(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
+(*(x, y), *(x, z)) → *(x, +(y, z))
+(+(x, y), z) → +(x, +(y, z))
+(*(x, y), +(*(x, z), u)) → +(*(x, +(y, z)), u)
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Polynomial interpretation [POLO]:
POL(*(x1, x2)) = 1 + x1 + x2
POL(+(x1, x2)) = x1 + x2
POL(u) = 0
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
+(*(x, y), *(x, z)) → *(x, +(y, z))
+(*(x, y), +(*(x, z), u)) → +(*(x, +(y, z)), u)
(2) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
+(+(x, y), z) → +(x, +(y, z))
Q is empty.
(3) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Recursive path order with status [RPO].
Quasi-Precedence:
trivial
Status:
+2: [1,2]
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
+(+(x, y), z) → +(x, +(y, z))
(4) Obligation:
Q restricted rewrite system:
R is empty.
Q is empty.
(5) RisEmptyProof (EQUIVALENT transformation)
The TRS R is empty. Hence, termination is trivially proven.
(6) TRUE
(7) RisEmptyProof (EQUIVALENT transformation)
The TRS R is empty. Hence, termination is trivially proven.
(8) TRUE
(9) RisEmptyProof (EQUIVALENT transformation)
The TRS R is empty. Hence, termination is trivially proven.
(10) TRUE