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:

+2(*2(x, y), *2(x, z)) -> *2(x, +2(y, z))
+2(+2(x, y), z) -> +2(x, +2(y, z))
+2(*2(x, y), +2(*2(x, z), u)) -> +2(*2(x, +2(y, z)), u)

Q is empty.


↳ QTRS
  ↳ DependencyPairsProof

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

+2(*2(x, y), *2(x, z)) -> *2(x, +2(y, z))
+2(+2(x, y), z) -> +2(x, +2(y, z))
+2(*2(x, y), +2(*2(x, z), u)) -> +2(*2(x, +2(y, z)), u)

Q is empty.

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

+12(+2(x, y), z) -> +12(y, z)
+12(*2(x, y), +2(*2(x, z), u)) -> +12(y, z)
+12(*2(x, y), *2(x, z)) -> +12(y, z)
+12(*2(x, y), +2(*2(x, z), u)) -> +12(*2(x, +2(y, z)), u)
+12(+2(x, y), z) -> +12(x, +2(y, z))

The TRS R consists of the following rules:

+2(*2(x, y), *2(x, z)) -> *2(x, +2(y, z))
+2(+2(x, y), z) -> +2(x, +2(y, z))
+2(*2(x, y), +2(*2(x, z), u)) -> +2(*2(x, +2(y, z)), u)

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:

+12(+2(x, y), z) -> +12(y, z)
+12(*2(x, y), +2(*2(x, z), u)) -> +12(y, z)
+12(*2(x, y), *2(x, z)) -> +12(y, z)
+12(*2(x, y), +2(*2(x, z), u)) -> +12(*2(x, +2(y, z)), u)
+12(+2(x, y), z) -> +12(x, +2(y, z))

The TRS R consists of the following rules:

+2(*2(x, y), *2(x, z)) -> *2(x, +2(y, z))
+2(+2(x, y), z) -> +2(x, +2(y, z))
+2(*2(x, y), +2(*2(x, z), u)) -> +2(*2(x, +2(y, z)), u)

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

↳ QTRS
  ↳ DependencyPairsProof
    ↳ QDP
      ↳ DependencyGraphProof
        ↳ QDP

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

+12(+2(x, y), z) -> +12(y, z)
+12(*2(x, y), +2(*2(x, z), u)) -> +12(y, z)
+12(*2(x, y), *2(x, z)) -> +12(y, z)
+12(+2(x, y), z) -> +12(x, +2(y, z))

The TRS R consists of the following rules:

+2(*2(x, y), *2(x, z)) -> *2(x, +2(y, z))
+2(+2(x, y), z) -> +2(x, +2(y, z))
+2(*2(x, y), +2(*2(x, z), u)) -> +2(*2(x, +2(y, z)), u)

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