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(a(a(a(b(x1))))) → b(b(a(a(a(a(a(x1)))))))
Q is empty.
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS Reverse
↳ QTRS Reverse
Q restricted rewrite system:
The TRS R consists of the following rules:
a(a(a(a(b(x1))))) → b(b(a(a(a(a(a(x1)))))))
Q is empty.
The TRS is overlay and locally confluent. By [19] we can switch to innermost.
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QTRS Reverse
↳ QTRS Reverse
Q restricted rewrite system:
The TRS R consists of the following rules:
a(a(a(a(b(x1))))) → b(b(a(a(a(a(a(x1)))))))
The set Q consists of the following terms:
a(a(a(a(b(x0)))))
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(a(a(a(b(x1))))) → A(x1)
A(a(a(a(b(x1))))) → A(a(x1))
A(a(a(a(b(x1))))) → A(a(a(a(a(x1)))))
A(a(a(a(b(x1))))) → A(a(a(x1)))
A(a(a(a(b(x1))))) → A(a(a(a(x1))))
The TRS R consists of the following rules:
a(a(a(a(b(x1))))) → b(b(a(a(a(a(a(x1)))))))
The set Q consists of the following terms:
a(a(a(a(b(x0)))))
We have to consider all minimal (P,Q,R)-chains.
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A(a(a(a(b(x1))))) → A(x1)
A(a(a(a(b(x1))))) → A(a(x1))
A(a(a(a(b(x1))))) → A(a(a(a(a(x1)))))
A(a(a(a(b(x1))))) → A(a(a(x1)))
A(a(a(a(b(x1))))) → A(a(a(a(x1))))
The TRS R consists of the following rules:
a(a(a(a(b(x1))))) → b(b(a(a(a(a(a(x1)))))))
The set Q consists of the following terms:
a(a(a(a(b(x0)))))
We have to consider all minimal (P,Q,R)-chains.
We use the modular non-overlap check [17] to decrease Q to the empty set.
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A(a(a(a(b(x1))))) → A(x1)
A(a(a(a(b(x1))))) → A(a(x1))
A(a(a(a(b(x1))))) → A(a(a(a(a(x1)))))
A(a(a(a(b(x1))))) → A(a(a(x1)))
A(a(a(a(b(x1))))) → A(a(a(a(x1))))
The TRS R consists of the following rules:
a(a(a(a(b(x1))))) → b(b(a(a(a(a(a(x1)))))))
Q is empty.
We have to consider all (P,Q,R)-chains.
By narrowing [15] the rule A(a(a(a(b(x1))))) → A(a(a(a(a(x1))))) at position [0] we obtained the following new rules:
A(a(a(a(b(b(x0)))))) → A(b(b(a(a(a(a(a(x0))))))))
A(a(a(a(b(a(a(b(x0)))))))) → A(a(a(b(b(a(a(a(a(a(x0))))))))))
A(a(a(a(b(a(b(x0))))))) → A(a(b(b(a(a(a(a(a(x0)))))))))
A(a(a(a(b(a(a(a(b(x0))))))))) → A(a(a(a(b(b(a(a(a(a(a(x0)))))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A(a(a(a(b(x1))))) → A(x1)
A(a(a(a(b(a(b(x0))))))) → A(a(b(b(a(a(a(a(a(x0)))))))))
A(a(a(a(b(b(x0)))))) → A(b(b(a(a(a(a(a(x0))))))))
A(a(a(a(b(x1))))) → A(a(x1))
A(a(a(a(b(a(a(b(x0)))))))) → A(a(a(b(b(a(a(a(a(a(x0))))))))))
A(a(a(a(b(x1))))) → A(a(a(x1)))
A(a(a(a(b(a(a(a(b(x0))))))))) → A(a(a(a(b(b(a(a(a(a(a(x0)))))))))))
A(a(a(a(b(x1))))) → A(a(a(a(x1))))
The TRS R consists of the following rules:
a(a(a(a(b(x1))))) → b(b(a(a(a(a(a(x1)))))))
The set Q consists of the following terms:
a(a(a(a(b(x0)))))
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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A(a(a(a(b(x1))))) → A(x1)
A(a(a(a(b(x1))))) → A(a(x1))
A(a(a(a(b(x1))))) → A(a(a(x1)))
A(a(a(a(b(a(a(a(b(x0))))))))) → A(a(a(a(b(b(a(a(a(a(a(x0)))))))))))
A(a(a(a(b(x1))))) → A(a(a(a(x1))))
The TRS R consists of the following rules:
a(a(a(a(b(x1))))) → b(b(a(a(a(a(a(x1)))))))
The set Q consists of the following terms:
a(a(a(a(b(x0)))))
We have to consider all minimal (P,Q,R)-chains.
By forward instantiating [14] the rule A(a(a(a(b(x1))))) → A(a(a(x1))) we obtained the following new rules:
A(a(a(a(b(a(b(a(a(a(y_1)))))))))) → A(a(a(a(b(a(a(a(y_1))))))))
A(a(a(a(b(a(y_1)))))) → A(a(a(a(y_1))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A(a(a(a(b(a(y_1)))))) → A(a(a(a(y_1))))
A(a(a(a(b(a(b(a(a(a(y_1)))))))))) → A(a(a(a(b(a(a(a(y_1))))))))
A(a(a(a(b(x1))))) → A(x1)
A(a(a(a(b(x1))))) → A(a(x1))
A(a(a(a(b(x1))))) → A(a(a(a(x1))))
A(a(a(a(b(a(a(a(b(x0))))))))) → A(a(a(a(b(b(a(a(a(a(a(x0)))))))))))
The TRS R consists of the following rules:
a(a(a(a(b(x1))))) → b(b(a(a(a(a(a(x1)))))))
The set Q consists of the following terms:
a(a(a(a(b(x0)))))
We have to consider all minimal (P,Q,R)-chains.
By forward instantiating [14] the rule A(a(a(a(b(x1))))) → A(a(x1)) we obtained the following new rules:
A(a(a(a(b(a(a(b(a(b(a(a(a(y_0))))))))))))) → A(a(a(a(b(a(b(a(a(a(y_0))))))))))
A(a(a(a(b(a(a(y_1))))))) → A(a(a(a(y_1))))
A(a(a(a(b(a(a(b(a(y_0))))))))) → A(a(a(a(b(a(y_0))))))
A(a(a(a(b(a(a(b(a(a(a(y_1))))))))))) → A(a(a(a(b(a(a(a(y_1))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A(a(a(a(b(a(a(b(a(b(a(a(a(y_0))))))))))))) → A(a(a(a(b(a(b(a(a(a(y_0))))))))))
A(a(a(a(b(x1))))) → A(x1)
A(a(a(a(b(a(b(a(a(a(y_1)))))))))) → A(a(a(a(b(a(a(a(y_1))))))))
A(a(a(a(b(a(y_1)))))) → A(a(a(a(y_1))))
A(a(a(a(b(a(a(y_1))))))) → A(a(a(a(y_1))))
A(a(a(a(b(a(a(b(a(y_0))))))))) → A(a(a(a(b(a(y_0))))))
A(a(a(a(b(a(a(a(b(x0))))))))) → A(a(a(a(b(b(a(a(a(a(a(x0)))))))))))
A(a(a(a(b(x1))))) → A(a(a(a(x1))))
A(a(a(a(b(a(a(b(a(a(a(y_1))))))))))) → A(a(a(a(b(a(a(a(y_1))))))))
The TRS R consists of the following rules:
a(a(a(a(b(x1))))) → b(b(a(a(a(a(a(x1)))))))
The set Q consists of the following terms:
a(a(a(a(b(x0)))))
We have to consider all minimal (P,Q,R)-chains.
By forward instantiating [14] the rule A(a(a(a(b(x1))))) → A(x1) we obtained the following new rules:
A(a(a(a(b(a(a(a(b(y_0))))))))) → A(a(a(a(b(y_0)))))
A(a(a(a(b(a(a(a(b(a(a(b(a(a(a(y_0))))))))))))))) → A(a(a(a(b(a(a(b(a(a(a(y_0)))))))))))
A(a(a(a(b(a(a(a(b(a(a(a(b(y_0))))))))))))) → A(a(a(a(b(a(a(a(b(y_0)))))))))
A(a(a(a(b(a(a(a(b(a(b(a(a(a(y_0)))))))))))))) → A(a(a(a(b(a(b(a(a(a(y_0))))))))))
A(a(a(a(b(a(a(a(b(a(y_0)))))))))) → A(a(a(a(b(a(y_0))))))
A(a(a(a(b(a(a(a(b(a(a(b(a(y_0))))))))))))) → A(a(a(a(b(a(a(b(a(y_0)))))))))
A(a(a(a(b(a(a(a(b(a(a(y_0))))))))))) → A(a(a(a(b(a(a(y_0)))))))
A(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(y_0))))))))))))))))) → A(a(a(a(b(a(a(b(a(b(a(a(a(y_0)))))))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A(a(a(a(b(a(a(a(b(a(a(a(b(y_0))))))))))))) → A(a(a(a(b(a(a(a(b(y_0)))))))))
A(a(a(a(b(a(a(y_1))))))) → A(a(a(a(y_1))))
A(a(a(a(b(a(a(a(b(x0))))))))) → A(a(a(a(b(b(a(a(a(a(a(x0)))))))))))
A(a(a(a(b(a(a(b(a(a(a(y_1))))))))))) → A(a(a(a(b(a(a(a(y_1))))))))
A(a(a(a(b(a(a(a(b(y_0))))))))) → A(a(a(a(b(y_0)))))
A(a(a(a(b(a(a(a(b(a(a(b(a(a(a(y_0))))))))))))))) → A(a(a(a(b(a(a(b(a(a(a(y_0)))))))))))
A(a(a(a(b(a(a(b(a(b(a(a(a(y_0))))))))))))) → A(a(a(a(b(a(b(a(a(a(y_0))))))))))
A(a(a(a(b(a(b(a(a(a(y_1)))))))))) → A(a(a(a(b(a(a(a(y_1))))))))
A(a(a(a(b(a(y_1)))))) → A(a(a(a(y_1))))
A(a(a(a(b(a(a(a(b(a(b(a(a(a(y_0)))))))))))))) → A(a(a(a(b(a(b(a(a(a(y_0))))))))))
A(a(a(a(b(a(a(a(b(a(y_0)))))))))) → A(a(a(a(b(a(y_0))))))
A(a(a(a(b(a(a(a(b(a(a(b(a(y_0))))))))))))) → A(a(a(a(b(a(a(b(a(y_0)))))))))
A(a(a(a(b(a(a(b(a(y_0))))))))) → A(a(a(a(b(a(y_0))))))
A(a(a(a(b(a(a(a(b(a(a(y_0))))))))))) → A(a(a(a(b(a(a(y_0)))))))
A(a(a(a(b(x1))))) → A(a(a(a(x1))))
A(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(y_0))))))))))))))))) → A(a(a(a(b(a(a(b(a(b(a(a(a(y_0)))))))))))))
The TRS R consists of the following rules:
a(a(a(a(b(x1))))) → b(b(a(a(a(a(a(x1)))))))
The set Q consists of the following terms:
a(a(a(a(b(x0)))))
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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q restricted rewrite system:
The TRS R consists of the following rules:
a(a(a(a(b(x1))))) → b(b(a(a(a(a(a(x1)))))))
A(a(a(a(b(a(a(a(b(a(a(a(b(y_0))))))))))))) → A(a(a(a(b(a(a(a(b(y_0)))))))))
A(a(a(a(b(a(a(y_1))))))) → A(a(a(a(y_1))))
A(a(a(a(b(a(a(a(b(x0))))))))) → A(a(a(a(b(b(a(a(a(a(a(x0)))))))))))
A(a(a(a(b(a(a(b(a(a(a(y_1))))))))))) → A(a(a(a(b(a(a(a(y_1))))))))
A(a(a(a(b(a(a(a(b(y_0))))))))) → A(a(a(a(b(y_0)))))
A(a(a(a(b(a(a(a(b(a(a(b(a(a(a(y_0))))))))))))))) → A(a(a(a(b(a(a(b(a(a(a(y_0)))))))))))
A(a(a(a(b(a(a(b(a(b(a(a(a(y_0))))))))))))) → A(a(a(a(b(a(b(a(a(a(y_0))))))))))
A(a(a(a(b(a(b(a(a(a(y_1)))))))))) → A(a(a(a(b(a(a(a(y_1))))))))
A(a(a(a(b(a(y_1)))))) → A(a(a(a(y_1))))
A(a(a(a(b(a(a(a(b(a(b(a(a(a(y_0)))))))))))))) → A(a(a(a(b(a(b(a(a(a(y_0))))))))))
A(a(a(a(b(a(a(a(b(a(y_0)))))))))) → A(a(a(a(b(a(y_0))))))
A(a(a(a(b(a(a(a(b(a(a(b(a(y_0))))))))))))) → A(a(a(a(b(a(a(b(a(y_0)))))))))
A(a(a(a(b(a(a(b(a(y_0))))))))) → A(a(a(a(b(a(y_0))))))
A(a(a(a(b(a(a(a(b(a(a(y_0))))))))))) → A(a(a(a(b(a(a(y_0)))))))
A(a(a(a(b(x1))))) → A(a(a(a(x1))))
A(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(y_0))))))))))))))))) → A(a(a(a(b(a(a(b(a(b(a(a(a(y_0)))))))))))))
The set Q consists of the following terms:
a(a(a(a(b(x0)))))
We have reversed the following QTRS:
The set of rules R is
a(a(a(a(b(x1))))) → b(b(a(a(a(a(a(x1)))))))
A(a(a(a(b(a(a(a(b(a(a(a(b(y_0))))))))))))) → A(a(a(a(b(a(a(a(b(y_0)))))))))
A(a(a(a(b(a(a(y_1))))))) → A(a(a(a(y_1))))
A(a(a(a(b(a(a(a(b(x0))))))))) → A(a(a(a(b(b(a(a(a(a(a(x0)))))))))))
A(a(a(a(b(a(a(b(a(a(a(y_1))))))))))) → A(a(a(a(b(a(a(a(y_1))))))))
A(a(a(a(b(a(a(a(b(y_0))))))))) → A(a(a(a(b(y_0)))))
A(a(a(a(b(a(a(a(b(a(a(b(a(a(a(y_0))))))))))))))) → A(a(a(a(b(a(a(b(a(a(a(y_0)))))))))))
A(a(a(a(b(a(a(b(a(b(a(a(a(y_0))))))))))))) → A(a(a(a(b(a(b(a(a(a(y_0))))))))))
A(a(a(a(b(a(b(a(a(a(y_1)))))))))) → A(a(a(a(b(a(a(a(y_1))))))))
A(a(a(a(b(a(y_1)))))) → A(a(a(a(y_1))))
A(a(a(a(b(a(a(a(b(a(b(a(a(a(y_0)))))))))))))) → A(a(a(a(b(a(b(a(a(a(y_0))))))))))
A(a(a(a(b(a(a(a(b(a(y_0)))))))))) → A(a(a(a(b(a(y_0))))))
A(a(a(a(b(a(a(a(b(a(a(b(a(y_0))))))))))))) → A(a(a(a(b(a(a(b(a(y_0)))))))))
A(a(a(a(b(a(a(b(a(y_0))))))))) → A(a(a(a(b(a(y_0))))))
A(a(a(a(b(a(a(a(b(a(a(y_0))))))))))) → A(a(a(a(b(a(a(y_0)))))))
A(a(a(a(b(x1))))) → A(a(a(a(x1))))
A(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(y_0))))))))))))))))) → A(a(a(a(b(a(a(b(a(b(a(a(a(y_0)))))))))))))
The set Q is {a(a(a(a(b(x0)))))}.
We have obtained the following QTRS:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The set Q is empty.
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q restricted rewrite system:
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have reversed the following QTRS:
The set of rules R is
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The set Q is empty.
We have obtained the following QTRS:
a(a(a(a(b(x))))) → b(b(a(a(a(a(a(x)))))))
A(a(a(a(b(a(a(a(b(a(a(a(b(x))))))))))))) → A(a(a(a(b(a(a(a(b(x)))))))))
A(a(a(a(b(a(a(x))))))) → A(a(a(a(x))))
A(a(a(a(b(a(a(a(b(x))))))))) → A(a(a(a(b(b(a(a(a(a(a(x)))))))))))
A(a(a(a(b(a(a(b(a(a(a(x))))))))))) → A(a(a(a(b(a(a(a(x))))))))
A(a(a(a(b(a(a(a(b(x))))))))) → A(a(a(a(b(x)))))
A(a(a(a(b(a(a(a(b(a(a(b(a(a(a(x))))))))))))))) → A(a(a(a(b(a(a(b(a(a(a(x)))))))))))
A(a(a(a(b(a(a(b(a(b(a(a(a(x))))))))))))) → A(a(a(a(b(a(b(a(a(a(x))))))))))
A(a(a(a(b(a(b(a(a(a(x)))))))))) → A(a(a(a(b(a(a(a(x))))))))
A(a(a(a(b(a(x)))))) → A(a(a(a(x))))
A(a(a(a(b(a(a(a(b(a(b(a(a(a(x)))))))))))))) → A(a(a(a(b(a(b(a(a(a(x))))))))))
A(a(a(a(b(a(a(a(b(a(x)))))))))) → A(a(a(a(b(a(x))))))
A(a(a(a(b(a(a(a(b(a(a(b(a(x))))))))))))) → A(a(a(a(b(a(a(b(a(x)))))))))
A(a(a(a(b(a(a(b(a(x))))))))) → A(a(a(a(b(a(x))))))
A(a(a(a(b(a(a(a(b(a(a(x))))))))))) → A(a(a(a(b(a(a(x)))))))
A(a(a(a(b(x))))) → A(a(a(a(x))))
A(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(x))))))))))))))))) → A(a(a(a(b(a(a(b(a(b(a(a(a(x)))))))))))))
The set Q is empty.
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ DependencyPairsProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q restricted rewrite system:
The TRS R consists of the following rules:
a(a(a(a(b(x))))) → b(b(a(a(a(a(a(x)))))))
A(a(a(a(b(a(a(a(b(a(a(a(b(x))))))))))))) → A(a(a(a(b(a(a(a(b(x)))))))))
A(a(a(a(b(a(a(x))))))) → A(a(a(a(x))))
A(a(a(a(b(a(a(a(b(x))))))))) → A(a(a(a(b(b(a(a(a(a(a(x)))))))))))
A(a(a(a(b(a(a(b(a(a(a(x))))))))))) → A(a(a(a(b(a(a(a(x))))))))
A(a(a(a(b(a(a(a(b(x))))))))) → A(a(a(a(b(x)))))
A(a(a(a(b(a(a(a(b(a(a(b(a(a(a(x))))))))))))))) → A(a(a(a(b(a(a(b(a(a(a(x)))))))))))
A(a(a(a(b(a(a(b(a(b(a(a(a(x))))))))))))) → A(a(a(a(b(a(b(a(a(a(x))))))))))
A(a(a(a(b(a(b(a(a(a(x)))))))))) → A(a(a(a(b(a(a(a(x))))))))
A(a(a(a(b(a(x)))))) → A(a(a(a(x))))
A(a(a(a(b(a(a(a(b(a(b(a(a(a(x)))))))))))))) → A(a(a(a(b(a(b(a(a(a(x))))))))))
A(a(a(a(b(a(a(a(b(a(x)))))))))) → A(a(a(a(b(a(x))))))
A(a(a(a(b(a(a(a(b(a(a(b(a(x))))))))))))) → A(a(a(a(b(a(a(b(a(x)))))))))
A(a(a(a(b(a(a(b(a(x))))))))) → A(a(a(a(b(a(x))))))
A(a(a(a(b(a(a(a(b(a(a(x))))))))))) → A(a(a(a(b(a(a(x)))))))
A(a(a(a(b(x))))) → A(a(a(a(x))))
A(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(x))))))))))))))))) → A(a(a(a(b(a(a(b(a(b(a(a(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:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → B(a(b(a(a(a(A(x)))))))
B(a(a(a(a(x))))) → A1(a(a(a(a(b(b(x)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(a(a(b(a(a(b(a(a(a(A(x)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → B(a(b(a(a(a(A(x)))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(a(b(a(a(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
B(a(a(a(b(a(a(a(A(x))))))))) → B(b(a(a(a(A(x))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(b(a(a(b(a(a(a(A(x))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(A(x))))))))))) → A1(a(a(b(a(a(a(A(x))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(b(a(a(b(a(a(a(A(x)))))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(A(x)))))))))) → A1(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
A1(a(a(b(a(b(a(a(a(A(x)))))))))) → A1(a(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → B(a(b(a(a(a(A(x)))))))
B(a(a(a(a(x))))) → A1(a(a(a(a(b(b(x)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(a(a(b(a(a(b(a(a(a(A(x)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → B(a(b(a(a(a(A(x)))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(a(b(a(a(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
B(a(a(a(b(a(a(a(A(x))))))))) → B(b(a(a(a(A(x))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(b(a(a(b(a(a(a(A(x))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(A(x))))))))))) → A1(a(a(b(a(a(a(A(x))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(b(a(a(b(a(a(a(A(x)))))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(A(x)))))))))) → A1(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
A1(a(a(b(a(b(a(a(a(A(x)))))))))) → A1(a(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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(x))))))))) → B(b(a(a(a(A(x)))))) at position [0] we obtained the following new rules:
B(a(a(a(b(a(a(a(A(x0))))))))) → B(a(a(a(A(x0)))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
B(a(a(a(b(a(a(a(A(x0))))))))) → B(a(a(a(A(x0)))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → B(a(b(a(a(a(A(x)))))))
B(a(a(a(a(x))))) → A1(a(a(a(a(b(b(x)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(a(a(b(a(a(b(a(a(a(A(x)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → B(a(b(a(a(a(A(x)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(a(b(a(a(b(a(a(a(A(x))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(b(a(a(b(a(a(a(A(x))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(A(x))))))))))) → A1(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(b(a(a(b(a(a(a(A(x)))))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(A(x)))))))))) → A1(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
A1(a(a(b(a(b(a(a(a(A(x)))))))))) → A1(a(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → B(a(b(a(a(a(A(x)))))))
B(a(a(a(a(x))))) → A1(a(a(a(a(b(b(x)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(a(a(b(a(a(b(a(a(a(A(x)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → B(a(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(a(b(a(a(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(b(a(a(b(a(a(a(A(x))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(A(x))))))))))) → A1(a(a(b(a(a(a(A(x))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(b(a(a(b(a(a(a(A(x)))))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(A(x)))))))))) → A1(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
A1(a(a(b(a(b(a(a(a(A(x)))))))))) → A1(a(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(a(b(a(a(a(A(x))))))))))) → A1(a(a(b(a(a(a(A(x)))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(a(b(a(a(a(A(x0))))))))))) → A1(a(a(a(A(x0)))))
A1(a(a(b(a(a(b(a(a(a(A(x0))))))))))) → A1(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(A(x0))))))))))) → A1(a(a(a(a(A(x0))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(a(b(a(a(a(A(x0))))))))))) → A1(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → B(a(b(a(a(a(A(x)))))))
B(a(a(a(a(x))))) → A1(a(a(a(a(b(b(x)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(A(x0))))))))))) → A1(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(a(a(b(a(a(b(a(a(a(A(x)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → B(a(b(a(a(a(A(x)))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(a(b(a(a(a(A(x0))))))))))) → A1(a(a(a(A(x0)))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(a(b(a(a(b(a(a(a(A(x))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(b(a(a(b(a(a(a(A(x))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(b(a(a(b(a(a(a(A(x)))))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(A(x)))))))))) → A1(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
A1(a(a(b(a(b(a(a(a(A(x)))))))))) → A1(a(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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 3 less nodes.
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → B(a(b(a(a(a(A(x)))))))
B(a(a(a(a(x))))) → A1(a(a(a(a(b(b(x)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(a(a(b(a(a(b(a(a(a(A(x)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → B(a(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(a(b(a(a(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(b(a(a(b(a(a(a(A(x))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(b(a(a(b(a(a(a(A(x)))))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(A(x)))))))))) → A1(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
A1(a(a(b(a(b(a(a(a(A(x)))))))))) → A1(a(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(a(A(x)))))))))) → A1(a(a(b(a(a(a(A(x)))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(a(A(x0)))))))))) → A1(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(A(x0)))))))))) → A1(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(A(x0)))))))))) → A1(a(a(a(A(x0)))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))
A1(a(a(b(a(b(a(a(a(A(x0)))))))))) → A1(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → B(a(b(a(a(a(A(x)))))))
B(a(a(a(a(x))))) → A1(a(a(a(a(b(b(x)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(a(a(b(a(a(b(a(a(a(A(x)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → B(a(b(a(a(a(A(x)))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(a(b(a(a(b(a(a(a(A(x))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(b(a(a(b(a(a(a(A(x))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(b(a(a(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(a(A(x0)))))))))) → A1(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(A(x0)))))))))) → A1(a(a(a(A(x0)))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
A1(a(a(b(a(b(a(a(a(A(x)))))))))) → A1(a(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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 3 less nodes.
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → B(a(b(a(a(a(A(x)))))))
B(a(a(a(a(x))))) → A1(a(a(a(a(b(b(x)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(a(a(b(a(a(b(a(a(a(A(x)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → B(a(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(a(b(a(a(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(b(a(a(b(a(a(a(A(x))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(b(a(a(b(a(a(a(A(x)))))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
A1(a(a(b(a(b(a(a(a(A(x)))))))))) → A1(a(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(a(A(x)))))))))) → A1(a(b(a(a(a(A(x))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(a(A(x0)))))))))) → A1(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(A(x0)))))))))) → A1(a(a(a(A(x0)))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → B(a(b(a(a(a(A(x)))))))
B(a(a(a(a(x))))) → A1(a(a(a(a(b(b(x)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(a(a(b(a(a(b(a(a(a(A(x)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → B(a(b(a(a(a(A(x)))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(a(b(a(a(b(a(a(a(A(x))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(b(a(a(b(a(a(a(A(x))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(b(a(a(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(a(A(x0)))))))))) → A1(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(A(x0)))))))))) → A1(a(a(a(A(x0)))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → B(a(b(a(a(a(A(x)))))))
B(a(a(a(a(x))))) → A1(a(a(a(a(b(b(x)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(a(a(b(a(a(b(a(a(a(A(x)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → B(a(b(a(a(a(A(x)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(a(b(a(a(b(a(a(a(A(x))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(b(a(a(b(a(a(a(A(x))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(b(a(a(b(a(a(a(A(x)))))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(a(b(a(a(b(a(a(a(A(x)))))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → B(a(b(a(a(a(A(x)))))))
B(a(a(a(a(x))))) → A1(a(a(a(a(b(b(x)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(a(a(b(a(a(b(a(a(a(A(x)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → B(a(b(a(a(a(A(x)))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(b(a(a(b(a(a(a(A(x))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(b(a(a(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(a(a(b(a(a(b(a(a(a(A(x))))))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → B(a(b(a(a(a(A(x)))))))
B(a(a(a(a(x))))) → A1(a(a(a(a(b(b(x)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → B(a(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(b(a(a(b(a(a(a(A(x))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(b(a(a(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → A1(b(a(a(b(a(a(a(A(x))))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → B(a(b(a(a(a(A(x)))))))
B(a(a(a(a(x))))) → A1(a(a(a(a(b(b(x)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → B(a(b(a(a(a(A(x)))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(b(a(a(b(a(a(a(A(x))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(b(a(a(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → B(a(a(b(a(a(a(A(x)))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(A(x0)))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → B(a(b(a(a(a(A(x)))))))
B(a(a(a(a(x))))) → A1(a(a(a(a(b(b(x)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → B(a(b(a(a(a(A(x)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(b(a(a(b(a(a(a(A(x))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(A(x0)))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(b(a(a(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → B(a(b(a(a(a(A(x)))))))
B(a(a(a(a(x))))) → A1(a(a(a(a(b(b(x)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → B(a(b(a(a(a(A(x)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(b(a(a(b(a(a(a(A(x))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(b(a(a(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x)))))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → B(a(b(a(a(a(A(x)))))))
B(a(a(a(a(x))))) → A1(a(a(a(a(b(b(x)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → B(a(b(a(a(a(A(x)))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(b(a(a(b(a(a(a(A(x))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(b(a(a(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(a(b(a(b(a(a(a(A(x))))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → B(a(b(a(a(a(A(x)))))))
B(a(a(a(a(x))))) → A1(a(a(a(a(b(b(x)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → B(a(b(a(a(a(A(x)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(b(a(a(b(a(a(a(A(x))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(b(a(a(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(b(a(a(a(A(x)))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → B(a(b(a(a(a(A(x)))))))
B(a(a(a(a(x))))) → A1(a(a(a(a(b(b(x)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → B(a(b(a(a(a(A(x)))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(b(a(a(b(a(a(a(A(x))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(b(a(a(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → B(a(b(a(a(a(A(x))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(A(x0)))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))
B(a(a(a(a(x))))) → A1(a(a(a(a(b(b(x)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(A(x0)))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → B(a(b(a(a(a(A(x)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(b(a(a(b(a(a(a(A(x))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(b(a(a(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))
B(a(a(a(a(x))))) → A1(a(a(a(a(b(b(x)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → B(a(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(b(a(a(b(a(a(a(A(x))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(b(a(a(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x)))))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))
B(a(a(a(a(x))))) → A1(a(a(a(a(b(b(x)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(b(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → B(a(b(a(a(a(A(x)))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(b(a(a(b(a(a(a(A(x))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(b(a(a(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(a(b(a(b(a(a(a(A(x))))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))
B(a(a(a(a(x))))) → A1(a(a(a(a(b(b(x)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → B(a(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(b(a(a(b(a(a(a(A(x))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(b(a(a(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(b(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → A1(b(a(b(a(a(a(A(x)))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))
B(a(a(a(a(x))))) → A1(a(a(a(a(b(b(x)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → B(a(b(a(a(a(A(x)))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(b(a(a(b(a(a(a(A(x))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(b(a(a(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → B(a(b(a(a(a(A(x))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(A(x0)))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))
B(a(a(a(a(x))))) → A1(a(a(a(a(b(b(x)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(A(x0)))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(b(a(a(b(a(a(a(A(x))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(b(a(a(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))
B(a(a(a(a(x))))) → A1(a(a(a(a(b(b(x)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(b(a(a(b(a(a(a(A(x))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(b(a(a(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → A1(b(a(a(b(a(a(a(A(x))))))))) at position [0] we obtained the following new rules:
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))
B(a(a(a(a(x))))) → A1(a(a(a(a(b(b(x)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → B(b(x))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(b(a(a(b(a(a(a(A(x))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(b(a(a(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → B(a(a(b(a(a(a(A(x)))))))) at position [0] we obtained the following new rules:
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(A(x0)))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(b(a(a(b(a(a(a(A(x))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(A(x0)))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → A1(a(a(a(a(b(b(x)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(b(a(a(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))
B(a(a(a(a(x))))) → A1(a(a(a(a(b(b(x)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → B(b(x))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(b(a(a(b(a(a(a(A(x))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(b(a(a(b(a(a(a(A(x)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(b(a(a(b(a(a(a(A(x))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → A1(a(a(a(a(b(b(x)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(b(a(a(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(b(a(a(b(a(a(a(A(x))))))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(b(a(a(b(a(a(a(A(x))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(a(b(b(x)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(b(a(a(b(a(a(a(A(x)))))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → A1(a(a(a(a(b(b(x)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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(x))))) → A1(a(a(a(a(b(b(x))))))) at position [0] we obtained the following new rules:
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(b(a(a(b(a(a(a(A(x))))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → B(a(a(b(a(a(a(A(x)))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(A(x0)))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(A(x0)))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(a(A(x0))))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(y0))))))))))))))) → A1(a(a(a(a(a(a(b(b(a(A(y0)))))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(y0))))))))))))))) → A1(a(a(a(a(a(a(b(b(a(A(y0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(A(x0))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(a(A(x0)))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(a(A(x0)))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(b(a(a(a(a(A(x0)))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(y0))))))))))))))) → A1(a(a(a(a(a(a(b(b(A(y0))))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(y0))))))))))))))) → A1(a(a(a(a(a(a(b(b(A(y0))))))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(a(A(x0)))))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(y0))))))))))))))) → A1(a(a(a(a(a(a(a(b(b(a(A(y0))))))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(y0))))))))))))))) → A1(a(a(a(a(a(a(a(b(b(a(A(y0))))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(A(x0)))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(a(A(x0)))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(a(A(x0)))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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 3 less nodes.
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(b(a(a(a(a(A(x0))))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(y0))))))))))))))) → A1(a(a(a(a(a(a(a(b(b(A(y0)))))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(y0))))))))))))))) → A1(a(a(a(a(a(a(a(b(b(A(y0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(A(x0))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(y0))))))))))))))) → A1(a(a(a(a(a(b(b(A(y0)))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(y0))))))))))))))) → A1(a(a(a(a(a(b(b(A(y0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(A(x0)))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(a(A(x0)))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(a(a(a(A(x0)))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → A1(b(a(a(a(a(a(A(x0)))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(y0))))))))))))))) → A1(a(a(a(a(a(b(b(a(A(y0))))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(y0))))))))))))))) → A1(a(a(a(a(a(b(b(a(A(y0))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → A1(a(a(a(b(b(x))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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(x))))) → A1(a(a(a(b(b(x)))))) at position [0] we obtained the following new rules:
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(x))))) → A1(a(a(b(b(x)))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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(x))))) → A1(a(a(b(b(x))))) at position [0] we obtained the following new rules:
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(A(x0)))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(A(x0)))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(A(x0))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(A(x0)))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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 3 less nodes.
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → A1(a(b(b(x))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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(x))))) → A1(a(b(b(x)))) at position [0] we obtained the following new rules:
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(x))))) → A1(b(b(x)))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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(x))))) → A1(b(b(x))) at position [0] we obtained the following new rules:
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(A(x0))))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(b(a(a(a(A(y0))))))))))))) → A1(a(a(a(a(a(a(a(b(b(A(y0)))))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(y0))))))))))))) → A1(a(a(a(a(a(a(a(b(b(A(y0)))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
B(a(a(a(a(x))))) → B(b(x))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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(x))))) → B(b(x)) at position [0] we obtained the following new rules:
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → B(a(a(a(A(x0)))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → B(a(a(a(A(x0)))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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(x))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x))))))))))) at position [0] we obtained the following new rules:
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(A(x0))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(A(x0)))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(A(x0))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(A(x0)))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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(x))))))))) → A1(a(a(a(b(b(a(a(a(A(x)))))))))) at position [0] we obtained the following new rules:
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(A(x0)))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(b(a(a(a(A(y0))))))))))))) → A1(a(a(a(a(a(a(b(b(A(y0))))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(y0))))))))))))) → A1(a(a(a(a(a(a(b(b(A(y0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(a(b(b(a(a(a(A(x)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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(x))))))))) → A1(a(a(b(b(a(a(a(A(x))))))))) at position [0] we obtained the following new rules:
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0)))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(A(x0)))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(A(x0)))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(a(b(b(a(a(a(A(x))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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(x))))))))) → A1(a(b(b(a(a(a(A(x)))))))) at position [0] we obtained the following new rules:
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(b(a(a(a(A(y0))))))))))))) → A1(a(a(a(a(a(b(b(A(y0)))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(y0))))))))))))) → A1(a(a(a(a(a(b(b(A(y0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x))))))))) → A1(b(b(a(a(a(A(x)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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(x))))))))) → A1(b(b(a(a(a(A(x))))))) at position [0] we obtained the following new rules:
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(A(x0)))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(a(A(x0)))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(a(A(x0)))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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 3 less nodes.
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(x))))) → B(x)
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(b(a(a(a(a(A(x0))))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(y0)))))))))))))) → A1(a(a(a(a(a(a(a(b(b(A(y0)))))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(y0)))))))))))))) → A1(a(a(a(a(a(a(a(b(b(A(y0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → B(x)
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(A(x0))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(a(A(x0)))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(a(A(x0)))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → B(x)
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(b(a(a(a(a(A(x0)))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(y0)))))))))))))) → A1(a(a(a(a(a(a(b(b(A(y0))))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(y0)))))))))))))) → A1(a(a(a(a(a(a(b(b(A(y0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(A(x0)))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(a(A(x0)))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(a(a(a(A(x0)))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → B(x)
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → A1(b(a(a(a(a(A(x0))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(y0)))))))))))))) → A1(a(a(a(a(a(b(b(A(y0)))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(y0)))))))))))))) → A1(a(a(a(a(a(b(b(A(y0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → B(x)
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(A(x0))))))) at position [0] we obtained the following new rules:
A1(b(a(a(b(a(a(a(b(a(a(a(A(y0))))))))))))) → A1(a(a(a(a(a(b(b(A(y0)))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(y0))))))))))))) → A1(a(a(a(a(a(b(b(A(y0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → B(x)
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(A(x0)))))) at position [0] we obtained the following new rules:
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(A(x0)))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → B(x)
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(A(x0)))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(A(x0)))))))) at position [0] we obtained the following new rules:
A1(b(a(a(b(a(a(a(b(a(a(a(A(y0))))))))))))) → A1(a(a(a(a(a(b(b(a(A(y0))))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → B(x)
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(y0))))))))))))) → A1(a(a(a(a(a(b(b(a(A(y0))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(A(x0)))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → B(x)
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0)))))))))) at position [0] we obtained the following new rules:
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(a(a(a(A(x0)))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(a(a(a(A(x0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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 3 less nodes.
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(A(x0))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(A(x0)))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(A(x0)))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → B(x)
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(a(A(x0)))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(y0))))))))))))))))) → A1(a(a(a(a(a(b(b(a(A(y0))))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → B(x)
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(y0))))))))))))))))) → A1(a(a(a(a(a(b(b(a(A(y0))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(a(A(x0))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(y0))))))))))))))))) → A1(a(a(a(a(a(b(b(A(y0)))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → B(x)
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(y0))))))))))))))))) → A1(a(a(a(a(a(b(b(A(y0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(a(a(A(x0)))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(A(x0)))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(A(x0)))))
B(a(a(a(a(x))))) → B(x)
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0))))))))) at position [0] we obtained the following new rules:
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(A(x0))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(x)
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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 3 less nodes.
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0)))))))) at position [0] we obtained the following new rules:
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(A(x0)))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(A(x0)))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(x)
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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 3 less nodes.
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0))))))) at position [0] we obtained the following new rules:
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(A(x0)))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(A(x0)))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0)))))) at position [0] we obtained the following new rules:
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(A(x0)))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(A(x0))))))))) → A1(a(a(a(A(x0)))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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(a(a(a(b(a(a(a(A(x0))))))))))))) → B(b(a(a(a(A(x0)))))) at position [0] we obtained the following new rules:
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(A(x0)))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(A(x0)))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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(x0))))))))) → A1(a(a(a(a(b(a(a(a(A(x0)))))))))) at position [0] we obtained the following new rules:
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(a(a(a(A(x0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(a(a(A(x0))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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 3 less nodes.
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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(x0))))))))) → A1(a(a(a(b(a(a(a(A(x0))))))))) at position [0] we obtained the following new rules:
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(a(a(A(x0))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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 3 less nodes.
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(b(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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(x0))))))))) → A1(a(a(b(a(a(a(A(x0)))))))) at position [0] we obtained the following new rules:
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(A(x0)))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(a(A(x0)))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(A(x0)))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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 3 less nodes.
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(b(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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(x0))))))))) → A1(a(b(a(a(a(A(x0))))))) at position [0] we obtained the following new rules:
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(A(x0)))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(A(x0))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(A(x0)))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(b(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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(x0))))))))) → A1(b(a(a(a(A(x0)))))) at position [0] we obtained the following new rules:
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(A(x0)))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
B(a(a(a(b(a(a(a(A(x0))))))))) → A1(a(a(a(A(x0)))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(a(b(a(a(a(A(x0)))))))))))))) → B(a(a(a(a(A(x0))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(A(x0))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(A(x0)))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
We found the following model for the rules of the TRS R.
Interpretation over the domain with elements from 0 to 1.A1: 0
B: 0
a: 0
A: 1
b: 0
By semantic labelling [33] we obtain the following labelled TRS:Q DP problem:
The TRS P consists of the following rules:
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(a.0(b.0(a.0(a.0(a.0(a.1(A.1(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))) → B.0(a.0(a.0(a.0(a.1(A.0(x0))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))
A1.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))))
A1.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → B.0(a.0(a.0(a.0(a.1(A.0(x0))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))
A1.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))
A1.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0)))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))
B.0(a.0(a.0(a.0(a.0(x))))) → B.0(x)
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → B.0(a.0(a.0(a.0(a.1(A.0(x0))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(a.0(a.0(a.0(a.1(A.0(x0))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))) → B.0(a.0(a.0(a.0(a.1(A.1(x0))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0)))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → B.0(a.0(a.0(a.0(a.1(A.1(x0))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.1(A.1(x0))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))
B.0(a.0(a.0(a.0(a.1(x))))) → B.1(x)
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(b.0(a.0(b.0(a.0(a.0(a.0(a.1(A.1(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(b.0(a.0(b.0(a.0(a.0(a.0(a.1(A.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))
A1.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))
A1.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))) → B.0(a.0(a.0(a.0(a.1(A.0(x0))))))
A1.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))) → B.0(a.0(a.0(a.0(a.1(A.1(x0))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(a.0(b.0(a.0(a.0(a.0(a.1(A.0(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))
A1.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → B.0(a.0(a.0(a.0(a.1(A.1(x0))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(a.0(a.0(a.0(a.1(A.1(x0))))))
The TRS R consists of the following rules:
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))
a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))) → a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))) → a.0(b.0(a.0(a.0(a.1(A.1(x))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))) → b.0(a.0(a.0(a.1(A.1(x)))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))) → b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))
b.0(a.0(a.0(a.1(A.0(x))))) → a.0(a.0(a.1(A.0(x))))
a.0(b.0(a.0(a.0(a.1(A.1(x)))))) → a.0(a.0(a.1(A.1(x))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))
b.0(a.0(a.0(a.0(a.1(x))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.1(x)))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))) → a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))
a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))) → a.0(b.0(a.0(a.0(a.1(A.0(x))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))
a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))) → a.0(a.0(a.1(A.0(x))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))) → b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))) → a.0(b.0(a.0(a.0(a.1(A.0(x))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))) → a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))
b.0(a.0(a.0(a.1(A.1(x))))) → a.0(a.0(a.1(A.1(x))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))
a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))) → a.0(a.0(a.1(A.1(x))))
a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))) → a.0(b.0(a.0(a.0(a.1(A.1(x))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))
a.0(b.0(a.0(a.0(a.1(A.0(x)))))) → a.0(a.0(a.1(A.0(x))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))) → b.0(a.0(a.0(a.1(A.0(x)))))
b.0(a.0(a.0(a.0(a.0(x))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.0(x)))))))
a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))) → a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ SemLabProof
↳ QDP
↳ DependencyGraphProof
↳ SemLabProof2
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(a.0(b.0(a.0(a.0(a.0(a.1(A.1(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))) → B.0(a.0(a.0(a.0(a.1(A.0(x0))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))
A1.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))))
A1.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → B.0(a.0(a.0(a.0(a.1(A.0(x0))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))
A1.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))
A1.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0)))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))
B.0(a.0(a.0(a.0(a.0(x))))) → B.0(x)
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → B.0(a.0(a.0(a.0(a.1(A.0(x0))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(a.0(a.0(a.0(a.1(A.0(x0))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))) → B.0(a.0(a.0(a.0(a.1(A.1(x0))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0)))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → B.0(a.0(a.0(a.0(a.1(A.1(x0))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.1(A.1(x0))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))
B.0(a.0(a.0(a.0(a.1(x))))) → B.1(x)
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(b.0(a.0(b.0(a.0(a.0(a.0(a.1(A.1(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(b.0(a.0(b.0(a.0(a.0(a.0(a.1(A.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))
A1.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))
A1.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))) → B.0(a.0(a.0(a.0(a.1(A.0(x0))))))
A1.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))) → B.0(a.0(a.0(a.0(a.1(A.1(x0))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(a.0(b.0(a.0(a.0(a.0(a.1(A.0(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))
A1.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → B.0(a.0(a.0(a.0(a.1(A.1(x0))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(a.0(a.0(a.0(a.1(A.1(x0))))))
The TRS R consists of the following rules:
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))
a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))) → a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))) → a.0(b.0(a.0(a.0(a.1(A.1(x))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))) → b.0(a.0(a.0(a.1(A.1(x)))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))) → b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))
b.0(a.0(a.0(a.1(A.0(x))))) → a.0(a.0(a.1(A.0(x))))
a.0(b.0(a.0(a.0(a.1(A.1(x)))))) → a.0(a.0(a.1(A.1(x))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))
b.0(a.0(a.0(a.0(a.1(x))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.1(x)))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))) → a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))
a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))) → a.0(b.0(a.0(a.0(a.1(A.0(x))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))
a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))) → a.0(a.0(a.1(A.0(x))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))) → b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))) → a.0(b.0(a.0(a.0(a.1(A.0(x))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))) → a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))
b.0(a.0(a.0(a.1(A.1(x))))) → a.0(a.0(a.1(A.1(x))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))
a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))) → a.0(a.0(a.1(A.1(x))))
a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))) → a.0(b.0(a.0(a.0(a.1(A.1(x))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))
a.0(b.0(a.0(a.0(a.1(A.0(x)))))) → a.0(a.0(a.1(A.0(x))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))) → b.0(a.0(a.0(a.1(A.0(x)))))
b.0(a.0(a.0(a.0(a.0(x))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.0(x)))))))
a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))) → a.0(a.0(b.0(a.0(a.0(a.1(A.0(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 11 less nodes.
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ SemLabProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ RuleRemovalProof
↳ SemLabProof2
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(a.0(b.0(a.0(a.0(a.0(a.1(A.1(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))
A1.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))
A1.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))
A1.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0)))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))
B.0(a.0(a.0(a.0(a.0(x))))) → B.0(x)
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0)))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.1(A.1(x0))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(b.0(a.0(b.0(a.0(a.0(a.0(a.1(A.1(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(b.0(a.0(b.0(a.0(a.0(a.0(a.1(A.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))
A1.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(a.0(b.0(a.0(a.0(a.0(a.1(A.0(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))
The TRS R consists of the following rules:
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))
a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))) → a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))) → a.0(b.0(a.0(a.0(a.1(A.1(x))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))) → b.0(a.0(a.0(a.1(A.1(x)))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))) → b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))
b.0(a.0(a.0(a.1(A.0(x))))) → a.0(a.0(a.1(A.0(x))))
a.0(b.0(a.0(a.0(a.1(A.1(x)))))) → a.0(a.0(a.1(A.1(x))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))
b.0(a.0(a.0(a.0(a.1(x))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.1(x)))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))) → a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))
a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))) → a.0(b.0(a.0(a.0(a.1(A.0(x))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))
a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))) → a.0(a.0(a.1(A.0(x))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))) → b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))) → a.0(b.0(a.0(a.0(a.1(A.0(x))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))) → a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))
b.0(a.0(a.0(a.1(A.1(x))))) → a.0(a.0(a.1(A.1(x))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))
a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))) → a.0(a.0(a.1(A.1(x))))
a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))) → a.0(b.0(a.0(a.0(a.1(A.1(x))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))
a.0(b.0(a.0(a.0(a.1(A.0(x)))))) → a.0(a.0(a.1(A.0(x))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))) → b.0(a.0(a.0(a.1(A.0(x)))))
b.0(a.0(a.0(a.0(a.0(x))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.0(x)))))))
a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))) → a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the rule removal processor [15] with the following polynomial ordering [25], at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented.
Strictly oriented dependency pairs:
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0)))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0)))))))))
Strictly oriented rules of the TRS R:
b.0(a.0(a.0(a.0(a.1(x))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.1(x)))))))
Used ordering: POLO with Polynomial interpretation [25]:
POL(A.0(x1)) = x1
POL(A.1(x1)) = x1
POL(A1.0(x1)) = x1
POL(B.0(x1)) = x1
POL(a.0(x1)) = x1
POL(a.1(x1)) = 1 + x1
POL(b.0(x1)) = x1
POL(b.1(x1)) = x1
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ SemLabProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ RuleRemovalProof
↳ QDP
↳ DependencyGraphProof
↳ SemLabProof2
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(a.0(b.0(a.0(a.0(a.0(a.1(A.1(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))
A1.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))
A1.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))
A1.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))
B.0(a.0(a.0(a.0(a.0(x))))) → B.0(x)
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0)))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.1(A.1(x0))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(b.0(a.0(b.0(a.0(a.0(a.0(a.1(A.1(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(b.0(a.0(b.0(a.0(a.0(a.0(a.1(A.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))
A1.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(a.0(b.0(a.0(a.0(a.0(a.1(A.0(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))
The TRS R consists of the following rules:
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))
a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))) → a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))) → a.0(b.0(a.0(a.0(a.1(A.1(x))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))) → b.0(a.0(a.0(a.1(A.1(x)))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))) → b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))
b.0(a.0(a.0(a.1(A.0(x))))) → a.0(a.0(a.1(A.0(x))))
a.0(b.0(a.0(a.0(a.1(A.1(x)))))) → a.0(a.0(a.1(A.1(x))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))) → a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))
a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))) → a.0(b.0(a.0(a.0(a.1(A.0(x))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))
a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))) → a.0(a.0(a.1(A.0(x))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))) → b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))) → a.0(b.0(a.0(a.0(a.1(A.0(x))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))) → a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))
b.0(a.0(a.0(a.1(A.1(x))))) → a.0(a.0(a.1(A.1(x))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))
a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))) → a.0(a.0(a.1(A.1(x))))
a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))) → a.0(b.0(a.0(a.0(a.1(A.1(x))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))
a.0(b.0(a.0(a.0(a.1(A.0(x)))))) → a.0(a.0(a.1(A.0(x))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))) → b.0(a.0(a.0(a.1(A.0(x)))))
b.0(a.0(a.0(a.0(a.0(x))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.0(x)))))))
a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))) → a.0(a.0(b.0(a.0(a.0(a.1(A.0(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 6 less nodes.
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ SemLabProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ RuleRemovalProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ SemLabProof2
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))
A1.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))
A1.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))
A1.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))
B.0(a.0(a.0(a.0(a.0(x))))) → B.0(x)
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0)))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))
A1.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))
The TRS R consists of the following rules:
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))
a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))) → a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))) → a.0(b.0(a.0(a.0(a.1(A.1(x))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))) → b.0(a.0(a.0(a.1(A.1(x)))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))) → b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))
b.0(a.0(a.0(a.1(A.0(x))))) → a.0(a.0(a.1(A.0(x))))
a.0(b.0(a.0(a.0(a.1(A.1(x)))))) → a.0(a.0(a.1(A.1(x))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))) → a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))
a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))) → a.0(b.0(a.0(a.0(a.1(A.0(x))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))
a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))) → a.0(a.0(a.1(A.0(x))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))) → b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))) → a.0(b.0(a.0(a.0(a.1(A.0(x))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))) → a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))
b.0(a.0(a.0(a.1(A.1(x))))) → a.0(a.0(a.1(A.1(x))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))
a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))) → a.0(a.0(a.1(A.1(x))))
a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))) → a.0(b.0(a.0(a.0(a.1(A.1(x))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))
a.0(b.0(a.0(a.0(a.1(A.0(x)))))) → a.0(a.0(a.1(A.0(x))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))) → b.0(a.0(a.0(a.1(A.0(x)))))
b.0(a.0(a.0(a.0(a.0(x))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.0(x)))))))
a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))) → a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
As can be seen after transforming the QDP problem by semantic labelling [33] and then some rule deleting processors, only certain labelled rules and pairs can be used.
Hence, we only have to consider all unlabelled pairs and rules (without the decreasing rules for quasi-models).
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ Narrowing
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → A1(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) at position [0] we obtained the following new rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(a(b(a(a(a(a(A(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(a(b(a(a(a(a(a(A(x0))))))))))))
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(a(b(a(a(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(a(b(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(x))))) → B(x)
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
We found the following model for the rules of the TRS R.
Interpretation over the domain with elements from 0 to 1.A1: 0
B: 0
a: 0
A: 1
b: 0
By semantic labelling [33] we obtain the following labelled TRS:Q DP problem:
The TRS P consists of the following rules:
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))
A1.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))
A1.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))
A1.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0)))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))
B.0(a.0(a.0(a.0(a.0(x))))) → B.0(x)
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0)))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.1(A.1(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))
B.0(a.0(a.0(a.0(a.1(x))))) → B.1(x)
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.1(A.0(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))
A1.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0)))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0))))))))))))
The TRS R consists of the following rules:
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))
a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))) → a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))) → a.0(b.0(a.0(a.0(a.1(A.1(x))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))) → b.0(a.0(a.0(a.1(A.1(x)))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))) → b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))
b.0(a.0(a.0(a.1(A.0(x))))) → a.0(a.0(a.1(A.0(x))))
a.0(b.0(a.0(a.0(a.1(A.1(x)))))) → a.0(a.0(a.1(A.1(x))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))
b.0(a.0(a.0(a.0(a.1(x))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.1(x)))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))) → a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))
a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))) → a.0(b.0(a.0(a.0(a.1(A.0(x))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))
a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))) → a.0(a.0(a.1(A.0(x))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))) → b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))) → a.0(b.0(a.0(a.0(a.1(A.0(x))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))) → a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))
b.0(a.0(a.0(a.1(A.1(x))))) → a.0(a.0(a.1(A.1(x))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))
a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))) → a.0(a.0(a.1(A.1(x))))
a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))) → a.0(b.0(a.0(a.0(a.1(A.1(x))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))
a.0(b.0(a.0(a.0(a.1(A.0(x)))))) → a.0(a.0(a.1(A.0(x))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))) → b.0(a.0(a.0(a.1(A.0(x)))))
b.0(a.0(a.0(a.0(a.0(x))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.0(x)))))))
a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))) → a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ QDP
↳ DependencyGraphProof
↳ SemLabProof2
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))
A1.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))
A1.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))
A1.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0)))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))
B.0(a.0(a.0(a.0(a.0(x))))) → B.0(x)
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0)))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.1(A.1(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))
B.0(a.0(a.0(a.0(a.1(x))))) → B.1(x)
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.1(A.0(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))
A1.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0)))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0))))))))))))
The TRS R consists of the following rules:
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))
a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))) → a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))) → a.0(b.0(a.0(a.0(a.1(A.1(x))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))) → b.0(a.0(a.0(a.1(A.1(x)))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))) → b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))
b.0(a.0(a.0(a.1(A.0(x))))) → a.0(a.0(a.1(A.0(x))))
a.0(b.0(a.0(a.0(a.1(A.1(x)))))) → a.0(a.0(a.1(A.1(x))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))
b.0(a.0(a.0(a.0(a.1(x))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.1(x)))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))) → a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))
a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))) → a.0(b.0(a.0(a.0(a.1(A.0(x))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))
a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))) → a.0(a.0(a.1(A.0(x))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))) → b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))) → a.0(b.0(a.0(a.0(a.1(A.0(x))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))) → a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))
b.0(a.0(a.0(a.1(A.1(x))))) → a.0(a.0(a.1(A.1(x))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))
a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))) → a.0(a.0(a.1(A.1(x))))
a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))) → a.0(b.0(a.0(a.0(a.1(A.1(x))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))
a.0(b.0(a.0(a.0(a.1(A.0(x)))))) → a.0(a.0(a.1(A.0(x))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))) → b.0(a.0(a.0(a.1(A.0(x)))))
b.0(a.0(a.0(a.0(a.0(x))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.0(x)))))))
a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))) → a.0(a.0(b.0(a.0(a.0(a.1(A.0(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ RuleRemovalProof
↳ SemLabProof2
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))
A1.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))
A1.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))
A1.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0)))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))
B.0(a.0(a.0(a.0(a.0(x))))) → B.0(x)
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0)))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.1(A.1(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.1(A.0(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))
A1.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0)))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0))))))))))))
The TRS R consists of the following rules:
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))
a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))) → a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))) → a.0(b.0(a.0(a.0(a.1(A.1(x))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))) → b.0(a.0(a.0(a.1(A.1(x)))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))) → b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))
b.0(a.0(a.0(a.1(A.0(x))))) → a.0(a.0(a.1(A.0(x))))
a.0(b.0(a.0(a.0(a.1(A.1(x)))))) → a.0(a.0(a.1(A.1(x))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))
b.0(a.0(a.0(a.0(a.1(x))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.1(x)))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))) → a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))
a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))) → a.0(b.0(a.0(a.0(a.1(A.0(x))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))
a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))) → a.0(a.0(a.1(A.0(x))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))) → b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))) → a.0(b.0(a.0(a.0(a.1(A.0(x))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))) → a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))
b.0(a.0(a.0(a.1(A.1(x))))) → a.0(a.0(a.1(A.1(x))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))
a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))) → a.0(a.0(a.1(A.1(x))))
a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))) → a.0(b.0(a.0(a.0(a.1(A.1(x))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))
a.0(b.0(a.0(a.0(a.1(A.0(x)))))) → a.0(a.0(a.1(A.0(x))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))) → b.0(a.0(a.0(a.1(A.0(x)))))
b.0(a.0(a.0(a.0(a.0(x))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.0(x)))))))
a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))) → a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the rule removal processor [15] with the following polynomial ordering [25], at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented.
Strictly oriented dependency pairs:
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0)))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.1(x0))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.1(x0)))))))))
Strictly oriented rules of the TRS R:
b.0(a.0(a.0(a.0(a.1(x))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.1(x)))))))
Used ordering: POLO with Polynomial interpretation [25]:
POL(A.0(x1)) = x1
POL(A.1(x1)) = x1
POL(A1.0(x1)) = x1
POL(B.0(x1)) = x1
POL(a.0(x1)) = x1
POL(a.1(x1)) = 1 + x1
POL(b.0(x1)) = x1
POL(b.1(x1)) = x1
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ RuleRemovalProof
↳ QDP
↳ DependencyGraphProof
↳ SemLabProof2
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))
A1.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))
A1.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))
A1.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))
B.0(a.0(a.0(a.0(a.0(x))))) → B.0(x)
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0)))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.1(A.1(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.1(A.0(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))
A1.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))
The TRS R consists of the following rules:
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))
a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))) → a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))) → a.0(b.0(a.0(a.0(a.1(A.1(x))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))) → b.0(a.0(a.0(a.1(A.1(x)))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))) → b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))
b.0(a.0(a.0(a.1(A.0(x))))) → a.0(a.0(a.1(A.0(x))))
a.0(b.0(a.0(a.0(a.1(A.1(x)))))) → a.0(a.0(a.1(A.1(x))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))) → a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))
a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))) → a.0(b.0(a.0(a.0(a.1(A.0(x))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))
a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))) → a.0(a.0(a.1(A.0(x))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))) → b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))) → a.0(b.0(a.0(a.0(a.1(A.0(x))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))) → a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))
b.0(a.0(a.0(a.1(A.1(x))))) → a.0(a.0(a.1(A.1(x))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))
a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))) → a.0(a.0(a.1(A.1(x))))
a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))) → a.0(b.0(a.0(a.0(a.1(A.1(x))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))
a.0(b.0(a.0(a.0(a.1(A.0(x)))))) → a.0(a.0(a.1(A.0(x))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))) → b.0(a.0(a.0(a.1(A.0(x)))))
b.0(a.0(a.0(a.0(a.0(x))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.0(x)))))))
a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))) → a.0(a.0(b.0(a.0(a.0(a.1(A.0(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
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ RuleRemovalProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ SemLabProof2
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))
A1.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))
A1.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))
A1.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))
B.0(a.0(a.0(a.0(a.0(x))))) → B.0(x)
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0)))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0)))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → A1.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.1(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → B.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(x0))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(a.0(b.0(a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))
A1.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))) → B.0(a.0(a.0(a.0(a.0(a.1(A.1(x0)))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))))))))) → B.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x0))))))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))
B.0(a.0(a.0(a.0(a.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))) → A1.0(b.0(b.0(a.0(a.0(a.1(A.0(x0)))))))
A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x0))))))))))))))))) → A1.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(a.0(a.1(A.0(x0))))))))))))
The TRS R consists of the following rules:
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))
a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))) → a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))) → a.0(b.0(a.0(a.0(a.1(A.1(x))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))) → b.0(a.0(a.0(a.1(A.1(x)))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))) → b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))
b.0(a.0(a.0(a.1(A.0(x))))) → a.0(a.0(a.1(A.0(x))))
a.0(b.0(a.0(a.0(a.1(A.1(x)))))) → a.0(a.0(a.1(A.1(x))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))) → a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))
a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))) → a.0(b.0(a.0(a.0(a.1(A.0(x))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))
a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))) → a.0(a.0(a.1(A.0(x))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))) → b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))) → a.0(b.0(a.0(a.0(a.1(A.0(x))))))
a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))))) → a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))
b.0(a.0(a.0(a.1(A.1(x))))) → a.0(a.0(a.1(A.1(x))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))
a.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))) → a.0(a.0(a.1(A.1(x))))
a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))) → a.0(b.0(a.0(a.0(a.1(A.1(x))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.1(x)))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.1(x))))))))))
a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))))))))) → a.0(a.0(a.0(b.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))
a.0(a.0(a.0(b.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))) → a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))
a.0(b.0(a.0(a.0(a.1(A.0(x)))))) → a.0(a.0(a.1(A.0(x))))
b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))) → b.0(a.0(a.0(a.1(A.0(x)))))
b.0(a.0(a.0(a.0(a.0(x))))) → a.0(a.0(a.0(a.0(a.0(b.0(b.0(x)))))))
a.0(a.0(b.0(a.0(a.0(a.0(b.0(a.0(a.0(a.1(A.0(x))))))))))) → a.0(a.0(b.0(a.0(a.0(a.1(A.0(x)))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
As can be seen after transforming the QDP problem by semantic labelling [33] and then some rule deleting processors, only certain labelled rules and pairs can be used.
Hence, we only have to consider all unlabelled pairs and rules (without the decreasing rules for quasi-models).
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(a(b(a(a(a(a(a(A(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(b(a(a(a(A(x0)))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(a(b(a(a(a(a(a(A(x0)))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(b(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(b(b(a(a(a(b(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → B(a(a(a(a(a(b(b(x0))))))))
A1(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(x0))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(b(a(a(a(a(a(b(b(x0)))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(b(a(b(a(a(a(a(a(A(x0))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0))))))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(a(a(a(b(a(a(a(a(a(b(b(x0)))))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(a(b(b(a(a(a(A(x0))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(b(a(a(a(b(a(a(a(A(x0))))))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(b(b(a(a(a(b(a(a(a(A(x0)))))))))))
B(a(a(a(a(x))))) → B(x)
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(a(b(a(a(a(a(a(b(b(x0))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(b(a(a(a(a(a(A(x0)))))))))
A1(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → A1(a(a(a(a(b(b(a(a(a(b(a(a(a(A(x0)))))))))))))))
A1(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x0))))))))))))))))) → B(a(a(a(a(a(A(x0)))))))
B(a(a(a(a(a(a(a(b(a(a(a(A(x0))))))))))))) → A1(b(a(a(a(a(a(b(b(a(a(a(A(x0)))))))))))))
B(a(a(a(a(a(a(a(a(x0))))))))) → A1(b(a(a(a(a(a(b(b(x0)))))))))
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
We have reversed the following QTRS:
The set of rules R is
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
b(a(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → b(a(a(a(b(a(a(a(A(x)))))))))
a(a(b(a(a(a(A(x))))))) → a(a(a(A(x))))
b(a(a(a(b(a(a(a(A(x))))))))) → a(a(a(a(a(b(b(a(a(a(A(x)))))))))))
a(a(a(b(a(a(b(a(a(a(A(x))))))))))) → a(a(a(b(a(a(a(A(x))))))))
b(a(a(a(b(a(a(a(A(x))))))))) → b(a(a(a(A(x)))))
a(a(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))) → a(a(a(b(a(a(b(a(a(a(A(x)))))))))))
a(a(a(b(a(b(a(a(b(a(a(a(A(x))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(a(a(b(a(b(a(a(a(A(x)))))))))) → a(a(a(b(a(a(a(A(x))))))))
a(b(a(a(a(A(x)))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(a(b(a(a(a(A(x)))))))))))))) → a(a(a(b(a(b(a(a(a(A(x))))))))))
a(b(a(a(a(b(a(a(a(A(x)))))))))) → a(b(a(a(a(A(x))))))
a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))) → a(b(a(a(b(a(a(a(A(x)))))))))
a(b(a(a(b(a(a(a(A(x))))))))) → a(b(a(a(a(A(x))))))
a(a(b(a(a(a(b(a(a(a(A(x))))))))))) → a(a(b(a(a(a(A(x)))))))
b(a(a(a(A(x))))) → a(a(a(A(x))))
a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(A(x))))))))))))))))) → a(a(a(b(a(b(a(a(b(a(a(a(A(x)))))))))))))
The set Q is empty.
We have obtained the following QTRS:
a(a(a(a(b(x))))) → b(b(a(a(a(a(a(x)))))))
A(a(a(a(b(a(a(a(b(a(a(a(b(x))))))))))))) → A(a(a(a(b(a(a(a(b(x)))))))))
A(a(a(a(b(a(a(x))))))) → A(a(a(a(x))))
A(a(a(a(b(a(a(a(b(x))))))))) → A(a(a(a(b(b(a(a(a(a(a(x)))))))))))
A(a(a(a(b(a(a(b(a(a(a(x))))))))))) → A(a(a(a(b(a(a(a(x))))))))
A(a(a(a(b(a(a(a(b(x))))))))) → A(a(a(a(b(x)))))
A(a(a(a(b(a(a(a(b(a(a(b(a(a(a(x))))))))))))))) → A(a(a(a(b(a(a(b(a(a(a(x)))))))))))
A(a(a(a(b(a(a(b(a(b(a(a(a(x))))))))))))) → A(a(a(a(b(a(b(a(a(a(x))))))))))
A(a(a(a(b(a(b(a(a(a(x)))))))))) → A(a(a(a(b(a(a(a(x))))))))
A(a(a(a(b(a(x)))))) → A(a(a(a(x))))
A(a(a(a(b(a(a(a(b(a(b(a(a(a(x)))))))))))))) → A(a(a(a(b(a(b(a(a(a(x))))))))))
A(a(a(a(b(a(a(a(b(a(x)))))))))) → A(a(a(a(b(a(x))))))
A(a(a(a(b(a(a(a(b(a(a(b(a(x))))))))))))) → A(a(a(a(b(a(a(b(a(x)))))))))
A(a(a(a(b(a(a(b(a(x))))))))) → A(a(a(a(b(a(x))))))
A(a(a(a(b(a(a(a(b(a(a(x))))))))))) → A(a(a(a(b(a(a(x)))))))
A(a(a(a(b(x))))) → A(a(a(a(x))))
A(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(x))))))))))))))))) → A(a(a(a(b(a(a(b(a(b(a(a(a(x)))))))))))))
The set Q is empty.
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ MNOCProof
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ ForwardInstantiation
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
Q restricted rewrite system:
The TRS R consists of the following rules:
a(a(a(a(b(x))))) → b(b(a(a(a(a(a(x)))))))
A(a(a(a(b(a(a(a(b(a(a(a(b(x))))))))))))) → A(a(a(a(b(a(a(a(b(x)))))))))
A(a(a(a(b(a(a(x))))))) → A(a(a(a(x))))
A(a(a(a(b(a(a(a(b(x))))))))) → A(a(a(a(b(b(a(a(a(a(a(x)))))))))))
A(a(a(a(b(a(a(b(a(a(a(x))))))))))) → A(a(a(a(b(a(a(a(x))))))))
A(a(a(a(b(a(a(a(b(x))))))))) → A(a(a(a(b(x)))))
A(a(a(a(b(a(a(a(b(a(a(b(a(a(a(x))))))))))))))) → A(a(a(a(b(a(a(b(a(a(a(x)))))))))))
A(a(a(a(b(a(a(b(a(b(a(a(a(x))))))))))))) → A(a(a(a(b(a(b(a(a(a(x))))))))))
A(a(a(a(b(a(b(a(a(a(x)))))))))) → A(a(a(a(b(a(a(a(x))))))))
A(a(a(a(b(a(x)))))) → A(a(a(a(x))))
A(a(a(a(b(a(a(a(b(a(b(a(a(a(x)))))))))))))) → A(a(a(a(b(a(b(a(a(a(x))))))))))
A(a(a(a(b(a(a(a(b(a(x)))))))))) → A(a(a(a(b(a(x))))))
A(a(a(a(b(a(a(a(b(a(a(b(a(x))))))))))))) → A(a(a(a(b(a(a(b(a(x)))))))))
A(a(a(a(b(a(a(b(a(x))))))))) → A(a(a(a(b(a(x))))))
A(a(a(a(b(a(a(a(b(a(a(x))))))))))) → A(a(a(a(b(a(a(x)))))))
A(a(a(a(b(x))))) → A(a(a(a(x))))
A(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(x))))))))))))))))) → A(a(a(a(b(a(a(b(a(b(a(a(a(x)))))))))))))
Q is empty.
We have reversed the following QTRS:
The set of rules R is
a(a(a(a(b(x1))))) → b(b(a(a(a(a(a(x1)))))))
The set Q is empty.
We have obtained the following QTRS:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
The set Q is empty.
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
Q restricted rewrite system:
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
Q is empty.
We have reversed the following QTRS:
The set of rules R is
a(a(a(a(b(x1))))) → b(b(a(a(a(a(a(x1)))))))
The set Q is empty.
We have obtained the following QTRS:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
The set Q is empty.
↳ QTRS
↳ Overlay + Local Confluence
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS
Q restricted rewrite system:
The TRS R consists of the following rules:
b(a(a(a(a(x))))) → a(a(a(a(a(b(b(x)))))))
Q is empty.