(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
:(:(:(:(C, x), y), z), u) → :(:(x, z), :(:(:(x, y), z), u))
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Lexicographic path order with status [LPO].
Precedence:
C > :2
Status:
:2: [1,2]
C: []
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
:(:(:(:(C, x), y), z), u) → :(:(x, z), :(:(:(x, y), z), u))
(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