(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
+(-(x, y), z) → -(+(x, z), y)
-(+(x, y), y) → x
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Lexicographic path order with status [LPO].
Quasi-Precedence:
[+2, -2]
Status:
-2: [2,1]
+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, z), y)
-(+(x, y), y) → x
(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