(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