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:

f2(f2(f2(a, x), y), z) -> f2(f2(x, z), f2(y, z))
f2(f2(b, x), y) -> x
f2(c, y) -> y

Q is empty.


QTRS
  ↳ Non-Overlap Check

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

f2(f2(f2(a, x), y), z) -> f2(f2(x, z), f2(y, z))
f2(f2(b, x), y) -> x
f2(c, y) -> y

Q is empty.

The TRS is non-overlapping. Hence, we can switch to innermost.

↳ QTRS
  ↳ Non-Overlap Check
QTRS
      ↳ DependencyPairsProof

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

f2(f2(f2(a, x), y), z) -> f2(f2(x, z), f2(y, z))
f2(f2(b, x), y) -> x
f2(c, y) -> y

The set Q consists of the following terms:

f2(f2(f2(a, x0), x1), x2)
f2(f2(b, x0), x1)
f2(c, x0)


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

F2(f2(f2(a, x), y), z) -> F2(x, z)
F2(f2(f2(a, x), y), z) -> F2(f2(x, z), f2(y, z))
F2(f2(f2(a, x), y), z) -> F2(y, z)

The TRS R consists of the following rules:

f2(f2(f2(a, x), y), z) -> f2(f2(x, z), f2(y, z))
f2(f2(b, x), y) -> x
f2(c, y) -> y

The set Q consists of the following terms:

f2(f2(f2(a, x0), x1), x2)
f2(f2(b, x0), x1)
f2(c, x0)

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

↳ QTRS
  ↳ Non-Overlap Check
    ↳ QTRS
      ↳ DependencyPairsProof
QDP

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

F2(f2(f2(a, x), y), z) -> F2(x, z)
F2(f2(f2(a, x), y), z) -> F2(f2(x, z), f2(y, z))
F2(f2(f2(a, x), y), z) -> F2(y, z)

The TRS R consists of the following rules:

f2(f2(f2(a, x), y), z) -> f2(f2(x, z), f2(y, z))
f2(f2(b, x), y) -> x
f2(c, y) -> y

The set Q consists of the following terms:

f2(f2(f2(a, x0), x1), x2)
f2(f2(b, x0), x1)
f2(c, x0)

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