Termination w.r.t. Q of the following Term Rewriting System could not be shown:
Q restricted rewrite system:
The TRS R consists of the following rules:
b(a(b(b(b(a(b(b(x1)))))))) → b(b(a(b(b(b(a(b(a(b(b(b(a(b(x1))))))))))))))
Q is empty.
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
Q restricted rewrite system:
The TRS R consists of the following rules:
b(a(b(b(b(a(b(b(x1)))))))) → b(b(a(b(b(b(a(b(a(b(b(b(a(b(x1))))))))))))))
Q is empty.
We have reversed the following QTRS:
The set of rules R is
b(a(b(b(b(a(b(b(x1)))))))) → b(b(a(b(b(b(a(b(a(b(b(b(a(b(x1))))))))))))))
The set Q is empty.
We have obtained the following QTRS:
b(b(a(b(b(b(a(b(x)))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
The set Q is empty.
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
Q restricted rewrite system:
The TRS R consists of the following rules:
b(b(a(b(b(b(a(b(x)))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
Q is empty.
We were given the following TRS:
b(a(b(b(b(a(b(b(x1)))))))) → b(b(a(b(b(b(a(b(a(b(b(b(a(b(x1))))))))))))))
By stripping symbols from the only rule of the system, we obtained the following TRS:
a(b(b(b(a(b(b(x1))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(x1)))))))))))))
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
Q restricted rewrite system:
The TRS R consists of the following rules:
a(b(b(b(a(b(b(x1))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(x1)))))))))))))
Q is empty.
We have reversed the following QTRS:
The set of rules R is
b(a(b(b(b(a(b(b(x1)))))))) → b(b(a(b(b(b(a(b(a(b(b(b(a(b(x1))))))))))))))
The set Q is empty.
We have obtained the following QTRS:
b(b(a(b(b(b(a(b(x)))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
The set Q is empty.
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ QTRS
↳ Strip Symbols Proof
↳ DependencyPairsProof
Q restricted rewrite system:
The TRS R consists of the following rules:
b(b(a(b(b(b(a(b(x)))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
Q is empty.
We were given the following TRS:
b(b(a(b(b(b(a(b(x)))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
By stripping symbols from the only rule of the system, we obtained the following TRS:
b(a(b(b(b(a(b(x))))))) → a(b(b(b(a(b(a(b(b(b(a(b(b(x)))))))))))))
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ QTRS
↳ Strip Symbols Proof
↳ QTRS
↳ DependencyPairsProof
Q restricted rewrite system:
The TRS R consists of the following rules:
b(a(b(b(b(a(b(x))))))) → a(b(b(b(a(b(a(b(b(b(a(b(b(x)))))))))))))
Q is empty.
Using Dependency Pairs [1,15] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:
B(a(b(b(b(a(b(b(x1)))))))) → B(b(a(b(x1))))
B(a(b(b(b(a(b(b(x1)))))))) → B(a(b(a(b(b(b(a(b(x1)))))))))
B(a(b(b(b(a(b(b(x1)))))))) → B(b(b(a(b(x1)))))
B(a(b(b(b(a(b(b(x1)))))))) → B(a(b(b(b(a(b(a(b(b(b(a(b(x1)))))))))))))
B(a(b(b(b(a(b(b(x1)))))))) → B(a(b(x1)))
B(a(b(b(b(a(b(b(x1)))))))) → B(b(a(b(b(b(a(b(a(b(b(b(a(b(x1))))))))))))))
B(a(b(b(b(a(b(b(x1)))))))) → B(b(b(a(b(a(b(b(b(a(b(x1)))))))))))
B(a(b(b(b(a(b(b(x1)))))))) → B(a(b(b(b(a(b(x1)))))))
B(a(b(b(b(a(b(b(x1)))))))) → B(b(a(b(a(b(b(b(a(b(x1))))))))))
The TRS R consists of the following rules:
b(a(b(b(b(a(b(b(x1)))))))) → b(b(a(b(b(b(a(b(a(b(b(b(a(b(x1))))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
Q DP problem:
The TRS P consists of the following rules:
B(a(b(b(b(a(b(b(x1)))))))) → B(b(a(b(x1))))
B(a(b(b(b(a(b(b(x1)))))))) → B(a(b(a(b(b(b(a(b(x1)))))))))
B(a(b(b(b(a(b(b(x1)))))))) → B(b(b(a(b(x1)))))
B(a(b(b(b(a(b(b(x1)))))))) → B(a(b(b(b(a(b(a(b(b(b(a(b(x1)))))))))))))
B(a(b(b(b(a(b(b(x1)))))))) → B(a(b(x1)))
B(a(b(b(b(a(b(b(x1)))))))) → B(b(a(b(b(b(a(b(a(b(b(b(a(b(x1))))))))))))))
B(a(b(b(b(a(b(b(x1)))))))) → B(b(b(a(b(a(b(b(b(a(b(x1)))))))))))
B(a(b(b(b(a(b(b(x1)))))))) → B(a(b(b(b(a(b(x1)))))))
B(a(b(b(b(a(b(b(x1)))))))) → B(b(a(b(a(b(b(b(a(b(x1))))))))))
The TRS R consists of the following rules:
b(a(b(b(b(a(b(b(x1)))))))) → b(b(a(b(b(b(a(b(a(b(b(b(a(b(x1))))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 5 less nodes.
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
Q DP problem:
The TRS P consists of the following rules:
B(a(b(b(b(a(b(b(x1)))))))) → B(a(b(a(b(b(b(a(b(x1)))))))))
B(a(b(b(b(a(b(b(x1)))))))) → B(a(b(b(b(a(b(a(b(b(b(a(b(x1)))))))))))))
B(a(b(b(b(a(b(b(x1)))))))) → B(a(b(x1)))
B(a(b(b(b(a(b(b(x1)))))))) → B(a(b(b(b(a(b(x1)))))))
The TRS R consists of the following rules:
b(a(b(b(b(a(b(b(x1)))))))) → b(b(a(b(b(b(a(b(a(b(b(b(a(b(x1))))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B(a(b(b(b(a(b(b(x1)))))))) → B(a(b(a(b(b(b(a(b(x1))))))))) at position [0,0] we obtained the following new rules:
B(a(b(b(b(a(b(b(b(x0))))))))) → B(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x0))))))))))))))))
B(a(b(b(b(a(b(b(a(b(b(b(a(b(b(x0))))))))))))))) → B(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x0))))))))))))))))))))))
B(a(b(b(b(a(b(b(b(b(a(b(b(x0))))))))))))) → B(a(b(a(b(b(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x0))))))))))))))))))))
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
Q DP problem:
The TRS P consists of the following rules:
B(a(b(b(b(a(b(b(b(x0))))))))) → B(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x0))))))))))))))))
B(a(b(b(b(a(b(b(a(b(b(b(a(b(b(x0))))))))))))))) → B(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x0))))))))))))))))))))))
B(a(b(b(b(a(b(b(b(b(a(b(b(x0))))))))))))) → B(a(b(a(b(b(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x0))))))))))))))))))))
B(a(b(b(b(a(b(b(x1)))))))) → B(a(b(b(b(a(b(a(b(b(b(a(b(x1)))))))))))))
B(a(b(b(b(a(b(b(x1)))))))) → B(a(b(x1)))
B(a(b(b(b(a(b(b(x1)))))))) → B(a(b(b(b(a(b(x1)))))))
The TRS R consists of the following rules:
b(a(b(b(b(a(b(b(x1)))))))) → b(b(a(b(b(b(a(b(a(b(b(b(a(b(x1))))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B(a(b(b(b(a(b(b(x1)))))))) → B(a(b(b(b(a(b(a(b(b(b(a(b(x1))))))))))))) at position [0,0] we obtained the following new rules:
B(a(b(b(b(a(b(b(a(b(b(b(a(b(b(x0))))))))))))))) → B(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x0))))))))))))))))))))))))))
B(a(b(b(b(a(b(b(b(b(a(b(b(x0))))))))))))) → B(a(b(b(b(a(b(a(b(b(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x0))))))))))))))))))))))))
B(a(b(b(b(a(b(b(b(x0))))))))) → B(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x0))))))))))))))))))))
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ SemLabProof2
Q DP problem:
The TRS P consists of the following rules:
B(a(b(b(b(a(b(b(b(x0))))))))) → B(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x0))))))))))))))))
B(a(b(b(b(a(b(b(a(b(b(b(a(b(b(x0))))))))))))))) → B(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x0))))))))))))))))))))))
B(a(b(b(b(a(b(b(b(b(a(b(b(x0))))))))))))) → B(a(b(a(b(b(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x0))))))))))))))))))))
B(a(b(b(b(a(b(b(x1)))))))) → B(a(b(x1)))
B(a(b(b(b(a(b(b(b(x0))))))))) → B(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x0))))))))))))))))))))
B(a(b(b(b(a(b(b(a(b(b(b(a(b(b(x0))))))))))))))) → B(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x0))))))))))))))))))))))))))
B(a(b(b(b(a(b(b(x1)))))))) → B(a(b(b(b(a(b(x1)))))))
B(a(b(b(b(a(b(b(b(b(a(b(b(x0))))))))))))) → B(a(b(b(b(a(b(a(b(b(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x0))))))))))))))))))))))))
The TRS R consists of the following rules:
b(a(b(b(b(a(b(b(x1)))))))) → b(b(a(b(b(b(a(b(a(b(b(b(a(b(x1))))))))))))))
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.B: 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.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(b.0(x0))))))))) → B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(x0))))))))))))))))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(x1)))))))) → B.1(a.0(b.0(x1)))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(x1)))))))) → B.1(a.0(b.0(b.0(b.1(a.0(b.1(x1)))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(x1)))))))) → B.1(a.0(b.1(x1)))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(b.0(b.1(a.0(b.0(b.0(x0))))))))))))) → B.1(a.0(b.1(a.0(b.0(b.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(x0))))))))))))))))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(x0))))))))))))))) → B.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(x0))))))))))))))))))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(b.0(b.1(a.0(b.0(b.1(x0))))))))))))) → B.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(x0))))))))))))))))))))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(b.0(x0))))))))) → B.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(x0))))))))))))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(b.1(x0))))))))) → B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(x0))))))))))))))))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(b.0(b.1(a.0(b.0(b.0(x0))))))))))))) → B.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(x0))))))))))))))))))))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(x0))))))))))))))) → B.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(x0))))))))))))))))))))))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(b.1(x0))))))))) → B.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(x0))))))))))))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(x0))))))))))))))) → B.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(x0))))))))))))))))))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(b.0(b.1(a.0(b.0(b.1(x0))))))))))))) → B.1(a.0(b.1(a.0(b.0(b.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(x0))))))))))))))))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(x0))))))))))))))) → B.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(x0))))))))))))))))))))))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(x1)))))))) → B.1(a.0(b.0(b.0(b.1(a.0(b.0(x1)))))))
The TRS R consists of the following rules:
b.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(x1)))))))) → b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(x1))))))))))))))
b.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(x1)))))))) → b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(x1))))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ QDP
↳ DependencyGraphProof
↳ SemLabProof2
Q DP problem:
The TRS P consists of the following rules:
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(b.0(x0))))))))) → B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(x0))))))))))))))))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(x1)))))))) → B.1(a.0(b.0(x1)))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(x1)))))))) → B.1(a.0(b.0(b.0(b.1(a.0(b.1(x1)))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(x1)))))))) → B.1(a.0(b.1(x1)))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(b.0(b.1(a.0(b.0(b.0(x0))))))))))))) → B.1(a.0(b.1(a.0(b.0(b.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(x0))))))))))))))))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(x0))))))))))))))) → B.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(x0))))))))))))))))))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(b.0(b.1(a.0(b.0(b.1(x0))))))))))))) → B.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(x0))))))))))))))))))))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(b.0(x0))))))))) → B.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(x0))))))))))))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(b.1(x0))))))))) → B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(x0))))))))))))))))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(b.0(b.1(a.0(b.0(b.0(x0))))))))))))) → B.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(x0))))))))))))))))))))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(x0))))))))))))))) → B.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(x0))))))))))))))))))))))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(b.1(x0))))))))) → B.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(x0))))))))))))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(x0))))))))))))))) → B.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(x0))))))))))))))))))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(b.0(b.1(a.0(b.0(b.1(x0))))))))))))) → B.1(a.0(b.1(a.0(b.0(b.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(x0))))))))))))))))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(x0))))))))))))))) → B.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(x0))))))))))))))))))))))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(x1)))))))) → B.1(a.0(b.0(b.0(b.1(a.0(b.0(x1)))))))
The TRS R consists of the following rules:
b.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(x1)))))))) → b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(x1))))))))))))))
b.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(x1)))))))) → b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(x1))))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 4 less nodes.
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ SemLabProof2
Q DP problem:
The TRS P consists of the following rules:
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(b.1(x0))))))))) → B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(x0))))))))))))))))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(b.0(x0))))))))) → B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(x0))))))))))))))))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(x1)))))))) → B.1(a.0(b.0(b.0(b.1(a.0(b.1(x1)))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(x1)))))))) → B.1(a.0(b.0(x1)))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(x0))))))))))))))) → B.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(x0))))))))))))))))))))))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(b.1(x0))))))))) → B.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(x0))))))))))))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(x1)))))))) → B.1(a.0(b.1(x1)))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(x0))))))))))))))) → B.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(x0))))))))))))))))))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(x0))))))))))))))) → B.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(x0))))))))))))))))))))))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(x0))))))))))))))) → B.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(x0))))))))))))))))))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(x1)))))))) → B.1(a.0(b.0(b.0(b.1(a.0(b.0(x1)))))))
B.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(b.0(x0))))))))) → B.1(a.0(b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(x0))))))))))))))))
The TRS R consists of the following rules:
b.1(a.0(b.0(b.0(b.1(a.0(b.0(b.0(x1)))))))) → b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.0(x1))))))))))))))
b.1(a.0(b.0(b.0(b.1(a.0(b.0(b.1(x1)))))))) → b.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(a.0(b.0(b.0(b.1(a.0(b.1(x1))))))))))))))
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
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ QDPToSRSProof
Q DP problem:
The TRS P consists of the following rules:
B(a(b(b(b(a(b(b(b(x0))))))))) → B(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x0))))))))))))))))
B(a(b(b(b(a(b(b(a(b(b(b(a(b(b(x0))))))))))))))) → B(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x0))))))))))))))))))))))
B(a(b(b(b(a(b(b(x1)))))))) → B(a(b(x1)))
B(a(b(b(b(a(b(b(b(x0))))))))) → B(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x0))))))))))))))))))))
B(a(b(b(b(a(b(b(a(b(b(b(a(b(b(x0))))))))))))))) → B(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x0))))))))))))))))))))))))))
B(a(b(b(b(a(b(b(x1)))))))) → B(a(b(b(b(a(b(x1)))))))
The TRS R consists of the following rules:
b(a(b(b(b(a(b(b(x1)))))))) → b(b(a(b(b(b(a(b(a(b(b(b(a(b(x1))))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The finiteness of this DP problem is implied by strong termination of a SRS due to [12].
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
Q restricted rewrite system:
The TRS R consists of the following rules:
b(a(b(b(b(a(b(b(x1)))))))) → b(b(a(b(b(b(a(b(a(b(b(b(a(b(x1))))))))))))))
B(a(b(b(b(a(b(b(b(x0))))))))) → B(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x0))))))))))))))))
B(a(b(b(b(a(b(b(a(b(b(b(a(b(b(x0))))))))))))))) → B(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x0))))))))))))))))))))))
B(a(b(b(b(a(b(b(x1)))))))) → B(a(b(x1)))
B(a(b(b(b(a(b(b(b(x0))))))))) → B(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x0))))))))))))))))))))
B(a(b(b(b(a(b(b(a(b(b(b(a(b(b(x0))))))))))))))) → B(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x0))))))))))))))))))))))))))
B(a(b(b(b(a(b(b(x1)))))))) → B(a(b(b(b(a(b(x1)))))))
Q is empty.
We have reversed the following QTRS:
The set of rules R is
b(a(b(b(b(a(b(b(x1)))))))) → b(b(a(b(b(b(a(b(a(b(b(b(a(b(x1))))))))))))))
B(a(b(b(b(a(b(b(b(x0))))))))) → B(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x0))))))))))))))))
B(a(b(b(b(a(b(b(a(b(b(b(a(b(b(x0))))))))))))))) → B(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x0))))))))))))))))))))))
B(a(b(b(b(a(b(b(x1)))))))) → B(a(b(x1)))
B(a(b(b(b(a(b(b(b(x0))))))))) → B(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x0))))))))))))))))))))
B(a(b(b(b(a(b(b(a(b(b(b(a(b(b(x0))))))))))))))) → B(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x0))))))))))))))))))))))))))
B(a(b(b(b(a(b(b(x1)))))))) → B(a(b(b(b(a(b(x1)))))))
The set Q is empty.
We have obtained the following QTRS:
b(b(a(b(b(b(a(b(x)))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(B(x)))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(b(b(b(a(B(x)))))))
The set Q is empty.
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
Q restricted rewrite system:
The TRS R consists of the following rules:
b(b(a(b(b(b(a(b(x)))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(B(x)))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(b(b(b(a(B(x)))))))
Q is empty.
We have reversed the following QTRS:
The set of rules R is
b(b(a(b(b(b(a(b(x)))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(B(x)))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(b(b(b(a(B(x)))))))
The set Q is empty.
We have obtained the following QTRS:
b(a(b(b(b(a(b(b(x)))))))) → b(b(a(b(b(b(a(b(a(b(b(b(a(b(x))))))))))))))
B(a(b(b(b(a(b(b(b(x))))))))) → B(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x))))))))))))))))
B(a(b(b(b(a(b(b(a(b(b(b(a(b(b(x))))))))))))))) → B(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x))))))))))))))))))))))
B(a(b(b(b(a(b(b(x)))))))) → B(a(b(x)))
B(a(b(b(b(a(b(b(b(x))))))))) → B(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x))))))))))))))))))))
B(a(b(b(b(a(b(b(a(b(b(b(a(b(b(x))))))))))))))) → B(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x))))))))))))))))))))))))))
B(a(b(b(b(a(b(b(x)))))))) → B(a(b(b(b(a(b(x)))))))
The set Q is empty.
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
Q restricted rewrite system:
The TRS R consists of the following rules:
b(a(b(b(b(a(b(b(x)))))))) → b(b(a(b(b(b(a(b(a(b(b(b(a(b(x))))))))))))))
B(a(b(b(b(a(b(b(b(x))))))))) → B(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x))))))))))))))))
B(a(b(b(b(a(b(b(a(b(b(b(a(b(b(x))))))))))))))) → B(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x))))))))))))))))))))))
B(a(b(b(b(a(b(b(x)))))))) → B(a(b(x)))
B(a(b(b(b(a(b(b(b(x))))))))) → B(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x))))))))))))))))))))
B(a(b(b(b(a(b(b(a(b(b(b(a(b(b(x))))))))))))))) → B(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x))))))))))))))))))))))))))
B(a(b(b(b(a(b(b(x)))))))) → B(a(b(b(b(a(b(x)))))))
Q is empty.
We have reversed the following QTRS:
The set of rules R is
b(b(a(b(b(b(a(b(x)))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(B(x)))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(b(b(b(a(B(x)))))))
The set Q is empty.
We have obtained the following QTRS:
b(a(b(b(b(a(b(b(x)))))))) → b(b(a(b(b(b(a(b(a(b(b(b(a(b(x))))))))))))))
B(a(b(b(b(a(b(b(b(x))))))))) → B(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x))))))))))))))))
B(a(b(b(b(a(b(b(a(b(b(b(a(b(b(x))))))))))))))) → B(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x))))))))))))))))))))))
B(a(b(b(b(a(b(b(x)))))))) → B(a(b(x)))
B(a(b(b(b(a(b(b(b(x))))))))) → B(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x))))))))))))))))))))
B(a(b(b(b(a(b(b(a(b(b(b(a(b(b(x))))))))))))))) → B(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x))))))))))))))))))))))))))
B(a(b(b(b(a(b(b(x)))))))) → B(a(b(b(b(a(b(x)))))))
The set Q is empty.
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS
↳ DependencyPairsProof
Q restricted rewrite system:
The TRS R consists of the following rules:
b(a(b(b(b(a(b(b(x)))))))) → b(b(a(b(b(b(a(b(a(b(b(b(a(b(x))))))))))))))
B(a(b(b(b(a(b(b(b(x))))))))) → B(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x))))))))))))))))
B(a(b(b(b(a(b(b(a(b(b(b(a(b(b(x))))))))))))))) → B(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x))))))))))))))))))))))
B(a(b(b(b(a(b(b(x)))))))) → B(a(b(x)))
B(a(b(b(b(a(b(b(b(x))))))))) → B(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x))))))))))))))))))))
B(a(b(b(b(a(b(b(a(b(b(b(a(b(b(x))))))))))))))) → B(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(x))))))))))))))))))))))))))
B(a(b(b(b(a(b(b(x)))))))) → B(a(b(b(b(a(b(x)))))))
Q is empty.
Using Dependency Pairs [1,15] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(b(a(b(b(a(b(b(b(a(B(x)))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(a(b(a(B(x)))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(a(b(b(b(a(b(a(B(x)))))))))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(a(b(a(b(b(b(a(b(b(a(B(x))))))))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(a(b(b(b(a(b(b(a(B(x))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(B(x))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(a(B(x))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x)))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(a(b(b(b(a(b(a(b(b(b(a(B(x)))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(a(b(b(a(B(x))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(a(b(b(b(a(B(x))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(a(b(a(b(b(b(a(b(b(x)))))))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(b(b(a(b(a(b(b(b(a(b(b(a(B(x))))))))))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(b(a(b(a(B(x)))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(a(b(b(x))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x)))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x)))))))))))))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(a(b(a(b(b(b(a(b(b(x))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(a(b(a(b(b(b(a(B(x)))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(a(b(b(b(a(b(b(x))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(x))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x)))))))))))))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(a(b(b(x)))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(b(a(b(b(x))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(b(b(a(b(b(a(B(x))))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(b(a(b(a(b(b(b(a(b(b(a(B(x)))))))))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(b(a(b(a(b(b(b(a(B(x)))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(a(b(b(b(a(b(a(B(x)))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(b(a(b(b(a(B(x)))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(a(b(b(a(b(b(b(a(B(x))))))))))
The TRS R consists of the following rules:
b(b(a(b(b(b(a(b(x)))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(B(x)))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(b(b(b(a(B(x)))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
Q DP problem:
The TRS P consists of the following rules:
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(b(a(b(b(a(b(b(b(a(B(x)))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(a(b(a(B(x)))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(a(b(b(b(a(b(a(B(x)))))))))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(a(b(a(b(b(b(a(b(b(a(B(x))))))))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(a(b(b(b(a(b(b(a(B(x))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(B(x))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(a(B(x))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x)))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(a(b(b(b(a(b(a(b(b(b(a(B(x)))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(a(b(b(a(B(x))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(a(b(b(b(a(B(x))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(a(b(a(b(b(b(a(b(b(x)))))))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(b(b(a(b(a(b(b(b(a(b(b(a(B(x))))))))))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(b(a(b(a(B(x)))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(a(b(b(x))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x)))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x)))))))))))))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(a(b(a(b(b(b(a(b(b(x))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(a(b(a(b(b(b(a(B(x)))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(a(b(b(b(a(b(b(x))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(x))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x)))))))))))))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(a(b(b(x)))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(b(a(b(b(x))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(b(b(a(b(b(a(B(x))))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(b(a(b(a(b(b(b(a(b(b(a(B(x)))))))))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(b(a(b(a(b(b(b(a(B(x)))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(a(b(b(b(a(b(a(B(x)))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(b(a(b(b(a(B(x)))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(a(b(b(a(b(b(b(a(B(x))))))))))
The TRS R consists of the following rules:
b(b(a(b(b(b(a(b(x)))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(B(x)))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(b(b(b(a(B(x)))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 40 less nodes.
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
Q DP problem:
The TRS P consists of the following rules:
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(a(b(b(x)))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(b(a(b(b(x))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x)))))))))))))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(b(a(b(b(a(b(b(b(a(B(x)))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(B(x))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(a(b(b(b(a(b(a(B(x)))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(x))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))
The TRS R consists of the following rules:
b(b(a(b(b(b(a(b(x)))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(B(x)))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(b(b(b(a(B(x)))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(B(x)))))))))))))) at position [0] we obtained the following new rules:
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(y0))))))))))))))) → B1(b(b(a(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(y0))))))))))))))))))))
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
Q DP problem:
The TRS P consists of the following rules:
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(a(b(b(x)))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(b(a(b(b(x))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(b(a(b(b(a(b(b(b(a(B(x)))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x)))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(y0))))))))))))))) → B1(b(b(a(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(y0))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(B(x))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(a(b(b(b(a(b(a(B(x)))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(x))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))
The TRS R consists of the following rules:
b(b(a(b(b(b(a(b(x)))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(B(x)))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(b(b(b(a(B(x)))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 1 less node.
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
Q DP problem:
The TRS P consists of the following rules:
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(a(b(b(x)))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(b(a(b(b(x))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x)))))))))))))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(b(a(b(b(a(b(b(b(a(B(x)))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(B(x))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(a(b(b(b(a(b(a(B(x)))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(x))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))
The TRS R consists of the following rules:
b(b(a(b(b(b(a(b(x)))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(B(x)))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(b(b(b(a(B(x)))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))) at position [0,0,0] we obtained the following new rules:
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(y0))))))))))))))) → B1(b(a(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(y0)))))))))))))))))))
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
Q DP problem:
The TRS P consists of the following rules:
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(a(b(b(x)))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(y0))))))))))))))) → B1(b(a(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(y0)))))))))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(b(a(b(b(x))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(b(a(b(b(a(b(b(b(a(B(x)))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x)))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(B(x))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(x))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))
The TRS R consists of the following rules:
b(b(a(b(b(b(a(b(x)))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(B(x)))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(b(b(b(a(B(x)))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 1 less node.
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
Q DP problem:
The TRS P consists of the following rules:
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(a(b(b(x)))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(b(a(b(b(x))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x)))))))))))))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(b(a(b(b(a(b(b(b(a(B(x)))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(B(x))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(x))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))
The TRS R consists of the following rules:
b(b(a(b(b(b(a(b(x)))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(B(x)))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(b(b(b(a(B(x)))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B1(b(b(a(b(b(b(a(B(x))))))))) → B1(b(b(a(b(b(a(b(b(b(a(B(x)))))))))))) at position [0] we obtained the following new rules:
B1(b(b(a(b(b(b(a(B(x0))))))))) → B1(b(b(a(b(a(B(x0)))))))
B1(b(b(a(b(b(b(a(B(x0))))))))) → B1(b(b(a(b(a(b(b(b(a(B(x0)))))))))))
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
Q DP problem:
The TRS P consists of the following rules:
B1(b(b(a(b(b(b(a(B(x0))))))))) → B1(b(b(a(b(a(B(x0)))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(a(b(b(x)))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))
B1(b(b(a(b(b(b(a(B(x0))))))))) → B1(b(b(a(b(a(b(b(b(a(B(x0)))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(b(a(b(b(x))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(b(a(b(b(a(b(b(b(a(B(x)))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x)))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(B(x))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(x))
The TRS R consists of the following rules:
b(b(a(b(b(b(a(b(x)))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(B(x)))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(b(b(b(a(B(x)))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 2 less nodes.
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
Q DP problem:
The TRS P consists of the following rules:
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(a(b(b(x)))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(b(a(b(b(x))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x)))))))))))))))))
B1(b(b(a(b(b(b(a(B(x))))))))) → B1(b(a(b(b(a(b(b(b(a(B(x)))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(B(x))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(x))
The TRS R consists of the following rules:
b(b(a(b(b(b(a(b(x)))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(B(x)))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(b(b(b(a(B(x)))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B1(b(b(a(b(b(b(a(B(x))))))))) → B1(b(a(b(b(a(b(b(b(a(B(x))))))))))) at position [0,0,0] we obtained the following new rules:
B1(b(b(a(b(b(b(a(B(x0))))))))) → B1(b(a(b(a(b(b(b(a(B(x0))))))))))
B1(b(b(a(b(b(b(a(B(x0))))))))) → B1(b(a(b(a(B(x0))))))
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
Q DP problem:
The TRS P consists of the following rules:
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(a(b(b(x)))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(b(a(b(b(x))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x)))))))))))))))))
B1(b(b(a(b(b(b(a(B(x0))))))))) → B1(b(a(b(a(B(x0))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(B(x))))))))))
B1(b(b(a(b(b(b(a(B(x0))))))))) → B1(b(a(b(a(b(b(b(a(B(x0))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(x))
The TRS R consists of the following rules:
b(b(a(b(b(b(a(b(x)))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(B(x)))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(b(b(b(a(B(x)))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 2 less nodes.
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
Q DP problem:
The TRS P consists of the following rules:
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(a(b(b(x)))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(b(a(b(b(x))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x)))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(B(x))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(x))
The TRS R consists of the following rules:
b(b(a(b(b(b(a(b(x)))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(B(x)))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(b(b(b(a(B(x)))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x)))))))))))))))))) at position [0] we obtained the following new rules:
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(y0))))))))))))))) → B1(b(b(a(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(y0))))))))))))))))))))))))
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
Q DP problem:
The TRS P consists of the following rules:
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(a(b(b(x)))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(b(a(b(b(x))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x)))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(B(x))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(y0))))))))))))))) → B1(b(b(a(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(y0))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(x))
The TRS R consists of the following rules:
b(b(a(b(b(b(a(b(x)))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(B(x)))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(b(b(b(a(B(x)))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 1 less node.
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
Q DP problem:
The TRS P consists of the following rules:
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(a(b(b(x)))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(b(a(b(b(x))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x)))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(B(x))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(x))
The TRS R consists of the following rules:
b(b(a(b(b(b(a(b(x)))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(B(x)))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(b(b(b(a(B(x)))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))) at position [0,0,0] we obtained the following new rules:
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(y0))))))))))))))) → B1(b(a(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(y0)))))))))))))))))))))))
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
Q DP problem:
The TRS P consists of the following rules:
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(a(b(b(x)))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(b(a(b(b(x))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(y0))))))))))))))) → B1(b(a(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(y0)))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(B(x))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(x))
The TRS R consists of the following rules:
b(b(a(b(b(b(a(b(x)))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(B(x)))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(b(b(b(a(B(x)))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 1 less node.
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
Q DP problem:
The TRS P consists of the following rules:
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(a(b(b(x)))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(b(a(b(b(x))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(B(x))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(x))
The TRS R consists of the following rules:
b(b(a(b(b(b(a(b(x)))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(B(x)))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(b(b(b(a(B(x)))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B1(b(a(b(b(b(a(b(x)))))))) → B1(b(b(a(b(b(x)))))) at position [0] we obtained the following new rules:
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x0)))))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x0)))))))))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(B(x0))))))))))) → B1(b(a(b(b(b(a(B(x0))))))))
B1(b(a(b(b(b(a(b(b(b(a(b(b(b(a(B(x0)))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(a(b(b(b(a(B(x0)))))))))))))) → B1(b(b(a(b(a(B(x0)))))))
B1(b(a(b(b(b(a(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x0)))))))))))))))))))))))
B1(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0))))))))))))))))))))) → B1(b(b(a(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x0))))))))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(x0))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(b(b(x0)))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(b(x0))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(x0)))))))))))))))))))
B1(b(a(b(b(b(a(b(a(b(b(b(a(b(x0)))))))))))))) → B1(b(b(a(b(a(b(b(b(a(b(a(b(b(b(a(b(b(x0))))))))))))))))))
B1(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0))))))))))))))))))))) → B1(b(b(a(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x0))))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0))))))))))))))) → B1(b(b(a(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x0))))))))))))))))))))
B1(b(a(b(b(b(a(b(a(b(b(b(a(B(x0)))))))))))))) → B1(b(b(a(b(a(b(b(b(a(B(x0)))))))))))
B1(b(a(b(b(b(a(b(b(b(a(b(b(b(a(B(x0)))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x0)))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(B(x0))))))))))) → B1(b(a(B(x0))))
B1(b(a(b(b(b(a(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x0)))))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0))))))))))))))) → B1(b(b(a(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(B(x0))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0))))))))))))))) → B1(b(b(a(b(b(a(B(x0))))))))
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
Q DP problem:
The TRS P consists of the following rules:
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x0)))))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x0)))))))))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(B(x0))))))))))) → B1(b(a(b(b(b(a(B(x0))))))))
B1(b(a(b(b(b(a(b(b(b(a(b(b(b(a(B(x0)))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(a(b(b(b(a(B(x0)))))))))))))) → B1(b(b(a(b(a(B(x0)))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(B(x))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(x))
B1(b(a(b(b(b(a(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x0)))))))))))))))))))))))
B1(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0))))))))))))))))))))) → B1(b(b(a(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x0))))))))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(a(b(b(x)))))
B1(b(a(b(b(b(a(b(b(a(b(x0))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(b(b(x0)))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(b(x0))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(x0)))))))))))))))))))
B1(b(a(b(b(b(a(b(a(b(b(b(a(b(x0)))))))))))))) → B1(b(b(a(b(a(b(b(b(a(b(a(b(b(b(a(b(b(x0))))))))))))))))))
B1(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0))))))))))))))))))))) → B1(b(b(a(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x0))))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(a(b(b(b(a(B(x0)))))))))))))) → B1(b(b(a(b(a(b(b(b(a(B(x0)))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0))))))))))))))) → B1(b(b(a(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x0))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(B(x0))))))))))) → B1(b(a(B(x0))))
B1(b(a(b(b(b(a(b(b(b(a(b(b(b(a(B(x0)))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x0)))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x0)))))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0))))))))))))))) → B1(b(b(a(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(B(x0))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0))))))))))))))) → B1(b(b(a(b(b(a(B(x0))))))))
The TRS R consists of the following rules:
b(b(a(b(b(b(a(b(x)))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(B(x)))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(b(b(b(a(B(x)))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 10 less nodes.
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
Q DP problem:
The TRS P consists of the following rules:
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x0)))))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x0)))))))))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(b(a(b(b(b(a(B(x0)))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(B(x))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(x))
B1(b(a(b(b(b(a(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x0)))))))))))))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(a(b(b(x)))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(x0))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(b(b(x0)))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(b(x0))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(x0)))))))))))))))))))
B1(b(a(b(b(b(a(b(b(b(a(b(b(b(a(B(x0)))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x0)))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x0)))))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(B(x0))))))))))))
The TRS R consists of the following rules:
b(b(a(b(b(b(a(b(x)))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(B(x)))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(b(b(b(a(B(x)))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B1(b(a(b(b(b(a(b(b(b(a(b(b(b(a(B(x0)))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x0))))))))))))))))))))) at position [0] we obtained the following new rules:
B1(b(a(b(b(b(a(b(b(b(a(b(b(b(a(B(y0)))))))))))))))) → B1(b(b(a(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(b(a(B(y0)))))))))))))))))))))))))))
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
Q DP problem:
The TRS P consists of the following rules:
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x0)))))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x0)))))))))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(b(a(b(b(b(a(B(y0)))))))))))))))) → B1(b(b(a(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(b(a(B(y0)))))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(b(a(b(b(b(a(B(x0)))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(B(x))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x0)))))))))))))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(x))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(a(b(b(x)))))
B1(b(a(b(b(b(a(b(b(a(b(x0))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(b(b(x0)))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(b(x0))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(x0)))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x0)))))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(B(x0))))))))))))
The TRS R consists of the following rules:
b(b(a(b(b(b(a(b(x)))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(B(x)))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(b(b(b(a(B(x)))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 1 less node.
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
Q DP problem:
The TRS P consists of the following rules:
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(a(b(b(x)))))
B1(b(a(b(b(b(a(b(b(a(b(x0))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(b(b(x0)))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x0)))))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(b(x0))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(x0)))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x0)))))))))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(b(a(b(b(b(a(B(x0)))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(B(x))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x0)))))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x0)))))))))))))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(x))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(B(x0))))))))))))
The TRS R consists of the following rules:
b(b(a(b(b(b(a(b(x)))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(B(x)))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(b(b(b(a(B(x)))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))) at position [0] we obtained the following new rules:
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0))))))))))))))) → B1(b(b(a(b(a(B(x0)))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0))))))))))))))) → B1(b(b(a(b(a(b(b(b(a(B(x0)))))))))))
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
Q DP problem:
The TRS P consists of the following rules:
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0))))))))))))))) → B1(b(b(a(b(a(B(x0)))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x0)))))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x0)))))))))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(b(a(b(b(b(a(B(x0)))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(B(x))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(x))
B1(b(a(b(b(b(a(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x0)))))))))))))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(a(b(b(x)))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(x0))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(b(b(x0)))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(b(x0))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(x0)))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0))))))))))))))) → B1(b(b(a(b(a(b(b(b(a(B(x0)))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x0)))))))))))))))))))))))))))
The TRS R consists of the following rules:
b(b(a(b(b(b(a(b(x)))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(B(x)))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(b(b(b(a(B(x)))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 2 less nodes.
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ 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
Q DP problem:
The TRS P consists of the following rules:
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(a(b(b(x)))))
B1(b(a(b(b(b(a(b(b(a(b(x0))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(b(b(x0)))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x0)))))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(b(x0))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(x0)))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x0)))))))))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(b(a(b(b(b(a(B(x0)))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(B(x))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x0)))))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x0)))))))))))))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(x))
The TRS R consists of the following rules:
b(b(a(b(b(b(a(b(x)))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(B(x)))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(b(b(b(a(B(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.B: 1
a: x0
B1: 0
b: 0
By semantic labelling [33] we obtain the following labelled TRS:Q DP problem:
The TRS P consists of the following rules:
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x))))))))))))))) → B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x0)))))))))))))))))))))) → B1.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x0)))))))))))))))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x0)))))))))))))))))))))) → B1.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.1(a.1(B.1(x0)))))))))))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x0)))))))))))))))))) → B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x0)))))))))))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x0)))))))))))))))))))))) → B1.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x0)))))))))))))))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x0)))))))))))))))) → B1.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x0)))))))))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(x)))))))) → B1.0(b.0(x))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x0)))))))))))))))))))))) → B1.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.1(a.1(B.0(x0)))))))))))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x))))))))))))))) → B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.1(a.1(B.0(x))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.1(x0))))))))))) → B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.1(x0)))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.1(x)))))))) → B1.0(b.1(x))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x0)))))))))))))))))) → B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x0)))))))))))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.1(x)))))))) → B1.0(b.0(a.0(b.0(b.1(x)))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x0)))))))))))))))))) → B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.1(a.1(B.0(x0)))))))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x0)))))))))))))))) → B1.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x0)))))))))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x))))))))))))))) → B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.1(a.1(B.1(x))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x))))))))))))))) → B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(x0))))))))))) → B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(x0)))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x0)))))))))))))))))) → B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.1(a.1(B.1(x0)))))))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(x0))))))))))))))) → B1.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(x0)))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(x)))))))) → B1.0(b.0(a.0(b.0(b.0(x)))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.1(x0))))))))))))))) → B1.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.1(x0)))))))))))))))))))
The TRS R consists of the following rules:
b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.1(x)))))))) → b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.1(x))))))))))))))
b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x))))))))))))))) → b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x))))))))))))))))))))))))))
b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x)))))))) → b.1(a.1(B.0(x)))
b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x))))))))))))))) → b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.1(a.1(B.0(x))))))))))))))))))))))
b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x)))))))) → b.1(a.1(B.1(x)))
b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(x)))))))) → b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(x))))))))))))))
b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x)))))))) → b.0(a.0(b.0(b.0(b.1(a.1(B.1(x)))))))
b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x)))))))) → b.0(a.0(b.0(b.0(b.1(a.1(B.0(x)))))))
b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x))))))))))))))) → b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.1(a.1(B.1(x))))))))))))))))))))))
b.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x))))))))) → b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x))))))))))))))))))))
b.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x))))))))) → b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.1(a.1(B.1(x))))))))))))))))
b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x))))))))))))))) → b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x))))))))))))))))))))))))))
b.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x))))))))) → b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x))))))))))))))))))))
b.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x))))))))) → b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.1(a.1(B.0(x))))))))))))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ 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
Q DP problem:
The TRS P consists of the following rules:
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x))))))))))))))) → B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x0)))))))))))))))))))))) → B1.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x0)))))))))))))))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x0)))))))))))))))))))))) → B1.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.1(a.1(B.1(x0)))))))))))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x0)))))))))))))))))) → B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x0)))))))))))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x0)))))))))))))))))))))) → B1.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x0)))))))))))))))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x0)))))))))))))))) → B1.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x0)))))))))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(x)))))))) → B1.0(b.0(x))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x0)))))))))))))))))))))) → B1.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.1(a.1(B.0(x0)))))))))))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x))))))))))))))) → B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.1(a.1(B.0(x))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.1(x0))))))))))) → B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.1(x0)))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.1(x)))))))) → B1.0(b.1(x))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x0)))))))))))))))))) → B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x0)))))))))))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.1(x)))))))) → B1.0(b.0(a.0(b.0(b.1(x)))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x0)))))))))))))))))) → B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.1(a.1(B.0(x0)))))))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x0)))))))))))))))) → B1.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x0)))))))))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x))))))))))))))) → B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.1(a.1(B.1(x))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x))))))))))))))) → B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(x0))))))))))) → B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(x0)))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x0)))))))))))))))))) → B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.1(a.1(B.1(x0)))))))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(x0))))))))))))))) → B1.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(x0)))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(x)))))))) → B1.0(b.0(a.0(b.0(b.0(x)))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.1(x0))))))))))))))) → B1.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.1(x0)))))))))))))))))))
The TRS R consists of the following rules:
b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.1(x)))))))) → b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.1(x))))))))))))))
b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x))))))))))))))) → b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x))))))))))))))))))))))))))
b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x)))))))) → b.1(a.1(B.0(x)))
b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x))))))))))))))) → b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.1(a.1(B.0(x))))))))))))))))))))))
b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x)))))))) → b.1(a.1(B.1(x)))
b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(x)))))))) → b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(x))))))))))))))
b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x)))))))) → b.0(a.0(b.0(b.0(b.1(a.1(B.1(x)))))))
b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x)))))))) → b.0(a.0(b.0(b.0(b.1(a.1(B.0(x)))))))
b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x))))))))))))))) → b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.1(a.1(B.1(x))))))))))))))))))))))
b.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x))))))))) → b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x))))))))))))))))))))
b.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x))))))))) → b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.1(a.1(B.1(x))))))))))))))))
b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x))))))))))))))) → b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x))))))))))))))))))))))))))
b.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x))))))))) → b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x))))))))))))))))))))
b.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x))))))))) → b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.1(a.1(B.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 4 less nodes.
↳ QTRS
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ 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
↳ SemLabProof2
Q DP problem:
The TRS P consists of the following rules:
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x))))))))))))))) → B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x0)))))))))))))))))))))) → B1.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x0)))))))))))))))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x0)))))))))))))))))))))) → B1.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.1(a.1(B.1(x0)))))))))))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x0)))))))))))))))))) → B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x0)))))))))))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x0)))))))))))))))))))))) → B1.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x0)))))))))))))))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x0)))))))))))))))) → B1.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x0)))))))))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(x)))))))) → B1.0(b.0(x))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x0)))))))))))))))))))))) → B1.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.1(a.1(B.0(x0)))))))))))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.1(x0))))))))))) → B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.1(x0)))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x0)))))))))))))))))) → B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x0)))))))))))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x0)))))))))))))))))) → B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.1(a.1(B.0(x0)))))))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x0)))))))))))))))) → B1.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x0)))))))))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x))))))))))))))) → B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(x0))))))))))) → B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(x0)))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x0)))))))))))))))))) → B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.1(a.1(B.1(x0)))))))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(x0))))))))))))))) → B1.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(x0)))))))))))))))))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(x)))))))) → B1.0(b.0(a.0(b.0(b.0(x)))))
B1.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.1(x0))))))))))))))) → B1.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.1(x0)))))))))))))))))))
The TRS R consists of the following rules:
b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.1(x)))))))) → b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.1(x))))))))))))))
b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x))))))))))))))) → b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x))))))))))))))))))))))))))
b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x)))))))) → b.1(a.1(B.0(x)))
b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x))))))))))))))) → b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.1(a.1(B.0(x))))))))))))))))))))))
b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x)))))))) → b.1(a.1(B.1(x)))
b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(x)))))))) → b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(x))))))))))))))
b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x)))))))) → b.0(a.0(b.0(b.0(b.1(a.1(B.1(x)))))))
b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x)))))))) → b.0(a.0(b.0(b.0(b.1(a.1(B.0(x)))))))
b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x))))))))))))))) → b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.1(a.1(B.1(x))))))))))))))))))))))
b.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x))))))))) → b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x))))))))))))))))))))
b.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x))))))))) → b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.1(a.1(B.1(x))))))))))))))))
b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x))))))))))))))) → b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x))))))))))))))))))))))))))
b.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x))))))))) → b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.1(x))))))))))))))))))))
b.0(b.0(b.0(a.0(b.0(b.0(b.1(a.1(B.0(x))))))))) → b.0(a.0(b.0(b.0(b.0(a.0(b.0(a.0(b.0(b.0(b.0(a.0(b.0(b.1(a.1(B.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
↳ QTRS Reverse
↳ Strip Symbols Proof
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ 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
Q DP problem:
The TRS P consists of the following rules:
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(a(b(b(x)))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(x0))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(b(b(x0)))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x0)))))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(b(x0))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(x0)))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x0)))))))))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(b(a(b(b(b(a(B(x0)))))))))))))))) → B1(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x0)))))))))))))))))))))))))))
B1(b(a(b(b(b(a(b(b(a(b(b(a(b(b(b(a(B(x0)))))))))))))))))) → B1(b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x0)))))))))))))))))))))))
B1(b(a(b(b(b(a(b(x)))))))) → B1(b(x))
The TRS R consists of the following rules:
b(b(a(b(b(b(a(b(x)))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(x))))))))))))))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(B(x))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(B(x))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(B(x)))
b(b(b(a(b(b(b(a(B(x))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))))))))
b(b(a(b(b(b(a(b(b(a(b(b(b(a(B(x))))))))))))))) → b(a(b(b(b(a(b(a(b(b(b(a(b(b(a(b(b(b(a(b(a(b(b(b(a(B(x))))))))))))))))))))))))))
b(b(a(b(b(b(a(B(x)))))))) → b(a(b(b(b(a(B(x)))))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.