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:

b2(y, z) -> f1(c3(c3(y, z, z), a, a))
b2(b2(z, y), a) -> z
c3(f1(z), f1(c3(a, x, a)), y) -> c3(f1(b2(x, z)), c3(z, y, a), a)

Q is empty.


↳ QTRS
  ↳ DependencyPairsProof

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

b2(y, z) -> f1(c3(c3(y, z, z), a, a))
b2(b2(z, y), a) -> z
c3(f1(z), f1(c3(a, x, a)), y) -> c3(f1(b2(x, z)), c3(z, y, a), a)

Q is empty.

Using Dependency Pairs [1,13] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:

B2(y, z) -> C3(y, z, z)
C3(f1(z), f1(c3(a, x, a)), y) -> B2(x, z)
C3(f1(z), f1(c3(a, x, a)), y) -> C3(f1(b2(x, z)), c3(z, y, a), a)
B2(y, z) -> C3(c3(y, z, z), a, a)
C3(f1(z), f1(c3(a, x, a)), y) -> C3(z, y, a)

The TRS R consists of the following rules:

b2(y, z) -> f1(c3(c3(y, z, z), a, a))
b2(b2(z, y), a) -> z
c3(f1(z), f1(c3(a, x, a)), y) -> c3(f1(b2(x, z)), c3(z, y, a), a)

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

↳ QTRS
  ↳ DependencyPairsProof
    ↳ QDP
      ↳ DependencyGraphProof

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

B2(y, z) -> C3(y, z, z)
C3(f1(z), f1(c3(a, x, a)), y) -> B2(x, z)
C3(f1(z), f1(c3(a, x, a)), y) -> C3(f1(b2(x, z)), c3(z, y, a), a)
B2(y, z) -> C3(c3(y, z, z), a, a)
C3(f1(z), f1(c3(a, x, a)), y) -> C3(z, y, a)

The TRS R consists of the following rules:

b2(y, z) -> f1(c3(c3(y, z, z), a, a))
b2(b2(z, y), a) -> z
c3(f1(z), f1(c3(a, x, a)), y) -> c3(f1(b2(x, z)), c3(z, y, a), a)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [13,14,18] contains 1 SCC with 1 less node.

↳ QTRS
  ↳ DependencyPairsProof
    ↳ QDP
      ↳ DependencyGraphProof
        ↳ QDP

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

B2(y, z) -> C3(y, z, z)
C3(f1(z), f1(c3(a, x, a)), y) -> B2(x, z)
C3(f1(z), f1(c3(a, x, a)), y) -> C3(f1(b2(x, z)), c3(z, y, a), a)
C3(f1(z), f1(c3(a, x, a)), y) -> C3(z, y, a)

The TRS R consists of the following rules:

b2(y, z) -> f1(c3(c3(y, z, z), a, a))
b2(b2(z, y), a) -> z
c3(f1(z), f1(c3(a, x, a)), y) -> c3(f1(b2(x, z)), c3(z, y, a), a)

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