Termination w.r.t. Q of the given QTRS could not be shown:

(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:
Lexicographic path order with status [LPO].
Quasi-Precedence:

g₁ > [f₁, h₁, i₁]
a > b > [f₁, h₁, i₁]

Status:

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

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.