a(a(b(x0))))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(b(a(x))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(x)))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(A(x))))))))))))))))
b(a(a(a(a(b(A(x))))))) → a(b(A(x)))
b(a(a(a(a(b(A(x))))))) → A(x)
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(A(x))))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(x)))))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B(a(a(a(a(b(a(x))))))) → B(a(a(a(a(b(b(a(a(a(a(b(x)))))))))))) at position [0,0,0,0,0] we obtained the following new rules:
B(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(A(x0))))))))))))))))) → B(a(a(a(a(b(b(a(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(x0))))))))))))))))))))))))))
B(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(A(x0))))))))))))))))) → B(a(a(a(a(b(b(a(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(A(x0)))))))))))))))))))))))))
B(a(a(a(a(b(a(a(a(a(a(b(A(x0))))))))))))) → B(a(a(a(a(b(b(a(a(a(a(a(b(A(x0))))))))))))))
B(a(a(a(a(b(a(A(x0)))))))) → B(a(a(a(a(b(A(x0)))))))
B(a(a(a(a(b(a(a(a(a(a(b(a(x0))))))))))))) → B(a(a(a(a(b(b(a(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(x0))))))))))))))))))))))))
B(a(a(a(a(b(a(A(x0)))))))) → B(a(a(a(a(b(a(b(A(x0)))))))))
B(a(a(a(a(b(a(a(x0)))))))) → B(a(a(a(a(b(a(b(a(a(a(a(b(b(a(a(a(a(b(x0)))))))))))))))))))
B(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(A(x0))))))))))))))))) → B(a(a(a(a(b(b(a(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(A(x0)))))))))))))))))))))))))))
B(a(a(a(a(b(a(a(a(a(a(b(A(x0))))))))))))) → B(a(a(a(a(b(b(a(a(a(a(A(x0))))))))))))
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
Q DP problem:
The TRS P consists of the following rules:
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(b(a(a(a(a(b(a(a(A(x)))))))))))))))
B(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(A(x0))))))))))))))))) → B(a(a(a(a(b(b(a(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(x0))))))))))))))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(b(a(a(a(a(b(A(x)))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(a(A(x)))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(a(a(A(x)))))))))
B(a(a(a(a(b(a(a(a(a(a(b(a(x0))))))))))))) → B(a(a(a(a(b(b(a(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(x0))))))))))))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(a(A(x))))))))
B(a(a(a(a(b(a(A(x0)))))))) → B(a(a(a(a(b(a(b(A(x0)))))))))
B(a(a(a(a(b(a(x))))))) → B(x)
B(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(A(x0))))))))))))))))) → B(a(a(a(a(b(b(a(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(A(x0)))))))))))))))))))))))))))
B(a(a(a(a(b(a(a(x0)))))))) → B(a(a(a(a(b(a(b(a(a(a(a(b(b(a(a(a(a(b(x0)))))))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(b(a(a(a(a(b(a(A(x))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(a(a(A(x))))))))))
B(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(A(x0))))))))))))))))) → B(a(a(a(a(b(b(a(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(A(x0)))))))))))))))))))))))))
B(a(a(a(a(b(a(a(a(a(a(b(A(x0))))))))))))) → B(a(a(a(a(b(b(a(a(a(a(a(b(A(x0))))))))))))))
B(a(a(a(a(b(a(x))))))) → B(a(a(a(a(b(x))))))
B(a(a(a(a(b(a(A(x0)))))))) → B(a(a(a(a(b(A(x0)))))))
B(a(a(a(a(b(a(a(a(a(a(b(A(x0))))))))))))) → B(a(a(a(a(b(b(a(a(a(a(A(x0))))))))))))
B(a(a(a(a(b(a(a(x0)))))))) → B(a(b(a(a(a(a(b(b(a(a(a(a(b(x0))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(A(x))))))))
The TRS R consists of the following rules:
b(a(a(a(a(b(a(x))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(x)))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(A(x))))))))))))))))
b(a(a(a(a(b(A(x))))))) → a(b(A(x)))
b(a(a(a(a(b(A(x))))))) → A(x)
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(A(x))))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(x)))))))))))))))
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 7 less nodes.
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
Q DP problem:
The TRS P consists of the following rules:
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(b(a(a(a(a(b(a(a(A(x)))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(b(a(a(a(a(b(A(x)))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(a(A(x)))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(a(a(A(x)))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(a(A(x))))))))
B(a(a(a(a(b(a(A(x0)))))))) → B(a(a(a(a(b(a(b(A(x0)))))))))
B(a(a(a(a(b(a(x))))))) → B(x)
B(a(a(a(a(b(a(a(x0)))))))) → B(a(a(a(a(b(a(b(a(a(a(a(b(b(a(a(a(a(b(x0)))))))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(b(a(a(a(a(b(a(A(x))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(a(a(A(x))))))))))
B(a(a(a(a(b(a(x))))))) → B(a(a(a(a(b(x))))))
B(a(a(a(a(b(a(a(x0)))))))) → B(a(b(a(a(a(a(b(b(a(a(a(a(b(x0))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(A(x))))))))
The TRS R consists of the following rules:
b(a(a(a(a(b(a(x))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(x)))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(A(x))))))))))))))))
b(a(a(a(a(b(A(x))))))) → a(b(A(x)))
b(a(a(a(a(b(A(x))))))) → A(x)
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(A(x))))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(x)))))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(b(a(a(a(a(b(a(a(A(x))))))))))))))) at position [0,0,0,0,0] we obtained the following new rules:
B(a(a(a(b(a(a(a(a(b(A(y0))))))))))) → B(a(a(a(a(b(a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(y0)))))))))))))))))))))
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
Q DP problem:
The TRS P consists of the following rules:
B(a(a(a(b(a(a(a(a(b(A(y0))))))))))) → B(a(a(a(a(b(a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(y0)))))))))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(a(A(x)))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(b(a(a(a(a(b(A(x)))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(a(a(A(x)))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(a(A(x))))))))
B(a(a(a(a(b(a(A(x0)))))))) → B(a(a(a(a(b(a(b(A(x0)))))))))
B(a(a(a(a(b(a(x))))))) → B(x)
B(a(a(a(a(b(a(a(x0)))))))) → B(a(a(a(a(b(a(b(a(a(a(a(b(b(a(a(a(a(b(x0)))))))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(b(a(a(a(a(b(a(A(x))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(a(a(A(x))))))))))
B(a(a(a(a(b(a(x))))))) → B(a(a(a(a(b(x))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(A(x))))))))
B(a(a(a(a(b(a(a(x0)))))))) → B(a(b(a(a(a(a(b(b(a(a(a(a(b(x0))))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(b(a(x))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(x)))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(A(x))))))))))))))))
b(a(a(a(a(b(A(x))))))) → a(b(A(x)))
b(a(a(a(a(b(A(x))))))) → A(x)
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(A(x))))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(x)))))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(a(a(A(x)))))))))) at position [0] we obtained the following new rules:
B(a(a(a(b(a(a(a(a(b(A(y0))))))))))) → B(a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(y0))))))))))))))))
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
Q DP problem:
The TRS P consists of the following rules:
B(a(a(a(b(a(a(a(a(b(A(y0))))))))))) → B(a(a(a(a(b(a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(y0)))))))))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(b(a(a(a(a(b(A(x)))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(a(A(x)))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(a(a(A(x)))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(a(A(x))))))))
B(a(a(a(a(b(a(A(x0)))))))) → B(a(a(a(a(b(a(b(A(x0)))))))))
B(a(a(a(a(b(a(x))))))) → B(x)
B(a(a(a(a(b(a(a(x0)))))))) → B(a(a(a(a(b(a(b(a(a(a(a(b(b(a(a(a(a(b(x0)))))))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(y0))))))))))) → B(a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(y0))))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(b(a(a(a(a(b(a(A(x))))))))))))))
B(a(a(a(a(b(a(x))))))) → B(a(a(a(a(b(x))))))
B(a(a(a(a(b(a(a(x0)))))))) → B(a(b(a(a(a(a(b(b(a(a(a(a(b(x0))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(A(x))))))))
The TRS R consists of the following rules:
b(a(a(a(a(b(a(x))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(x)))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(A(x))))))))))))))))
b(a(a(a(a(b(A(x))))))) → a(b(A(x)))
b(a(a(a(a(b(A(x))))))) → A(x)
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(A(x))))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(x)))))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(b(a(a(a(a(b(A(x))))))))))))) at position [0,0,0,0,0] we obtained the following new rules:
B(a(a(a(b(a(a(a(a(b(A(x0))))))))))) → B(a(a(a(a(b(a(b(A(x0)))))))))
B(a(a(a(b(a(a(a(a(b(A(x0))))))))))) → B(a(a(a(a(b(A(x0)))))))
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
Q DP problem:
The TRS P consists of the following rules:
B(a(a(a(b(a(a(a(a(b(A(x0))))))))))) → B(a(a(a(a(b(A(x0)))))))
B(a(a(a(b(a(a(a(a(b(A(y0))))))))))) → B(a(a(a(a(b(a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(y0)))))))))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(a(A(x)))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(a(a(A(x)))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(a(A(x))))))))
B(a(a(a(a(b(a(A(x0)))))))) → B(a(a(a(a(b(a(b(A(x0)))))))))
B(a(a(a(a(b(a(x))))))) → B(x)
B(a(a(a(a(b(a(a(x0)))))))) → B(a(a(a(a(b(a(b(a(a(a(a(b(b(a(a(a(a(b(x0)))))))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(y0))))))))))) → B(a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(y0))))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(b(a(a(a(a(b(a(A(x))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x0))))))))))) → B(a(a(a(a(b(a(b(A(x0)))))))))
B(a(a(a(a(b(a(x))))))) → B(a(a(a(a(b(x))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(A(x))))))))
B(a(a(a(a(b(a(a(x0)))))))) → B(a(b(a(a(a(a(b(b(a(a(a(a(b(x0))))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(b(a(x))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(x)))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(A(x))))))))))))))))
b(a(a(a(a(b(A(x))))))) → a(b(A(x)))
b(a(a(a(a(b(A(x))))))) → A(x)
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(A(x))))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(x)))))))))))))))
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 1 less node.
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
Q DP problem:
The TRS P consists of the following rules:
B(a(a(a(b(a(a(a(a(b(A(y0))))))))))) → B(a(a(a(a(b(a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(y0)))))))))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(a(A(x)))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(a(a(A(x)))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(a(A(x))))))))
B(a(a(a(a(b(a(A(x0)))))))) → B(a(a(a(a(b(a(b(A(x0)))))))))
B(a(a(a(a(b(a(x))))))) → B(x)
B(a(a(a(a(b(a(a(x0)))))))) → B(a(a(a(a(b(a(b(a(a(a(a(b(b(a(a(a(a(b(x0)))))))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(y0))))))))))) → B(a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(y0))))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(b(a(a(a(a(b(a(A(x))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x0))))))))))) → B(a(a(a(a(b(a(b(A(x0)))))))))
B(a(a(a(a(b(a(x))))))) → B(a(a(a(a(b(x))))))
B(a(a(a(a(b(a(a(x0)))))))) → B(a(b(a(a(a(a(b(b(a(a(a(a(b(x0))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(A(x))))))))
The TRS R consists of the following rules:
b(a(a(a(a(b(a(x))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(x)))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(A(x))))))))))))))))
b(a(a(a(a(b(A(x))))))) → a(b(A(x)))
b(a(a(a(a(b(A(x))))))) → A(x)
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(A(x))))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(x)))))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(A(x)))))))) at position [0] we obtained the following new rules:
B(a(a(a(b(a(a(a(a(b(A(x0))))))))))) → B(A(x0))
B(a(a(a(b(a(a(a(a(b(A(x0))))))))))) → B(a(b(A(x0))))
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
Q DP problem:
The TRS P consists of the following rules:
B(a(a(a(b(a(a(a(a(b(A(y0))))))))))) → B(a(a(a(a(b(a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(y0)))))))))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(a(A(x)))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(a(a(A(x)))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(a(A(x))))))))
B(a(a(a(a(b(a(A(x0)))))))) → B(a(a(a(a(b(a(b(A(x0)))))))))
B(a(a(a(a(b(a(x))))))) → B(x)
B(a(a(a(a(b(a(a(x0)))))))) → B(a(a(a(a(b(a(b(a(a(a(a(b(b(a(a(a(a(b(x0)))))))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(y0))))))))))) → B(a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(y0))))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x0))))))))))) → B(a(b(A(x0))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(b(a(a(a(a(b(a(A(x))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x0))))))))))) → B(a(a(a(a(b(a(b(A(x0)))))))))
B(a(a(a(b(a(a(a(a(b(A(x0))))))))))) → B(A(x0))
B(a(a(a(a(b(a(x))))))) → B(a(a(a(a(b(x))))))
B(a(a(a(a(b(a(a(x0)))))))) → B(a(b(a(a(a(a(b(b(a(a(a(a(b(x0))))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(b(a(x))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(x)))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(A(x))))))))))))))))
b(a(a(a(a(b(A(x))))))) → a(b(A(x)))
b(a(a(a(a(b(A(x))))))) → A(x)
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(A(x))))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(x)))))))))))))))
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 2 less nodes.
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
Q DP problem:
The TRS P consists of the following rules:
B(a(a(a(b(a(a(a(a(b(A(x0))))))))))) → B(a(a(a(a(b(a(b(A(x0)))))))))
B(a(a(a(b(a(a(a(a(b(A(y0))))))))))) → B(a(a(a(a(b(a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(y0)))))))))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(a(A(x)))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(a(a(A(x)))))))))
B(a(a(a(a(b(a(x))))))) → B(a(a(a(a(b(x))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(a(A(x))))))))
B(a(a(a(a(b(a(A(x0)))))))) → B(a(a(a(a(b(a(b(A(x0)))))))))
B(a(a(a(a(b(a(x))))))) → B(x)
B(a(a(a(a(b(a(a(x0)))))))) → B(a(a(a(a(b(a(b(a(a(a(a(b(b(a(a(a(a(b(x0)))))))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(y0))))))))))) → B(a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(y0))))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(b(a(a(a(a(b(a(A(x))))))))))))))
B(a(a(a(a(b(a(a(x0)))))))) → B(a(b(a(a(a(a(b(b(a(a(a(a(b(x0))))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(b(a(x))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(x)))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(A(x))))))))))))))))
b(a(a(a(a(b(A(x))))))) → a(b(A(x)))
b(a(a(a(a(b(A(x))))))) → A(x)
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(A(x))))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(x)))))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(b(a(a(a(a(b(a(A(x)))))))))))))) at position [0,0,0,0,0] we obtained the following new rules:
B(a(a(a(b(a(a(a(a(b(A(y0))))))))))) → B(a(a(a(a(b(a(b(a(a(a(a(b(b(a(a(a(a(b(A(y0))))))))))))))))))))
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
Q DP problem:
The TRS P consists of the following rules:
B(a(a(a(b(a(a(a(a(b(A(y0))))))))))) → B(a(a(a(a(b(a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(y0)))))))))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(a(A(x)))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(a(a(A(x)))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(a(A(x))))))))
B(a(a(a(a(b(a(A(x0)))))))) → B(a(a(a(a(b(a(b(A(x0)))))))))
B(a(a(a(a(b(a(x))))))) → B(x)
B(a(a(a(a(b(a(a(x0)))))))) → B(a(a(a(a(b(a(b(a(a(a(a(b(b(a(a(a(a(b(x0)))))))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(y0))))))))))) → B(a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(y0))))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x0))))))))))) → B(a(a(a(a(b(a(b(A(x0)))))))))
B(a(a(a(a(b(a(x))))))) → B(a(a(a(a(b(x))))))
B(a(a(a(b(a(a(a(a(b(A(y0))))))))))) → B(a(a(a(a(b(a(b(a(a(a(a(b(b(a(a(a(a(b(A(y0))))))))))))))))))))
B(a(a(a(a(b(a(a(x0)))))))) → B(a(b(a(a(a(a(b(b(a(a(a(a(b(x0))))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(b(a(x))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(x)))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(A(x))))))))))))))))
b(a(a(a(a(b(A(x))))))) → a(b(A(x)))
b(a(a(a(a(b(A(x))))))) → A(x)
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(A(x))))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(x)))))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(b(a(a(a(a(b(a(A(x))))))))) at position [0] we obtained the following new rules:
B(a(a(a(b(a(a(a(a(b(A(y0))))))))))) → B(a(b(a(a(a(a(b(b(a(a(a(a(b(A(y0)))))))))))))))
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
B(a(a(a(b(a(a(a(a(b(A(y0))))))))))) → B(a(a(a(a(b(a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(y0)))))))))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(a(a(A(x)))))))))
B(a(a(a(b(a(a(a(a(b(A(x))))))))))) → B(a(a(a(a(b(a(A(x))))))))
B(a(a(a(a(b(a(A(x0)))))))) → B(a(a(a(a(b(a(b(A(x0)))))))))
B(a(a(a(a(b(a(x))))))) → B(x)
B(a(a(a(a(b(a(a(x0)))))))) → B(a(a(a(a(b(a(b(a(a(a(a(b(b(a(a(a(a(b(x0)))))))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(y0))))))))))) → B(a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(y0))))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(x0))))))))))) → B(a(a(a(a(b(a(b(A(x0)))))))))
B(a(a(a(a(b(a(x))))))) → B(a(a(a(a(b(x))))))
B(a(a(a(b(a(a(a(a(b(A(y0))))))))))) → B(a(b(a(a(a(a(b(b(a(a(a(a(b(A(y0)))))))))))))))
B(a(a(a(b(a(a(a(a(b(A(y0))))))))))) → B(a(a(a(a(b(a(b(a(a(a(a(b(b(a(a(a(a(b(A(y0))))))))))))))))))))
B(a(a(a(a(b(a(a(x0)))))))) → B(a(b(a(a(a(a(b(b(a(a(a(a(b(x0))))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(b(a(x))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(x)))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(A(x))))))))))))))))
b(a(a(a(a(b(A(x))))))) → a(b(A(x)))
b(a(a(a(a(b(A(x))))))) → A(x)
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(A(x))))))))))))))
b(a(a(a(b(a(a(a(a(b(A(x))))))))))) → a(b(a(a(a(a(b(b(a(a(a(a(b(a(A(x)))))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.