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:

f3(0, 1, x) -> f3(g1(x), g1(x), x)
f3(g1(x), y, z) -> g1(f3(x, y, z))
f3(x, g1(y), z) -> g1(f3(x, y, z))
f3(x, y, g1(z)) -> g1(f3(x, y, z))

Q is empty.


QTRS
  ↳ DependencyPairsProof

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

f3(0, 1, x) -> f3(g1(x), g1(x), x)
f3(g1(x), y, z) -> g1(f3(x, y, z))
f3(x, g1(y), z) -> g1(f3(x, y, z))
f3(x, y, g1(z)) -> g1(f3(x, y, z))

Q is empty.

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

F3(g1(x), y, z) -> F3(x, y, z)
F3(0, 1, x) -> F3(g1(x), g1(x), x)
F3(x, y, g1(z)) -> F3(x, y, z)
F3(x, g1(y), z) -> F3(x, y, z)

The TRS R consists of the following rules:

f3(0, 1, x) -> f3(g1(x), g1(x), x)
f3(g1(x), y, z) -> g1(f3(x, y, z))
f3(x, g1(y), z) -> g1(f3(x, y, z))
f3(x, y, g1(z)) -> g1(f3(x, y, z))

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

↳ QTRS
  ↳ DependencyPairsProof
QDP
      ↳ QDPAfsSolverProof

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

F3(g1(x), y, z) -> F3(x, y, z)
F3(0, 1, x) -> F3(g1(x), g1(x), x)
F3(x, y, g1(z)) -> F3(x, y, z)
F3(x, g1(y), z) -> F3(x, y, z)

The TRS R consists of the following rules:

f3(0, 1, x) -> f3(g1(x), g1(x), x)
f3(g1(x), y, z) -> g1(f3(x, y, z))
f3(x, g1(y), z) -> g1(f3(x, y, z))
f3(x, y, g1(z)) -> g1(f3(x, y, z))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using an argument filtering and a montonic ordering, at least one Dependency Pair of this SCC can be strictly oriented.

F3(x, y, g1(z)) -> F3(x, y, z)
Used argument filtering: F3(x1, x2, x3)  =  x3
g1(x1)  =  g1(x1)
Used ordering: Quasi Precedence: trivial


↳ QTRS
  ↳ DependencyPairsProof
    ↳ QDP
      ↳ QDPAfsSolverProof
QDP

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

F3(g1(x), y, z) -> F3(x, y, z)
F3(0, 1, x) -> F3(g1(x), g1(x), x)
F3(x, g1(y), z) -> F3(x, y, z)

The TRS R consists of the following rules:

f3(0, 1, x) -> f3(g1(x), g1(x), x)
f3(g1(x), y, z) -> g1(f3(x, y, z))
f3(x, g1(y), z) -> g1(f3(x, y, z))
f3(x, y, g1(z)) -> g1(f3(x, y, z))

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