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:

+(x, +(y, z)) → +(+(x, y), z)
*(x, +(y, z)) → +(*(x, y), *(x, z))
+(+(x, *(y, z)), *(y, u)) → +(x, *(y, +(z, u)))

Q is empty.


↳ QTRS
  ↳ DependencyPairsProof

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

+(x, +(y, z)) → +(+(x, y), z)
*(x, +(y, z)) → +(*(x, y), *(x, z))
+(+(x, *(y, z)), *(y, u)) → +(x, *(y, +(z, u)))

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:

+1(+(x, *(y, z)), *(y, u)) → +1(z, u)
+1(+(x, *(y, z)), *(y, u)) → *1(y, +(z, u))
*1(x, +(y, z)) → +1(*(x, y), *(x, z))
+1(+(x, *(y, z)), *(y, u)) → +1(x, *(y, +(z, u)))
*1(x, +(y, z)) → *1(x, z)
*1(x, +(y, z)) → *1(x, y)
+1(x, +(y, z)) → +1(x, y)
+1(x, +(y, z)) → +1(+(x, y), z)

The TRS R consists of the following rules:

+(x, +(y, z)) → +(+(x, y), z)
*(x, +(y, z)) → +(*(x, y), *(x, z))
+(+(x, *(y, z)), *(y, u)) → +(x, *(y, +(z, u)))

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

↳ QTRS
  ↳ DependencyPairsProof
    ↳ QDP
      ↳ EdgeDeletionProof

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

+1(+(x, *(y, z)), *(y, u)) → +1(z, u)
+1(+(x, *(y, z)), *(y, u)) → *1(y, +(z, u))
*1(x, +(y, z)) → +1(*(x, y), *(x, z))
+1(+(x, *(y, z)), *(y, u)) → +1(x, *(y, +(z, u)))
*1(x, +(y, z)) → *1(x, z)
*1(x, +(y, z)) → *1(x, y)
+1(x, +(y, z)) → +1(x, y)
+1(x, +(y, z)) → +1(+(x, y), z)

The TRS R consists of the following rules:

+(x, +(y, z)) → +(+(x, y), z)
*(x, +(y, z)) → +(*(x, y), *(x, z))
+(+(x, *(y, z)), *(y, u)) → +(x, *(y, +(z, u)))

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

↳ QTRS
  ↳ DependencyPairsProof
    ↳ QDP
      ↳ EdgeDeletionProof
        ↳ QDP

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

+1(+(x, *(y, z)), *(y, u)) → *1(y, +(z, u))
+1(+(x, *(y, z)), *(y, u)) → +1(z, u)
*1(x, +(y, z)) → +1(*(x, y), *(x, z))
*1(x, +(y, z)) → *1(x, z)
+1(+(x, *(y, z)), *(y, u)) → +1(x, *(y, +(z, u)))
+1(x, +(y, z)) → +1(x, y)
*1(x, +(y, z)) → *1(x, y)
+1(x, +(y, z)) → +1(+(x, y), z)

The TRS R consists of the following rules:

+(x, +(y, z)) → +(+(x, y), z)
*(x, +(y, z)) → +(*(x, y), *(x, z))
+(+(x, *(y, z)), *(y, u)) → +(x, *(y, +(z, u)))

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