(0) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

f(g(x), y, y) → g(f(x, x, y))

Q is empty.

(1) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Recursive path order with status [RPO].
Precedence:
f3 > g1

Status:
f3: [1,2,3]
g1: multiset
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

f(g(x), y, y) → g(f(x, x, y))


(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