(0) Obligation:

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

f(h(x)) → f(i(x))
g(i(x)) → g(h(x))
h(a) → b
i(a) → b

Q is empty.

(1) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Recursive path order with status [RPO].
Quasi-Precedence:
[h1, i1] > b > [f1, g1]
a > b > [f1, g1]

Status:
i1: [1]
f1: [1]
a: multiset
g1: [1]
h1: [1]
b: multiset

With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

h(a) → b
i(a) → b


(2) Obligation:

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

f(h(x)) → f(i(x))
g(i(x)) → g(h(x))

Q is empty.