(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
*(x, +(y, z)) → +(*(x, y), *(x, z))
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)
*1(x, +(y, z)) → *1(x, z)
The TRS R consists of the following rules:
*(x, +(y, z)) → +(*(x, y), *(x, z))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
(3) QDPOrderProof (EQUIVALENT transformation)
We use the reduction pair processor [LPAR04].
The following pairs can be oriented strictly and are deleted.
*1(x, +(y, z)) → *1(x, y)
*1(x, +(y, z)) → *1(x, z)
The remaining pairs can at least be oriented weakly.
Used ordering: Lexicographic path order with status [LPO].
Quasi-Precedence:
+2 > *^12
Status:
*^12: [2,1]
+2: [2,1]
The following usable rules [FROCOS05] were oriented:
none
(4) Obligation:
Q DP problem:
P is empty.
The TRS R consists of the following rules:
*(x, +(y, z)) → +(*(x, y), *(x, z))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
(5) PisEmptyProof (EQUIVALENT transformation)
The TRS P is empty. Hence, there is no (P,Q,R) chain.
(6) TRUE