(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: [1,2]
-2: [2,1]

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