Termination w.r.t. Q of the following Term Rewriting System could not be shown:
Q restricted rewrite system:
The TRS R consists of the following rules:
a(a(a(x1))) → b(b(c(a(a(x1)))))
b(b(x1)) → c(a(b(x1)))
c(x1) → x1
Q is empty.
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QTRS Reverse
Q restricted rewrite system:
The TRS R consists of the following rules:
a(a(a(x1))) → b(b(c(a(a(x1)))))
b(b(x1)) → c(a(b(x1)))
c(x1) → x1
Q is empty.
We have reversed the following QTRS:
The set of rules R is
a(a(a(x1))) → b(b(c(a(a(x1)))))
b(b(x1)) → c(a(b(x1)))
c(x1) → x1
The set Q is empty.
We have obtained the following QTRS:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
The set Q is empty.
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ DependencyPairsProof
↳ QTRS Reverse
Q restricted rewrite system:
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → 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(b(x1)) → A(b(x1))
B(b(x1)) → C(a(b(x1)))
A(a(a(x1))) → C(a(a(x1)))
A(a(a(x1))) → B(c(a(a(x1))))
A(a(a(x1))) → B(b(c(a(a(x1)))))
The TRS R consists of the following rules:
a(a(a(x1))) → b(b(c(a(a(x1)))))
b(b(x1)) → c(a(b(x1)))
c(x1) → x1
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
B(b(x1)) → A(b(x1))
B(b(x1)) → C(a(b(x1)))
A(a(a(x1))) → C(a(a(x1)))
A(a(a(x1))) → B(c(a(a(x1))))
A(a(a(x1))) → B(b(c(a(a(x1)))))
The TRS R consists of the following rules:
a(a(a(x1))) → b(b(c(a(a(x1)))))
b(b(x1)) → c(a(b(x1)))
c(x1) → 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 2 less nodes.
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
B(b(x1)) → A(b(x1))
A(a(a(x1))) → B(c(a(a(x1))))
A(a(a(x1))) → B(b(c(a(a(x1)))))
The TRS R consists of the following rules:
a(a(a(x1))) → b(b(c(a(a(x1)))))
b(b(x1)) → c(a(b(x1)))
c(x1) → x1
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B(b(x1)) → A(b(x1)) at position [0] we obtained the following new rules:
B(b(b(x0))) → A(c(a(b(x0))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
B(b(b(x0))) → A(c(a(b(x0))))
A(a(a(x1))) → B(c(a(a(x1))))
A(a(a(x1))) → B(b(c(a(a(x1)))))
The TRS R consists of the following rules:
a(a(a(x1))) → b(b(c(a(a(x1)))))
b(b(x1)) → c(a(b(x1)))
c(x1) → x1
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A(a(a(x1))) → B(b(c(a(a(x1))))) at position [0] we obtained the following new rules:
A(a(a(a(a(x0))))) → B(b(c(a(b(b(c(a(a(x0)))))))))
A(a(a(y0))) → B(b(a(a(y0))))
A(a(a(a(x0)))) → B(b(c(b(b(c(a(a(x0))))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A(a(a(a(a(x0))))) → B(b(c(a(b(b(c(a(a(x0)))))))))
B(b(b(x0))) → A(c(a(b(x0))))
A(a(a(a(x0)))) → B(b(c(b(b(c(a(a(x0))))))))
A(a(a(y0))) → B(b(a(a(y0))))
A(a(a(x1))) → B(c(a(a(x1))))
The TRS R consists of the following rules:
a(a(a(x1))) → b(b(c(a(a(x1)))))
b(b(x1)) → c(a(b(x1)))
c(x1) → x1
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A(a(a(x1))) → B(c(a(a(x1)))) at position [0] we obtained the following new rules:
A(a(a(a(a(x0))))) → B(c(a(b(b(c(a(a(x0))))))))
A(a(a(a(x0)))) → B(c(b(b(c(a(a(x0)))))))
A(a(a(y0))) → B(a(a(y0)))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
B(b(b(x0))) → A(c(a(b(x0))))
A(a(a(a(a(x0))))) → B(b(c(a(b(b(c(a(a(x0)))))))))
A(a(a(y0))) → B(a(a(y0)))
A(a(a(a(x0)))) → B(b(c(b(b(c(a(a(x0))))))))
A(a(a(a(a(x0))))) → B(c(a(b(b(c(a(a(x0))))))))
A(a(a(a(x0)))) → B(c(b(b(c(a(a(x0)))))))
A(a(a(y0))) → B(b(a(a(y0))))
The TRS R consists of the following rules:
a(a(a(x1))) → b(b(c(a(a(x1)))))
b(b(x1)) → c(a(b(x1)))
c(x1) → 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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
Q restricted rewrite system:
The TRS R consists of the following rules:
a(a(a(x1))) → b(b(c(a(a(x1)))))
b(b(x1)) → c(a(b(x1)))
c(x1) → x1
B(b(b(x0))) → A(c(a(b(x0))))
A(a(a(a(a(x0))))) → B(b(c(a(b(b(c(a(a(x0)))))))))
A(a(a(y0))) → B(a(a(y0)))
A(a(a(a(x0)))) → B(b(c(b(b(c(a(a(x0))))))))
A(a(a(a(a(x0))))) → B(c(a(b(b(c(a(a(x0))))))))
A(a(a(a(x0)))) → B(c(b(b(c(a(a(x0)))))))
A(a(a(y0))) → B(b(a(a(y0))))
Q is empty.
We have reversed the following QTRS:
The set of rules R is
a(a(a(x1))) → b(b(c(a(a(x1)))))
b(b(x1)) → c(a(b(x1)))
c(x1) → x1
B(b(b(x0))) → A(c(a(b(x0))))
A(a(a(a(a(x0))))) → B(b(c(a(b(b(c(a(a(x0)))))))))
A(a(a(y0))) → B(a(a(y0)))
A(a(a(a(x0)))) → B(b(c(b(b(c(a(a(x0))))))))
A(a(a(a(a(x0))))) → B(c(a(b(b(c(a(a(x0))))))))
A(a(a(a(x0)))) → B(c(b(b(c(a(a(x0)))))))
A(a(a(y0))) → B(b(a(a(y0))))
The set Q is empty.
We have obtained the following QTRS:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
The set Q is empty.
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QTRS Reverse
Q restricted rewrite system:
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have reversed the following QTRS:
The set of rules R is
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
The set Q is empty.
We have obtained the following QTRS:
a(a(a(x))) → b(b(c(a(a(x)))))
b(b(x)) → c(a(b(x)))
c(x) → x
B(b(b(x))) → A(c(a(b(x))))
A(a(a(a(a(x))))) → B(b(c(a(b(b(c(a(a(x)))))))))
A(a(a(x))) → B(a(a(x)))
A(a(a(a(x)))) → B(b(c(b(b(c(a(a(x))))))))
A(a(a(a(a(x))))) → B(c(a(b(b(c(a(a(x))))))))
A(a(a(a(x)))) → B(c(b(b(c(a(a(x)))))))
A(a(a(x))) → B(b(a(a(x))))
The set Q is empty.
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QTRS Reverse
Q restricted rewrite system:
The TRS R consists of the following rules:
a(a(a(x))) → b(b(c(a(a(x)))))
b(b(x)) → c(a(b(x)))
c(x) → x
B(b(b(x))) → A(c(a(b(x))))
A(a(a(a(a(x))))) → B(b(c(a(b(b(c(a(a(x)))))))))
A(a(a(x))) → B(a(a(x)))
A(a(a(a(x)))) → B(b(c(b(b(c(a(a(x))))))))
A(a(a(a(a(x))))) → B(c(a(b(b(c(a(a(x))))))))
A(a(a(a(x)))) → B(c(b(b(c(a(a(x)))))))
A(a(a(x))) → B(b(a(a(x))))
Q is empty.
We have reversed the following QTRS:
The set of rules R is
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
The set Q is empty.
We have obtained the following QTRS:
a(a(a(x))) → b(b(c(a(a(x)))))
b(b(x)) → c(a(b(x)))
c(x) → x
B(b(b(x))) → A(c(a(b(x))))
A(a(a(a(a(x))))) → B(b(c(a(b(b(c(a(a(x)))))))))
A(a(a(x))) → B(a(a(x)))
A(a(a(a(x)))) → B(b(c(b(b(c(a(a(x))))))))
A(a(a(a(a(x))))) → B(c(a(b(b(c(a(a(x))))))))
A(a(a(a(x)))) → B(c(b(b(c(a(a(x)))))))
A(a(a(x))) → B(b(a(a(x))))
The set Q is empty.
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ QTRS
↳ DependencyPairsProof
↳ QTRS Reverse
Q restricted rewrite system:
The TRS R consists of the following rules:
a(a(a(x))) → b(b(c(a(a(x)))))
b(b(x)) → c(a(b(x)))
c(x) → x
B(b(b(x))) → A(c(a(b(x))))
A(a(a(a(a(x))))) → B(b(c(a(b(b(c(a(a(x)))))))))
A(a(a(x))) → B(a(a(x)))
A(a(a(a(x)))) → B(b(c(b(b(c(a(a(x))))))))
A(a(a(a(a(x))))) → B(c(a(b(b(c(a(a(x))))))))
A(a(a(a(x)))) → B(c(b(b(c(a(a(x)))))))
A(a(a(x))) → B(b(a(a(x))))
Q is empty.
Using Dependency Pairs [1,15] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(a(A(x))))) → B1(a(c(B(x))))
A1(a(a(A(x)))) → C(b(b(c(b(B(x))))))
A1(a(a(a(A(x))))) → A1(c(b(B(x))))
A1(a(a(A(x)))) → B1(B(x))
A1(a(a(a(A(x))))) → C(b(B(x)))
B1(b(B(x))) → B1(a(c(A(x))))
A1(a(a(x))) → A1(a(c(b(b(x)))))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(b(B(x)))))))))
A1(a(a(x))) → A1(c(b(b(x))))
B1(b(B(x))) → A1(c(A(x)))
B1(b(x)) → A1(c(x))
A1(a(A(x))) → A1(a(b(B(x))))
B1(b(B(x))) → C(A(x))
A1(a(a(a(A(x))))) → C(b(b(a(c(B(x))))))
A1(a(a(A(x)))) → B1(c(b(B(x))))
A1(a(a(a(A(x))))) → B1(a(c(b(B(x)))))
A1(a(a(a(A(x))))) → B1(B(x))
B1(b(x)) → B1(a(c(x)))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(x)))) → A1(c(b(b(c(B(x))))))
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(B(x)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(b(B(x))))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(A(x)))) → C(b(B(x)))
A1(a(a(x))) → B1(b(x))
A1(a(A(x))) → B1(B(x))
A1(a(A(x))) → A1(b(B(x)))
A1(a(a(A(x)))) → B1(c(B(x)))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(B(x))))))))
A1(a(a(a(A(x))))) → A1(c(B(x)))
A1(a(A(x))) → A1(a(B(x)))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(x)))) → C(b(b(c(B(x)))))
A1(a(a(x))) → C(b(b(x)))
A1(a(a(a(A(x))))) → C(b(b(a(c(b(B(x)))))))
A1(a(a(A(x)))) → A1(c(b(b(c(b(B(x)))))))
A1(a(a(A(x)))) → C(B(x))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(x)))) → A1(a(c(b(b(c(B(x)))))))
A1(a(a(A(x)))) → A1(a(c(b(b(c(b(B(x))))))))
A1(a(A(x))) → A1(B(x))
A1(a(a(a(A(x))))) → C(B(x))
B1(b(x)) → C(x)
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(a(A(x))))) → B1(a(c(B(x))))
A1(a(a(A(x)))) → C(b(b(c(b(B(x))))))
A1(a(a(a(A(x))))) → A1(c(b(B(x))))
A1(a(a(A(x)))) → B1(B(x))
A1(a(a(a(A(x))))) → C(b(B(x)))
B1(b(B(x))) → B1(a(c(A(x))))
A1(a(a(x))) → A1(a(c(b(b(x)))))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(b(B(x)))))))))
A1(a(a(x))) → A1(c(b(b(x))))
B1(b(B(x))) → A1(c(A(x)))
B1(b(x)) → A1(c(x))
A1(a(A(x))) → A1(a(b(B(x))))
B1(b(B(x))) → C(A(x))
A1(a(a(a(A(x))))) → C(b(b(a(c(B(x))))))
A1(a(a(A(x)))) → B1(c(b(B(x))))
A1(a(a(a(A(x))))) → B1(a(c(b(B(x)))))
A1(a(a(a(A(x))))) → B1(B(x))
B1(b(x)) → B1(a(c(x)))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(x)))) → A1(c(b(b(c(B(x))))))
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(B(x)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(b(B(x))))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(A(x)))) → C(b(B(x)))
A1(a(a(x))) → B1(b(x))
A1(a(A(x))) → B1(B(x))
A1(a(A(x))) → A1(b(B(x)))
A1(a(a(A(x)))) → B1(c(B(x)))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(B(x))))))))
A1(a(a(a(A(x))))) → A1(c(B(x)))
A1(a(A(x))) → A1(a(B(x)))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(x)))) → C(b(b(c(B(x)))))
A1(a(a(x))) → C(b(b(x)))
A1(a(a(a(A(x))))) → C(b(b(a(c(b(B(x)))))))
A1(a(a(A(x)))) → A1(c(b(b(c(b(B(x)))))))
A1(a(a(A(x)))) → C(B(x))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(x)))) → A1(a(c(b(b(c(B(x)))))))
A1(a(a(A(x)))) → A1(a(c(b(b(c(b(B(x))))))))
A1(a(A(x))) → A1(B(x))
A1(a(a(a(A(x))))) → C(B(x))
B1(b(x)) → C(x)
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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 18 less nodes.
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(a(A(x))))) → B1(a(c(B(x))))
A1(a(a(a(A(x))))) → A1(c(b(B(x))))
B1(b(B(x))) → B1(a(c(A(x))))
A1(a(a(x))) → A1(a(c(b(b(x)))))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(b(B(x)))))))))
A1(a(a(x))) → A1(c(b(b(x))))
B1(b(B(x))) → A1(c(A(x)))
B1(b(x)) → A1(c(x))
A1(a(a(A(x)))) → B1(c(b(B(x))))
A1(a(a(a(A(x))))) → B1(a(c(b(B(x)))))
B1(b(x)) → B1(a(c(x)))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(B(x)))))))
A1(a(a(A(x)))) → A1(c(b(b(c(B(x))))))
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(b(B(x))))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(x)))) → B1(c(B(x)))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(B(x))))))))
A1(a(a(a(A(x))))) → A1(c(B(x)))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(x)))) → A1(c(b(b(c(b(B(x)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(x)))) → A1(a(c(b(b(c(B(x)))))))
A1(a(a(A(x)))) → A1(a(c(b(b(c(b(B(x))))))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B1(b(x)) → B1(a(c(x))) at position [0] we obtained the following new rules:
B1(b(x0)) → B1(a(x0))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(a(A(x))))) → B1(a(c(B(x))))
A1(a(a(a(A(x))))) → A1(c(b(B(x))))
A1(a(a(x))) → A1(a(c(b(b(x)))))
B1(b(B(x))) → B1(a(c(A(x))))
A1(a(a(x))) → A1(c(b(b(x))))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(b(B(x)))))))))
B1(b(x)) → A1(c(x))
B1(b(B(x))) → A1(c(A(x)))
A1(a(a(A(x)))) → B1(c(b(B(x))))
A1(a(a(a(A(x))))) → B1(a(c(b(B(x)))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(x)))) → A1(c(b(b(c(B(x))))))
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(B(x)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(b(B(x))))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(x)))) → B1(c(B(x)))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(B(x))))))))
A1(a(a(a(A(x))))) → A1(c(B(x)))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(x)))) → A1(c(b(b(c(b(B(x)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(x)))) → A1(a(c(b(b(c(B(x)))))))
A1(a(a(A(x)))) → A1(a(c(b(b(c(b(B(x))))))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B1(b(x)) → A1(c(x)) at position [0] we obtained the following new rules:
B1(b(x0)) → A1(x0)
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(a(A(x))))) → B1(a(c(B(x))))
A1(a(a(a(A(x))))) → A1(c(b(B(x))))
B1(b(B(x))) → B1(a(c(A(x))))
A1(a(a(x))) → A1(a(c(b(b(x)))))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(b(B(x)))))))))
A1(a(a(x))) → A1(c(b(b(x))))
B1(b(B(x))) → A1(c(A(x)))
A1(a(a(A(x)))) → B1(c(b(B(x))))
A1(a(a(a(A(x))))) → B1(a(c(b(B(x)))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(B(x)))))))
A1(a(a(A(x)))) → A1(c(b(b(c(B(x))))))
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(b(B(x))))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(x)))) → B1(c(B(x)))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(B(x))))))))
A1(a(a(a(A(x))))) → A1(c(B(x)))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(x)))) → A1(c(b(b(c(b(B(x)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
B1(b(x0)) → A1(x0)
A1(a(a(A(x)))) → A1(a(c(b(b(c(B(x)))))))
A1(a(a(A(x)))) → A1(a(c(b(b(c(b(B(x))))))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B1(b(B(x))) → B1(a(c(A(x)))) at position [0] we obtained the following new rules:
B1(b(B(y0))) → B1(a(A(y0)))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(a(A(x))))) → B1(a(c(B(x))))
A1(a(a(a(A(x))))) → A1(c(b(B(x))))
B1(b(B(y0))) → B1(a(A(y0)))
A1(a(a(x))) → A1(a(c(b(b(x)))))
A1(a(a(x))) → A1(c(b(b(x))))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(b(B(x)))))))))
B1(b(B(x))) → A1(c(A(x)))
A1(a(a(A(x)))) → B1(c(b(B(x))))
A1(a(a(a(A(x))))) → B1(a(c(b(B(x)))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(x)))) → A1(c(b(b(c(B(x))))))
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(B(x)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(b(B(x))))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(x)))) → B1(c(B(x)))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(B(x))))))))
A1(a(a(a(A(x))))) → A1(c(B(x)))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(x)))) → A1(c(b(b(c(b(B(x)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
B1(b(x0)) → A1(x0)
A1(a(a(A(x)))) → A1(a(c(b(b(c(B(x)))))))
A1(a(a(A(x)))) → A1(a(c(b(b(c(b(B(x))))))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(a(A(x))))) → B1(a(c(B(x))))
A1(a(a(a(A(x))))) → A1(c(b(B(x))))
A1(a(a(x))) → A1(a(c(b(b(x)))))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(b(B(x)))))))))
A1(a(a(x))) → A1(c(b(b(x))))
B1(b(B(x))) → A1(c(A(x)))
A1(a(a(A(x)))) → B1(c(b(B(x))))
A1(a(a(a(A(x))))) → B1(a(c(b(B(x)))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(B(x)))))))
A1(a(a(A(x)))) → A1(c(b(b(c(B(x))))))
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(b(B(x))))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(x)))) → B1(c(B(x)))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(B(x))))))))
A1(a(a(a(A(x))))) → A1(c(B(x)))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(x)))) → A1(c(b(b(c(b(B(x)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
B1(b(x0)) → A1(x0)
A1(a(a(A(x)))) → A1(a(c(b(b(c(B(x)))))))
A1(a(a(A(x)))) → A1(a(c(b(b(c(b(B(x))))))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B1(b(B(x))) → A1(c(A(x))) at position [0] we obtained the following new rules:
B1(b(B(y0))) → A1(A(y0))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(a(A(x))))) → B1(a(c(B(x))))
A1(a(a(a(A(x))))) → A1(c(b(B(x))))
A1(a(a(x))) → A1(a(c(b(b(x)))))
A1(a(a(x))) → A1(c(b(b(x))))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(b(B(x)))))))))
A1(a(a(A(x)))) → B1(c(b(B(x))))
A1(a(a(a(A(x))))) → B1(a(c(b(B(x)))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(x)))) → A1(c(b(b(c(B(x))))))
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(B(x)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(b(B(x))))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(x)))) → B1(c(B(x)))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(B(x))))))))
A1(a(a(a(A(x))))) → A1(c(B(x)))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(x)))) → A1(c(b(b(c(b(B(x)))))))
B1(b(B(y0))) → A1(A(y0))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
B1(b(x0)) → A1(x0)
A1(a(a(A(x)))) → A1(a(c(b(b(c(B(x)))))))
A1(a(a(A(x)))) → A1(a(c(b(b(c(b(B(x))))))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(a(A(x))))) → B1(a(c(B(x))))
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(b(B(x))))))))
A1(a(a(a(A(x))))) → A1(c(b(B(x))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(x))) → A1(a(c(b(b(x)))))
A1(a(a(x))) → B1(b(x))
A1(a(a(x))) → A1(c(b(b(x))))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(b(B(x)))))))))
A1(a(a(A(x)))) → B1(c(B(x)))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(B(x))))))))
A1(a(a(a(A(x))))) → A1(c(B(x)))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(x)))) → B1(c(b(B(x))))
A1(a(a(a(A(x))))) → B1(a(c(b(B(x)))))
A1(a(a(A(x)))) → A1(c(b(b(c(b(B(x)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
B1(b(x0)) → A1(x0)
A1(a(a(A(x)))) → A1(a(c(b(b(c(B(x)))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(x)))) → A1(a(c(b(b(c(b(B(x))))))))
A1(a(a(A(x)))) → A1(c(b(b(c(B(x))))))
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(B(x)))))))
A1(a(a(x))) → B1(x)
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(x))))) → B1(a(c(b(B(x))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → B1(a(b(B(y0))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(a(A(x))))) → B1(a(c(B(x))))
A1(a(a(a(A(x))))) → A1(c(b(B(x))))
A1(a(a(x))) → A1(a(c(b(b(x)))))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(b(B(x)))))))))
A1(a(a(x))) → A1(c(b(b(x))))
A1(a(a(A(x)))) → B1(c(b(B(x))))
A1(a(a(a(A(y0))))) → B1(a(b(B(y0))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(B(x)))))))
A1(a(a(A(x)))) → A1(c(b(b(c(B(x))))))
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(b(B(x))))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(x)))) → B1(c(B(x)))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(B(x))))))))
A1(a(a(a(A(x))))) → A1(c(B(x)))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(x)))) → A1(c(b(b(c(b(B(x)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
B1(b(x0)) → A1(x0)
A1(a(a(A(x)))) → A1(a(c(b(b(c(B(x)))))))
A1(a(a(A(x)))) → A1(a(c(b(b(c(b(B(x))))))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(a(A(x))))) → B1(a(c(B(x))))
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(b(B(x))))))))
A1(a(a(a(A(x))))) → A1(c(b(B(x))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(x))) → A1(a(c(b(b(x)))))
A1(a(a(x))) → B1(b(x))
A1(a(a(x))) → A1(c(b(b(x))))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(b(B(x)))))))))
A1(a(a(A(x)))) → B1(c(B(x)))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(B(x))))))))
A1(a(a(a(A(x))))) → A1(c(B(x)))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(x)))) → B1(c(b(B(x))))
A1(a(a(A(x)))) → A1(c(b(b(c(b(B(x)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
B1(b(x0)) → A1(x0)
A1(a(a(A(x)))) → A1(a(c(b(b(c(B(x)))))))
A1(a(a(A(x)))) → A1(a(c(b(b(c(b(B(x))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(x)))) → A1(c(b(b(c(B(x))))))
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(B(x)))))))
A1(a(a(x))) → B1(x)
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(x))))) → A1(c(b(B(x)))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(b(B(y0)))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(a(A(x))))) → B1(a(c(B(x))))
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(b(B(x))))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(x))) → B1(b(x))
A1(a(a(x))) → A1(a(c(b(b(x)))))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(b(B(x)))))))))
A1(a(a(x))) → A1(c(b(b(x))))
A1(a(a(A(x)))) → B1(c(B(x)))
A1(a(a(a(A(y0))))) → A1(b(B(y0)))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(B(x))))))))
A1(a(a(a(A(x))))) → A1(c(B(x)))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(x)))) → B1(c(b(B(x))))
A1(a(a(A(x)))) → A1(c(b(b(c(b(B(x)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
B1(b(x0)) → A1(x0)
A1(a(a(A(x)))) → A1(a(c(b(b(c(B(x)))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(x)))) → A1(a(c(b(b(c(b(B(x))))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(B(x)))))))
A1(a(a(A(x)))) → A1(c(b(b(c(B(x))))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(a(A(x))))) → B1(a(c(B(x))))
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(b(B(x))))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(x))) → A1(a(c(b(b(x)))))
A1(a(a(x))) → B1(b(x))
A1(a(a(x))) → A1(c(b(b(x))))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(b(B(x)))))))))
A1(a(a(A(x)))) → B1(c(B(x)))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(B(x))))))))
A1(a(a(a(A(x))))) → A1(c(B(x)))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(x)))) → B1(c(b(B(x))))
A1(a(a(A(x)))) → A1(c(b(b(c(b(B(x)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
B1(b(x0)) → A1(x0)
A1(a(a(A(x)))) → A1(a(c(b(b(c(B(x)))))))
A1(a(a(A(x)))) → A1(a(c(b(b(c(b(B(x))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(x)))) → A1(c(b(b(c(B(x))))))
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(B(x)))))))
A1(a(a(x))) → B1(x)
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(A(x)))) → B1(c(b(B(x)))) at position [0] we obtained the following new rules:
A1(a(a(A(y0)))) → B1(b(B(y0)))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(a(A(x))))) → B1(a(c(B(x))))
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(b(B(x))))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(x))) → B1(b(x))
A1(a(a(x))) → A1(a(c(b(b(x)))))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(b(B(x)))))))))
A1(a(a(x))) → A1(c(b(b(x))))
A1(a(a(A(x)))) → B1(c(B(x)))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(B(x))))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(x))))) → A1(c(B(x)))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(x)))) → A1(c(b(b(c(b(B(x)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
B1(b(x0)) → A1(x0)
A1(a(a(A(x)))) → A1(a(c(b(b(c(B(x)))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(x)))) → A1(a(c(b(b(c(b(B(x))))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(B(x)))))))
A1(a(a(A(x)))) → A1(c(b(b(c(B(x))))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(x))))) → B1(a(c(B(x)))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → B1(a(B(y0)))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(b(B(x))))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(x))) → A1(a(c(b(b(x)))))
A1(a(a(x))) → B1(b(x))
A1(a(a(x))) → A1(c(b(b(x))))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(b(B(x)))))))))
A1(a(a(A(x)))) → B1(c(B(x)))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(B(x))))))))
A1(a(a(a(A(x))))) → A1(c(B(x)))
A1(a(a(A(y0)))) → B1(b(B(y0)))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(x)))) → A1(c(b(b(c(b(B(x)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
B1(b(x0)) → A1(x0)
A1(a(a(A(x)))) → A1(a(c(b(b(c(B(x)))))))
A1(a(a(A(x)))) → A1(a(c(b(b(c(b(B(x))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(a(A(y0))))) → B1(a(B(y0)))
A1(a(a(A(x)))) → A1(c(b(b(c(B(x))))))
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(B(x)))))))
A1(a(a(x))) → B1(x)
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(b(B(x))))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(x))) → A1(a(c(b(b(x)))))
A1(a(a(x))) → B1(b(x))
A1(a(a(x))) → A1(c(b(b(x))))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(b(B(x)))))))))
A1(a(a(A(x)))) → B1(c(B(x)))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(B(x))))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(x))))) → A1(c(B(x)))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(x)))) → A1(c(b(b(c(b(B(x)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
B1(b(x0)) → A1(x0)
A1(a(a(A(x)))) → A1(a(c(b(b(c(B(x)))))))
A1(a(a(A(x)))) → A1(a(c(b(b(c(b(B(x))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(x)))) → A1(c(b(b(c(B(x))))))
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(B(x)))))))
A1(a(a(x))) → B1(x)
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(x))))) → A1(c(B(x))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(B(y0))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(b(B(x))))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(x))) → B1(b(x))
A1(a(a(x))) → A1(a(c(b(b(x)))))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(b(B(x)))))))))
A1(a(a(x))) → A1(c(b(b(x))))
A1(a(a(A(x)))) → B1(c(B(x)))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(B(x))))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(x)))) → A1(c(b(b(c(b(B(x)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(a(A(y0))))) → A1(B(y0))
B1(b(x0)) → A1(x0)
A1(a(a(A(x)))) → A1(a(c(b(b(c(B(x)))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(x)))) → A1(a(c(b(b(c(b(B(x))))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(B(x)))))))
A1(a(a(A(x)))) → A1(c(b(b(c(B(x))))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(b(B(x))))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(x))) → A1(a(c(b(b(x)))))
A1(a(a(x))) → B1(b(x))
A1(a(a(x))) → A1(c(b(b(x))))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(b(B(x)))))))))
A1(a(a(A(x)))) → B1(c(B(x)))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(B(x))))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(x)))) → A1(c(b(b(c(b(B(x)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
B1(b(x0)) → A1(x0)
A1(a(a(A(x)))) → A1(a(c(b(b(c(B(x)))))))
A1(a(a(A(x)))) → A1(a(c(b(b(c(b(B(x))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(x)))) → A1(c(b(b(c(B(x))))))
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(B(x)))))))
A1(a(a(x))) → B1(x)
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(A(x)))) → B1(c(B(x))) at position [0] we obtained the following new rules:
A1(a(a(A(y0)))) → B1(B(y0))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(b(B(x))))))))
A1(a(a(A(y0)))) → B1(B(y0))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(x))) → B1(b(x))
A1(a(a(x))) → A1(a(c(b(b(x)))))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(b(B(x)))))))))
A1(a(a(x))) → A1(c(b(b(x))))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(B(x))))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(x)))) → A1(c(b(b(c(b(B(x)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
B1(b(x0)) → A1(x0)
A1(a(a(A(x)))) → A1(a(c(b(b(c(B(x)))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(x)))) → A1(a(c(b(b(c(b(B(x))))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(B(x)))))))
A1(a(a(A(x)))) → A1(c(b(b(c(B(x))))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(b(B(x))))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(x))) → A1(a(c(b(b(x)))))
A1(a(a(x))) → B1(b(x))
A1(a(a(x))) → A1(c(b(b(x))))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(b(B(x)))))))))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(B(x))))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(x)))) → A1(c(b(b(c(b(B(x)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
B1(b(x0)) → A1(x0)
A1(a(a(A(x)))) → A1(a(c(b(b(c(B(x)))))))
A1(a(a(A(x)))) → A1(a(c(b(b(c(b(B(x))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(x)))) → A1(c(b(b(c(B(x))))))
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(B(x)))))))
A1(a(a(x))) → B1(x)
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(x))) → A1(a(c(b(b(x))))) at position [0] we obtained the following new rules:
A1(a(a(B(x0)))) → A1(a(c(b(a(c(A(x0)))))))
A1(a(a(x0))) → A1(a(c(b(a(c(x0))))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(b(B(x))))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(b(B(x)))))))))
A1(a(a(x))) → A1(c(b(b(x))))
A1(a(a(x0))) → A1(a(c(b(a(c(x0))))))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(B(x))))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(B(x0)))) → A1(a(c(b(a(c(A(x0)))))))
A1(a(a(A(x)))) → A1(c(b(b(c(b(B(x)))))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
B1(b(x0)) → A1(x0)
A1(a(a(A(x)))) → A1(a(c(b(b(c(B(x)))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(x)))) → A1(a(c(b(b(c(b(B(x))))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(B(x)))))))
A1(a(a(A(x)))) → A1(c(b(b(c(B(x))))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(x))) → A1(c(b(b(x)))) at position [0] we obtained the following new rules:
A1(a(a(x0))) → A1(c(b(a(c(x0)))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(B(x0)))) → A1(c(b(a(c(A(x0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(x0))) → A1(c(b(a(c(x0)))))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(b(B(x)))))))))
A1(a(a(x0))) → A1(a(c(b(a(c(x0))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(B(x0)))) → A1(c(b(a(c(A(x0))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(B(x)))))))
A1(a(a(A(x)))) → A1(c(b(b(c(B(x))))))
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(b(B(x))))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(B(x))))))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(B(x0)))) → A1(a(c(b(a(c(A(x0)))))))
A1(a(a(A(x)))) → A1(c(b(b(c(b(B(x)))))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(A(x)))) → A1(a(c(b(b(c(B(x)))))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(A(x)))) → A1(a(c(b(b(c(b(B(x))))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(b(B(x))))))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(c(b(B(y0))))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(x0))) → A1(c(b(a(c(x0)))))
A1(a(a(x0))) → A1(a(c(b(a(c(x0))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(B(x0)))) → A1(c(b(a(c(A(x0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(c(b(B(y0))))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(x)))) → A1(c(b(b(c(B(x))))))
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(B(x)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(b(B(x))))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(B(x))))))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(B(x0)))) → A1(a(c(b(a(c(A(x0)))))))
A1(a(a(A(x)))) → A1(c(b(b(c(b(B(x)))))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(A(x)))) → A1(a(c(b(b(c(B(x)))))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(A(x)))) → A1(a(c(b(b(c(b(B(x))))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(x))))) → A1(c(b(b(a(c(b(B(x)))))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(x0))) → A1(c(b(a(c(x0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(c(b(B(y0)))))))))
A1(a(a(x0))) → A1(a(c(b(a(c(x0))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(B(x0)))) → A1(c(b(a(c(A(x0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(c(b(B(y0))))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(B(x)))))))
A1(a(a(A(x)))) → A1(c(b(b(c(B(x))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(B(x))))))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(B(x0)))) → A1(a(c(b(a(c(A(x0)))))))
A1(a(a(A(x)))) → A1(c(b(b(c(b(B(x)))))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
B1(b(x0)) → A1(x0)
A1(a(a(A(x)))) → A1(a(c(b(b(c(B(x)))))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(A(x)))) → A1(a(c(b(b(c(b(B(x))))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(A(x)))) → A1(a(c(b(b(c(b(B(x)))))))) at position [0] we obtained the following new rules:
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(c(b(B(y0)))))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(x0))) → A1(c(b(a(c(x0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(c(b(B(y0)))))))))
A1(a(a(x0))) → A1(a(c(b(a(c(x0))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(B(x0)))) → A1(c(b(a(c(A(x0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(c(b(B(y0))))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(x)))) → A1(c(b(b(c(B(x))))))
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(B(x)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(B(x))))))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(B(x0)))) → A1(a(c(b(a(c(A(x0)))))))
A1(a(a(A(x)))) → A1(c(b(b(c(b(B(x)))))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(A(x)))) → A1(a(c(b(b(c(B(x)))))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(A(x)))) → A1(c(b(b(c(b(B(x))))))) at position [0] we obtained the following new rules:
A1(a(a(A(y0)))) → A1(c(b(a(c(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(x0))) → A1(c(b(a(c(x0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(c(b(B(y0)))))))))
A1(a(a(x0))) → A1(a(c(b(a(c(x0))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(B(x0)))) → A1(c(b(a(c(A(x0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(c(b(B(y0))))))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(B(x)))))))
A1(a(a(A(x)))) → A1(c(b(b(c(B(x))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(B(x))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(c(b(B(y0))))))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(B(x0)))) → A1(a(c(b(a(c(A(x0)))))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
B1(b(x0)) → A1(x0)
A1(a(a(A(x)))) → A1(a(c(b(b(c(B(x)))))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(x))))) → A1(a(c(b(b(a(c(B(x)))))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(c(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(x0))) → A1(c(b(a(c(x0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(c(b(B(y0)))))))))
A1(a(a(x0))) → A1(a(c(b(a(c(x0))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(B(x0)))) → A1(c(b(a(c(A(x0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(c(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(c(b(B(y0))))))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(A(x)))) → A1(c(b(b(c(B(x))))))
A1(a(a(a(A(x))))) → A1(c(b(b(a(c(B(x)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(c(b(a(c(c(b(B(y0))))))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(B(x0)))) → A1(a(c(b(a(c(A(x0)))))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(A(x)))) → A1(a(c(b(b(c(B(x)))))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(x))))) → A1(c(b(b(a(c(B(x))))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(c(B(y0))))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(x0))) → A1(c(b(a(c(x0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(c(x0))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(B(x0)))) → A1(c(b(a(c(A(x0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(c(b(B(y0))))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(c(B(y0)))))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(x)))) → A1(c(b(b(c(B(x))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(c(b(a(c(c(b(B(y0))))))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(B(x0)))) → A1(a(c(b(a(c(A(x0)))))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(c(B(y0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
B1(b(x0)) → A1(x0)
A1(a(a(A(x)))) → A1(a(c(b(b(c(B(x)))))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(A(x)))) → A1(a(c(b(b(c(B(x))))))) at position [0] we obtained the following new rules:
A1(a(a(A(y0)))) → A1(a(c(b(a(c(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(x0))) → A1(c(b(a(c(x0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(c(x0))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(c(B(y0))))))))
A1(a(a(B(x0)))) → A1(c(b(a(c(A(x0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(c(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(c(b(B(y0))))))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(A(x)))) → A1(c(b(b(c(B(x))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(c(b(B(y0))))))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(B(x0)))) → A1(a(c(b(a(c(A(x0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(A(x)))) → A1(c(b(b(c(B(x)))))) at position [0] we obtained the following new rules:
A1(a(a(A(y0)))) → A1(c(b(a(c(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(x0))) → A1(c(b(a(c(x0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(c(x0))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(c(B(y0))))))))
A1(a(a(B(x0)))) → A1(c(b(a(c(A(x0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(c(b(B(y0))))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(c(B(y0)))))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
A1(a(a(A(y0)))) → A1(c(b(a(c(c(b(B(y0))))))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(B(x0)))) → A1(a(c(b(a(c(A(x0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(c(B(y0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(B(x0)))) → A1(a(c(b(a(c(A(x0))))))) at position [0] we obtained the following new rules:
A1(a(a(B(y0)))) → A1(a(c(b(a(A(y0))))))
A1(a(a(B(y0)))) → A1(a(b(a(c(A(y0))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(x0))) → A1(c(b(a(c(x0)))))
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(c(b(B(y0)))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(c(x0))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(c(B(y0))))))))
A1(a(a(B(x0)))) → A1(c(b(a(c(A(x0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(c(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(c(b(B(y0))))))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(B(y0)))) → A1(a(b(a(c(A(y0))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(B(y0)))) → A1(a(c(b(a(A(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(x0))) → A1(a(c(b(a(c(x0)))))) at position [0] we obtained the following new rules:
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(y0))) → A1(a(b(a(c(y0)))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(x0))) → A1(c(b(a(c(x0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(y0))) → A1(a(b(a(c(y0)))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(c(B(y0))))))))
A1(a(a(B(x0)))) → A1(c(b(a(c(A(x0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(c(b(B(y0))))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(c(B(y0)))))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(B(y0)))) → A1(a(b(a(c(A(y0))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
A1(a(a(A(y0)))) → A1(c(b(a(c(c(b(B(y0))))))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(B(y0)))) → A1(a(c(b(a(A(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(c(B(y0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(x0))) → A1(c(b(a(c(x0))))) at position [0] we obtained the following new rules:
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(a(c(y0))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(c(b(B(y0)))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(y0))) → A1(a(b(a(c(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(c(B(y0))))))))
A1(a(a(B(x0)))) → A1(c(b(a(c(A(x0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(c(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(c(b(B(y0))))))))))
A1(a(a(y0))) → A1(b(a(c(y0))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(B(y0)))) → A1(a(b(a(c(A(y0))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(B(y0)))) → A1(a(c(b(a(A(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(B(x0)))) → A1(c(b(a(c(A(x0)))))) at position [0] we obtained the following new rules:
A1(a(a(B(y0)))) → A1(c(b(a(A(y0)))))
A1(a(a(B(y0)))) → A1(b(a(c(A(y0)))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(y0))) → A1(a(b(a(c(y0)))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(c(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(c(b(B(y0))))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(c(B(y0)))))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(y0))) → A1(b(a(c(y0))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(B(y0)))) → A1(b(a(c(A(y0)))))
A1(a(a(B(y0)))) → A1(a(b(a(c(A(y0))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
A1(a(a(A(y0)))) → A1(c(b(a(c(c(b(B(y0))))))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(B(y0)))) → A1(c(b(a(A(y0)))))
A1(a(a(B(y0)))) → A1(a(c(b(a(A(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(c(B(y0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(c(b(B(y0)))))))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(b(B(y0)))))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(y0))) → A1(a(b(a(c(y0)))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(c(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(b(B(y0)))))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(B(y0)))) → A1(b(a(c(A(y0)))))
A1(a(a(B(y0)))) → A1(a(b(a(c(A(y0))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(c(B(y0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(c(b(B(y0)))))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(c(B(y0))))))))
A1(a(a(y0))) → A1(b(a(c(y0))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(b(B(y0)))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(c(b(B(y0))))))))
A1(a(a(B(y0)))) → A1(c(b(a(A(y0)))))
A1(a(a(B(y0)))) → A1(a(c(b(a(A(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(c(b(B(y0))))))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(b(B(y0))))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(y0))) → A1(a(b(a(c(y0)))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(c(B(y0)))))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(B(y0)))) → A1(b(a(c(A(y0)))))
A1(a(a(B(y0)))) → A1(a(b(a(c(A(y0))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(c(b(B(y0)))))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(c(B(y0))))))))
A1(a(a(y0))) → A1(b(a(c(y0))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(b(B(y0))))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(b(B(y0)))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(c(b(B(y0))))))))
A1(a(a(B(y0)))) → A1(a(c(b(a(A(y0))))))
A1(a(a(B(y0)))) → A1(c(b(a(A(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(A(y0)))) → A1(a(c(b(a(c(c(b(B(y0))))))))) at position [0] we obtained the following new rules:
A1(a(a(A(y0)))) → A1(a(b(a(c(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(b(B(y0))))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(a(b(a(c(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(y0))) → A1(a(b(a(c(y0)))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(c(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(b(B(y0)))))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(B(y0)))) → A1(b(a(c(A(y0)))))
A1(a(a(B(y0)))) → A1(a(b(a(c(A(y0))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(c(B(y0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(c(B(y0))))))))
A1(a(a(y0))) → A1(b(a(c(y0))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(b(B(y0))))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(b(B(y0)))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(b(B(y0))))))))
A1(a(a(B(y0)))) → A1(c(b(a(A(y0)))))
A1(a(a(B(y0)))) → A1(a(c(b(a(A(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(A(y0)))) → A1(c(b(a(c(c(b(B(y0)))))))) at position [0] we obtained the following new rules:
A1(a(a(A(y0)))) → A1(b(a(c(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(b(B(y0)))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(a(b(a(c(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(y0))) → A1(a(b(a(c(y0)))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(c(B(y0)))))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(B(y0)))) → A1(b(a(c(A(y0)))))
A1(a(a(B(y0)))) → A1(a(b(a(c(A(y0))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(A(y0)))) → A1(b(a(c(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(c(B(y0))))))))
A1(a(a(y0))) → A1(b(a(c(y0))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(b(B(y0))))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(b(B(y0)))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(b(B(y0))))))))
A1(a(a(B(y0)))) → A1(a(c(b(a(A(y0))))))
A1(a(a(B(y0)))) → A1(c(b(a(A(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(c(B(y0))))))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(B(y0))))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(a(b(a(c(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(y0))) → A1(a(b(a(c(y0)))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(b(B(y0)))))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(B(y0)))) → A1(b(a(c(A(y0)))))
A1(a(a(B(y0)))) → A1(a(b(a(c(A(y0))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(c(B(y0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(A(y0)))) → A1(b(a(c(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(c(B(y0))))))))
A1(a(a(y0))) → A1(b(a(c(y0))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(b(B(y0))))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(b(B(y0)))))))
A1(a(a(B(y0)))) → A1(c(b(a(A(y0)))))
A1(a(a(B(y0)))) → A1(a(c(b(a(A(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(c(B(y0)))))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(B(y0)))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(a(b(a(c(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(y0))) → A1(a(b(a(c(y0)))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(b(B(y0)))))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(B(y0)))) → A1(b(a(c(A(y0)))))
A1(a(a(B(y0)))) → A1(a(b(a(c(A(y0))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(A(y0)))) → A1(b(a(c(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(c(B(y0))))))))
A1(a(a(y0))) → A1(b(a(c(y0))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(b(B(y0))))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(b(B(y0))))))))
A1(a(a(B(y0)))) → A1(a(c(b(a(A(y0))))))
A1(a(a(B(y0)))) → A1(c(b(a(A(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(B(y0)))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(A(y0)))) → A1(a(c(b(a(c(c(B(y0)))))))) at position [0] we obtained the following new rules:
A1(a(a(A(y0)))) → A1(a(b(a(c(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(B(y0)))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(a(b(a(c(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(y0))) → A1(a(b(a(c(y0)))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(b(B(y0)))))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(B(y0)))) → A1(b(a(c(A(y0)))))
A1(a(a(B(y0)))) → A1(a(b(a(c(A(y0))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(A(y0)))) → A1(b(a(c(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(c(B(y0)))))))
A1(a(a(y0))) → A1(b(a(c(y0))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(b(B(y0))))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(b(B(y0)))))))
A1(a(a(B(y0)))) → A1(c(b(a(A(y0)))))
A1(a(a(B(y0)))) → A1(a(c(b(a(A(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(B(y0)))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(A(y0)))) → A1(c(b(a(c(c(B(y0))))))) at position [0] we obtained the following new rules:
A1(a(a(A(y0)))) → A1(c(b(a(c(B(y0))))))
A1(a(a(A(y0)))) → A1(b(a(c(c(B(y0))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(a(b(a(c(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → A1(c(b(a(c(B(y0))))))
A1(a(a(y0))) → A1(a(b(a(c(y0)))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(b(B(y0)))))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(y0)))) → A1(b(a(c(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(y0)))) → A1(a(c(b(a(c(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(B(y0)))) → A1(b(a(c(A(y0)))))
A1(a(a(B(y0)))) → A1(a(b(a(c(A(y0))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(A(y0)))) → A1(b(a(c(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(c(B(y0)))))))
A1(a(a(y0))) → A1(b(a(c(y0))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(b(B(y0))))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(b(B(y0))))))))
A1(a(a(B(y0)))) → A1(a(c(b(a(A(y0))))))
A1(a(a(B(y0)))) → A1(c(b(a(A(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(B(y0)))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(B(y0)))) → A1(a(c(b(a(A(y0)))))) at position [0] we obtained the following new rules:
A1(a(a(B(y0)))) → A1(a(b(a(A(y0)))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(a(b(a(c(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(y0))) → A1(a(b(a(c(y0)))))
A1(a(a(A(y0)))) → A1(c(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(b(B(y0)))))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(B(y0)))) → A1(a(b(a(A(y0)))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(y0)))) → A1(b(a(c(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(B(y0)))) → A1(b(a(c(A(y0)))))
A1(a(a(B(y0)))) → A1(a(b(a(c(A(y0))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(A(y0)))) → A1(b(a(c(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(c(B(y0)))))))
A1(a(a(y0))) → A1(b(a(c(y0))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(b(B(y0))))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(b(B(y0)))))))
A1(a(a(B(y0)))) → A1(c(b(a(A(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(B(y0)))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(a(b(a(c(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → A1(c(b(a(c(B(y0))))))
A1(a(a(y0))) → A1(a(b(a(c(y0)))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(b(B(y0)))))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(y0)))) → A1(b(a(c(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(B(y0)))) → A1(b(a(c(A(y0)))))
A1(a(a(B(y0)))) → A1(a(b(a(c(A(y0))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(A(y0)))) → A1(b(a(c(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(c(B(y0)))))))
A1(a(a(y0))) → A1(b(a(c(y0))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(b(B(y0))))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(b(B(y0)))))))
A1(a(a(B(y0)))) → A1(c(b(a(A(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(B(y0)))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(B(y0)))) → A1(a(b(a(c(A(y0)))))) at position [0] we obtained the following new rules:
A1(a(a(B(y0)))) → A1(a(b(a(A(y0)))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(a(b(a(c(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(y0))) → A1(a(b(a(c(y0)))))
A1(a(a(A(y0)))) → A1(c(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(b(B(y0)))))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(B(y0)))) → A1(a(b(a(A(y0)))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(y0)))) → A1(b(a(c(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(y0)))) → A1(a(c(b(a(c(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(B(y0)))) → A1(b(a(c(A(y0)))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(A(y0)))) → A1(b(a(c(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(c(B(y0)))))))
A1(a(a(y0))) → A1(b(a(c(y0))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(b(B(y0))))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(b(B(y0))))))))
A1(a(a(B(y0)))) → A1(c(b(a(A(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(B(y0)))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(a(b(a(c(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → A1(c(b(a(c(B(y0))))))
A1(a(a(y0))) → A1(a(b(a(c(y0)))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(b(B(y0)))))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(y0)))) → A1(b(a(c(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(B(y0)))) → A1(b(a(c(A(y0)))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(A(y0)))) → A1(b(a(c(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(c(B(y0)))))))
A1(a(a(y0))) → A1(b(a(c(y0))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(b(B(y0))))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(b(B(y0)))))))
A1(a(a(B(y0)))) → A1(c(b(a(A(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(B(y0)))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(y0))) → A1(a(b(a(c(y0))))) at position [0] we obtained the following new rules:
A1(a(a(x0))) → A1(a(b(a(x0))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(a(b(a(c(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → A1(c(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(b(B(y0)))))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(y0)))) → A1(b(a(c(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(y0)))) → A1(a(c(b(a(c(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(B(y0)))) → A1(b(a(c(A(y0)))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(A(y0)))) → A1(b(a(c(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(c(B(y0)))))))
A1(a(a(y0))) → A1(b(a(c(y0))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(b(B(y0))))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(b(B(y0))))))))
A1(a(a(B(y0)))) → A1(c(b(a(A(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(B(y0)))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(y0))) → A1(b(a(c(y0)))) at position [0] we obtained the following new rules:
A1(a(a(x0))) → A1(b(a(x0)))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(a(b(a(c(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → A1(c(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(b(B(y0)))))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(A(y0)))) → A1(b(a(c(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(B(y0)))) → A1(b(a(c(A(y0)))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(A(y0)))) → A1(b(a(c(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(c(B(y0)))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(b(B(y0))))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(b(B(y0)))))))
A1(a(a(B(y0)))) → A1(c(b(a(A(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(B(y0)))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(B(y0)))) → A1(c(b(a(A(y0))))) at position [0] we obtained the following new rules:
A1(a(a(B(y0)))) → A1(b(a(A(y0))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(a(b(a(c(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → A1(c(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(b(B(y0)))))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(y0)))) → A1(b(a(c(c(B(y0))))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(y0)))) → A1(a(c(b(a(c(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(B(y0)))) → A1(b(a(c(A(y0)))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(B(y0)))) → A1(b(a(A(y0))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(A(y0)))) → A1(b(a(c(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(b(B(y0))))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(B(y0)))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(a(b(a(c(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → A1(c(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(b(B(y0)))))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(A(y0)))) → A1(b(a(c(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(B(y0)))) → A1(b(a(c(A(y0)))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(A(y0)))) → A1(b(a(c(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(c(B(y0)))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(b(B(y0))))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(B(y0)))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(B(y0)))) → A1(b(a(c(A(y0))))) at position [0] we obtained the following new rules:
A1(a(a(B(y0)))) → A1(b(a(A(y0))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(a(b(a(c(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → A1(c(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(b(B(y0)))))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(y0)))) → A1(b(a(c(c(B(y0))))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(y0)))) → A1(a(c(b(a(c(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(B(y0)))) → A1(b(a(A(y0))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(A(y0)))) → A1(b(a(c(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(b(B(y0))))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(B(y0)))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(a(b(a(c(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → A1(c(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(b(B(y0)))))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(A(y0)))) → A1(b(a(c(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(A(y0)))) → A1(b(a(c(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(c(B(y0)))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(b(B(y0))))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(B(y0)))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(b(B(y0))))))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(b(B(y0))))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(a(b(a(c(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → A1(c(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(b(B(y0)))))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(y0)))) → A1(b(a(c(c(B(y0))))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(y0)))) → A1(a(c(b(a(c(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(A(y0)))) → A1(b(a(c(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(b(B(y0))))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(b(B(y0))))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(B(y0)))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(b(B(y0))))))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(b(B(y0))))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(a(b(a(c(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → A1(c(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(A(y0)))) → A1(b(a(c(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(A(y0)))) → A1(b(a(c(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(b(B(y0))))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(c(B(y0)))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(b(B(y0))))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(b(B(y0)))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(B(y0)))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(b(B(y0))))))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(b(B(y0))))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(a(b(a(c(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → A1(c(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(y0)))) → A1(b(a(c(c(B(y0))))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(y0)))) → A1(a(c(b(a(c(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(b(B(y0))))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(A(y0)))) → A1(b(a(c(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(b(B(y0))))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(b(B(y0))))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(B(y0)))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(b(B(y0)))))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(c(b(a(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(b(B(y0)))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(a(b(a(c(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → A1(c(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(A(y0)))) → A1(b(a(c(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(A(y0)))) → A1(b(a(c(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(b(B(y0))))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(c(B(y0)))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(b(B(y0))))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(B(y0)))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(b(B(y0)))))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(c(b(a(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(b(B(y0)))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(a(b(a(c(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → A1(c(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(y0)))) → A1(b(a(c(c(B(y0))))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(y0)))) → A1(a(c(b(a(c(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(b(B(y0))))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(A(y0)))) → A1(b(a(c(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(b(B(y0))))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(b(B(y0))))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(B(y0)))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(b(B(y0)))))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(b(a(c(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(b(B(y0)))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(a(b(a(c(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(b(B(y0)))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → A1(c(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(A(y0)))) → A1(b(a(c(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(A(y0)))) → A1(b(a(c(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(b(B(y0))))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(c(B(y0)))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(B(y0)))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(A(y0)))) → A1(a(b(a(c(c(b(B(y0)))))))) at position [0] we obtained the following new rules:
A1(a(a(A(y0)))) → A1(a(b(a(c(b(B(y0)))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → A1(c(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(y0)))) → A1(b(a(c(c(B(y0))))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(y0)))) → A1(a(c(b(a(c(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(b(B(y0))))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(A(y0)))) → A1(b(a(c(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(b(B(y0))))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(b(B(y0)))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(B(y0)))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(A(y0)))) → A1(a(c(b(a(c(b(B(y0)))))))) at position [0] we obtained the following new rules:
A1(a(a(A(y0)))) → A1(a(c(b(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(b(B(y0)))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(b(B(y0)))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → A1(c(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(A(y0)))) → A1(b(a(c(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(A(y0)))) → A1(b(a(c(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(b(B(y0))))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(b(B(y0)))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(B(y0)))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(A(y0)))) → A1(b(a(c(c(b(B(y0))))))) at position [0] we obtained the following new rules:
A1(a(a(A(y0)))) → A1(b(a(c(b(B(y0))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → A1(c(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(y0)))) → A1(b(a(c(c(B(y0))))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(y0)))) → A1(a(c(b(a(c(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(b(B(y0))))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(A(y0)))) → A1(a(c(b(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(b(B(y0))))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(b(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(B(y0)))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(A(y0)))) → A1(c(b(a(c(b(B(y0))))))) at position [0] we obtained the following new rules:
A1(a(a(A(y0)))) → A1(c(b(a(b(B(y0))))))
A1(a(a(A(y0)))) → A1(b(a(c(b(B(y0))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(b(B(y0)))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → A1(c(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(A(y0)))) → A1(b(a(c(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(A(y0)))) → A1(a(c(b(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(b(B(y0))))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(b(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(B(y0)))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(c(B(y0)))))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → A1(c(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(y0)))) → A1(b(a(c(c(B(y0))))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(y0)))) → A1(a(c(b(a(c(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(b(B(y0))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(A(y0)))) → A1(a(c(b(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(b(B(y0))))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(b(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(B(y0)))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(y0))))) → A1(a(c(b(a(c(a(B(y0)))))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(b(B(y0)))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → A1(c(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(A(y0)))) → A1(b(a(c(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(b(B(y0))))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(B(y0))))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(b(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(B(y0)))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(c(B(y0)))))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → A1(c(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(y0)))) → A1(b(a(c(c(B(y0))))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(y0)))) → A1(a(c(b(a(c(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(b(B(y0))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(b(B(y0))))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(b(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(B(y0)))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(y0))))) → A1(c(b(a(c(a(B(y0))))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(b(B(y0)))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → A1(c(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(A(y0)))) → A1(b(a(c(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(b(B(y0))))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(A(y0)))) → A1(a(b(a(c(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(y0))))) → A1(b(a(c(a(c(B(y0))))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → A1(c(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(y0)))) → A1(b(a(c(c(B(y0))))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(y0)))) → A1(a(c(b(a(c(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(b(B(y0))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(b(B(y0))))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(y0))))) → A1(c(b(a(a(c(B(y0))))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(b(B(y0)))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → A1(c(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(A(y0)))) → A1(b(a(c(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(c(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(b(B(y0))))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(A(y0)))) → A1(a(b(a(c(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(A(y0)))) → A1(a(b(a(c(c(B(y0))))))) at position [0] we obtained the following new rules:
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → A1(c(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(y0)))) → A1(b(a(c(c(B(y0))))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(y0)))) → A1(a(c(b(a(c(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(b(B(y0))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(b(B(y0))))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(A(y0)))) → A1(a(c(b(a(c(B(y0))))))) at position [0] we obtained the following new rules:
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(b(B(y0)))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → A1(c(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(A(y0)))) → A1(b(a(c(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(b(B(y0))))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(A(y0)))) → A1(c(b(a(c(B(y0)))))) at position [0] we obtained the following new rules:
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(A(y0)))) → A1(b(a(c(c(B(y0))))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(b(B(y0))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(b(B(y0))))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(A(y0)))) → A1(b(a(c(c(B(y0)))))) at position [0] we obtained the following new rules:
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(b(B(y0)))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(b(B(y0))))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(b(B(y0)))))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(a(b(a(a(b(B(y0)))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(b(B(y0))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(b(B(y0)))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(b(B(y0)))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(b(B(y0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(b(B(y0)))))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(a(b(a(a(b(B(y0)))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(b(B(y0)))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(b(B(y0)))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(c(b(a(b(B(y0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(b(B(y0)))))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(a(b(a(a(b(B(y0)))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(b(B(y0)))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(b(B(y0)))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(A(y0)))) → A1(c(b(a(b(B(y0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(y0))))) → A1(c(b(a(a(b(B(y0))))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(b(a(a(b(B(y0))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(b(B(y0))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(b(B(y0)))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(A(y0)))) → A1(c(b(a(b(B(y0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(y0))))) → A1(b(a(c(a(b(B(y0))))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(b(a(a(b(B(y0))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(b(B(y0))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(b(B(y0)))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(A(y0)))) → A1(c(b(a(b(B(y0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(y0))))) → A1(b(a(a(c(b(B(y0))))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(b(a(a(b(B(y0))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(b(B(y0))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(A(y0)))) → A1(c(b(a(b(B(y0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(A(y0)))) → A1(a(b(a(c(b(B(y0))))))) at position [0] we obtained the following new rules:
A1(a(a(A(y0)))) → A1(a(b(a(b(B(y0))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(a(b(a(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(a(c(b(a(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(b(B(y0))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(A(y0)))) → A1(a(c(b(a(b(B(y0))))))) at position [0] we obtained the following new rules:
A1(a(a(A(y0)))) → A1(a(b(a(b(B(y0))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(A(y0)))) → A1(c(b(a(b(B(y0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(a(b(a(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(b(B(y0))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(A(y0)))) → A1(b(a(c(b(B(y0)))))) at position [0] we obtained the following new rules:
A1(a(a(A(y0)))) → A1(b(a(b(B(y0)))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(y0)))) → A1(b(a(b(B(y0)))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(A(y0)))) → A1(c(b(a(b(B(y0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(A(y0)))) → A1(c(b(a(b(B(y0)))))) at position [0] we obtained the following new rules:
A1(a(a(A(y0)))) → A1(b(a(b(B(y0)))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(y0)))) → A1(b(a(b(B(y0)))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(y0))))) → A1(a(b(a(a(c(B(y0))))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(a(b(a(a(B(y0))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(y0))))) → A1(a(c(b(a(a(B(y0))))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(a(b(a(a(B(y0))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0)))))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(y0))))) → A1(a(b(a(c(a(B(y0))))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(a(b(a(a(B(y0))))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(a(a(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(y0))))) → A1(c(b(a(a(B(y0)))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(b(a(a(B(y0)))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(B(y0)))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0))))))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(y0))))) → A1(b(a(c(a(B(y0)))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(b(a(a(B(y0)))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(B(y0)))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(a(A(y0))))) → A1(b(a(a(c(B(y0)))))) at position [0] we obtained the following new rules:
A1(a(a(a(A(y0))))) → A1(b(a(a(B(y0)))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(a(A(y0))))) → A1(b(a(a(B(y0)))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(A(y0)))) → A1(a(b(a(c(B(y0)))))) at position [0] we obtained the following new rules:
A1(a(a(A(y0)))) → A1(a(b(a(B(y0)))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(A(y0)))) → A1(a(b(a(B(y0)))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(A(y0)))) → A1(a(c(b(a(B(y0)))))) at position [0] we obtained the following new rules:
A1(a(a(A(y0)))) → A1(a(b(a(B(y0)))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(A(y0)))) → A1(a(b(a(B(y0)))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(a(c(B(y0)))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(A(y0)))) → A1(b(a(c(B(y0))))) at position [0] we obtained the following new rules:
A1(a(a(A(y0)))) → A1(b(a(B(y0))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(a(B(y0))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(y0)))) → A1(c(b(a(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule A1(a(a(A(y0)))) → A1(c(b(a(B(y0))))) at position [0] we obtained the following new rules:
A1(a(a(A(y0)))) → A1(b(a(B(y0))))
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(y0)))) → A1(b(a(B(y0))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → B1(b(B(y0)))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(A(x)))) → B1(b(c(B(x))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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.c: x0
A1: 0
B: 1
a: 0
A: 0
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:
A1.0(a.0(a.0(A.0(y0)))) → A1.0(b.0(b.1(c.1(B.0(y0)))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(c.0(b.0(b.0(a.1(B.1(y0))))))
A1.0(a.0(a.1(x0))) → A1.0(c.0(b.0(a.1(x0))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.0(b.0(b.0(c.0(b.1(B.1(y0)))))))
A1.0(a.0(a.0(b.0(x0)))) → A1.0(a.0(c.0(b.0(b.0(a.0(c.0(x0)))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(c.0(b.0(b.0(a.0(b.1(B.0(y0)))))))
A1.0(a.0(a.1(x0))) → A1.0(a.0(c.0(b.0(a.1(x0)))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.0(b.0(b.1(c.1(B.1(y0))))))
A1.0(a.0(a.0(y0))) → A1.0(a.0(b.0(b.0(y0))))
A1.0(a.0(a.0(a.0(A.0(x))))) → B1.0(b.0(a.0(c.0(b.1(B.0(x))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.0(b.0(b.0(a.1(c.1(B.0(y0)))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(c.0(b.0(b.0(b.1(B.1(y0))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(b.0(b.1(c.1(B.1(y0)))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.0(c.0(b.0(b.0(b.1(B.1(y0)))))))
B1.0(b.1(x0)) → A1.1(x0)
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.0(b.0(b.0(c.0(b.1(B.0(y0)))))))
A1.0(a.0(a.0(x0))) → A1.0(a.0(c.0(b.0(a.0(x0)))))
A1.0(a.0(a.1(y0))) → A1.0(a.0(b.0(b.1(y0))))
A1.0(a.0(a.0(b.1(B.1(x0))))) → A1.0(a.0(c.0(b.0(b.0(a.0(c.0(A.1(x0))))))))
A1.0(a.0(a.0(b.1(x0)))) → A1.0(c.0(b.0(b.0(a.1(c.1(x0))))))
A1.0(a.0(a.0(y0))) → A1.0(b.0(b.0(y0)))
B1.0(b.0(x0)) → B1.0(a.0(x0))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(c.0(b.0(b.1(B.1(y0)))))
A1.0(a.0(a.1(x))) → B1.0(b.1(x))
A1.0(a.0(a.1(y0))) → A1.0(b.0(b.1(y0)))
A1.0(a.0(a.0(A.1(x)))) → B1.0(b.1(c.1(B.1(x))))
A1.0(a.0(a.0(b.1(B.0(x0))))) → A1.0(c.0(b.0(b.0(a.0(c.0(A.0(x0)))))))
A1.0(a.0(a.0(b.0(x0)))) → A1.0(c.0(b.0(b.0(a.0(c.0(x0))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(b.0(b.0(a.0(c.0(b.1(B.1(y0)))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(b.0(b.0(a.0(c.0(b.1(B.0(y0)))))))
A1.0(a.0(a.0(A.0(y0)))) → B1.0(b.1(B.0(y0)))
A1.0(a.0(a.0(x))) → B1.0(b.0(x))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.0(b.0(b.0(a.0(c.0(b.1(B.0(y0))))))))
A1.0(a.0(a.0(A.1(x)))) → B1.0(b.0(c.0(b.1(B.1(x)))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.0(c.0(b.0(b.0(a.0(b.1(B.1(y0))))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.0(b.0(b.0(a.1(c.1(B.1(y0)))))))
A1.0(a.0(a.0(A.1(y0)))) → B1.0(b.1(B.1(y0)))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.0(c.0(b.0(b.0(a.0(b.1(B.0(y0))))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.0(c.0(b.0(b.0(b.1(B.0(y0)))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.0(c.0(b.0(b.1(B.0(y0))))))
A1.0(a.0(a.0(b.1(x0)))) → A1.0(a.0(c.0(b.0(b.0(a.1(c.1(x0)))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(b.0(b.0(c.0(b.1(B.1(y0))))))
A1.0(a.0(a.1(x0))) → A1.0(b.0(a.1(x0)))
A1.0(a.0(a.0(x0))) → A1.0(a.0(b.0(a.0(x0))))
A1.0(a.0(a.0(A.0(x)))) → B1.0(b.0(c.0(b.1(B.0(x)))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(c.0(b.0(b.0(a.0(b.1(B.1(y0)))))))
A1.0(a.0(a.0(a.0(A.0(x))))) → B1.0(b.0(a.1(c.1(B.0(x)))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.0(c.0(b.0(b.0(a.1(B.1(y0)))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.0(c.0(b.0(b.0(a.1(B.0(y0)))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.0(b.0(b.0(a.0(c.0(b.1(B.1(y0))))))))
A1.0(a.0(a.0(x0))) → A1.0(b.0(a.0(x0)))
A1.0(a.0(a.0(a.0(A.1(x))))) → B1.0(b.0(a.1(c.1(B.1(x)))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(b.0(b.0(c.0(b.1(B.0(y0))))))
A1.0(a.0(a.0(b.1(B.0(x0))))) → A1.0(a.0(c.0(b.0(b.0(a.0(c.0(A.0(x0))))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(b.0(b.0(a.1(c.1(B.1(y0))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.0(b.0(b.1(c.1(B.0(y0))))))
B1.0(b.0(x0)) → A1.0(x0)
A1.0(a.0(a.1(x))) → B1.1(x)
A1.0(a.0(a.1(x0))) → A1.0(a.0(b.0(a.1(x0))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(b.0(b.0(a.1(c.1(B.0(y0))))))
B1.0(b.1(x0)) → B1.0(a.1(x0))
A1.0(a.0(a.0(x0))) → A1.0(c.0(b.0(a.0(x0))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.0(c.0(b.0(b.1(B.1(y0))))))
A1.0(a.0(a.0(x))) → B1.0(x)
A1.0(a.0(a.0(b.1(B.1(x0))))) → A1.0(c.0(b.0(b.0(a.0(c.0(A.1(x0)))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(c.0(b.0(b.1(B.0(y0)))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(c.0(b.0(b.0(a.1(B.0(y0))))))
A1.0(a.0(a.0(a.0(A.1(x))))) → B1.0(b.0(a.0(c.0(b.1(B.1(x))))))
A1.0(a.0(a.0(A.0(x)))) → B1.0(b.1(c.1(B.0(x))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(c.0(b.0(b.0(b.1(B.0(y0))))))
The TRS R consists of the following rules:
a.0(a.0(a.0(A.0(x)))) → a.0(a.0(c.0(b.0(b.1(c.1(B.0(x)))))))
a.0(a.0(A.1(x))) → a.0(a.1(B.1(x)))
a.0(a.0(a.0(x))) → a.0(a.0(c.0(b.0(b.0(x)))))
c.1(x) → x
a.0(a.0(a.0(a.0(A.1(x))))) → a.0(a.0(c.0(b.0(b.0(a.1(c.1(B.1(x))))))))
a.0(a.0(A.0(x))) → a.0(a.1(B.0(x)))
a.0(a.0(a.0(a.0(A.0(x))))) → a.0(a.0(c.0(b.0(b.0(a.1(c.1(B.0(x))))))))
a.0(a.0(a.0(A.1(x)))) → a.0(a.0(c.0(b.0(b.0(c.0(b.1(B.1(x))))))))
b.0(b.0(x)) → b.0(a.0(c.0(x)))
a.0(a.0(a.1(x))) → a.0(a.0(c.0(b.0(b.1(x)))))
a.0(a.0(a.0(A.1(x)))) → a.0(a.0(c.0(b.0(b.1(c.1(B.1(x)))))))
b.0(b.1(x)) → b.0(a.1(c.1(x)))
a.0(a.0(a.0(a.0(A.0(x))))) → a.0(a.0(c.0(b.0(b.0(a.0(c.0(b.1(B.0(x)))))))))
a.0(a.0(A.1(x))) → a.0(a.0(b.1(B.1(x))))
a.0(a.0(a.0(A.0(x)))) → a.0(a.0(c.0(b.0(b.0(c.0(b.1(B.0(x))))))))
b.0(b.1(B.1(x))) → b.0(a.0(c.0(A.1(x))))
a.0(a.0(a.0(a.0(A.1(x))))) → a.0(a.0(c.0(b.0(b.0(a.0(c.0(b.1(B.1(x)))))))))
c.0(x) → x
a.0(a.0(A.0(x))) → a.0(a.0(b.1(B.0(x))))
b.0(b.1(B.0(x))) → b.0(a.0(c.0(A.0(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ SemLabProof
↳ QDP
↳ DependencyGraphProof
↳ SemLabProof2
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1.0(a.0(a.0(A.0(y0)))) → A1.0(b.0(b.1(c.1(B.0(y0)))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(c.0(b.0(b.0(a.1(B.1(y0))))))
A1.0(a.0(a.1(x0))) → A1.0(c.0(b.0(a.1(x0))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.0(b.0(b.0(c.0(b.1(B.1(y0)))))))
A1.0(a.0(a.0(b.0(x0)))) → A1.0(a.0(c.0(b.0(b.0(a.0(c.0(x0)))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(c.0(b.0(b.0(a.0(b.1(B.0(y0)))))))
A1.0(a.0(a.1(x0))) → A1.0(a.0(c.0(b.0(a.1(x0)))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.0(b.0(b.1(c.1(B.1(y0))))))
A1.0(a.0(a.0(y0))) → A1.0(a.0(b.0(b.0(y0))))
A1.0(a.0(a.0(a.0(A.0(x))))) → B1.0(b.0(a.0(c.0(b.1(B.0(x))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.0(b.0(b.0(a.1(c.1(B.0(y0)))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(c.0(b.0(b.0(b.1(B.1(y0))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(b.0(b.1(c.1(B.1(y0)))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.0(c.0(b.0(b.0(b.1(B.1(y0)))))))
B1.0(b.1(x0)) → A1.1(x0)
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.0(b.0(b.0(c.0(b.1(B.0(y0)))))))
A1.0(a.0(a.0(x0))) → A1.0(a.0(c.0(b.0(a.0(x0)))))
A1.0(a.0(a.1(y0))) → A1.0(a.0(b.0(b.1(y0))))
A1.0(a.0(a.0(b.1(B.1(x0))))) → A1.0(a.0(c.0(b.0(b.0(a.0(c.0(A.1(x0))))))))
A1.0(a.0(a.0(b.1(x0)))) → A1.0(c.0(b.0(b.0(a.1(c.1(x0))))))
A1.0(a.0(a.0(y0))) → A1.0(b.0(b.0(y0)))
B1.0(b.0(x0)) → B1.0(a.0(x0))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(c.0(b.0(b.1(B.1(y0)))))
A1.0(a.0(a.1(x))) → B1.0(b.1(x))
A1.0(a.0(a.1(y0))) → A1.0(b.0(b.1(y0)))
A1.0(a.0(a.0(A.1(x)))) → B1.0(b.1(c.1(B.1(x))))
A1.0(a.0(a.0(b.1(B.0(x0))))) → A1.0(c.0(b.0(b.0(a.0(c.0(A.0(x0)))))))
A1.0(a.0(a.0(b.0(x0)))) → A1.0(c.0(b.0(b.0(a.0(c.0(x0))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(b.0(b.0(a.0(c.0(b.1(B.1(y0)))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(b.0(b.0(a.0(c.0(b.1(B.0(y0)))))))
A1.0(a.0(a.0(A.0(y0)))) → B1.0(b.1(B.0(y0)))
A1.0(a.0(a.0(x))) → B1.0(b.0(x))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.0(b.0(b.0(a.0(c.0(b.1(B.0(y0))))))))
A1.0(a.0(a.0(A.1(x)))) → B1.0(b.0(c.0(b.1(B.1(x)))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.0(c.0(b.0(b.0(a.0(b.1(B.1(y0))))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.0(b.0(b.0(a.1(c.1(B.1(y0)))))))
A1.0(a.0(a.0(A.1(y0)))) → B1.0(b.1(B.1(y0)))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.0(c.0(b.0(b.0(a.0(b.1(B.0(y0))))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.0(c.0(b.0(b.0(b.1(B.0(y0)))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.0(c.0(b.0(b.1(B.0(y0))))))
A1.0(a.0(a.0(b.1(x0)))) → A1.0(a.0(c.0(b.0(b.0(a.1(c.1(x0)))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(b.0(b.0(c.0(b.1(B.1(y0))))))
A1.0(a.0(a.1(x0))) → A1.0(b.0(a.1(x0)))
A1.0(a.0(a.0(x0))) → A1.0(a.0(b.0(a.0(x0))))
A1.0(a.0(a.0(A.0(x)))) → B1.0(b.0(c.0(b.1(B.0(x)))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(c.0(b.0(b.0(a.0(b.1(B.1(y0)))))))
A1.0(a.0(a.0(a.0(A.0(x))))) → B1.0(b.0(a.1(c.1(B.0(x)))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.0(c.0(b.0(b.0(a.1(B.1(y0)))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.0(c.0(b.0(b.0(a.1(B.0(y0)))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.0(b.0(b.0(a.0(c.0(b.1(B.1(y0))))))))
A1.0(a.0(a.0(x0))) → A1.0(b.0(a.0(x0)))
A1.0(a.0(a.0(a.0(A.1(x))))) → B1.0(b.0(a.1(c.1(B.1(x)))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(b.0(b.0(c.0(b.1(B.0(y0))))))
A1.0(a.0(a.0(b.1(B.0(x0))))) → A1.0(a.0(c.0(b.0(b.0(a.0(c.0(A.0(x0))))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(b.0(b.0(a.1(c.1(B.1(y0))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.0(b.0(b.1(c.1(B.0(y0))))))
B1.0(b.0(x0)) → A1.0(x0)
A1.0(a.0(a.1(x))) → B1.1(x)
A1.0(a.0(a.1(x0))) → A1.0(a.0(b.0(a.1(x0))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(b.0(b.0(a.1(c.1(B.0(y0))))))
B1.0(b.1(x0)) → B1.0(a.1(x0))
A1.0(a.0(a.0(x0))) → A1.0(c.0(b.0(a.0(x0))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.0(c.0(b.0(b.1(B.1(y0))))))
A1.0(a.0(a.0(x))) → B1.0(x)
A1.0(a.0(a.0(b.1(B.1(x0))))) → A1.0(c.0(b.0(b.0(a.0(c.0(A.1(x0)))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(c.0(b.0(b.1(B.0(y0)))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(c.0(b.0(b.0(a.1(B.0(y0))))))
A1.0(a.0(a.0(a.0(A.1(x))))) → B1.0(b.0(a.0(c.0(b.1(B.1(x))))))
A1.0(a.0(a.0(A.0(x)))) → B1.0(b.1(c.1(B.0(x))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(c.0(b.0(b.0(b.1(B.0(y0))))))
The TRS R consists of the following rules:
a.0(a.0(a.0(A.0(x)))) → a.0(a.0(c.0(b.0(b.1(c.1(B.0(x)))))))
a.0(a.0(A.1(x))) → a.0(a.1(B.1(x)))
a.0(a.0(a.0(x))) → a.0(a.0(c.0(b.0(b.0(x)))))
c.1(x) → x
a.0(a.0(a.0(a.0(A.1(x))))) → a.0(a.0(c.0(b.0(b.0(a.1(c.1(B.1(x))))))))
a.0(a.0(A.0(x))) → a.0(a.1(B.0(x)))
a.0(a.0(a.0(a.0(A.0(x))))) → a.0(a.0(c.0(b.0(b.0(a.1(c.1(B.0(x))))))))
a.0(a.0(a.0(A.1(x)))) → a.0(a.0(c.0(b.0(b.0(c.0(b.1(B.1(x))))))))
b.0(b.0(x)) → b.0(a.0(c.0(x)))
a.0(a.0(a.1(x))) → a.0(a.0(c.0(b.0(b.1(x)))))
a.0(a.0(a.0(A.1(x)))) → a.0(a.0(c.0(b.0(b.1(c.1(B.1(x)))))))
b.0(b.1(x)) → b.0(a.1(c.1(x)))
a.0(a.0(a.0(a.0(A.0(x))))) → a.0(a.0(c.0(b.0(b.0(a.0(c.0(b.1(B.0(x)))))))))
a.0(a.0(A.1(x))) → a.0(a.0(b.1(B.1(x))))
a.0(a.0(a.0(A.0(x)))) → a.0(a.0(c.0(b.0(b.0(c.0(b.1(B.0(x))))))))
b.0(b.1(B.1(x))) → b.0(a.0(c.0(A.1(x))))
a.0(a.0(a.0(a.0(A.1(x))))) → a.0(a.0(c.0(b.0(b.0(a.0(c.0(b.1(B.1(x)))))))))
c.0(x) → x
a.0(a.0(A.0(x))) → a.0(a.0(b.1(B.0(x))))
b.0(b.1(B.0(x))) → b.0(a.0(c.0(A.0(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 10 less nodes.
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ 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
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1.0(a.0(a.0(A.0(y0)))) → A1.0(b.0(b.1(c.1(B.0(y0)))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(c.0(b.0(b.0(a.1(B.1(y0))))))
A1.0(a.0(a.1(x0))) → A1.0(c.0(b.0(a.1(x0))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.0(b.0(b.0(c.0(b.1(B.1(y0)))))))
A1.0(a.0(a.0(b.0(x0)))) → A1.0(a.0(c.0(b.0(b.0(a.0(c.0(x0)))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(c.0(b.0(b.0(a.0(b.1(B.0(y0)))))))
A1.0(a.0(a.1(x0))) → A1.0(a.0(c.0(b.0(a.1(x0)))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.0(b.0(b.1(c.1(B.1(y0))))))
A1.0(a.0(a.0(y0))) → A1.0(a.0(b.0(b.0(y0))))
A1.0(a.0(a.0(a.0(A.0(x))))) → B1.0(b.0(a.0(c.0(b.1(B.0(x))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.0(b.0(b.0(a.1(c.1(B.0(y0)))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(c.0(b.0(b.0(b.1(B.1(y0))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(b.0(b.1(c.1(B.1(y0)))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.0(c.0(b.0(b.0(b.1(B.1(y0)))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.0(b.0(b.0(c.0(b.1(B.0(y0)))))))
A1.0(a.0(a.0(x0))) → A1.0(a.0(c.0(b.0(a.0(x0)))))
A1.0(a.0(a.1(y0))) → A1.0(a.0(b.0(b.1(y0))))
A1.0(a.0(a.0(b.1(x0)))) → A1.0(c.0(b.0(b.0(a.1(c.1(x0))))))
A1.0(a.0(a.0(b.1(B.1(x0))))) → A1.0(a.0(c.0(b.0(b.0(a.0(c.0(A.1(x0))))))))
A1.0(a.0(a.0(y0))) → A1.0(b.0(b.0(y0)))
B1.0(b.0(x0)) → B1.0(a.0(x0))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(c.0(b.0(b.1(B.1(y0)))))
A1.0(a.0(a.1(y0))) → A1.0(b.0(b.1(y0)))
A1.0(a.0(a.0(b.0(x0)))) → A1.0(c.0(b.0(b.0(a.0(c.0(x0))))))
A1.0(a.0(a.0(b.1(B.0(x0))))) → A1.0(c.0(b.0(b.0(a.0(c.0(A.0(x0)))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(b.0(b.0(a.0(c.0(b.1(B.1(y0)))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(b.0(b.0(a.0(c.0(b.1(B.0(y0)))))))
A1.0(a.0(a.0(x))) → B1.0(b.0(x))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.0(b.0(b.0(a.0(c.0(b.1(B.0(y0))))))))
A1.0(a.0(a.0(A.1(x)))) → B1.0(b.0(c.0(b.1(B.1(x)))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.0(c.0(b.0(b.0(a.0(b.1(B.1(y0))))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.0(b.0(b.0(a.1(c.1(B.1(y0)))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.0(c.0(b.0(b.0(a.0(b.1(B.0(y0))))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.0(c.0(b.0(b.0(b.1(B.0(y0)))))))
A1.0(a.0(a.0(b.1(x0)))) → A1.0(a.0(c.0(b.0(b.0(a.1(c.1(x0)))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(b.0(b.0(c.0(b.1(B.1(y0))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.0(c.0(b.0(b.1(B.0(y0))))))
A1.0(a.0(a.0(x0))) → A1.0(a.0(b.0(a.0(x0))))
A1.0(a.0(a.0(A.0(x)))) → B1.0(b.0(c.0(b.1(B.0(x)))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(c.0(b.0(b.0(a.0(b.1(B.1(y0)))))))
A1.0(a.0(a.0(a.0(A.0(x))))) → B1.0(b.0(a.1(c.1(B.0(x)))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.0(c.0(b.0(b.0(a.1(B.1(y0)))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.0(c.0(b.0(b.0(a.1(B.0(y0)))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.0(b.0(b.0(a.0(c.0(b.1(B.1(y0))))))))
A1.0(a.0(a.0(x0))) → A1.0(b.0(a.0(x0)))
A1.0(a.0(a.0(a.0(A.1(x))))) → B1.0(b.0(a.1(c.1(B.1(x)))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(b.0(b.0(c.0(b.1(B.0(y0))))))
A1.0(a.0(a.0(b.1(B.0(x0))))) → A1.0(a.0(c.0(b.0(b.0(a.0(c.0(A.0(x0))))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(b.0(b.0(a.1(c.1(B.1(y0))))))
B1.0(b.0(x0)) → A1.0(x0)
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.0(b.0(b.1(c.1(B.0(y0))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(b.0(b.0(a.1(c.1(B.0(y0))))))
A1.0(a.0(a.0(x0))) → A1.0(c.0(b.0(a.0(x0))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.0(c.0(b.0(b.1(B.1(y0))))))
A1.0(a.0(a.0(x))) → B1.0(x)
A1.0(a.0(a.0(b.1(B.1(x0))))) → A1.0(c.0(b.0(b.0(a.0(c.0(A.1(x0)))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(c.0(b.0(b.1(B.0(y0)))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(c.0(b.0(b.0(a.1(B.0(y0))))))
A1.0(a.0(a.0(a.0(A.1(x))))) → B1.0(b.0(a.0(c.0(b.1(B.1(x))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(c.0(b.0(b.0(b.1(B.0(y0))))))
The TRS R consists of the following rules:
a.0(a.0(a.0(A.0(x)))) → a.0(a.0(c.0(b.0(b.1(c.1(B.0(x)))))))
a.0(a.0(A.1(x))) → a.0(a.1(B.1(x)))
a.0(a.0(a.0(x))) → a.0(a.0(c.0(b.0(b.0(x)))))
c.1(x) → x
a.0(a.0(a.0(a.0(A.1(x))))) → a.0(a.0(c.0(b.0(b.0(a.1(c.1(B.1(x))))))))
a.0(a.0(A.0(x))) → a.0(a.1(B.0(x)))
a.0(a.0(a.0(a.0(A.0(x))))) → a.0(a.0(c.0(b.0(b.0(a.1(c.1(B.0(x))))))))
a.0(a.0(a.0(A.1(x)))) → a.0(a.0(c.0(b.0(b.0(c.0(b.1(B.1(x))))))))
b.0(b.0(x)) → b.0(a.0(c.0(x)))
a.0(a.0(a.1(x))) → a.0(a.0(c.0(b.0(b.1(x)))))
a.0(a.0(a.0(A.1(x)))) → a.0(a.0(c.0(b.0(b.1(c.1(B.1(x)))))))
b.0(b.1(x)) → b.0(a.1(c.1(x)))
a.0(a.0(a.0(a.0(A.0(x))))) → a.0(a.0(c.0(b.0(b.0(a.0(c.0(b.1(B.0(x)))))))))
a.0(a.0(A.1(x))) → a.0(a.0(b.1(B.1(x))))
a.0(a.0(a.0(A.0(x)))) → a.0(a.0(c.0(b.0(b.0(c.0(b.1(B.0(x))))))))
b.0(b.1(B.1(x))) → b.0(a.0(c.0(A.1(x))))
a.0(a.0(a.0(a.0(A.1(x))))) → a.0(a.0(c.0(b.0(b.0(a.0(c.0(b.1(B.1(x)))))))))
c.0(x) → x
a.0(a.0(A.0(x))) → a.0(a.0(b.1(B.0(x))))
b.0(b.1(B.0(x))) → b.0(a.0(c.0(A.0(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
As can be seen after transforming the QDP problem by semantic labelling [33] and then some rule deleting processors, only certain labelled rules and pairs can be used.
Hence, we only have to consider all unlabelled pairs and rules (without the decreasing rules for quasi-models).
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ 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
↳ SemLabProof
↳ SemLabProof2
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(x0))) → A1(b(a(x0)))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
B1(b(x0)) → B1(a(x0))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
B1(b(x0)) → A1(x0)
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
We found the following quasi-model for the rules of the TRS R.
Interpretation over the domain with elements from 0 to 1.c: 1
A1: 0
B: 0
a: 0
A: 0
B1: 0
b: 1
By semantic labelling [33] we obtain the following labelled TRS:Q DP problem:
The TRS P consists of the following rules:
A1.0(a.0(a.0(A.0(y0)))) → A1.0(b.1(b.1(c.0(B.0(y0)))))
A1.0(a.0(a.1(x0))) → A1.1(c.1(b.0(a.1(x0))))
A1.0(a.0(a.0(A.0(y0)))) → A1.1(c.1(b.1(b.1(b.0(B.0(y0))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.1(c.1(b.1(b.0(a.0(B.0(y0))))))
A1.0(a.0(a.0(y0))) → A1.0(b.1(b.0(y0)))
A1.0(a.0(a.0(A.0(x)))) → B1.1(b.1(c.1(b.0(B.0(x)))))
A1.0(a.0(a.1(b.1(x0)))) → A1.0(a.1(c.1(b.1(b.0(a.1(c.1(x0)))))))
A1.0(a.0(a.0(x0))) → A1.0(a.1(c.1(b.0(a.0(x0)))))
A1.0(a.0(a.0(a.0(A.0(x))))) → B1.1(b.0(a.1(c.1(b.0(B.0(x))))))
A1.0(a.0(a.0(x0))) → A1.1(c.1(b.0(a.0(x0))))
A1.0(a.0(a.1(x))) → B1.0(b.1(x))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(b.1(b.0(a.1(c.0(B.1(y0))))))
A1.0(a.0(a.1(x0))) → A1.0(a.1(b.0(a.1(x0))))
A1.0(a.0(a.0(A.1(x)))) → B1.1(b.1(c.1(b.0(B.1(x)))))
A1.0(a.0(a.0(A.1(y0)))) → A1.1(c.1(b.1(b.1(b.0(B.1(y0))))))
A1.0(a.0(a.0(a.0(A.0(x))))) → B1.1(b.0(a.1(c.0(B.0(x)))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.1(c.1(b.1(b.0(B.1(y0))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.1(c.1(b.1(b.0(a.1(b.0(B.0(y0)))))))
A1.0(a.0(a.0(x))) → B1.0(b.0(x))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.1(b.1(b.1(c.1(b.0(B.1(y0)))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.1(c.1(b.1(b.0(B.0(y0)))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.1(b.1(b.0(a.1(c.1(b.0(B.1(y0)))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.1(c.1(b.1(b.0(B.1(y0)))))
A1.0(a.0(a.1(x0))) → A1.0(a.1(c.1(b.0(a.1(x0)))))
A1.0(a.0(a.0(a.0(A.1(x))))) → B1.0(b.0(a.1(c.0(B.1(x)))))
A1.0(a.0(a.0(x0))) → A1.0(c.1(b.0(a.0(x0))))
A1.0(a.0(a.1(b.0(x0)))) → A1.0(c.1(b.1(b.0(a.1(c.0(x0))))))
A1.0(a.0(a.1(x0))) → A1.0(c.1(b.0(a.1(x0))))
A1.0(a.0(a.0(a.0(A.1(x))))) → B1.0(b.0(a.1(c.1(b.0(B.1(x))))))
A1.0(a.0(a.0(a.0(A.0(x))))) → B1.0(b.0(a.1(c.1(b.0(B.0(x))))))
A1.0(a.0(a.0(a.0(A.1(x))))) → B1.1(b.0(a.1(c.0(B.1(x)))))
A1.0(a.0(a.0(x0))) → A1.0(b.0(a.0(x0)))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.1(b.1(b.0(a.1(c.1(b.0(B.0(y0)))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(b.1(b.0(a.1(c.0(B.0(y0))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.1(c.1(b.1(b.0(a.0(B.1(y0))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.1(b.1(b.1(c.0(B.0(y0)))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.1(c.1(b.1(b.1(b.0(B.1(y0)))))))
A1.0(a.0(a.0(a.0(A.0(x))))) → B1.0(b.0(a.1(c.0(B.0(x)))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(c.1(b.1(b.0(a.0(B.0(y0))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(c.1(b.1(b.0(B.0(y0)))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(b.1(b.1(c.1(b.0(B.0(y0))))))
A1.0(a.0(a.0(x))) → B1.1(b.0(x))
A1.0(a.0(a.1(b.0(B.0(x0))))) → A1.0(a.1(c.1(b.1(b.0(a.1(c.0(A.0(x0))))))))
A1.0(a.0(a.1(b.1(x0)))) → A1.1(c.1(b.1(b.0(a.1(c.1(x0))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.1(b.1(b.0(a.1(c.1(b.0(B.0(y0))))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.1(b.1(b.1(c.1(b.0(B.0(y0)))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.1(b.1(b.0(a.1(c.1(b.0(B.1(y0))))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(c.1(b.1(b.0(a.0(B.1(y0))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.1(b.1(b.0(a.1(c.0(B.0(y0))))))
A1.0(a.0(a.1(y0))) → A1.1(b.1(b.1(y0)))
A1.0(a.0(a.0(a.0(A.1(x))))) → B1.1(b.0(a.1(c.1(b.0(B.1(x))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.1(c.1(b.1(b.0(a.0(B.1(y0)))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.1(c.1(b.1(b.0(a.1(b.0(B.1(y0))))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.1(b.1(b.1(c.0(B.0(y0))))))
A1.0(a.0(a.1(b.0(B.0(x0))))) → A1.0(c.1(b.1(b.0(a.1(c.0(A.0(x0)))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(b.1(b.0(a.1(c.1(b.0(B.0(y0)))))))
A1.0(a.0(a.1(y0))) → A1.0(a.1(b.1(b.1(y0))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.1(b.1(b.0(a.1(c.0(B.0(y0)))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.1(b.1(b.1(c.1(b.0(B.0(y0))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.1(b.1(b.0(a.1(c.0(B.1(y0))))))
B1.1(b.1(x0)) → A1.1(x0)
B1.1(b.1(x0)) → A1.0(x0)
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(c.1(b.1(b.0(a.1(b.0(B.1(y0)))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(c.1(b.1(b.1(b.0(B.0(y0))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(c.1(b.1(b.0(B.1(y0)))))
A1.0(a.0(a.1(b.0(x0)))) → A1.1(c.1(b.1(b.0(a.1(c.0(x0))))))
A1.0(a.0(a.0(y0))) → A1.0(a.1(b.1(b.0(y0))))
B1.1(b.0(x0)) → B1.0(a.0(x0))
A1.0(a.0(a.1(b.0(B.0(x0))))) → A1.1(c.1(b.1(b.0(a.1(c.0(A.0(x0)))))))
A1.0(a.0(a.1(y0))) → A1.0(b.1(b.1(y0)))
B1.1(b.1(x0)) → B1.0(a.1(x0))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(b.1(b.0(a.1(c.1(b.0(B.1(y0)))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.1(b.1(b.1(c.0(B.1(y0))))))
A1.0(a.0(a.1(b.0(x0)))) → A1.0(a.1(c.1(b.1(b.0(a.1(c.0(x0)))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(c.1(b.1(b.0(a.1(b.0(B.0(y0)))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.1(c.1(b.1(b.0(a.1(b.0(B.1(y0)))))))
A1.0(a.0(a.1(b.0(B.1(x0))))) → A1.0(a.1(c.1(b.1(b.0(a.1(c.0(A.1(x0))))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(b.1(b.1(c.1(b.0(B.1(y0))))))
A1.0(a.0(a.1(x0))) → A1.0(b.0(a.1(x0)))
A1.0(a.0(a.0(x0))) → A1.0(a.1(b.0(a.0(x0))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.1(c.1(b.1(b.1(b.0(B.0(y0)))))))
A1.0(a.0(a.1(b.0(B.1(x0))))) → A1.0(c.1(b.1(b.0(a.1(c.0(A.1(x0)))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.1(c.1(b.1(b.0(a.0(B.0(y0)))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(c.1(b.1(b.1(b.0(B.1(y0))))))
A1.0(a.0(a.0(y0))) → A1.1(b.1(b.0(y0)))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.1(b.1(b.0(a.1(c.0(B.1(y0)))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.1(c.1(b.1(b.0(B.0(y0))))))
A1.0(a.0(a.1(x))) → B1.1(x)
A1.0(a.0(a.0(A.1(x)))) → B1.0(b.1(c.1(b.0(B.1(x)))))
A1.0(a.0(a.0(x0))) → A1.1(b.0(a.0(x0)))
B1.1(b.0(x0)) → A1.0(x0)
A1.0(a.0(a.1(x0))) → A1.1(b.0(a.1(x0)))
A1.0(a.0(a.1(x))) → B1.0(x)
A1.0(a.0(a.1(x))) → B1.1(b.1(x))
A1.0(a.0(a.0(x))) → B1.0(x)
A1.0(a.0(a.1(b.0(B.1(x0))))) → A1.1(c.1(b.1(b.0(a.1(c.0(A.1(x0)))))))
A1.0(a.0(a.0(A.0(x)))) → B1.0(b.1(c.1(b.0(B.0(x)))))
A1.0(a.0(a.0(A.1(y0)))) → A1.1(b.1(b.1(c.0(B.1(y0)))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.1(c.1(b.1(b.0(a.1(b.0(B.0(y0))))))))
A1.0(a.0(a.1(b.1(x0)))) → A1.0(c.1(b.1(b.0(a.1(c.1(x0))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.1(b.1(b.1(c.1(b.0(B.1(y0))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(b.1(b.1(c.0(B.1(y0)))))
The TRS R consists of the following rules:
c.1(x) → x
A.1(x0) → A.0(x0)
b.1(x0) → b.0(x0)
a.0(a.0(a.0(x))) → a.0(a.1(c.1(b.1(b.0(x)))))
a.1(x0) → a.0(x0)
b.1(b.1(x)) → b.0(a.1(c.1(x)))
a.0(a.0(a.0(A.0(x)))) → a.0(a.1(c.1(b.1(b.1(c.0(B.0(x)))))))
a.0(a.0(a.0(a.0(A.1(x))))) → a.0(a.1(c.1(b.1(b.0(a.1(c.1(b.0(B.1(x)))))))))
a.0(a.0(A.0(x))) → a.0(a.0(B.0(x)))
b.1(b.0(B.0(x))) → b.0(a.1(c.0(A.0(x))))
a.0(a.0(a.0(A.0(x)))) → a.0(a.1(c.1(b.1(b.1(c.1(b.0(B.0(x))))))))
a.0(a.0(a.0(a.0(A.0(x))))) → a.0(a.1(c.1(b.1(b.0(a.1(c.1(b.0(B.0(x)))))))))
a.0(a.0(a.0(A.1(x)))) → a.0(a.1(c.1(b.1(b.1(c.1(b.0(B.1(x))))))))
a.0(a.0(A.1(x))) → a.0(a.1(b.0(B.1(x))))
B.1(x0) → B.0(x0)
a.0(a.0(a.0(A.1(x)))) → a.0(a.1(c.1(b.1(b.1(c.0(B.1(x)))))))
c.0(x) → x
c.1(x0) → c.0(x0)
b.1(b.0(x)) → b.0(a.1(c.0(x)))
a.0(a.0(A.0(x))) → a.0(a.1(b.0(B.0(x))))
b.1(b.0(B.1(x))) → b.0(a.1(c.0(A.1(x))))
a.0(a.0(a.1(x))) → a.0(a.1(c.1(b.1(b.1(x)))))
a.0(a.0(a.0(a.0(A.0(x))))) → a.0(a.1(c.1(b.1(b.0(a.1(c.0(B.0(x))))))))
a.0(a.0(a.0(a.0(A.1(x))))) → a.0(a.1(c.1(b.1(b.0(a.1(c.0(B.1(x))))))))
a.0(a.0(A.1(x))) → a.0(a.0(B.1(x)))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ 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
↳ SemLabProof
↳ QDP
↳ DependencyGraphProof
↳ SemLabProof2
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1.0(a.0(a.0(A.0(y0)))) → A1.0(b.1(b.1(c.0(B.0(y0)))))
A1.0(a.0(a.1(x0))) → A1.1(c.1(b.0(a.1(x0))))
A1.0(a.0(a.0(A.0(y0)))) → A1.1(c.1(b.1(b.1(b.0(B.0(y0))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.1(c.1(b.1(b.0(a.0(B.0(y0))))))
A1.0(a.0(a.0(y0))) → A1.0(b.1(b.0(y0)))
A1.0(a.0(a.0(A.0(x)))) → B1.1(b.1(c.1(b.0(B.0(x)))))
A1.0(a.0(a.1(b.1(x0)))) → A1.0(a.1(c.1(b.1(b.0(a.1(c.1(x0)))))))
A1.0(a.0(a.0(x0))) → A1.0(a.1(c.1(b.0(a.0(x0)))))
A1.0(a.0(a.0(a.0(A.0(x))))) → B1.1(b.0(a.1(c.1(b.0(B.0(x))))))
A1.0(a.0(a.0(x0))) → A1.1(c.1(b.0(a.0(x0))))
A1.0(a.0(a.1(x))) → B1.0(b.1(x))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(b.1(b.0(a.1(c.0(B.1(y0))))))
A1.0(a.0(a.1(x0))) → A1.0(a.1(b.0(a.1(x0))))
A1.0(a.0(a.0(A.1(x)))) → B1.1(b.1(c.1(b.0(B.1(x)))))
A1.0(a.0(a.0(A.1(y0)))) → A1.1(c.1(b.1(b.1(b.0(B.1(y0))))))
A1.0(a.0(a.0(a.0(A.0(x))))) → B1.1(b.0(a.1(c.0(B.0(x)))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.1(c.1(b.1(b.0(B.1(y0))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.1(c.1(b.1(b.0(a.1(b.0(B.0(y0)))))))
A1.0(a.0(a.0(x))) → B1.0(b.0(x))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.1(b.1(b.1(c.1(b.0(B.1(y0)))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.1(c.1(b.1(b.0(B.0(y0)))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.1(b.1(b.0(a.1(c.1(b.0(B.1(y0)))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.1(c.1(b.1(b.0(B.1(y0)))))
A1.0(a.0(a.1(x0))) → A1.0(a.1(c.1(b.0(a.1(x0)))))
A1.0(a.0(a.0(a.0(A.1(x))))) → B1.0(b.0(a.1(c.0(B.1(x)))))
A1.0(a.0(a.0(x0))) → A1.0(c.1(b.0(a.0(x0))))
A1.0(a.0(a.1(b.0(x0)))) → A1.0(c.1(b.1(b.0(a.1(c.0(x0))))))
A1.0(a.0(a.1(x0))) → A1.0(c.1(b.0(a.1(x0))))
A1.0(a.0(a.0(a.0(A.1(x))))) → B1.0(b.0(a.1(c.1(b.0(B.1(x))))))
A1.0(a.0(a.0(a.0(A.0(x))))) → B1.0(b.0(a.1(c.1(b.0(B.0(x))))))
A1.0(a.0(a.0(a.0(A.1(x))))) → B1.1(b.0(a.1(c.0(B.1(x)))))
A1.0(a.0(a.0(x0))) → A1.0(b.0(a.0(x0)))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.1(b.1(b.0(a.1(c.1(b.0(B.0(y0)))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(b.1(b.0(a.1(c.0(B.0(y0))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.1(c.1(b.1(b.0(a.0(B.1(y0))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.1(b.1(b.1(c.0(B.0(y0)))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.1(c.1(b.1(b.1(b.0(B.1(y0)))))))
A1.0(a.0(a.0(a.0(A.0(x))))) → B1.0(b.0(a.1(c.0(B.0(x)))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(c.1(b.1(b.0(a.0(B.0(y0))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(c.1(b.1(b.0(B.0(y0)))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(b.1(b.1(c.1(b.0(B.0(y0))))))
A1.0(a.0(a.0(x))) → B1.1(b.0(x))
A1.0(a.0(a.1(b.0(B.0(x0))))) → A1.0(a.1(c.1(b.1(b.0(a.1(c.0(A.0(x0))))))))
A1.0(a.0(a.1(b.1(x0)))) → A1.1(c.1(b.1(b.0(a.1(c.1(x0))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.1(b.1(b.0(a.1(c.1(b.0(B.0(y0))))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.1(b.1(b.1(c.1(b.0(B.0(y0)))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.1(b.1(b.0(a.1(c.1(b.0(B.1(y0))))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(c.1(b.1(b.0(a.0(B.1(y0))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.1(b.1(b.0(a.1(c.0(B.0(y0))))))
A1.0(a.0(a.1(y0))) → A1.1(b.1(b.1(y0)))
A1.0(a.0(a.0(a.0(A.1(x))))) → B1.1(b.0(a.1(c.1(b.0(B.1(x))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.1(c.1(b.1(b.0(a.0(B.1(y0)))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.1(c.1(b.1(b.0(a.1(b.0(B.1(y0))))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.1(b.1(b.1(c.0(B.0(y0))))))
A1.0(a.0(a.1(b.0(B.0(x0))))) → A1.0(c.1(b.1(b.0(a.1(c.0(A.0(x0)))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(b.1(b.0(a.1(c.1(b.0(B.0(y0)))))))
A1.0(a.0(a.1(y0))) → A1.0(a.1(b.1(b.1(y0))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.1(b.1(b.0(a.1(c.0(B.0(y0)))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.1(b.1(b.1(c.1(b.0(B.0(y0))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.1(b.1(b.0(a.1(c.0(B.1(y0))))))
B1.1(b.1(x0)) → A1.1(x0)
B1.1(b.1(x0)) → A1.0(x0)
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(c.1(b.1(b.0(a.1(b.0(B.1(y0)))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(c.1(b.1(b.1(b.0(B.0(y0))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(c.1(b.1(b.0(B.1(y0)))))
A1.0(a.0(a.1(b.0(x0)))) → A1.1(c.1(b.1(b.0(a.1(c.0(x0))))))
A1.0(a.0(a.0(y0))) → A1.0(a.1(b.1(b.0(y0))))
B1.1(b.0(x0)) → B1.0(a.0(x0))
A1.0(a.0(a.1(b.0(B.0(x0))))) → A1.1(c.1(b.1(b.0(a.1(c.0(A.0(x0)))))))
A1.0(a.0(a.1(y0))) → A1.0(b.1(b.1(y0)))
B1.1(b.1(x0)) → B1.0(a.1(x0))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(b.1(b.0(a.1(c.1(b.0(B.1(y0)))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.1(b.1(b.1(c.0(B.1(y0))))))
A1.0(a.0(a.1(b.0(x0)))) → A1.0(a.1(c.1(b.1(b.0(a.1(c.0(x0)))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(c.1(b.1(b.0(a.1(b.0(B.0(y0)))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.1(c.1(b.1(b.0(a.1(b.0(B.1(y0)))))))
A1.0(a.0(a.1(b.0(B.1(x0))))) → A1.0(a.1(c.1(b.1(b.0(a.1(c.0(A.1(x0))))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(b.1(b.1(c.1(b.0(B.1(y0))))))
A1.0(a.0(a.1(x0))) → A1.0(b.0(a.1(x0)))
A1.0(a.0(a.0(x0))) → A1.0(a.1(b.0(a.0(x0))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.1(c.1(b.1(b.1(b.0(B.0(y0)))))))
A1.0(a.0(a.1(b.0(B.1(x0))))) → A1.0(c.1(b.1(b.0(a.1(c.0(A.1(x0)))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.1(c.1(b.1(b.0(a.0(B.0(y0)))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(c.1(b.1(b.1(b.0(B.1(y0))))))
A1.0(a.0(a.0(y0))) → A1.1(b.1(b.0(y0)))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.1(b.1(b.0(a.1(c.0(B.1(y0)))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.1(c.1(b.1(b.0(B.0(y0))))))
A1.0(a.0(a.1(x))) → B1.1(x)
A1.0(a.0(a.0(A.1(x)))) → B1.0(b.1(c.1(b.0(B.1(x)))))
A1.0(a.0(a.0(x0))) → A1.1(b.0(a.0(x0)))
B1.1(b.0(x0)) → A1.0(x0)
A1.0(a.0(a.1(x0))) → A1.1(b.0(a.1(x0)))
A1.0(a.0(a.1(x))) → B1.0(x)
A1.0(a.0(a.1(x))) → B1.1(b.1(x))
A1.0(a.0(a.0(x))) → B1.0(x)
A1.0(a.0(a.1(b.0(B.1(x0))))) → A1.1(c.1(b.1(b.0(a.1(c.0(A.1(x0)))))))
A1.0(a.0(a.0(A.0(x)))) → B1.0(b.1(c.1(b.0(B.0(x)))))
A1.0(a.0(a.0(A.1(y0)))) → A1.1(b.1(b.1(c.0(B.1(y0)))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.1(c.1(b.1(b.0(a.1(b.0(B.0(y0))))))))
A1.0(a.0(a.1(b.1(x0)))) → A1.0(c.1(b.1(b.0(a.1(c.1(x0))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.1(b.1(b.1(c.1(b.0(B.1(y0))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(b.1(b.1(c.0(B.1(y0)))))
The TRS R consists of the following rules:
c.1(x) → x
A.1(x0) → A.0(x0)
b.1(x0) → b.0(x0)
a.0(a.0(a.0(x))) → a.0(a.1(c.1(b.1(b.0(x)))))
a.1(x0) → a.0(x0)
b.1(b.1(x)) → b.0(a.1(c.1(x)))
a.0(a.0(a.0(A.0(x)))) → a.0(a.1(c.1(b.1(b.1(c.0(B.0(x)))))))
a.0(a.0(a.0(a.0(A.1(x))))) → a.0(a.1(c.1(b.1(b.0(a.1(c.1(b.0(B.1(x)))))))))
a.0(a.0(A.0(x))) → a.0(a.0(B.0(x)))
b.1(b.0(B.0(x))) → b.0(a.1(c.0(A.0(x))))
a.0(a.0(a.0(A.0(x)))) → a.0(a.1(c.1(b.1(b.1(c.1(b.0(B.0(x))))))))
a.0(a.0(a.0(a.0(A.0(x))))) → a.0(a.1(c.1(b.1(b.0(a.1(c.1(b.0(B.0(x)))))))))
a.0(a.0(a.0(A.1(x)))) → a.0(a.1(c.1(b.1(b.1(c.1(b.0(B.1(x))))))))
a.0(a.0(A.1(x))) → a.0(a.1(b.0(B.1(x))))
B.1(x0) → B.0(x0)
a.0(a.0(a.0(A.1(x)))) → a.0(a.1(c.1(b.1(b.1(c.0(B.1(x)))))))
c.0(x) → x
c.1(x0) → c.0(x0)
b.1(b.0(x)) → b.0(a.1(c.0(x)))
a.0(a.0(A.0(x))) → a.0(a.1(b.0(B.0(x))))
b.1(b.0(B.1(x))) → b.0(a.1(c.0(A.1(x))))
a.0(a.0(a.1(x))) → a.0(a.1(c.1(b.1(b.1(x)))))
a.0(a.0(a.0(a.0(A.0(x))))) → a.0(a.1(c.1(b.1(b.0(a.1(c.0(B.0(x))))))))
a.0(a.0(a.0(a.0(A.1(x))))) → a.0(a.1(c.1(b.1(b.0(a.1(c.0(B.1(x))))))))
a.0(a.0(A.1(x))) → a.0(a.0(B.1(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 41 less nodes.
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ 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
↳ SemLabProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ RuleRemovalProof
↳ SemLabProof2
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.1(c.1(b.1(b.0(a.0(B.1(y0)))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(b.1(b.1(c.0(B.0(y0)))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.1(c.1(b.1(b.0(a.1(b.0(B.1(y0))))))))
A1.0(a.0(a.0(y0))) → A1.0(b.1(b.0(y0)))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.1(b.1(b.1(c.0(B.0(y0))))))
A1.0(a.0(a.0(A.0(x)))) → B1.1(b.1(c.1(b.0(B.0(x)))))
A1.0(a.0(a.1(b.1(x0)))) → A1.0(a.1(c.1(b.1(b.0(a.1(c.1(x0)))))))
A1.0(a.0(a.0(x0))) → A1.0(a.1(c.1(b.0(a.0(x0)))))
A1.0(a.0(a.1(b.0(B.0(x0))))) → A1.0(c.1(b.1(b.0(a.1(c.0(A.0(x0)))))))
A1.0(a.0(a.0(a.0(A.0(x))))) → B1.1(b.0(a.1(c.1(b.0(B.0(x))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(b.1(b.0(a.1(c.1(b.0(B.0(y0)))))))
A1.0(a.0(a.1(x0))) → A1.0(a.1(b.0(a.1(x0))))
A1.0(a.0(a.1(y0))) → A1.0(a.1(b.1(b.1(y0))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(b.1(b.0(a.1(c.0(B.1(y0))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.1(b.1(b.0(a.1(c.0(B.0(y0)))))))
A1.0(a.0(a.0(A.1(x)))) → B1.1(b.1(c.1(b.0(B.1(x)))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(c.1(b.1(b.0(B.1(y0)))))
B1.1(b.1(x0)) → A1.0(x0)
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(c.1(b.1(b.0(a.1(b.0(B.1(y0)))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(c.1(b.1(b.1(b.0(B.0(y0))))))
A1.0(a.0(a.0(a.0(A.0(x))))) → B1.1(b.0(a.1(c.0(B.0(x)))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.1(c.1(b.1(b.0(B.1(y0))))))
A1.0(a.0(a.0(y0))) → A1.0(a.1(b.1(b.0(y0))))
A1.0(a.0(a.1(y0))) → A1.0(b.1(b.1(y0)))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.1(b.1(b.1(c.1(b.0(B.1(y0)))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(b.1(b.0(a.1(c.1(b.0(B.1(y0)))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.1(b.1(b.1(c.0(B.1(y0))))))
A1.0(a.0(a.1(b.0(x0)))) → A1.0(a.1(c.1(b.1(b.0(a.1(c.0(x0)))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(c.1(b.1(b.0(a.1(b.0(B.0(y0)))))))
A1.0(a.0(a.1(x0))) → A1.0(a.1(c.1(b.0(a.1(x0)))))
A1.0(a.0(a.1(b.0(B.1(x0))))) → A1.0(a.1(c.1(b.1(b.0(a.1(c.0(A.1(x0))))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(b.1(b.1(c.1(b.0(B.1(y0))))))
A1.0(a.0(a.0(x0))) → A1.0(a.1(b.0(a.0(x0))))
A1.0(a.0(a.0(x0))) → A1.0(c.1(b.0(a.0(x0))))
A1.0(a.0(a.1(b.0(x0)))) → A1.0(c.1(b.1(b.0(a.1(c.0(x0))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.1(c.1(b.1(b.1(b.0(B.0(y0)))))))
A1.0(a.0(a.1(x0))) → A1.0(c.1(b.0(a.1(x0))))
A1.0(a.0(a.1(b.0(B.1(x0))))) → A1.0(c.1(b.1(b.0(a.1(c.0(A.1(x0)))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.1(c.1(b.1(b.0(a.0(B.0(y0)))))))
A1.0(a.0(a.0(a.0(A.1(x))))) → B1.1(b.0(a.1(c.0(B.1(x)))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(c.1(b.1(b.1(b.0(B.1(y0))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(b.1(b.0(a.1(c.0(B.0(y0))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.1(b.1(b.0(a.1(c.0(B.1(y0)))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.1(c.1(b.1(b.0(B.0(y0))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.1(c.1(b.1(b.1(b.0(B.1(y0)))))))
A1.0(a.0(a.1(x))) → B1.1(x)
A1.0(a.0(a.0(A.0(y0)))) → A1.0(c.1(b.1(b.0(B.0(y0)))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(c.1(b.1(b.0(a.0(B.0(y0))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(b.1(b.1(c.1(b.0(B.0(y0))))))
A1.0(a.0(a.0(x))) → B1.1(b.0(x))
B1.1(b.0(x0)) → A1.0(x0)
A1.0(a.0(a.1(b.0(B.0(x0))))) → A1.0(a.1(c.1(b.1(b.0(a.1(c.0(A.0(x0))))))))
A1.0(a.0(a.1(x))) → B1.1(b.1(x))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.1(b.1(b.0(a.1(c.1(b.0(B.0(y0))))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.1(b.1(b.1(c.1(b.0(B.0(y0)))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.1(b.1(b.0(a.1(c.1(b.0(B.1(y0))))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(c.1(b.1(b.0(a.0(B.1(y0))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.1(c.1(b.1(b.0(a.1(b.0(B.0(y0))))))))
A1.0(a.0(a.1(b.1(x0)))) → A1.0(c.1(b.1(b.0(a.1(c.1(x0))))))
A1.0(a.0(a.0(a.0(A.1(x))))) → B1.1(b.0(a.1(c.1(b.0(B.1(x))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(b.1(b.1(c.0(B.1(y0)))))
The TRS R consists of the following rules:
c.1(x) → x
A.1(x0) → A.0(x0)
b.1(x0) → b.0(x0)
a.0(a.0(a.0(x))) → a.0(a.1(c.1(b.1(b.0(x)))))
a.1(x0) → a.0(x0)
b.1(b.1(x)) → b.0(a.1(c.1(x)))
a.0(a.0(a.0(A.0(x)))) → a.0(a.1(c.1(b.1(b.1(c.0(B.0(x)))))))
a.0(a.0(a.0(a.0(A.1(x))))) → a.0(a.1(c.1(b.1(b.0(a.1(c.1(b.0(B.1(x)))))))))
a.0(a.0(A.0(x))) → a.0(a.0(B.0(x)))
b.1(b.0(B.0(x))) → b.0(a.1(c.0(A.0(x))))
a.0(a.0(a.0(A.0(x)))) → a.0(a.1(c.1(b.1(b.1(c.1(b.0(B.0(x))))))))
a.0(a.0(a.0(a.0(A.0(x))))) → a.0(a.1(c.1(b.1(b.0(a.1(c.1(b.0(B.0(x)))))))))
a.0(a.0(a.0(A.1(x)))) → a.0(a.1(c.1(b.1(b.1(c.1(b.0(B.1(x))))))))
a.0(a.0(A.1(x))) → a.0(a.1(b.0(B.1(x))))
B.1(x0) → B.0(x0)
a.0(a.0(a.0(A.1(x)))) → a.0(a.1(c.1(b.1(b.1(c.0(B.1(x)))))))
c.0(x) → x
c.1(x0) → c.0(x0)
b.1(b.0(x)) → b.0(a.1(c.0(x)))
a.0(a.0(A.0(x))) → a.0(a.1(b.0(B.0(x))))
b.1(b.0(B.1(x))) → b.0(a.1(c.0(A.1(x))))
a.0(a.0(a.1(x))) → a.0(a.1(c.1(b.1(b.1(x)))))
a.0(a.0(a.0(a.0(A.0(x))))) → a.0(a.1(c.1(b.1(b.0(a.1(c.0(B.0(x))))))))
a.0(a.0(a.0(a.0(A.1(x))))) → a.0(a.1(c.1(b.1(b.0(a.1(c.0(B.1(x))))))))
a.0(a.0(A.1(x))) → a.0(a.0(B.1(x)))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the rule removal processor [15] with the following polynomial ordering [25], at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented.
Strictly oriented rules of the TRS R:
A.1(x0) → A.0(x0)
B.1(x0) → B.0(x0)
Used ordering: POLO with Polynomial interpretation [25]:
POL(A.0(x1)) = x1
POL(A.1(x1)) = 1 + x1
POL(A1.0(x1)) = x1
POL(B.0(x1)) = x1
POL(B.1(x1)) = 1 + x1
POL(B1.1(x1)) = x1
POL(a.0(x1)) = x1
POL(a.1(x1)) = x1
POL(b.0(x1)) = x1
POL(b.1(x1)) = x1
POL(c.0(x1)) = x1
POL(c.1(x1)) = x1
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ 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
↳ SemLabProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ RuleRemovalProof
↳ QDP
↳ SemLabProof2
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.1(c.1(b.1(b.0(a.0(B.1(y0)))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(b.1(b.1(c.0(B.0(y0)))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.1(c.1(b.1(b.0(a.1(b.0(B.1(y0))))))))
A1.0(a.0(a.0(y0))) → A1.0(b.1(b.0(y0)))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.1(b.1(b.1(c.0(B.0(y0))))))
A1.0(a.0(a.0(A.0(x)))) → B1.1(b.1(c.1(b.0(B.0(x)))))
A1.0(a.0(a.1(b.1(x0)))) → A1.0(a.1(c.1(b.1(b.0(a.1(c.1(x0)))))))
A1.0(a.0(a.0(x0))) → A1.0(a.1(c.1(b.0(a.0(x0)))))
A1.0(a.0(a.1(b.0(B.0(x0))))) → A1.0(c.1(b.1(b.0(a.1(c.0(A.0(x0)))))))
A1.0(a.0(a.0(a.0(A.0(x))))) → B1.1(b.0(a.1(c.1(b.0(B.0(x))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(b.1(b.0(a.1(c.1(b.0(B.0(y0)))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(b.1(b.0(a.1(c.0(B.1(y0))))))
A1.0(a.0(a.1(x0))) → A1.0(a.1(b.0(a.1(x0))))
A1.0(a.0(a.1(y0))) → A1.0(a.1(b.1(b.1(y0))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.1(b.1(b.0(a.1(c.0(B.0(y0)))))))
A1.0(a.0(a.0(A.1(x)))) → B1.1(b.1(c.1(b.0(B.1(x)))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(c.1(b.1(b.1(b.0(B.0(y0))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(c.1(b.1(b.0(a.1(b.0(B.1(y0)))))))
B1.1(b.1(x0)) → A1.0(x0)
A1.0(a.0(a.0(A.1(y0)))) → A1.0(c.1(b.1(b.0(B.1(y0)))))
A1.0(a.0(a.0(a.0(A.0(x))))) → B1.1(b.0(a.1(c.0(B.0(x)))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.1(c.1(b.1(b.0(B.1(y0))))))
A1.0(a.0(a.0(y0))) → A1.0(a.1(b.1(b.0(y0))))
A1.0(a.0(a.1(y0))) → A1.0(b.1(b.1(y0)))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.1(b.1(b.1(c.1(b.0(B.1(y0)))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(b.1(b.0(a.1(c.1(b.0(B.1(y0)))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.1(b.1(b.1(c.0(B.1(y0))))))
A1.0(a.0(a.1(b.0(x0)))) → A1.0(a.1(c.1(b.1(b.0(a.1(c.0(x0)))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(c.1(b.1(b.0(a.1(b.0(B.0(y0)))))))
A1.0(a.0(a.1(x0))) → A1.0(a.1(c.1(b.0(a.1(x0)))))
A1.0(a.0(a.1(b.0(B.1(x0))))) → A1.0(a.1(c.1(b.1(b.0(a.1(c.0(A.1(x0))))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(b.1(b.1(c.1(b.0(B.1(y0))))))
A1.0(a.0(a.0(x0))) → A1.0(a.1(b.0(a.0(x0))))
A1.0(a.0(a.0(x0))) → A1.0(c.1(b.0(a.0(x0))))
A1.0(a.0(a.1(b.0(x0)))) → A1.0(c.1(b.1(b.0(a.1(c.0(x0))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.1(c.1(b.1(b.1(b.0(B.0(y0)))))))
A1.0(a.0(a.1(x0))) → A1.0(c.1(b.0(a.1(x0))))
A1.0(a.0(a.1(b.0(B.1(x0))))) → A1.0(c.1(b.1(b.0(a.1(c.0(A.1(x0)))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.1(c.1(b.1(b.0(a.0(B.0(y0)))))))
A1.0(a.0(a.0(a.0(A.1(x))))) → B1.1(b.0(a.1(c.0(B.1(x)))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(c.1(b.1(b.1(b.0(B.1(y0))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(b.1(b.0(a.1(c.0(B.0(y0))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.1(b.1(b.0(a.1(c.0(B.1(y0)))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.1(c.1(b.1(b.0(B.0(y0))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.1(c.1(b.1(b.1(b.0(B.1(y0)))))))
A1.0(a.0(a.1(x))) → B1.1(x)
A1.0(a.0(a.0(A.0(y0)))) → A1.0(c.1(b.1(b.0(B.0(y0)))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(c.1(b.1(b.0(a.0(B.0(y0))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(b.1(b.1(c.1(b.0(B.0(y0))))))
A1.0(a.0(a.0(x))) → B1.1(b.0(x))
B1.1(b.0(x0)) → A1.0(x0)
A1.0(a.0(a.1(b.0(B.0(x0))))) → A1.0(a.1(c.1(b.1(b.0(a.1(c.0(A.0(x0))))))))
A1.0(a.0(a.1(x))) → B1.1(b.1(x))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.1(b.1(b.1(c.1(b.0(B.0(y0)))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.1(b.1(b.0(a.1(c.1(b.0(B.0(y0))))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.1(b.1(b.0(a.1(c.1(b.0(B.1(y0))))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(c.1(b.1(b.0(a.0(B.1(y0))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.1(c.1(b.1(b.0(a.1(b.0(B.0(y0))))))))
A1.0(a.0(a.1(b.1(x0)))) → A1.0(c.1(b.1(b.0(a.1(c.1(x0))))))
A1.0(a.0(a.0(a.0(A.1(x))))) → B1.1(b.0(a.1(c.1(b.0(B.1(x))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(b.1(b.1(c.0(B.1(y0)))))
The TRS R consists of the following rules:
c.1(x) → x
b.1(x0) → b.0(x0)
a.0(a.0(a.0(x))) → a.0(a.1(c.1(b.1(b.0(x)))))
a.1(x0) → a.0(x0)
b.1(b.1(x)) → b.0(a.1(c.1(x)))
a.0(a.0(a.0(A.0(x)))) → a.0(a.1(c.1(b.1(b.1(c.0(B.0(x)))))))
a.0(a.0(a.0(a.0(A.1(x))))) → a.0(a.1(c.1(b.1(b.0(a.1(c.1(b.0(B.1(x)))))))))
a.0(a.0(A.0(x))) → a.0(a.0(B.0(x)))
b.1(b.0(B.0(x))) → b.0(a.1(c.0(A.0(x))))
a.0(a.0(a.0(A.0(x)))) → a.0(a.1(c.1(b.1(b.1(c.1(b.0(B.0(x))))))))
a.0(a.0(a.0(a.0(A.0(x))))) → a.0(a.1(c.1(b.1(b.0(a.1(c.1(b.0(B.0(x)))))))))
a.0(a.0(a.0(A.1(x)))) → a.0(a.1(c.1(b.1(b.1(c.1(b.0(B.1(x))))))))
a.0(a.0(A.1(x))) → a.0(a.1(b.0(B.1(x))))
a.0(a.0(a.0(A.1(x)))) → a.0(a.1(c.1(b.1(b.1(c.0(B.1(x)))))))
c.0(x) → x
c.1(x0) → c.0(x0)
b.1(b.0(x)) → b.0(a.1(c.0(x)))
a.0(a.0(A.0(x))) → a.0(a.1(b.0(B.0(x))))
b.1(b.0(B.1(x))) → b.0(a.1(c.0(A.1(x))))
a.0(a.0(a.1(x))) → a.0(a.1(c.1(b.1(b.1(x)))))
a.0(a.0(a.0(a.0(A.0(x))))) → a.0(a.1(c.1(b.1(b.0(a.1(c.0(B.0(x))))))))
a.0(a.0(a.0(a.0(A.1(x))))) → a.0(a.1(c.1(b.1(b.0(a.1(c.0(B.1(x))))))))
a.0(a.0(A.1(x))) → a.0(a.0(B.1(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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ 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
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(A(y0)))) → A1(b(b(c(B(y0)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(b(b(a(c(B(y0))))))
A1(a(a(x0))) → A1(a(c(b(a(x0)))))
A1(a(a(A(y0)))) → A1(c(b(b(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(b(B(y0))))))))
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(a(A(y0))))) → A1(a(c(b(b(a(B(y0)))))))
A1(a(a(x))) → B1(x)
A1(a(a(a(A(y0))))) → A1(c(b(b(a(b(B(y0)))))))
A1(a(a(a(A(y0))))) → A1(c(b(b(a(B(y0))))))
A1(a(a(b(B(x0))))) → A1(c(b(b(a(c(A(x0)))))))
A1(a(a(x))) → B1(b(x))
A1(a(a(A(y0)))) → A1(a(b(b(c(B(y0))))))
A1(a(a(A(y0)))) → A1(c(b(b(B(y0)))))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(A(y0)))) → A1(a(c(b(b(B(y0))))))
A1(a(a(x0))) → A1(a(b(a(x0))))
A1(a(a(b(B(x0))))) → A1(a(c(b(b(a(c(A(x0))))))))
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(B(y0)))))))
A1(a(a(A(y0)))) → A1(a(b(b(c(b(B(y0)))))))
A1(a(a(A(y0)))) → A1(b(b(c(b(B(y0))))))
A1(a(a(a(A(y0))))) → A1(a(b(b(a(c(b(B(y0))))))))
A1(a(a(b(x0)))) → A1(c(b(b(a(c(x0))))))
B1(b(x0)) → A1(x0)
A1(a(a(y0))) → A1(b(b(y0)))
A1(a(a(x0))) → A1(c(b(a(x0))))
A1(a(a(b(x0)))) → A1(a(c(b(b(a(c(x0)))))))
A1(a(a(y0))) → A1(a(b(b(y0))))
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(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.c: x0
A1: 0
B: 0
a: 0
A: 0
B1: 0
b: 1
By semantic labelling [33] we obtain the following labelled TRS:Q DP problem:
The TRS P consists of the following rules:
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.1(c.1(b.1(b.0(a.0(B.1(y0)))))))
A1.0(a.0(a.1(x0))) → A1.1(c.1(b.0(a.1(x0))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.1(b.1(b.0(a.0(c.0(B.0(y0))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.1(c.1(b.1(b.1(b.0(B.0(y0))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.1(c.1(b.1(b.0(a.1(b.0(B.1(y0))))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.1(c.1(b.1(b.0(a.0(B.0(y0))))))
A1.0(a.0(a.0(A.0(x)))) → B1.1(b.1(c.1(b.0(B.0(x)))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.1(b.1(b.0(a.0(c.0(B.1(y0)))))))
A1.0(a.0(a.1(b.1(x0)))) → A1.0(a.1(c.1(b.1(b.0(a.1(c.1(x0)))))))
A1.0(a.0(a.0(x0))) → A1.0(a.1(c.1(b.0(a.0(x0)))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.1(b.1(b.0(c.0(B.0(y0))))))
A1.0(a.0(a.0(a.0(A.0(x))))) → B1.1(b.0(a.1(c.1(b.0(B.0(x))))))
A1.0(a.0(a.0(x0))) → A1.1(c.1(b.0(a.0(x0))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.1(b.1(b.0(c.0(B.1(y0))))))
A1.0(a.0(a.1(x0))) → A1.0(a.1(b.0(a.1(x0))))
A1.0(a.0(a.1(y0))) → A1.0(a.1(b.1(b.1(y0))))
A1.0(a.0(a.1(b.0(B.1(x0))))) → A1.0(a.1(c.1(b.1(b.0(a.0(c.0(A.1(x0))))))))
A1.0(a.0(a.0(A.1(x)))) → B1.1(b.1(c.1(b.0(B.1(x)))))
A1.0(a.0(a.0(A.0(y0)))) → A1.1(b.1(b.1(c.1(b.0(B.0(y0))))))
B1.1(b.1(x0)) → A1.1(x0)
A1.0(a.0(a.0(A.1(y0)))) → A1.1(c.1(b.1(b.1(b.0(B.1(y0))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.1(c.1(b.1(b.0(B.1(y0))))))
A1.0(a.0(a.0(y0))) → A1.0(a.1(b.1(b.0(y0))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.1(c.1(b.1(b.0(a.1(b.0(B.0(y0)))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.1(b.1(b.1(c.1(b.0(B.1(y0)))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.1(c.1(b.1(b.0(B.0(y0)))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.1(b.1(b.0(a.0(c.0(B.0(y0)))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.1(b.1(b.0(a.1(c.1(b.0(B.1(y0)))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.1(b.1(b.0(a.0(c.0(B.1(y0))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.1(c.1(b.1(b.0(B.1(y0)))))
A1.0(a.0(a.1(x0))) → A1.0(a.1(c.1(b.0(a.1(x0)))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.1(c.1(b.1(b.0(a.1(b.0(B.1(y0)))))))
A1.0(a.0(a.1(b.0(x0)))) → A1.0(a.1(c.1(b.1(b.0(a.0(c.0(x0)))))))
A1.0(a.0(a.0(x0))) → A1.0(a.1(b.0(a.0(x0))))
A1.0(a.0(a.0(a.0(A.0(x))))) → B1.1(b.0(a.0(c.0(B.0(x)))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.1(c.1(b.1(b.1(b.0(B.0(y0)))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.1(b.1(b.0(c.0(B.1(y0)))))
A1.0(a.0(a.0(A.0(y0)))) → A1.1(b.1(b.0(c.0(B.0(y0)))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.1(c.1(b.1(b.0(a.0(B.0(y0)))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.1(b.1(b.0(a.1(c.1(b.0(B.0(y0)))))))
A1.0(a.0(a.1(b.0(x0)))) → A1.1(c.1(b.1(b.0(a.0(c.0(x0))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.1(c.1(b.1(b.0(a.0(B.1(y0))))))
A1.0(a.0(a.0(y0))) → A1.1(b.1(b.0(y0)))
A1.0(a.0(a.1(b.0(B.0(x0))))) → A1.1(c.1(b.1(b.0(a.0(c.0(A.0(x0)))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.1(c.1(b.1(b.0(B.0(y0))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.1(c.1(b.1(b.1(b.0(B.1(y0)))))))
A1.0(a.0(a.1(x))) → B1.1(x)
A1.0(a.0(a.0(x))) → B1.1(b.0(x))
B1.1(b.0(x0)) → A1.0(x0)
A1.0(a.0(a.0(a.0(A.1(x))))) → B1.1(b.0(a.0(c.0(B.1(x)))))
A1.0(a.0(a.1(b.0(B.0(x0))))) → A1.0(a.1(c.1(b.1(b.0(a.0(c.0(A.0(x0))))))))
A1.0(a.0(a.1(b.1(x0)))) → A1.1(c.1(b.1(b.0(a.1(c.1(x0))))))
A1.0(a.0(a.1(x))) → B1.1(b.1(x))
A1.0(a.0(a.0(x))) → B1.0(x)
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.1(b.1(b.0(a.1(c.1(b.0(B.0(y0))))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.1(b.1(b.1(c.1(b.0(B.0(y0)))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.1(b.1(b.0(a.1(c.1(b.0(B.1(y0))))))))
A1.0(a.0(a.1(b.0(B.1(x0))))) → A1.1(c.1(b.1(b.0(a.0(c.0(A.1(x0)))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.1(c.1(b.1(b.0(a.1(b.0(B.0(y0))))))))
A1.0(a.0(a.1(y0))) → A1.1(b.1(b.1(y0)))
A1.0(a.0(a.0(a.0(A.1(x))))) → B1.1(b.0(a.1(c.1(b.0(B.1(x))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.1(b.1(b.1(c.1(b.0(B.1(y0))))))
The TRS R consists of the following rules:
c.1(x) → x
a.0(a.0(A.0(x))) → a.0(a.1(b.0(B.0(x))))
b.1(b.0(B.1(x))) → b.0(a.0(c.0(A.1(x))))
a.0(a.0(a.0(x))) → a.0(a.1(c.1(b.1(b.0(x)))))
a.0(a.0(a.0(A.1(x)))) → a.0(a.1(c.1(b.1(b.0(c.0(B.1(x)))))))
b.1(b.0(B.0(x))) → b.0(a.0(c.0(A.0(x))))
b.1(b.1(x)) → b.0(a.1(c.1(x)))
a.0(a.0(a.0(a.0(A.1(x))))) → a.0(a.1(c.1(b.1(b.0(a.1(c.1(b.0(B.1(x)))))))))
a.0(a.0(a.1(x))) → a.0(a.1(c.1(b.1(b.1(x)))))
a.0(a.0(A.0(x))) → a.0(a.0(B.0(x)))
a.0(a.0(a.0(A.0(x)))) → a.0(a.1(c.1(b.1(b.1(c.1(b.0(B.0(x))))))))
a.0(a.0(a.0(a.0(A.0(x))))) → a.0(a.1(c.1(b.1(b.0(a.1(c.1(b.0(B.0(x)))))))))
a.0(a.0(a.0(A.1(x)))) → a.0(a.1(c.1(b.1(b.1(c.1(b.0(B.1(x))))))))
a.0(a.0(A.1(x))) → a.0(a.1(b.0(B.1(x))))
a.0(a.0(a.0(A.0(x)))) → a.0(a.1(c.1(b.1(b.0(c.0(B.0(x)))))))
a.0(a.0(a.0(a.0(A.1(x))))) → a.0(a.1(c.1(b.1(b.0(a.0(c.0(B.1(x))))))))
a.0(a.0(a.0(a.0(A.0(x))))) → a.0(a.1(c.1(b.1(b.0(a.0(c.0(B.0(x))))))))
c.0(x) → x
a.0(a.0(A.1(x))) → a.0(a.0(B.1(x)))
b.1(b.0(x)) → b.0(a.0(c.0(x)))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ 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
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ SemLabProof
↳ QDP
↳ DependencyGraphProof
↳ SemLabProof2
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.1(c.1(b.1(b.0(a.0(B.1(y0)))))))
A1.0(a.0(a.1(x0))) → A1.1(c.1(b.0(a.1(x0))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.1(b.1(b.0(a.0(c.0(B.0(y0))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.1(c.1(b.1(b.1(b.0(B.0(y0))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.1(c.1(b.1(b.0(a.1(b.0(B.1(y0))))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.1(c.1(b.1(b.0(a.0(B.0(y0))))))
A1.0(a.0(a.0(A.0(x)))) → B1.1(b.1(c.1(b.0(B.0(x)))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.1(b.1(b.0(a.0(c.0(B.1(y0)))))))
A1.0(a.0(a.1(b.1(x0)))) → A1.0(a.1(c.1(b.1(b.0(a.1(c.1(x0)))))))
A1.0(a.0(a.0(x0))) → A1.0(a.1(c.1(b.0(a.0(x0)))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.1(b.1(b.0(c.0(B.0(y0))))))
A1.0(a.0(a.0(a.0(A.0(x))))) → B1.1(b.0(a.1(c.1(b.0(B.0(x))))))
A1.0(a.0(a.0(x0))) → A1.1(c.1(b.0(a.0(x0))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.1(b.1(b.0(c.0(B.1(y0))))))
A1.0(a.0(a.1(x0))) → A1.0(a.1(b.0(a.1(x0))))
A1.0(a.0(a.1(y0))) → A1.0(a.1(b.1(b.1(y0))))
A1.0(a.0(a.1(b.0(B.1(x0))))) → A1.0(a.1(c.1(b.1(b.0(a.0(c.0(A.1(x0))))))))
A1.0(a.0(a.0(A.1(x)))) → B1.1(b.1(c.1(b.0(B.1(x)))))
A1.0(a.0(a.0(A.0(y0)))) → A1.1(b.1(b.1(c.1(b.0(B.0(y0))))))
B1.1(b.1(x0)) → A1.1(x0)
A1.0(a.0(a.0(A.1(y0)))) → A1.1(c.1(b.1(b.1(b.0(B.1(y0))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.1(c.1(b.1(b.0(B.1(y0))))))
A1.0(a.0(a.0(y0))) → A1.0(a.1(b.1(b.0(y0))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.1(c.1(b.1(b.0(a.1(b.0(B.0(y0)))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.1(b.1(b.1(c.1(b.0(B.1(y0)))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.1(c.1(b.1(b.0(B.0(y0)))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.1(b.1(b.0(a.0(c.0(B.0(y0)))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.1(b.1(b.0(a.1(c.1(b.0(B.1(y0)))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.1(b.1(b.0(a.0(c.0(B.1(y0))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.1(c.1(b.1(b.0(B.1(y0)))))
A1.0(a.0(a.1(x0))) → A1.0(a.1(c.1(b.0(a.1(x0)))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.1(c.1(b.1(b.0(a.1(b.0(B.1(y0)))))))
A1.0(a.0(a.1(b.0(x0)))) → A1.0(a.1(c.1(b.1(b.0(a.0(c.0(x0)))))))
A1.0(a.0(a.0(x0))) → A1.0(a.1(b.0(a.0(x0))))
A1.0(a.0(a.0(a.0(A.0(x))))) → B1.1(b.0(a.0(c.0(B.0(x)))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.1(c.1(b.1(b.1(b.0(B.0(y0)))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.1(b.1(b.0(c.0(B.1(y0)))))
A1.0(a.0(a.0(A.0(y0)))) → A1.1(b.1(b.0(c.0(B.0(y0)))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.1(c.1(b.1(b.0(a.0(B.0(y0)))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.1(b.1(b.0(a.1(c.1(b.0(B.0(y0)))))))
A1.0(a.0(a.1(b.0(x0)))) → A1.1(c.1(b.1(b.0(a.0(c.0(x0))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.1(c.1(b.1(b.0(a.0(B.1(y0))))))
A1.0(a.0(a.0(y0))) → A1.1(b.1(b.0(y0)))
A1.0(a.0(a.1(b.0(B.0(x0))))) → A1.1(c.1(b.1(b.0(a.0(c.0(A.0(x0)))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.1(c.1(b.1(b.0(B.0(y0))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.0(a.1(c.1(b.1(b.1(b.0(B.1(y0)))))))
A1.0(a.0(a.1(x))) → B1.1(x)
A1.0(a.0(a.0(x))) → B1.1(b.0(x))
B1.1(b.0(x0)) → A1.0(x0)
A1.0(a.0(a.0(a.0(A.1(x))))) → B1.1(b.0(a.0(c.0(B.1(x)))))
A1.0(a.0(a.1(b.0(B.0(x0))))) → A1.0(a.1(c.1(b.1(b.0(a.0(c.0(A.0(x0))))))))
A1.0(a.0(a.1(b.1(x0)))) → A1.1(c.1(b.1(b.0(a.1(c.1(x0))))))
A1.0(a.0(a.1(x))) → B1.1(b.1(x))
A1.0(a.0(a.0(x))) → B1.0(x)
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.1(b.1(b.0(a.1(c.1(b.0(B.0(y0))))))))
A1.0(a.0(a.0(A.0(y0)))) → A1.0(a.1(b.1(b.1(c.1(b.0(B.0(y0)))))))
A1.0(a.0(a.0(a.0(A.1(y0))))) → A1.0(a.1(b.1(b.0(a.1(c.1(b.0(B.1(y0))))))))
A1.0(a.0(a.1(b.0(B.1(x0))))) → A1.1(c.1(b.1(b.0(a.0(c.0(A.1(x0)))))))
A1.0(a.0(a.0(a.0(A.0(y0))))) → A1.0(a.1(c.1(b.1(b.0(a.1(b.0(B.0(y0))))))))
A1.0(a.0(a.1(y0))) → A1.1(b.1(b.1(y0)))
A1.0(a.0(a.0(a.0(A.1(x))))) → B1.1(b.0(a.1(c.1(b.0(B.1(x))))))
A1.0(a.0(a.0(A.1(y0)))) → A1.1(b.1(b.1(c.1(b.0(B.1(y0))))))
The TRS R consists of the following rules:
c.1(x) → x
a.0(a.0(A.0(x))) → a.0(a.1(b.0(B.0(x))))
b.1(b.0(B.1(x))) → b.0(a.0(c.0(A.1(x))))
a.0(a.0(a.0(x))) → a.0(a.1(c.1(b.1(b.0(x)))))
a.0(a.0(a.0(A.1(x)))) → a.0(a.1(c.1(b.1(b.0(c.0(B.1(x)))))))
b.1(b.0(B.0(x))) → b.0(a.0(c.0(A.0(x))))
b.1(b.1(x)) → b.0(a.1(c.1(x)))
a.0(a.0(a.0(a.0(A.1(x))))) → a.0(a.1(c.1(b.1(b.0(a.1(c.1(b.0(B.1(x)))))))))
a.0(a.0(a.1(x))) → a.0(a.1(c.1(b.1(b.1(x)))))
a.0(a.0(A.0(x))) → a.0(a.0(B.0(x)))
a.0(a.0(a.0(A.0(x)))) → a.0(a.1(c.1(b.1(b.1(c.1(b.0(B.0(x))))))))
a.0(a.0(a.0(a.0(A.0(x))))) → a.0(a.1(c.1(b.1(b.0(a.1(c.1(b.0(B.0(x)))))))))
a.0(a.0(a.0(A.1(x)))) → a.0(a.1(c.1(b.1(b.1(c.1(b.0(B.1(x))))))))
a.0(a.0(A.1(x))) → a.0(a.1(b.0(B.1(x))))
a.0(a.0(a.0(A.0(x)))) → a.0(a.1(c.1(b.1(b.0(c.0(B.0(x)))))))
a.0(a.0(a.0(a.0(A.1(x))))) → a.0(a.1(c.1(b.1(b.0(a.0(c.0(B.1(x))))))))
a.0(a.0(a.0(a.0(A.0(x))))) → a.0(a.1(c.1(b.1(b.0(a.0(c.0(B.0(x))))))))
c.0(x) → x
a.0(a.0(A.1(x))) → a.0(a.0(B.1(x)))
b.1(b.0(x)) → b.0(a.0(c.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 52 less nodes.
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ 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
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ SemLabProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ SemLabProof2
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1.0(a.0(a.0(a.0(A.0(x))))) → B1.1(b.0(a.1(c.1(b.0(B.0(x))))))
A1.0(a.0(a.1(x))) → B1.1(b.1(x))
A1.0(a.0(a.1(x))) → B1.1(x)
A1.0(a.0(a.0(A.0(x)))) → B1.1(b.1(c.1(b.0(B.0(x)))))
A1.0(a.0(a.0(x))) → B1.1(b.0(x))
A1.0(a.0(a.0(a.0(A.1(x))))) → B1.1(b.0(a.0(c.0(B.1(x)))))
B1.1(b.0(x0)) → A1.0(x0)
A1.0(a.0(a.0(A.1(x)))) → B1.1(b.1(c.1(b.0(B.1(x)))))
A1.0(a.0(a.0(a.0(A.1(x))))) → B1.1(b.0(a.1(c.1(b.0(B.1(x))))))
A1.0(a.0(a.0(a.0(A.0(x))))) → B1.1(b.0(a.0(c.0(B.0(x)))))
The TRS R consists of the following rules:
c.1(x) → x
a.0(a.0(A.0(x))) → a.0(a.1(b.0(B.0(x))))
b.1(b.0(B.1(x))) → b.0(a.0(c.0(A.1(x))))
a.0(a.0(a.0(x))) → a.0(a.1(c.1(b.1(b.0(x)))))
a.0(a.0(a.0(A.1(x)))) → a.0(a.1(c.1(b.1(b.0(c.0(B.1(x)))))))
b.1(b.0(B.0(x))) → b.0(a.0(c.0(A.0(x))))
b.1(b.1(x)) → b.0(a.1(c.1(x)))
a.0(a.0(a.0(a.0(A.1(x))))) → a.0(a.1(c.1(b.1(b.0(a.1(c.1(b.0(B.1(x)))))))))
a.0(a.0(a.1(x))) → a.0(a.1(c.1(b.1(b.1(x)))))
a.0(a.0(A.0(x))) → a.0(a.0(B.0(x)))
a.0(a.0(a.0(A.0(x)))) → a.0(a.1(c.1(b.1(b.1(c.1(b.0(B.0(x))))))))
a.0(a.0(a.0(a.0(A.0(x))))) → a.0(a.1(c.1(b.1(b.0(a.1(c.1(b.0(B.0(x)))))))))
a.0(a.0(a.0(A.1(x)))) → a.0(a.1(c.1(b.1(b.1(c.1(b.0(B.1(x))))))))
a.0(a.0(A.1(x))) → a.0(a.1(b.0(B.1(x))))
a.0(a.0(a.0(A.0(x)))) → a.0(a.1(c.1(b.1(b.0(c.0(B.0(x)))))))
a.0(a.0(a.0(a.0(A.1(x))))) → a.0(a.1(c.1(b.1(b.0(a.0(c.0(B.1(x))))))))
a.0(a.0(a.0(a.0(A.0(x))))) → a.0(a.1(c.1(b.1(b.0(a.0(c.0(B.0(x))))))))
c.0(x) → x
a.0(a.0(A.1(x))) → a.0(a.0(B.1(x)))
b.1(b.0(x)) → b.0(a.0(c.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
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ QDPToSRSProof
↳ QTRS
↳ QTRS Reverse
↳ QTRS
↳ QTRS Reverse
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ Narrowing
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ 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
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ SemLabProof
↳ SemLabProof2
↳ QDP
↳ QTRS Reverse
Q DP problem:
The TRS P consists of the following rules:
A1(a(a(a(A(x))))) → B1(b(a(c(b(B(x))))))
A1(a(a(x))) → B1(b(x))
B1(b(x0)) → A1(x0)
A1(a(a(A(x)))) → B1(b(c(b(B(x)))))
A1(a(a(a(A(x))))) → B1(b(a(c(B(x)))))
A1(a(a(x))) → B1(x)
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
b(b(B(x))) → b(a(c(A(x))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(b(B(x)))))))))
a(a(A(x))) → a(a(B(x)))
a(a(a(A(x)))) → a(a(c(b(b(c(b(B(x))))))))
a(a(a(a(A(x))))) → a(a(c(b(b(a(c(B(x))))))))
a(a(a(A(x)))) → a(a(c(b(b(c(B(x)))))))
a(a(A(x))) → a(a(b(B(x))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
We have reversed the following QTRS:
The set of rules R is
a(a(a(x1))) → b(b(c(a(a(x1)))))
b(b(x1)) → c(a(b(x1)))
c(x1) → x1
The set Q is empty.
We have obtained the following QTRS:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
The set Q is empty.
↳ QTRS
↳ QTRS Reverse
↳ DependencyPairsProof
↳ QTRS Reverse
↳ QTRS
Q restricted rewrite system:
The TRS R consists of the following rules:
a(a(a(x))) → a(a(c(b(b(x)))))
b(b(x)) → b(a(c(x)))
c(x) → x
Q is empty.