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(a) → f(b)
g(b) → g(a)
f(x) → g(x)

Q is empty.

(1) QTRSRRRProof (EQUIVALENT transformation)

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

f₁ > [a, b, g₁]

Status:

f₁: [1]
a: []
b: []
g₁: [1]

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

f(x) → g(x)

(2) Obligation:

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

f(a) → f(b)
g(b) → g(a)

Q is empty.