(0) Obligation:
Relative term rewrite system:
The relative TRS consists of the following R rules:
f(x) → x
g(x) → x
The relative TRS consists of the following S rules:
f(x) → g(x)
g(x) → f(x)
(1) RelTRSRRRProof (EQUIVALENT transformation)
We used the following monotonic ordering for rule removal:
Polynomial interpretation [POLO]:
POL(f(x1)) = 1 + x1
POL(g(x1)) = 1 + x1
With this ordering the following rules can be removed [MATRO] because they are oriented strictly:
Rules from R:
f(x) → x
g(x) → x
Rules from S:
none
(2) Obligation:
Relative term rewrite system:
R is empty.
The relative TRS consists of the following S rules:
f(x) → g(x)
g(x) → f(x)
(3) RIsEmptyProof (EQUIVALENT transformation)
The TRS R is empty. Hence, termination is trivially proven.
(4) YES