Termination w.r.t. Q proof of /tmp/tmppnRq3V/un02.srs

Termination w.r.t. Q of the following Term Rewriting System could not be shown:

Q restricted rewrite system:
The TRS R consists of the following rules:

b(a(a(b(b(x1))))) → b(a(a(a(a(b(b(x1)))))))
b(a(b(b(x1)))) → b(b(x1))
b(a(b(a(a(a(a(b(x1)))))))) → b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))))))))))
b(a(a(b(a(a(a(a(b(x1))))))))) → b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))
b(a(a(a(b(a(a(a(a(b(x1)))))))))) → b(x1)

Q is empty.

↳ QTRS

  ↳ QTRS Reverse

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

Q restricted rewrite system:
The TRS R consists of the following rules:

b(a(a(b(b(x1))))) → b(a(a(a(a(b(b(x1)))))))
b(a(b(b(x1)))) → b(b(x1))
b(a(b(a(a(a(a(b(x1)))))))) → b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))))))))))
b(a(a(b(a(a(a(a(b(x1))))))))) → b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))
b(a(a(a(b(a(a(a(a(b(x1)))))))))) → b(x1)

Q is empty.

We have reversed the following QTRS:
The set of rules R is

b(a(a(b(b(x1))))) → b(a(a(a(a(b(b(x1)))))))
b(a(b(b(x1)))) → b(b(x1))
b(a(b(a(a(a(a(b(x1)))))))) → b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))))))))))
b(a(a(b(a(a(a(a(b(x1))))))))) → b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))
b(a(a(a(b(a(a(a(a(b(x1)))))))))) → b(x1)

The set Q is empty.
We have obtained the following QTRS:

b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)

The set Q is empty.

↳ QTRS

  ↳ QTRS Reverse

    ↳ QTRS

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

Q restricted rewrite system:
The TRS R consists of the following rules:

b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)

Q is empty.

We have reversed the following QTRS:
The set of rules R is

b(a(a(b(b(x1))))) → b(a(a(a(a(b(b(x1)))))))
b(a(b(b(x1)))) → b(b(x1))
b(a(b(a(a(a(a(b(x1)))))))) → b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))))))))))
b(a(a(b(a(a(a(a(b(x1))))))))) → b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))
b(a(a(a(b(a(a(a(a(b(x1)))))))))) → b(x1)

The set Q is empty.
We have obtained the following QTRS:

b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)

The set Q is empty.

↳ QTRS

  ↳ QTRS Reverse

  ↳ QTRS Reverse

    ↳ QTRS

  ↳ DependencyPairsProof

Q restricted rewrite system:
The TRS R consists of the following rules:

b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)

Q is empty.

Using Dependency Pairs [1,15] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:

B(a(b(a(a(a(a(b(x1)))))))) → B(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))))))))))
B(a(a(b(a(a(a(a(b(x1))))))))) → B(a(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))
B(a(b(a(a(a(a(b(x1)))))))) → B(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))
B(a(a(b(a(a(a(a(b(x1))))))))) → B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))
B(a(b(a(a(a(a(b(x1)))))))) → B(a(a(a(b(a(a(a(a(b(x1))))))))))
B(a(a(b(a(a(a(a(b(x1))))))))) → B(a(a(a(b(a(a(a(a(b(x1))))))))))
B(a(b(a(a(a(a(b(x1)))))))) → B(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))))
B(a(a(b(b(x1))))) → B(a(a(a(a(b(b(x1)))))))

The TRS R consists of the following rules:

b(a(a(b(b(x1))))) → b(a(a(a(a(b(b(x1)))))))
b(a(b(b(x1)))) → b(b(x1))
b(a(b(a(a(a(a(b(x1)))))))) → b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))))))))))
b(a(a(b(a(a(a(a(b(x1))))))))) → b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))
b(a(a(a(b(a(a(a(a(b(x1)))))))))) → b(x1)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

↳ QTRS

  ↳ QTRS Reverse

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

Q DP problem:
The TRS P consists of the following rules:

B(a(b(a(a(a(a(b(x1)))))))) → B(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))))))))))
B(a(a(b(a(a(a(a(b(x1))))))))) → B(a(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))
B(a(b(a(a(a(a(b(x1)))))))) → B(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))
B(a(a(b(a(a(a(a(b(x1))))))))) → B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))
B(a(b(a(a(a(a(b(x1)))))))) → B(a(a(a(b(a(a(a(a(b(x1))))))))))
B(a(a(b(a(a(a(a(b(x1))))))))) → B(a(a(a(b(a(a(a(a(b(x1))))))))))
B(a(b(a(a(a(a(b(x1)))))))) → B(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))))
B(a(a(b(b(x1))))) → B(a(a(a(a(b(b(x1)))))))

The TRS R consists of the following rules:

b(a(a(b(b(x1))))) → b(a(a(a(a(b(b(x1)))))))
b(a(b(b(x1)))) → b(b(x1))
b(a(b(a(a(a(a(b(x1)))))))) → b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))))))))))
b(a(a(b(a(a(a(a(b(x1))))))))) → b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))
b(a(a(a(b(a(a(a(a(b(x1)))))))))) → b(x1)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 2 SCCs with 6 less nodes.

↳ QTRS

  ↳ QTRS Reverse

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

            ↳ Narrowing

          ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

B(a(b(a(a(a(a(b(x1)))))))) → B(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))

The TRS R consists of the following rules:

b(a(a(b(b(x1))))) → b(a(a(a(a(b(b(x1)))))))
b(a(b(b(x1)))) → b(b(x1))
b(a(b(a(a(a(a(b(x1)))))))) → b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))))))))))
b(a(a(b(a(a(a(a(b(x1))))))))) → b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))
b(a(a(a(b(a(a(a(a(b(x1)))))))))) → b(x1)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B(a(b(a(a(a(a(b(x1)))))))) → B(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))) at position [0,0] we obtained the following new rules:

B(a(b(a(a(a(a(b(a(a(b(b(x0)))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(x0))))))))))))))))))
B(a(b(a(a(a(a(b(a(b(a(a(a(a(b(x0))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))))))))
B(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))
B(a(b(a(a(a(a(b(a(b(b(x0))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(b(x0)))))))))))))
B(a(b(a(a(a(a(b(x0)))))))) → B(a(b(x0)))
B(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(x0)))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))

↳ QTRS

  ↳ QTRS Reverse

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

            ↳ Narrowing

              ↳ QDP

                ↳ QDPToSRSProof

          ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

B(a(b(a(a(a(a(b(a(b(b(x0))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(b(x0)))))))))))))
B(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))
B(a(b(a(a(a(a(b(x0)))))))) → B(a(b(x0)))
B(a(b(a(a(a(a(b(a(a(b(b(x0)))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(x0))))))))))))))))))
B(a(b(a(a(a(a(b(a(b(a(a(a(a(b(x0))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))))))))
B(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(x0)))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))

The TRS R consists of the following rules:

b(a(a(b(b(x1))))) → b(a(a(a(a(b(b(x1)))))))
b(a(b(b(x1)))) → b(b(x1))
b(a(b(a(a(a(a(b(x1)))))))) → b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))))))))))
b(a(a(b(a(a(a(a(b(x1))))))))) → b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))
b(a(a(a(b(a(a(a(a(b(x1)))))))))) → b(x1)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The finiteness of this DP problem is implied by strong termination of a SRS due to [12].

↳ QTRS

  ↳ QTRS Reverse

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

            ↳ Narrowing

              ↳ QDP

                ↳ QDPToSRSProof

                  ↳ QTRS

                    ↳ QTRS Reverse

          ↳ QDP

Q restricted rewrite system:
The TRS R consists of the following rules:

b(a(a(b(b(x1))))) → b(a(a(a(a(b(b(x1)))))))
b(a(b(b(x1)))) → b(b(x1))
b(a(b(a(a(a(a(b(x1)))))))) → b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))))))))))
b(a(a(b(a(a(a(a(b(x1))))))))) → b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))
b(a(a(a(b(a(a(a(a(b(x1)))))))))) → b(x1)
B(a(b(a(a(a(a(b(a(b(b(x0))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(b(x0)))))))))))))
B(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))
B(a(b(a(a(a(a(b(x0)))))))) → B(a(b(x0)))
B(a(b(a(a(a(a(b(a(a(b(b(x0)))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(x0))))))))))))))))))
B(a(b(a(a(a(a(b(a(b(a(a(a(a(b(x0))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))))))))
B(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(x0)))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))

Q is empty.

We have reversed the following QTRS:
The set of rules R is

b(a(a(b(b(x1))))) → b(a(a(a(a(b(b(x1)))))))
b(a(b(b(x1)))) → b(b(x1))
b(a(b(a(a(a(a(b(x1)))))))) → b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))))))))))
b(a(a(b(a(a(a(a(b(x1))))))))) → b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))
b(a(a(a(b(a(a(a(a(b(x1)))))))))) → b(x1)
B(a(b(a(a(a(a(b(a(b(b(x0))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(b(x0)))))))))))))
B(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))
B(a(b(a(a(a(a(b(x0)))))))) → B(a(b(x0)))
B(a(b(a(a(a(a(b(a(a(b(b(x0)))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(x0))))))))))))))))))
B(a(b(a(a(a(a(b(a(b(a(a(a(a(b(x0))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))))))))
B(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(x0)))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))

The set Q is empty.
We have obtained the following QTRS:

b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
b(b(a(b(a(a(a(a(b(a(B(x))))))))))) → b(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
b(a(a(a(a(b(a(B(x)))))))) → b(a(B(x)))
b(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))

The set Q is empty.

↳ QTRS

  ↳ QTRS Reverse

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

            ↳ Narrowing

              ↳ QDP

                ↳ QDPToSRSProof

                  ↳ QTRS

                    ↳ QTRS Reverse

                      ↳ QTRS

                        ↳ QTRS Reverse

                        ↳ QTRS Reverse

                        ↳ DependencyPairsProof

          ↳ QDP

Q restricted rewrite system:
The TRS R consists of the following rules:

b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
b(b(a(b(a(a(a(a(b(a(B(x))))))))))) → b(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
b(a(a(a(a(b(a(B(x)))))))) → b(a(B(x)))
b(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))

Q is empty.

We have reversed the following QTRS:
The set of rules R is

b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
b(b(a(b(a(a(a(a(b(a(B(x))))))))))) → b(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
b(a(a(a(a(b(a(B(x)))))))) → b(a(B(x)))
b(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))

The set Q is empty.
We have obtained the following QTRS:

b(a(a(b(b(x))))) → b(a(a(a(a(b(b(x)))))))
b(a(b(b(x)))) → b(b(x))
b(a(b(a(a(a(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(b(a(a(a(a(b(x))))))))) → b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x)))))))))))))))
b(a(a(a(b(a(a(a(a(b(x)))))))))) → b(x)
B(a(b(a(a(a(a(b(a(b(b(x))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(b(x)))))))))))))
B(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))
B(a(b(a(a(a(a(b(x)))))))) → B(a(b(x)))
B(a(b(a(a(a(a(b(a(a(b(b(x)))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(x))))))))))))))))))
B(a(b(a(a(a(a(b(a(b(a(a(a(a(b(x))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x)))))))))))))))))))))))))))))))))
B(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(x)))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))))))

The set Q is empty.

↳ QTRS

  ↳ QTRS Reverse

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

            ↳ Narrowing

              ↳ QDP

                ↳ QDPToSRSProof

                  ↳ QTRS

                    ↳ QTRS Reverse

                      ↳ QTRS

                        ↳ QTRS Reverse

                          ↳ QTRS

                        ↳ QTRS Reverse

                        ↳ DependencyPairsProof

          ↳ QDP

Q restricted rewrite system:
The TRS R consists of the following rules:

b(a(a(b(b(x))))) → b(a(a(a(a(b(b(x)))))))
b(a(b(b(x)))) → b(b(x))
b(a(b(a(a(a(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(b(a(a(a(a(b(x))))))))) → b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x)))))))))))))))
b(a(a(a(b(a(a(a(a(b(x)))))))))) → b(x)
B(a(b(a(a(a(a(b(a(b(b(x))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(b(x)))))))))))))
B(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))
B(a(b(a(a(a(a(b(x)))))))) → B(a(b(x)))
B(a(b(a(a(a(a(b(a(a(b(b(x)))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(x))))))))))))))))))
B(a(b(a(a(a(a(b(a(b(a(a(a(a(b(x))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x)))))))))))))))))))))))))))))))))
B(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(x)))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))))))

Q is empty.

We have reversed the following QTRS:
The set of rules R is

b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
b(b(a(b(a(a(a(a(b(a(B(x))))))))))) → b(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
b(a(a(a(a(b(a(B(x)))))))) → b(a(B(x)))
b(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))

The set Q is empty.
We have obtained the following QTRS:

b(a(a(b(b(x))))) → b(a(a(a(a(b(b(x)))))))
b(a(b(b(x)))) → b(b(x))
b(a(b(a(a(a(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(b(a(a(a(a(b(x))))))))) → b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x)))))))))))))))
b(a(a(a(b(a(a(a(a(b(x)))))))))) → b(x)
B(a(b(a(a(a(a(b(a(b(b(x))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(b(x)))))))))))))
B(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))
B(a(b(a(a(a(a(b(x)))))))) → B(a(b(x)))
B(a(b(a(a(a(a(b(a(a(b(b(x)))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(x))))))))))))))))))
B(a(b(a(a(a(a(b(a(b(a(a(a(a(b(x))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x)))))))))))))))))))))))))))))))))
B(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(x)))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))))))

The set Q is empty.

↳ QTRS

  ↳ QTRS Reverse

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

            ↳ Narrowing

              ↳ QDP

                ↳ QDPToSRSProof

                  ↳ QTRS

                    ↳ QTRS Reverse

                      ↳ QTRS

                        ↳ QTRS Reverse

                        ↳ QTRS Reverse

                          ↳ QTRS

                        ↳ DependencyPairsProof

          ↳ QDP

Q restricted rewrite system:
The TRS R consists of the following rules:

b(a(a(b(b(x))))) → b(a(a(a(a(b(b(x)))))))
b(a(b(b(x)))) → b(b(x))
b(a(b(a(a(a(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(b(a(a(a(a(b(x))))))))) → b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x)))))))))))))))
b(a(a(a(b(a(a(a(a(b(x)))))))))) → b(x)
B(a(b(a(a(a(a(b(a(b(b(x))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(b(x)))))))))))))
B(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))
B(a(b(a(a(a(a(b(x)))))))) → B(a(b(x)))
B(a(b(a(a(a(a(b(a(a(b(b(x)))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(x))))))))))))))))))
B(a(b(a(a(a(a(b(a(b(a(a(a(a(b(x))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x)))))))))))))))))))))))))))))))))
B(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(x)))))))))))))))) → B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))))))

Q is empty.

Using Dependency Pairs [1,15] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:

B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(x))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → B¹(a(a(a(b(a(B(x)))))))
B¹(a(a(a(a(b(a(a(b(x))))))))) → B¹(a(a(b(a(b(x))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → B¹(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))
B¹(b(a(b(a(a(a(a(b(a(B(x))))))))))) → B¹(a(a(a(b(a(B(x)))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(b(a(a(a(a(b(a(a(a(a(b(x)))))))))))))
B¹(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → B¹(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
B¹(a(a(a(a(b(a(a(b(x))))))))) → B¹(a(a(a(b(a(a(b(a(b(x))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(b(a(B(x)))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
B¹(b(a(b(x)))) → B¹(b(x))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → B¹(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))
B¹(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
B¹(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
B¹(b(a(b(a(a(a(a(b(a(B(x))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
B¹(b(a(b(a(a(a(a(b(a(B(x))))))))))) → B¹(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
B¹(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → B¹(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(a(a(a(a(b(x)))))))))))
B¹(b(a(a(b(x))))) → B¹(a(a(a(a(b(x))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x)))))))))))))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(x))))))
B¹(a(a(a(a(b(a(a(b(x))))))))) → B¹(a(b(x)))
B¹(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → B¹(a(a(a(b(a(B(x)))))))
B¹(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → B¹(a(a(a(b(a(B(x)))))))
B¹(b(a(a(b(x))))) → B¹(b(a(a(a(a(b(x)))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))

The TRS R consists of the following rules:

b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
b(b(a(b(a(a(a(a(b(a(B(x))))))))))) → b(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
b(a(a(a(a(b(a(B(x)))))))) → b(a(B(x)))
b(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

↳ QTRS

  ↳ QTRS Reverse

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

            ↳ Narrowing

              ↳ QDP

                ↳ QDPToSRSProof

                  ↳ QTRS

                    ↳ QTRS Reverse

                      ↳ QTRS

                        ↳ QTRS Reverse

                        ↳ QTRS Reverse

                        ↳ DependencyPairsProof

                          ↳ QDP

                            ↳ DependencyGraphProof

          ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(x))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → B¹(a(a(a(b(a(B(x)))))))
B¹(a(a(a(a(b(a(a(b(x))))))))) → B¹(a(a(b(a(b(x))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → B¹(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))
B¹(b(a(b(a(a(a(a(b(a(B(x))))))))))) → B¹(a(a(a(b(a(B(x)))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(b(a(a(a(a(b(a(a(a(a(b(x)))))))))))))
B¹(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → B¹(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
B¹(a(a(a(a(b(a(a(b(x))))))))) → B¹(a(a(a(b(a(a(b(a(b(x))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(b(a(B(x)))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
B¹(b(a(b(x)))) → B¹(b(x))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → B¹(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))
B¹(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
B¹(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
B¹(b(a(b(a(a(a(a(b(a(B(x))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
B¹(b(a(b(a(a(a(a(b(a(B(x))))))))))) → B¹(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
B¹(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → B¹(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(a(a(a(a(b(x)))))))))))
B¹(b(a(a(b(x))))) → B¹(a(a(a(a(b(x))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x)))))))))))))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(x))))))
B¹(a(a(a(a(b(a(a(b(x))))))))) → B¹(a(b(x)))
B¹(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → B¹(a(a(a(b(a(B(x)))))))
B¹(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → B¹(a(a(a(b(a(B(x)))))))
B¹(b(a(a(b(x))))) → B¹(b(a(a(a(a(b(x)))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))

The TRS R consists of the following rules:

b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
b(b(a(b(a(a(a(a(b(a(B(x))))))))))) → b(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
b(a(a(a(a(b(a(B(x)))))))) → b(a(B(x)))
b(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 2 SCCs with 22 less nodes.

↳ QTRS

  ↳ QTRS Reverse

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

            ↳ Narrowing

              ↳ QDP

                ↳ QDPToSRSProof

                  ↳ QTRS

                    ↳ QTRS Reverse

                      ↳ QTRS

                        ↳ QTRS Reverse

                        ↳ QTRS Reverse

                        ↳ DependencyPairsProof

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ Narrowing

                                ↳ QDP

          ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(x))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(a(a(a(a(b(x)))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(x))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))

The TRS R consists of the following rules:

b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
b(b(a(b(a(a(a(a(b(a(B(x))))))))))) → b(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
b(a(a(a(a(b(a(B(x)))))))) → b(a(B(x)))
b(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))) at position [0,0,0,0,0] we obtained the following new rules:

B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(y0))))))))))))))) → B¹(a(a(a(a(b(a(B(y0))))))))

↳ QTRS

  ↳ QTRS Reverse

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

            ↳ Narrowing

              ↳ QDP

                ↳ QDPToSRSProof

                  ↳ QTRS

                    ↳ QTRS Reverse

                      ↳ QTRS

                        ↳ QTRS Reverse

                        ↳ QTRS Reverse

                        ↳ DependencyPairsProof

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                ↳ QDP

          ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(x))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(y0))))))))))))))) → B¹(a(a(a(a(b(a(B(y0))))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(a(a(a(a(b(x)))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(x))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))

The TRS R consists of the following rules:

b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
b(b(a(b(a(a(a(a(b(a(B(x))))))))))) → b(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
b(a(a(a(a(b(a(B(x)))))))) → b(a(B(x)))
b(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 1 less node.

↳ QTRS

  ↳ QTRS Reverse

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

            ↳ Narrowing

              ↳ QDP

                ↳ QDPToSRSProof

                  ↳ QTRS

                    ↳ QTRS Reverse

                      ↳ QTRS

                        ↳ QTRS Reverse

                        ↳ QTRS Reverse

                        ↳ DependencyPairsProof

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ QDP

                                          ↳ Narrowing

                                ↳ QDP

          ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(x))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(a(a(a(a(b(x)))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(x))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))

The TRS R consists of the following rules:

b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
b(b(a(b(a(a(a(a(b(a(B(x))))))))))) → b(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
b(a(a(a(a(b(a(B(x)))))))) → b(a(B(x)))
b(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))) at position [0,0,0,0,0] we obtained the following new rules:

B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(y0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(B(y0)))))))))))))))))

↳ QTRS

  ↳ QTRS Reverse

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

            ↳ Narrowing

              ↳ QDP

                ↳ QDPToSRSProof

                  ↳ QTRS

                    ↳ QTRS Reverse

                      ↳ QTRS

                        ↳ QTRS Reverse

                        ↳ QTRS Reverse

                        ↳ DependencyPairsProof

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                ↳ QDP

          ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(x))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(a(a(a(a(b(x)))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(y0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(B(y0)))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(x))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))

The TRS R consists of the following rules:

b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
b(b(a(b(a(a(a(a(b(a(B(x))))))))))) → b(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
b(a(a(a(a(b(a(B(x)))))))) → b(a(B(x)))
b(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 1 less node.

↳ QTRS

  ↳ QTRS Reverse

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

            ↳ Narrowing

              ↳ QDP

                ↳ QDPToSRSProof

                  ↳ QTRS

                    ↳ QTRS Reverse

                      ↳ QTRS

                        ↳ QTRS Reverse

                        ↳ QTRS Reverse

                        ↳ DependencyPairsProof

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                ↳ QDP

          ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(x))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(a(a(a(a(b(x)))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(x))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))

The TRS R consists of the following rules:

b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
b(b(a(b(a(a(a(a(b(a(B(x))))))))))) → b(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
b(a(a(a(a(b(a(B(x)))))))) → b(a(B(x)))
b(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(a(a(a(a(b(x))))))))))) at position [0,0,0,0,0] we obtained the following new rules:

B¹(a(a(a(a(b(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(B(x0)))))))))) → B¹(a(a(a(a(b(a(B(x0))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(x0)))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(x0))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(x0)))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(x0))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(x0)))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))

↳ QTRS

  ↳ QTRS Reverse

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

            ↳ Narrowing

              ↳ QDP

                ↳ QDPToSRSProof

                  ↳ QTRS

                    ↳ QTRS Reverse

                      ↳ QTRS

                        ↳ QTRS Reverse

                        ↳ QTRS Reverse

                        ↳ DependencyPairsProof

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                ↳ QDP

          ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

B¹(a(a(a(a(b(a(a(b(x))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(B(x0)))))))))) → B¹(a(a(a(a(b(a(B(x0))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(x0)))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(x0))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(x0)))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(x0))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(x))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(x0)))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))

The TRS R consists of the following rules:

b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
b(b(a(b(a(a(a(a(b(a(B(x))))))))))) → b(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
b(a(a(a(a(b(a(B(x)))))))) → b(a(B(x)))
b(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 1 less node.

↳ QTRS

  ↳ QTRS Reverse

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

            ↳ Narrowing

              ↳ QDP

                ↳ QDPToSRSProof

                  ↳ QTRS

                    ↳ QTRS Reverse

                      ↳ QTRS

                        ↳ QTRS Reverse

                        ↳ QTRS Reverse

                        ↳ DependencyPairsProof

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                ↳ QDP

          ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

B¹(a(a(a(a(b(a(a(b(x))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(x0)))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(x0))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(x0)))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(x0))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(x))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(x0)))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))

The TRS R consists of the following rules:

b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
b(b(a(b(a(a(a(a(b(a(B(x))))))))))) → b(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
b(a(a(a(a(b(a(B(x)))))))) → b(a(B(x)))
b(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x)))))))))))))))))))))) at position [0,0,0,0,0] we obtained the following new rules:

B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(x0)))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(x0)))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(x0)))))))))))))))))
B¹(a(a(a(a(b(a(b(a(B(x0)))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(x0))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))

↳ QTRS

  ↳ QTRS Reverse

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

            ↳ Narrowing

              ↳ QDP

                ↳ QDPToSRSProof

                  ↳ QTRS

                    ↳ QTRS Reverse

                      ↳ QTRS

                        ↳ QTRS Reverse

                        ↳ QTRS Reverse

                        ↳ DependencyPairsProof

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ Narrowing

                                ↳ QDP

          ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

B¹(a(a(a(a(b(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(x0)))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(x))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(x0)))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(x0)))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(x0))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(x0))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(x0)))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(x0)))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(x0)))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(B(x0)))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(x0))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(x))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))

The TRS R consists of the following rules:

b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
b(b(a(b(a(a(a(a(b(a(B(x))))))))))) → b(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
b(a(a(a(a(b(a(B(x)))))))) → b(a(B(x)))
b(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B¹(a(a(a(a(b(a(a(b(x))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x))))))))))))))) at position [0,0,0,0,0] we obtained the following new rules:

B¹(a(a(a(a(b(a(a(b(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(a(b(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(x0))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(b(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(b(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(a(b(x0))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(a(a(a(a(b(x0)))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(B(x0)))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))))

↳ QTRS

  ↳ QTRS Reverse

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

            ↳ Narrowing

              ↳ QDP

                ↳ QDPToSRSProof

                  ↳ QTRS

                    ↳ QTRS Reverse

                      ↳ QTRS

                        ↳ QTRS Reverse

                        ↳ QTRS Reverse

                        ↳ DependencyPairsProof

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ Narrowing

                                                                ↳ QDP

                                                                  ↳ DependencyGraphProof

                                ↳ QDP

          ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

B¹(a(a(a(a(b(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(B(x0)))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(b(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(x0)))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(x0)))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(x0))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(x0)))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(x0)))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(a(b(x0))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(a(a(a(a(b(x0)))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(x0)))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(b(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(a(b(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(x0))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(x0))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(x0)))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(B(x0)))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(x0))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(x))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))

The TRS R consists of the following rules:

b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
b(b(a(b(a(a(a(a(b(a(B(x))))))))))) → b(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
b(a(a(a(a(b(a(B(x)))))))) → b(a(B(x)))
b(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 1 less node.

↳ QTRS

  ↳ QTRS Reverse

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

            ↳ Narrowing

              ↳ QDP

                ↳ QDPToSRSProof

                  ↳ QTRS

                    ↳ QTRS Reverse

                      ↳ QTRS

                        ↳ QTRS Reverse

                        ↳ QTRS Reverse

                        ↳ DependencyPairsProof

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ Narrowing

                                                                ↳ QDP

                                                                  ↳ DependencyGraphProof

                                                                    ↳ QDP

                                                                      ↳ Narrowing

                                ↳ QDP

          ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(x0)))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(b(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(a(b(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(x0))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(b(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(x0)))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(x0)))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(x0))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(x0)))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(x0))))))))))))
B¹(a(a(a(a(b(a(b(a(b(x0)))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(x0)))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(a(b(x0))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(a(a(a(a(b(x0)))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(B(x0)))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(x0))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(x))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))

The TRS R consists of the following rules:

b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
b(b(a(b(a(a(a(a(b(a(B(x))))))))))) → b(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
b(a(a(a(a(b(a(B(x)))))))) → b(a(B(x)))
b(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))))))))) at position [0,0,0,0,0] we obtained the following new rules:

B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(y0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(B(y0))))))))))))))))))))))))

↳ QTRS

  ↳ QTRS Reverse

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

            ↳ Narrowing

              ↳ QDP

                ↳ QDPToSRSProof

                  ↳ QTRS

                    ↳ QTRS Reverse

                      ↳ QTRS

                        ↳ QTRS Reverse

                        ↳ QTRS Reverse

                        ↳ DependencyPairsProof

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ Narrowing

                                                                ↳ QDP

                                                                  ↳ DependencyGraphProof

                                                                    ↳ QDP

                                                                      ↳ Narrowing

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                ↳ QDP

          ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

B¹(a(a(a(a(b(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(b(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(x0)))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(x0)))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(x0))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(x0)))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(x0)))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(a(b(x0))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(a(a(a(a(b(x0)))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(x0)))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(b(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(a(b(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(x0))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(x0))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(x0)))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(B(x0)))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(x0))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(x))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))

The TRS R consists of the following rules:

b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
b(b(a(b(a(a(a(a(b(a(B(x))))))))))) → b(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
b(a(a(a(a(b(a(B(x)))))))) → b(a(B(x)))
b(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))) at position [0,0,0,0,0] we obtained the following new rules:

B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(y0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(B(y0)))))))))))))

↳ QTRS

  ↳ QTRS Reverse

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

            ↳ Narrowing

              ↳ QDP

                ↳ QDPToSRSProof

                  ↳ QTRS

                    ↳ QTRS Reverse

                      ↳ QTRS

                        ↳ QTRS Reverse

                        ↳ QTRS Reverse

                        ↳ DependencyPairsProof

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ Narrowing

                                                                ↳ QDP

                                                                  ↳ DependencyGraphProof

                                                                    ↳ QDP

                                                                      ↳ Narrowing

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ Narrowing

                                ↳ QDP

          ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(x0)))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(b(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(a(b(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(x0))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(b(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(x0)))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(x0)))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(x0))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(x0)))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(x0))))))))))))
B¹(a(a(a(a(b(a(b(a(b(x0)))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(x0)))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(B(x0)))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(a(b(x0))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(a(a(a(a(b(x0)))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(x0))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(x))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))

The TRS R consists of the following rules:

b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
b(b(a(b(a(a(a(a(b(a(B(x))))))))))) → b(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
b(a(a(a(a(b(a(B(x)))))))) → b(a(B(x)))
b(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B¹(a(a(a(a(b(a(b(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))) at position [0,0,0,0,0] we obtained the following new rules:

B¹(a(a(a(a(b(a(b(b(a(b(a(a(a(a(b(a(B(y0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(B(y0))))))))))))))

↳ QTRS

  ↳ QTRS Reverse

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

            ↳ Narrowing

              ↳ QDP

                ↳ QDPToSRSProof

                  ↳ QTRS

                    ↳ QTRS Reverse

                      ↳ QTRS

                        ↳ QTRS Reverse

                        ↳ QTRS Reverse

                        ↳ DependencyPairsProof

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ Narrowing

                                                                ↳ QDP

                                                                  ↳ DependencyGraphProof

                                                                    ↳ QDP

                                                                      ↳ Narrowing

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ Narrowing

                                                                                ↳ QDP

                                                                                  ↳ DependencyGraphProof

                                ↳ QDP

          ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

B¹(a(a(a(a(b(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(x0)))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(b(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(a(b(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(a(a(a(a(b(a(B(y0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(B(y0))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(x0))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(b(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(x0)))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(x0)))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(x0))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(x0))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(x0)))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(x0)))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(x0)))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(a(b(x0))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(a(a(a(a(b(x0)))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(B(x0)))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(x0))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(x))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))

The TRS R consists of the following rules:

b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
b(b(a(b(a(a(a(a(b(a(B(x))))))))))) → b(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
b(a(a(a(a(b(a(B(x)))))))) → b(a(B(x)))
b(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 1 less node.

↳ QTRS

  ↳ QTRS Reverse

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

            ↳ Narrowing

              ↳ QDP

                ↳ QDPToSRSProof

                  ↳ QTRS

                    ↳ QTRS Reverse

                      ↳ QTRS

                        ↳ QTRS Reverse

                        ↳ QTRS Reverse

                        ↳ DependencyPairsProof

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ Narrowing

                                                                ↳ QDP

                                                                  ↳ DependencyGraphProof

                                                                    ↳ QDP

                                                                      ↳ Narrowing

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ Narrowing

                                                                                ↳ QDP

                                                                                  ↳ DependencyGraphProof

                                                                                    ↳ QDP

                                                                                      ↳ Narrowing

                                ↳ QDP

          ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(x0)))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(b(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(a(b(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(x0))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(b(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(x0)))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(x0)))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(x0))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(x0)))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(x0))))))))))))
B¹(a(a(a(a(b(a(b(a(b(x0)))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(x0)))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(a(b(x0))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(a(a(a(a(b(x0)))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(B(x0)))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(x0))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(x))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))

The TRS R consists of the following rules:

b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
b(b(a(b(a(a(a(a(b(a(B(x))))))))))) → b(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
b(a(a(a(a(b(a(B(x)))))))) → b(a(B(x)))
b(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))) at position [0,0,0,0,0] we obtained the following new rules:

B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))) → B¹(a(a(a(a(b(a(B(x0))))))))

↳ QTRS

  ↳ QTRS Reverse

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

            ↳ Narrowing

              ↳ QDP

                ↳ QDPToSRSProof

                  ↳ QTRS

                    ↳ QTRS Reverse

                      ↳ QTRS

                        ↳ QTRS Reverse

                        ↳ QTRS Reverse

                        ↳ DependencyPairsProof

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ Narrowing

                                                                ↳ QDP

                                                                  ↳ DependencyGraphProof

                                                                    ↳ QDP

                                                                      ↳ Narrowing

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ Narrowing

                                                                                ↳ QDP

                                                                                  ↳ DependencyGraphProof

                                                                                    ↳ QDP

                                                                                      ↳ Narrowing

                                                                                        ↳ QDP

                                                                                          ↳ DependencyGraphProof

                                ↳ QDP

          ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

B¹(a(a(a(a(b(a(b(a(b(x0)))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(b(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(a(b(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(x0))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))) → B¹(a(a(a(a(b(a(B(x0))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(b(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(x0)))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(x0)))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(x0))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(x0))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(x0)))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(x0)))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(x0)))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(B(x0)))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(a(b(x0))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(a(a(a(a(b(x0)))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(x0))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(x))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))

The TRS R consists of the following rules:

b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
b(b(a(b(a(a(a(a(b(a(B(x))))))))))) → b(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
b(a(a(a(a(b(a(B(x)))))))) → b(a(B(x)))
b(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 1 less node.

↳ QTRS

  ↳ QTRS Reverse

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

            ↳ Narrowing

              ↳ QDP

                ↳ QDPToSRSProof

                  ↳ QTRS

                    ↳ QTRS Reverse

                      ↳ QTRS

                        ↳ QTRS Reverse

                        ↳ QTRS Reverse

                        ↳ DependencyPairsProof

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ DependencyGraphProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ Narrowing

                                                                ↳ QDP

                                                                  ↳ DependencyGraphProof

                                                                    ↳ QDP

                                                                      ↳ Narrowing

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ Narrowing

                                                                                ↳ QDP

                                                                                  ↳ DependencyGraphProof

                                                                                    ↳ QDP

                                                                                      ↳ Narrowing

                                                                                        ↳ QDP

                                                                                          ↳ DependencyGraphProof

                                                                                            ↳ QDP

                                ↳ QDP

          ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(x0)))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(b(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(a(a(b(x0)))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(x0))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(b(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(x0)))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(x0)))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(x0))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(x0)))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(x0))))))))))))
B¹(a(a(a(a(b(a(b(a(b(x0)))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0)))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(b(x0))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(b(x0)))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(b(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(b(x0))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0))))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(a(b(x0))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(a(a(a(a(b(x0)))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(a(b(a(a(b(x0)))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x0))))))))))))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(B(x0)))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(B(x0)))))))))))))))))))
B¹(a(a(a(a(b(a(a(b(b(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(b(a(a(b(a(b(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))))))))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(x0)))))))))))) → B¹(a(a(a(a(b(x0))))))
B¹(a(a(a(a(b(a(b(x)))))))) → B¹(a(a(a(a(b(x))))))
B¹(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(B(x0))))))))))))))))))) → B¹(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x0)))))))))))))))))

The TRS R consists of the following rules:

b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
b(b(a(b(a(a(a(a(b(a(B(x))))))))))) → b(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
b(a(a(a(a(b(a(B(x)))))))) → b(a(B(x)))
b(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

↳ QTRS

  ↳ QTRS Reverse

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

            ↳ Narrowing

              ↳ QDP

                ↳ QDPToSRSProof

                  ↳ QTRS

                    ↳ QTRS Reverse

                      ↳ QTRS

                        ↳ QTRS Reverse

                        ↳ QTRS Reverse

                        ↳ DependencyPairsProof

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

          ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

B¹(b(a(b(a(a(a(a(b(a(B(x))))))))))) → B¹(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
B¹(b(a(b(x)))) → B¹(b(x))
B¹(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → B¹(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
B¹(b(a(a(b(x))))) → B¹(b(a(a(a(a(b(x)))))))

The TRS R consists of the following rules:

b(b(a(a(b(x))))) → b(b(a(a(a(a(b(x)))))))
b(b(a(b(x)))) → b(b(x))
b(a(a(a(a(b(a(b(x)))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(x))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(x)))))))))))))))
b(a(a(a(a(b(a(a(a(b(x)))))))))) → b(x)
b(b(a(b(a(a(a(a(b(a(B(x))))))))))) → b(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))
b(a(a(a(a(b(a(a(a(b(a(a(a(a(b(a(B(x))))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))
b(a(a(a(a(b(a(B(x)))))))) → b(a(B(x)))
b(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))) → b(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))
b(a(a(a(a(b(a(b(a(a(a(a(b(a(B(x))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(b(a(B(x)))))))))))))))))))))))))))))))))
b(a(a(a(a(b(a(a(b(a(a(a(a(b(a(B(x)))))))))))))))) → b(a(a(a(a(b(a(a(a(b(a(a(b(a(b(a(a(a(a(b(a(a(a(b(a(B(x))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

↳ QTRS

  ↳ QTRS Reverse

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

          ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

B(a(a(b(a(a(a(a(b(x1))))))))) → B(a(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))

The TRS R consists of the following rules:

b(a(a(b(b(x1))))) → b(a(a(a(a(b(b(x1)))))))
b(a(b(b(x1)))) → b(b(x1))
b(a(b(a(a(a(a(b(x1)))))))) → b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))))))))))
b(a(a(b(a(a(a(a(b(x1))))))))) → b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))
b(a(a(a(b(a(a(a(a(b(x1)))))))))) → b(x1)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.