(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
+(*(x, y), *(a, y)) → *(+(x, a), y)
*(*(x, y), z) → *(x, *(y, z))
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Lexicographic Path Order [LPO].
Precedence:
a > +2 > *2
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
+(*(x, y), *(a, y)) → *(+(x, a), y)
*(*(x, y), z) → *(x, *(y, z))
(2) Obligation:
Q restricted rewrite system:
R is empty.
Q is empty.
(3) RisEmptyProof (EQUIVALENT transformation)
The TRS R is empty. Hence, termination is trivially proven.
(4) TRUE