(0) Obligation:
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.
(1) DependencyPairsProof (EQUIVALENT transformation)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
(2) Obligation:
Q DP problem:
The TRS P consists of the following rules:
+1(x, +(y, z)) → +1(+(x, y), z)
+1(x, +(y, z)) → +1(x, y)
*1(x, +(y, z)) → +1(*(x, y), *(x, z))
*1(x, +(y, z)) → *1(x, y)
*1(x, +(y, z)) → *1(x, z)
+1(+(x, *(y, z)), *(y, u)) → +1(x, *(y, +(z, u)))
+1(+(x, *(y, z)), *(y, u)) → *1(y, +(z, u))
+1(+(x, *(y, z)), *(y, u)) → +1(z, u)
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.