Termination w.r.t. Q proof of /tmp/tmpTCoysN/un10.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(b(a(b(b(a(b(b(b(b(x1)))))))))) → b(b(b(b(b(a(b(b(a(b(b(a(b(x1)))))))))))))

Q is empty.

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

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

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

Q is empty.

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

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

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

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

The set Q is empty.

↳ QTRS

  ↳ QTRS Reverse

    ↳ QTRS

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

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

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

Q is empty.

We were given the following TRS:

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

By stripping symbols from the only rule of the system, we obtained the following TRS:

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

    ↳ QTRS

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

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

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

Q is empty.

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

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

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

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

The set Q is empty.

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

    ↳ QTRS

      ↳ Strip Symbols Proof

  ↳ DependencyPairsProof

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

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

Q is empty.

We were given the following TRS:

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

By stripping symbols from the only rule of the system, we obtained the following TRS:

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

    ↳ QTRS

      ↳ Strip Symbols Proof

        ↳ QTRS

  ↳ DependencyPairsProof

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

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

Q is empty.

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

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

The TRS R consists of the following rules:

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

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

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

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

The TRS R consists of the following rules:

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

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 6 less nodes.

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

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

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

The TRS R consists of the following rules:

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

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

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

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

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

The TRS R consists of the following rules:

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

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

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

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

The TRS R consists of the following rules:

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

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By forward instantiating [14] the rule B(b(a(b(b(a(b(b(b(b(x1)))))))))) → B(b(a(b(x1)))) we obtained the following new rules:

B(b(a(b(b(a(b(b(b(b(b(a(y_4)))))))))))) → B(b(a(b(b(a(y_4))))))

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

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

B(b(a(b(b(a(b(b(b(b(b(a(y_4)))))))))))) → B(b(a(b(b(a(y_4))))))
B(b(a(b(b(a(b(b(b(b(x1)))))))))) → B(b(a(b(b(a(b(x1)))))))
B(b(a(b(b(a(b(b(b(b(b(a(b(b(b(b(x0)))))))))))))))) → B(b(a(b(b(a(b(b(b(b(b(a(b(b(a(b(b(a(b(x0)))))))))))))))))))
B(b(a(b(b(a(b(b(b(b(b(a(b(b(a(b(b(b(b(x0))))))))))))))))))) → B(b(a(b(b(a(b(b(a(b(b(b(b(b(a(b(b(a(b(b(a(b(x0))))))))))))))))))))))

The TRS R consists of the following rules:

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

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

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

b(b(a(b(b(a(b(b(b(b(x1)))))))))) → b(b(b(b(b(a(b(b(a(b(b(a(b(x1)))))))))))))
B(b(a(b(b(a(b(b(b(b(b(a(y_4)))))))))))) → B(b(a(b(b(a(y_4))))))
B(b(a(b(b(a(b(b(b(b(x1)))))))))) → B(b(a(b(b(a(b(x1)))))))
B(b(a(b(b(a(b(b(b(b(b(a(b(b(b(b(x0)))))))))))))))) → B(b(a(b(b(a(b(b(b(b(b(a(b(b(a(b(b(a(b(x0)))))))))))))))))))
B(b(a(b(b(a(b(b(b(b(b(a(b(b(a(b(b(b(b(x0))))))))))))))))))) → B(b(a(b(b(a(b(b(a(b(b(b(b(b(a(b(b(a(b(b(a(b(x0))))))))))))))))))))))

Q is empty.

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

b(b(a(b(b(a(b(b(b(b(x1)))))))))) → b(b(b(b(b(a(b(b(a(b(b(a(b(x1)))))))))))))
B(b(a(b(b(a(b(b(b(b(b(a(y_4)))))))))))) → B(b(a(b(b(a(y_4))))))
B(b(a(b(b(a(b(b(b(b(x1)))))))))) → B(b(a(b(b(a(b(x1)))))))
B(b(a(b(b(a(b(b(b(b(b(a(b(b(b(b(x0)))))))))))))))) → B(b(a(b(b(a(b(b(b(b(b(a(b(b(a(b(b(a(b(x0)))))))))))))))))))
B(b(a(b(b(a(b(b(b(b(b(a(b(b(a(b(b(b(b(x0))))))))))))))))))) → B(b(a(b(b(a(b(b(a(b(b(b(b(b(a(b(b(a(b(b(a(b(x0))))))))))))))))))))))

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

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

The set Q is empty.

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

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

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

Q is empty.

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

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

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

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

The set Q is empty.

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                                ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

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

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

Q is empty.

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

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

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

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

The set Q is empty.

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                                ↳ QTRS

                              ↳ DependencyPairsProof

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

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

Q is empty.

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

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

The TRS R consists of the following rules:

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

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

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

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

The TRS R consists of the following rules:

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

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 12 less nodes.

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

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

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

The TRS R consists of the following rules:

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

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
We use the reduction pair processor [15].

The following pairs can be oriented strictly and are deleted.

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

The remaining pairs can at least be oriented weakly.

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

Used ordering: Polynomial Order [21,25] with Interpretation:

POL( B¹(x₁) ) = x₁

POL( b(x₁) ) = 1

POL( B(x₁) ) = max{0, x₁ - 1}

POL( a(x₁) ) = max{0, -1}

The following usable rules [17] were oriented:

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

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

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

The TRS R consists of the following rules:

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

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

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

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

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

The TRS R consists of the following rules:

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

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

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

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

The TRS R consists of the following rules:

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

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

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

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

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

The TRS R consists of the following rules:

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

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 2 less nodes.

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

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

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

The TRS R consists of the following rules:

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

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

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ DependencyGraphProof

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

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

The TRS R consists of the following rules:

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

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ DependencyGraphProof

                                                                ↳ QDP

                                                                  ↳ Narrowing

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

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

The TRS R consists of the following rules:

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

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

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ DependencyGraphProof

                                                                ↳ QDP

                                                                  ↳ Narrowing

                                                                    ↳ QDP

                                                                      ↳ DependencyGraphProof

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

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

The TRS R consists of the following rules:

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

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ DependencyGraphProof

                                                                ↳ QDP

                                                                  ↳ Narrowing

                                                                    ↳ QDP

                                                                      ↳ DependencyGraphProof

                                                                        ↳ QDP

                                                                          ↳ Narrowing

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

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

The TRS R consists of the following rules:

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

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

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ DependencyGraphProof

                                                                ↳ QDP

                                                                  ↳ Narrowing

                                                                    ↳ QDP

                                                                      ↳ DependencyGraphProof

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ DependencyGraphProof

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

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

The TRS R consists of the following rules:

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

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 3 less nodes.

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ DependencyGraphProof

                                                                ↳ QDP

                                                                  ↳ Narrowing

                                                                    ↳ QDP

                                                                      ↳ DependencyGraphProof

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ DependencyGraphProof

                                                                                ↳ QDP

                                                                                  ↳ Narrowing

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

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

The TRS R consists of the following rules:

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

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

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ DependencyGraphProof

                                                                ↳ QDP

                                                                  ↳ Narrowing

                                                                    ↳ QDP

                                                                      ↳ DependencyGraphProof

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ DependencyGraphProof

                                                                                ↳ QDP

                                                                                  ↳ Narrowing

                                                                                    ↳ QDP

                                                                                      ↳ DependencyGraphProof

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

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

The TRS R consists of the following rules:

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

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 3 less nodes.

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ DependencyGraphProof

                                                                ↳ QDP

                                                                  ↳ Narrowing

                                                                    ↳ QDP

                                                                      ↳ DependencyGraphProof

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ DependencyGraphProof

                                                                                ↳ QDP

                                                                                  ↳ Narrowing

                                                                                    ↳ QDP

                                                                                      ↳ DependencyGraphProof

                                                                                        ↳ QDP

                                                                                          ↳ Narrowing

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

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

The TRS R consists of the following rules:

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

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

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ DependencyGraphProof

                                                                ↳ QDP

                                                                  ↳ Narrowing

                                                                    ↳ QDP

                                                                      ↳ DependencyGraphProof

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ DependencyGraphProof

                                                                                ↳ QDP

                                                                                  ↳ Narrowing

                                                                                    ↳ QDP

                                                                                      ↳ DependencyGraphProof

                                                                                        ↳ QDP

                                                                                          ↳ Narrowing

                                                                                            ↳ QDP

                                                                                              ↳ DependencyGraphProof

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

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

The TRS R consists of the following rules:

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

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 3 less nodes.

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ DependencyGraphProof

                                                                ↳ QDP

                                                                  ↳ Narrowing

                                                                    ↳ QDP

                                                                      ↳ DependencyGraphProof

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ DependencyGraphProof

                                                                                ↳ QDP

                                                                                  ↳ Narrowing

                                                                                    ↳ QDP

                                                                                      ↳ DependencyGraphProof

                                                                                        ↳ QDP

                                                                                          ↳ Narrowing

                                                                                            ↳ QDP

                                                                                              ↳ DependencyGraphProof

                                                                                                ↳ QDP

                                                                                                  ↳ Narrowing

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

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

The TRS R consists of the following rules:

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

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

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ DependencyGraphProof

                                                                ↳ QDP

                                                                  ↳ Narrowing

                                                                    ↳ QDP

                                                                      ↳ DependencyGraphProof

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ DependencyGraphProof

                                                                                ↳ QDP

                                                                                  ↳ Narrowing

                                                                                    ↳ QDP

                                                                                      ↳ DependencyGraphProof

                                                                                        ↳ QDP

                                                                                          ↳ Narrowing

                                                                                            ↳ QDP

                                                                                              ↳ DependencyGraphProof

                                                                                                ↳ QDP

                                                                                                  ↳ Narrowing

                                                                                                    ↳ QDP

                                                                                                      ↳ DependencyGraphProof

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

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

The TRS R consists of the following rules:

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

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 2 less nodes.

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ DependencyGraphProof

                                                                ↳ QDP

                                                                  ↳ Narrowing

                                                                    ↳ QDP

                                                                      ↳ DependencyGraphProof

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ DependencyGraphProof

                                                                                ↳ QDP

                                                                                  ↳ Narrowing

                                                                                    ↳ QDP

                                                                                      ↳ DependencyGraphProof

                                                                                        ↳ QDP

                                                                                          ↳ Narrowing

                                                                                            ↳ QDP

                                                                                              ↳ DependencyGraphProof

                                                                                                ↳ QDP

                                                                                                  ↳ Narrowing

                                                                                                    ↳ QDP

                                                                                                      ↳ DependencyGraphProof

                                                                                                        ↳ QDP

                                                                                                          ↳ Narrowing

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

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

The TRS R consists of the following rules:

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

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

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ DependencyGraphProof

                                                                ↳ QDP

                                                                  ↳ Narrowing

                                                                    ↳ QDP

                                                                      ↳ DependencyGraphProof

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ DependencyGraphProof

                                                                                ↳ QDP

                                                                                  ↳ Narrowing

                                                                                    ↳ QDP

                                                                                      ↳ DependencyGraphProof

                                                                                        ↳ QDP

                                                                                          ↳ Narrowing

                                                                                            ↳ QDP

                                                                                              ↳ DependencyGraphProof

                                                                                                ↳ QDP

                                                                                                  ↳ Narrowing

                                                                                                    ↳ QDP

                                                                                                      ↳ DependencyGraphProof

                                                                                                        ↳ QDP

                                                                                                          ↳ Narrowing

                                                                                                            ↳ QDP

                                                                                                              ↳ DependencyGraphProof

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

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

The TRS R consists of the following rules:

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

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ DependencyGraphProof

                                                                ↳ QDP

                                                                  ↳ Narrowing

                                                                    ↳ QDP

                                                                      ↳ DependencyGraphProof

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ DependencyGraphProof

                                                                                ↳ QDP

                                                                                  ↳ Narrowing

                                                                                    ↳ QDP

                                                                                      ↳ DependencyGraphProof

                                                                                        ↳ QDP

                                                                                          ↳ Narrowing

                                                                                            ↳ QDP

                                                                                              ↳ DependencyGraphProof

                                                                                                ↳ QDP

                                                                                                  ↳ Narrowing

                                                                                                    ↳ QDP

                                                                                                      ↳ DependencyGraphProof

                                                                                                        ↳ QDP

                                                                                                          ↳ Narrowing

                                                                                                            ↳ QDP

                                                                                                              ↳ DependencyGraphProof

                                                                                                                ↳ QDP

                                                                                                                  ↳ Narrowing

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

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

The TRS R consists of the following rules:

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

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

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ DependencyGraphProof

                                                                ↳ QDP

                                                                  ↳ Narrowing

                                                                    ↳ QDP

                                                                      ↳ DependencyGraphProof

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ DependencyGraphProof

                                                                                ↳ QDP

                                                                                  ↳ Narrowing

                                                                                    ↳ QDP

                                                                                      ↳ DependencyGraphProof

                                                                                        ↳ QDP

                                                                                          ↳ Narrowing

                                                                                            ↳ QDP

                                                                                              ↳ DependencyGraphProof

                                                                                                ↳ QDP

                                                                                                  ↳ Narrowing

                                                                                                    ↳ QDP

                                                                                                      ↳ DependencyGraphProof

                                                                                                        ↳ QDP

                                                                                                          ↳ Narrowing

                                                                                                            ↳ QDP

                                                                                                              ↳ DependencyGraphProof

                                                                                                                ↳ QDP

                                                                                                                  ↳ Narrowing

                                                                                                                    ↳ QDP

                                                                                                                      ↳ DependencyGraphProof

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

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

The TRS R consists of the following rules:

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

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 2 less nodes.

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ DependencyGraphProof

                                                                ↳ QDP

                                                                  ↳ Narrowing

                                                                    ↳ QDP

                                                                      ↳ DependencyGraphProof

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ DependencyGraphProof

                                                                                ↳ QDP

                                                                                  ↳ Narrowing

                                                                                    ↳ QDP

                                                                                      ↳ DependencyGraphProof

                                                                                        ↳ QDP

                                                                                          ↳ Narrowing

                                                                                            ↳ QDP

                                                                                              ↳ DependencyGraphProof

                                                                                                ↳ QDP

                                                                                                  ↳ Narrowing

                                                                                                    ↳ QDP

                                                                                                      ↳ DependencyGraphProof

                                                                                                        ↳ QDP

                                                                                                          ↳ Narrowing

                                                                                                            ↳ QDP

                                                                                                              ↳ DependencyGraphProof

                                                                                                                ↳ QDP

                                                                                                                  ↳ Narrowing

                                                                                                                    ↳ QDP

                                                                                                                      ↳ DependencyGraphProof

                                                                                                                        ↳ QDP

                                                                                                                          ↳ Narrowing

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

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

The TRS R consists of the following rules:

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

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

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ DependencyGraphProof

                                                                ↳ QDP

                                                                  ↳ Narrowing

                                                                    ↳ QDP

                                                                      ↳ DependencyGraphProof

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ DependencyGraphProof

                                                                                ↳ QDP

                                                                                  ↳ Narrowing

                                                                                    ↳ QDP

                                                                                      ↳ DependencyGraphProof

                                                                                        ↳ QDP

                                                                                          ↳ Narrowing

                                                                                            ↳ QDP

                                                                                              ↳ DependencyGraphProof

                                                                                                ↳ QDP

                                                                                                  ↳ Narrowing

                                                                                                    ↳ QDP

                                                                                                      ↳ DependencyGraphProof

                                                                                                        ↳ QDP

                                                                                                          ↳ Narrowing

                                                                                                            ↳ QDP

                                                                                                              ↳ DependencyGraphProof

                                                                                                                ↳ QDP

                                                                                                                  ↳ Narrowing

                                                                                                                    ↳ QDP

                                                                                                                      ↳ DependencyGraphProof

                                                                                                                        ↳ QDP

                                                                                                                          ↳ Narrowing

                                                                                                                            ↳ QDP

                                                                                                                              ↳ DependencyGraphProof

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

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

The TRS R consists of the following rules:

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

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ DependencyGraphProof

                                                                ↳ QDP

                                                                  ↳ Narrowing

                                                                    ↳ QDP

                                                                      ↳ DependencyGraphProof

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ DependencyGraphProof

                                                                                ↳ QDP

                                                                                  ↳ Narrowing

                                                                                    ↳ QDP

                                                                                      ↳ DependencyGraphProof

                                                                                        ↳ QDP

                                                                                          ↳ Narrowing

                                                                                            ↳ QDP

                                                                                              ↳ DependencyGraphProof

                                                                                                ↳ QDP

                                                                                                  ↳ Narrowing

                                                                                                    ↳ QDP

                                                                                                      ↳ DependencyGraphProof

                                                                                                        ↳ QDP

                                                                                                          ↳ Narrowing

                                                                                                            ↳ QDP

                                                                                                              ↳ DependencyGraphProof

                                                                                                                ↳ QDP

                                                                                                                  ↳ Narrowing

                                                                                                                    ↳ QDP

                                                                                                                      ↳ DependencyGraphProof

                                                                                                                        ↳ QDP

                                                                                                                          ↳ Narrowing

                                                                                                                            ↳ QDP

                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                ↳ QDP

                                                                                                                                  ↳ Narrowing

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

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

The TRS R consists of the following rules:

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

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

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ DependencyGraphProof

                                                                ↳ QDP

                                                                  ↳ Narrowing

                                                                    ↳ QDP

                                                                      ↳ DependencyGraphProof

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ DependencyGraphProof

                                                                                ↳ QDP

                                                                                  ↳ Narrowing

                                                                                    ↳ QDP

                                                                                      ↳ DependencyGraphProof

                                                                                        ↳ QDP

                                                                                          ↳ Narrowing

                                                                                            ↳ QDP

                                                                                              ↳ DependencyGraphProof

                                                                                                ↳ QDP

                                                                                                  ↳ Narrowing

                                                                                                    ↳ QDP

                                                                                                      ↳ DependencyGraphProof

                                                                                                        ↳ QDP

                                                                                                          ↳ Narrowing

                                                                                                            ↳ QDP

                                                                                                              ↳ DependencyGraphProof

                                                                                                                ↳ QDP

                                                                                                                  ↳ Narrowing

                                                                                                                    ↳ QDP

                                                                                                                      ↳ DependencyGraphProof

                                                                                                                        ↳ QDP

                                                                                                                          ↳ Narrowing

                                                                                                                            ↳ QDP

                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                ↳ QDP

                                                                                                                                  ↳ Narrowing

                                                                                                                                    ↳ QDP

                                                                                                                                      ↳ DependencyGraphProof

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

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

The TRS R consists of the following rules:

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

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ DependencyGraphProof

                                                                ↳ QDP

                                                                  ↳ Narrowing

                                                                    ↳ QDP

                                                                      ↳ DependencyGraphProof

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ DependencyGraphProof

                                                                                ↳ QDP

                                                                                  ↳ Narrowing

                                                                                    ↳ QDP

                                                                                      ↳ DependencyGraphProof

                                                                                        ↳ QDP

                                                                                          ↳ Narrowing

                                                                                            ↳ QDP

                                                                                              ↳ DependencyGraphProof

                                                                                                ↳ QDP

                                                                                                  ↳ Narrowing

                                                                                                    ↳ QDP

                                                                                                      ↳ DependencyGraphProof

                                                                                                        ↳ QDP

                                                                                                          ↳ Narrowing

                                                                                                            ↳ QDP

                                                                                                              ↳ DependencyGraphProof

                                                                                                                ↳ QDP

                                                                                                                  ↳ Narrowing

                                                                                                                    ↳ QDP

                                                                                                                      ↳ DependencyGraphProof

                                                                                                                        ↳ QDP

                                                                                                                          ↳ Narrowing

                                                                                                                            ↳ QDP

                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                ↳ QDP

                                                                                                                                  ↳ Narrowing

                                                                                                                                    ↳ QDP

                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                        ↳ QDP

                                                                                                                                          ↳ Narrowing

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

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

The TRS R consists of the following rules:

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

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

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ DependencyGraphProof

                                                                ↳ QDP

                                                                  ↳ Narrowing

                                                                    ↳ QDP

                                                                      ↳ DependencyGraphProof

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ DependencyGraphProof

                                                                                ↳ QDP

                                                                                  ↳ Narrowing

                                                                                    ↳ QDP

                                                                                      ↳ DependencyGraphProof

                                                                                        ↳ QDP

                                                                                          ↳ Narrowing

                                                                                            ↳ QDP

                                                                                              ↳ DependencyGraphProof

                                                                                                ↳ QDP

                                                                                                  ↳ Narrowing

                                                                                                    ↳ QDP

                                                                                                      ↳ DependencyGraphProof

                                                                                                        ↳ QDP

                                                                                                          ↳ Narrowing

                                                                                                            ↳ QDP

                                                                                                              ↳ DependencyGraphProof

                                                                                                                ↳ QDP

                                                                                                                  ↳ Narrowing

                                                                                                                    ↳ QDP

                                                                                                                      ↳ DependencyGraphProof

                                                                                                                        ↳ QDP

                                                                                                                          ↳ Narrowing

                                                                                                                            ↳ QDP

                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                ↳ QDP

                                                                                                                                  ↳ Narrowing

                                                                                                                                    ↳ QDP

                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                        ↳ QDP

                                                                                                                                          ↳ Narrowing

                                                                                                                                            ↳ QDP

                                                                                                                                              ↳ DependencyGraphProof

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

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

The TRS R consists of the following rules:

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

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 2 less nodes.

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ DependencyGraphProof

                                                                ↳ QDP

                                                                  ↳ Narrowing

                                                                    ↳ QDP

                                                                      ↳ DependencyGraphProof

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ DependencyGraphProof

                                                                                ↳ QDP

                                                                                  ↳ Narrowing

                                                                                    ↳ QDP

                                                                                      ↳ DependencyGraphProof

                                                                                        ↳ QDP

                                                                                          ↳ Narrowing

                                                                                            ↳ QDP

                                                                                              ↳ DependencyGraphProof

                                                                                                ↳ QDP

                                                                                                  ↳ Narrowing

                                                                                                    ↳ QDP

                                                                                                      ↳ DependencyGraphProof

                                                                                                        ↳ QDP

                                                                                                          ↳ Narrowing

                                                                                                            ↳ QDP

                                                                                                              ↳ DependencyGraphProof

                                                                                                                ↳ QDP

                                                                                                                  ↳ Narrowing

                                                                                                                    ↳ QDP

                                                                                                                      ↳ DependencyGraphProof

                                                                                                                        ↳ QDP

                                                                                                                          ↳ Narrowing

                                                                                                                            ↳ QDP

                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                ↳ QDP

                                                                                                                                  ↳ Narrowing

                                                                                                                                    ↳ QDP

                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                        ↳ QDP

                                                                                                                                          ↳ Narrowing

                                                                                                                                            ↳ QDP

                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                ↳ QDP

                                                                                                                                                  ↳ Narrowing

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

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

The TRS R consists of the following rules:

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

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

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ DependencyGraphProof

                                                                ↳ QDP

                                                                  ↳ Narrowing

                                                                    ↳ QDP

                                                                      ↳ DependencyGraphProof

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ DependencyGraphProof

                                                                                ↳ QDP

                                                                                  ↳ Narrowing

                                                                                    ↳ QDP

                                                                                      ↳ DependencyGraphProof

                                                                                        ↳ QDP

                                                                                          ↳ Narrowing

                                                                                            ↳ QDP

                                                                                              ↳ DependencyGraphProof

                                                                                                ↳ QDP

                                                                                                  ↳ Narrowing

                                                                                                    ↳ QDP

                                                                                                      ↳ DependencyGraphProof

                                                                                                        ↳ QDP

                                                                                                          ↳ Narrowing

                                                                                                            ↳ QDP

                                                                                                              ↳ DependencyGraphProof

                                                                                                                ↳ QDP

                                                                                                                  ↳ Narrowing

                                                                                                                    ↳ QDP

                                                                                                                      ↳ DependencyGraphProof

                                                                                                                        ↳ QDP

                                                                                                                          ↳ Narrowing

                                                                                                                            ↳ QDP

                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                ↳ QDP

                                                                                                                                  ↳ Narrowing

                                                                                                                                    ↳ QDP

                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                        ↳ QDP

                                                                                                                                          ↳ Narrowing

                                                                                                                                            ↳ QDP

                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                ↳ QDP

                                                                                                                                                  ↳ Narrowing

                                                                                                                                                    ↳ QDP

                                                                                                                                                      ↳ DependencyGraphProof

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

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

The TRS R consists of the following rules:

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

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ DependencyGraphProof

                                                                ↳ QDP

                                                                  ↳ Narrowing

                                                                    ↳ QDP

                                                                      ↳ DependencyGraphProof

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ DependencyGraphProof

                                                                                ↳ QDP

                                                                                  ↳ Narrowing

                                                                                    ↳ QDP

                                                                                      ↳ DependencyGraphProof

                                                                                        ↳ QDP

                                                                                          ↳ Narrowing

                                                                                            ↳ QDP

                                                                                              ↳ DependencyGraphProof

                                                                                                ↳ QDP

                                                                                                  ↳ Narrowing

                                                                                                    ↳ QDP

                                                                                                      ↳ DependencyGraphProof

                                                                                                        ↳ QDP

                                                                                                          ↳ Narrowing

                                                                                                            ↳ QDP

                                                                                                              ↳ DependencyGraphProof

                                                                                                                ↳ QDP

                                                                                                                  ↳ Narrowing

                                                                                                                    ↳ QDP

                                                                                                                      ↳ DependencyGraphProof

                                                                                                                        ↳ QDP

                                                                                                                          ↳ Narrowing

                                                                                                                            ↳ QDP

                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                ↳ QDP

                                                                                                                                  ↳ Narrowing

                                                                                                                                    ↳ QDP

                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                        ↳ QDP

                                                                                                                                          ↳ Narrowing

                                                                                                                                            ↳ QDP

                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                ↳ QDP

                                                                                                                                                  ↳ Narrowing

                                                                                                                                                    ↳ QDP

                                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                                        ↳ QDP

                                                                                                                                                          ↳ Narrowing

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

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

The TRS R consists of the following rules:

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

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

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ DependencyGraphProof

                                                                ↳ QDP

                                                                  ↳ Narrowing

                                                                    ↳ QDP

                                                                      ↳ DependencyGraphProof

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ DependencyGraphProof

                                                                                ↳ QDP

                                                                                  ↳ Narrowing

                                                                                    ↳ QDP

                                                                                      ↳ DependencyGraphProof

                                                                                        ↳ QDP

                                                                                          ↳ Narrowing

                                                                                            ↳ QDP

                                                                                              ↳ DependencyGraphProof

                                                                                                ↳ QDP

                                                                                                  ↳ Narrowing

                                                                                                    ↳ QDP

                                                                                                      ↳ DependencyGraphProof

                                                                                                        ↳ QDP

                                                                                                          ↳ Narrowing

                                                                                                            ↳ QDP

                                                                                                              ↳ DependencyGraphProof

                                                                                                                ↳ QDP

                                                                                                                  ↳ Narrowing

                                                                                                                    ↳ QDP

                                                                                                                      ↳ DependencyGraphProof

                                                                                                                        ↳ QDP

                                                                                                                          ↳ Narrowing

                                                                                                                            ↳ QDP

                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                ↳ QDP

                                                                                                                                  ↳ Narrowing

                                                                                                                                    ↳ QDP

                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                        ↳ QDP

                                                                                                                                          ↳ Narrowing

                                                                                                                                            ↳ QDP

                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                ↳ QDP

                                                                                                                                                  ↳ Narrowing

                                                                                                                                                    ↳ QDP

                                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                                        ↳ QDP

                                                                                                                                                          ↳ Narrowing

                                                                                                                                                            ↳ QDP

                                                                                                                                                              ↳ DependencyGraphProof

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

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

The TRS R consists of the following rules:

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

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ DependencyGraphProof

                                                                ↳ QDP

                                                                  ↳ Narrowing

                                                                    ↳ QDP

                                                                      ↳ DependencyGraphProof

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ DependencyGraphProof

                                                                                ↳ QDP

                                                                                  ↳ Narrowing

                                                                                    ↳ QDP

                                                                                      ↳ DependencyGraphProof

                                                                                        ↳ QDP

                                                                                          ↳ Narrowing

                                                                                            ↳ QDP

                                                                                              ↳ DependencyGraphProof

                                                                                                ↳ QDP

                                                                                                  ↳ Narrowing

                                                                                                    ↳ QDP

                                                                                                      ↳ DependencyGraphProof

                                                                                                        ↳ QDP

                                                                                                          ↳ Narrowing

                                                                                                            ↳ QDP

                                                                                                              ↳ DependencyGraphProof

                                                                                                                ↳ QDP

                                                                                                                  ↳ Narrowing

                                                                                                                    ↳ QDP

                                                                                                                      ↳ DependencyGraphProof

                                                                                                                        ↳ QDP

                                                                                                                          ↳ Narrowing

                                                                                                                            ↳ QDP

                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                ↳ QDP

                                                                                                                                  ↳ Narrowing

                                                                                                                                    ↳ QDP

                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                        ↳ QDP

                                                                                                                                          ↳ Narrowing

                                                                                                                                            ↳ QDP

                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                ↳ QDP

                                                                                                                                                  ↳ Narrowing

                                                                                                                                                    ↳ QDP

                                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                                        ↳ QDP

                                                                                                                                                          ↳ Narrowing

                                                                                                                                                            ↳ QDP

                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Narrowing

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

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

The TRS R consists of the following rules:

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

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

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ DependencyGraphProof

                                                                ↳ QDP

                                                                  ↳ Narrowing

                                                                    ↳ QDP

                                                                      ↳ DependencyGraphProof

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ DependencyGraphProof

                                                                                ↳ QDP

                                                                                  ↳ Narrowing

                                                                                    ↳ QDP

                                                                                      ↳ DependencyGraphProof

                                                                                        ↳ QDP

                                                                                          ↳ Narrowing

                                                                                            ↳ QDP

                                                                                              ↳ DependencyGraphProof

                                                                                                ↳ QDP

                                                                                                  ↳ Narrowing

                                                                                                    ↳ QDP

                                                                                                      ↳ DependencyGraphProof

                                                                                                        ↳ QDP

                                                                                                          ↳ Narrowing

                                                                                                            ↳ QDP

                                                                                                              ↳ DependencyGraphProof

                                                                                                                ↳ QDP

                                                                                                                  ↳ Narrowing

                                                                                                                    ↳ QDP

                                                                                                                      ↳ DependencyGraphProof

                                                                                                                        ↳ QDP

                                                                                                                          ↳ Narrowing

                                                                                                                            ↳ QDP

                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                ↳ QDP

                                                                                                                                  ↳ Narrowing

                                                                                                                                    ↳ QDP

                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                        ↳ QDP

                                                                                                                                          ↳ Narrowing

                                                                                                                                            ↳ QDP

                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                ↳ QDP

                                                                                                                                                  ↳ Narrowing

                                                                                                                                                    ↳ QDP

                                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                                        ↳ QDP

                                                                                                                                                          ↳ Narrowing

                                                                                                                                                            ↳ QDP

                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Narrowing

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ DependencyGraphProof

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

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

The TRS R consists of the following rules:

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

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ DependencyGraphProof

                                                                ↳ QDP

                                                                  ↳ Narrowing

                                                                    ↳ QDP

                                                                      ↳ DependencyGraphProof

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ DependencyGraphProof

                                                                                ↳ QDP

                                                                                  ↳ Narrowing

                                                                                    ↳ QDP

                                                                                      ↳ DependencyGraphProof

                                                                                        ↳ QDP

                                                                                          ↳ Narrowing

                                                                                            ↳ QDP

                                                                                              ↳ DependencyGraphProof

                                                                                                ↳ QDP

                                                                                                  ↳ Narrowing

                                                                                                    ↳ QDP

                                                                                                      ↳ DependencyGraphProof

                                                                                                        ↳ QDP

                                                                                                          ↳ Narrowing

                                                                                                            ↳ QDP

                                                                                                              ↳ DependencyGraphProof

                                                                                                                ↳ QDP

                                                                                                                  ↳ Narrowing

                                                                                                                    ↳ QDP

                                                                                                                      ↳ DependencyGraphProof

                                                                                                                        ↳ QDP

                                                                                                                          ↳ Narrowing

                                                                                                                            ↳ QDP

                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                ↳ QDP

                                                                                                                                  ↳ Narrowing

                                                                                                                                    ↳ QDP

                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                        ↳ QDP

                                                                                                                                          ↳ Narrowing

                                                                                                                                            ↳ QDP

                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                ↳ QDP

                                                                                                                                                  ↳ Narrowing

                                                                                                                                                    ↳ QDP

                                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                                        ↳ QDP

                                                                                                                                                          ↳ Narrowing

                                                                                                                                                            ↳ QDP

                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Narrowing

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Narrowing

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

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

The TRS R consists of the following rules:

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

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

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ DependencyGraphProof

                                                                ↳ QDP

                                                                  ↳ Narrowing

                                                                    ↳ QDP

                                                                      ↳ DependencyGraphProof

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ DependencyGraphProof

                                                                                ↳ QDP

                                                                                  ↳ Narrowing

                                                                                    ↳ QDP

                                                                                      ↳ DependencyGraphProof

                                                                                        ↳ QDP

                                                                                          ↳ Narrowing

                                                                                            ↳ QDP

                                                                                              ↳ DependencyGraphProof

                                                                                                ↳ QDP

                                                                                                  ↳ Narrowing

                                                                                                    ↳ QDP

                                                                                                      ↳ DependencyGraphProof

                                                                                                        ↳ QDP

                                                                                                          ↳ Narrowing

                                                                                                            ↳ QDP

                                                                                                              ↳ DependencyGraphProof

                                                                                                                ↳ QDP

                                                                                                                  ↳ Narrowing

                                                                                                                    ↳ QDP

                                                                                                                      ↳ DependencyGraphProof

                                                                                                                        ↳ QDP

                                                                                                                          ↳ Narrowing

                                                                                                                            ↳ QDP

                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                ↳ QDP

                                                                                                                                  ↳ Narrowing

                                                                                                                                    ↳ QDP

                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                        ↳ QDP

                                                                                                                                          ↳ Narrowing

                                                                                                                                            ↳ QDP

                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                ↳ QDP

                                                                                                                                                  ↳ Narrowing

                                                                                                                                                    ↳ QDP

                                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                                        ↳ QDP

                                                                                                                                                          ↳ Narrowing

                                                                                                                                                            ↳ QDP

                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Narrowing

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Narrowing

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ DependencyGraphProof

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

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

The TRS R consists of the following rules:

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

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 2 less nodes.

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ DependencyGraphProof

                                                                ↳ QDP

                                                                  ↳ Narrowing

                                                                    ↳ QDP

                                                                      ↳ DependencyGraphProof

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ DependencyGraphProof

                                                                                ↳ QDP

                                                                                  ↳ Narrowing

                                                                                    ↳ QDP

                                                                                      ↳ DependencyGraphProof

                                                                                        ↳ QDP

                                                                                          ↳ Narrowing

                                                                                            ↳ QDP

                                                                                              ↳ DependencyGraphProof

                                                                                                ↳ QDP

                                                                                                  ↳ Narrowing

                                                                                                    ↳ QDP

                                                                                                      ↳ DependencyGraphProof

                                                                                                        ↳ QDP

                                                                                                          ↳ Narrowing

                                                                                                            ↳ QDP

                                                                                                              ↳ DependencyGraphProof

                                                                                                                ↳ QDP

                                                                                                                  ↳ Narrowing

                                                                                                                    ↳ QDP

                                                                                                                      ↳ DependencyGraphProof

                                                                                                                        ↳ QDP

                                                                                                                          ↳ Narrowing

                                                                                                                            ↳ QDP

                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                ↳ QDP

                                                                                                                                  ↳ Narrowing

                                                                                                                                    ↳ QDP

                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                        ↳ QDP

                                                                                                                                          ↳ Narrowing

                                                                                                                                            ↳ QDP

                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                ↳ QDP

                                                                                                                                                  ↳ Narrowing

                                                                                                                                                    ↳ QDP

                                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                                        ↳ QDP

                                                                                                                                                          ↳ Narrowing

                                                                                                                                                            ↳ QDP

                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Narrowing

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Narrowing

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Narrowing

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

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

The TRS R consists of the following rules:

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

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

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

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ DependencyGraphProof

                                                                ↳ QDP

                                                                  ↳ Narrowing

                                                                    ↳ QDP

                                                                      ↳ DependencyGraphProof

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ DependencyGraphProof

                                                                                ↳ QDP

                                                                                  ↳ Narrowing

                                                                                    ↳ QDP

                                                                                      ↳ DependencyGraphProof

                                                                                        ↳ QDP

                                                                                          ↳ Narrowing

                                                                                            ↳ QDP

                                                                                              ↳ DependencyGraphProof

                                                                                                ↳ QDP

                                                                                                  ↳ Narrowing

                                                                                                    ↳ QDP

                                                                                                      ↳ DependencyGraphProof

                                                                                                        ↳ QDP

                                                                                                          ↳ Narrowing

                                                                                                            ↳ QDP

                                                                                                              ↳ DependencyGraphProof

                                                                                                                ↳ QDP

                                                                                                                  ↳ Narrowing

                                                                                                                    ↳ QDP

                                                                                                                      ↳ DependencyGraphProof

                                                                                                                        ↳ QDP

                                                                                                                          ↳ Narrowing

                                                                                                                            ↳ QDP

                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                ↳ QDP

                                                                                                                                  ↳ Narrowing

                                                                                                                                    ↳ QDP

                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                        ↳ QDP

                                                                                                                                          ↳ Narrowing

                                                                                                                                            ↳ QDP

                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                ↳ QDP

                                                                                                                                                  ↳ Narrowing

                                                                                                                                                    ↳ QDP

                                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                                        ↳ QDP

                                                                                                                                                          ↳ Narrowing

                                                                                                                                                            ↳ QDP

                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Narrowing

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Narrowing

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Narrowing

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ DependencyGraphProof

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

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

The TRS R consists of the following rules:

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

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 2 less nodes.

↳ QTRS

  ↳ QTRS Reverse

  ↳ Strip Symbols Proof

  ↳ QTRS Reverse

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ QDPToSRSProof

                        ↳ QTRS

                          ↳ QTRS Reverse

                            ↳ QTRS

                              ↳ QTRS Reverse

                              ↳ QTRS Reverse

                              ↳ DependencyPairsProof

                                ↳ QDP

                                  ↳ DependencyGraphProof

                                    ↳ QDP

                                      ↳ QDPOrderProof

                                        ↳ QDP

                                          ↳ Narrowing

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ Narrowing

                                                    ↳ QDP

                                                      ↳ DependencyGraphProof

                                                        ↳ QDP

                                                          ↳ Narrowing

                                                            ↳ QDP

                                                              ↳ DependencyGraphProof

                                                                ↳ QDP

                                                                  ↳ Narrowing

                                                                    ↳ QDP

                                                                      ↳ DependencyGraphProof

                                                                        ↳ QDP

                                                                          ↳ Narrowing

                                                                            ↳ QDP

                                                                              ↳ DependencyGraphProof

                                                                                ↳ QDP

                                                                                  ↳ Narrowing

                                                                                    ↳ QDP

                                                                                      ↳ DependencyGraphProof

                                                                                        ↳ QDP

                                                                                          ↳ Narrowing

                                                                                            ↳ QDP

                                                                                              ↳ DependencyGraphProof

                                                                                                ↳ QDP

                                                                                                  ↳ Narrowing

                                                                                                    ↳ QDP

                                                                                                      ↳ DependencyGraphProof

                                                                                                        ↳ QDP

                                                                                                          ↳ Narrowing

                                                                                                            ↳ QDP

                                                                                                              ↳ DependencyGraphProof

                                                                                                                ↳ QDP

                                                                                                                  ↳ Narrowing

                                                                                                                    ↳ QDP

                                                                                                                      ↳ DependencyGraphProof

                                                                                                                        ↳ QDP

                                                                                                                          ↳ Narrowing

                                                                                                                            ↳ QDP

                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                ↳ QDP

                                                                                                                                  ↳ Narrowing

                                                                                                                                    ↳ QDP

                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                        ↳ QDP

                                                                                                                                          ↳ Narrowing

                                                                                                                                            ↳ QDP

                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                ↳ QDP

                                                                                                                                                  ↳ Narrowing

                                                                                                                                                    ↳ QDP

                                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                                        ↳ QDP

                                                                                                                                                          ↳ Narrowing

                                                                                                                                                            ↳ QDP

                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Narrowing

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Narrowing

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Narrowing

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                                                                        ↳ QDP

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

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

The TRS R consists of the following rules:

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

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