(0) Obligation:

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

f(x, g(x)) → x
f(x, h(y)) → f(h(x), y)

Q is empty.

(1) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Recursive path order with status [RPO].
Precedence:
f2 > h1
g1 > h1

Status:
f2: [2,1]
g1: multiset
h1: multiset
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

f(x, g(x)) → x
f(x, h(y)) → f(h(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