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.