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:

f(x, y, z) → g(x, y, z)
g(0, 1, x) → f(x, x, x)

Q is empty.


↳ QTRS
  ↳ AAECC Innermost

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

f(x, y, z) → g(x, y, z)
g(0, 1, x) → f(x, x, x)

Q is empty.

We have applied [15,7] to switch to innermost. The TRS R 1 is none

The TRS R 2 is

f(x, y, z) → g(x, y, z)
g(0, 1, x) → f(x, x, x)

The signature Sigma is {g, f}

↳ QTRS
  ↳ AAECC Innermost
    ↳ QTRS
      ↳ DependencyPairsProof

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

f(x, y, z) → g(x, y, z)
g(0, 1, x) → f(x, x, x)

The set Q consists of the following terms:

f(x0, x1, x2)
g(0, 1, 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:

G(0, 1, x) → F(x, x, x)
F(x, y, z) → G(x, y, z)

The TRS R consists of the following rules:

f(x, y, z) → g(x, y, z)
g(0, 1, x) → f(x, x, x)

The set Q consists of the following terms:

f(x0, x1, x2)
g(0, 1, x0)

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

↳ QTRS
  ↳ AAECC Innermost
    ↳ QTRS
      ↳ DependencyPairsProof
        ↳ QDP
          ↳ EdgeDeletionProof

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

G(0, 1, x) → F(x, x, x)
F(x, y, z) → G(x, y, z)

The TRS R consists of the following rules:

f(x, y, z) → g(x, y, z)
g(0, 1, x) → f(x, x, x)

The set Q consists of the following terms:

f(x0, x1, x2)
g(0, 1, x0)

We have to consider all minimal (P,Q,R)-chains.
We deleted some edges using various graph approximations

↳ QTRS
  ↳ AAECC Innermost
    ↳ QTRS
      ↳ DependencyPairsProof
        ↳ QDP
          ↳ EdgeDeletionProof
            ↳ QDP

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

G(0, 1, x) → F(x, x, x)
F(x, y, z) → G(x, y, z)

The TRS R consists of the following rules:

f(x, y, z) → g(x, y, z)
g(0, 1, x) → f(x, x, x)

The set Q consists of the following terms:

f(x0, x1, x2)
g(0, 1, x0)

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