(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
a → g(c)
g(a) → b
f(g(X), b) → f(a, X)
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Recursive path order with status [RPO].
Quasi-Precedence:
[a, b] > g1
[a, b] > c
Status:
f2: multiset
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
a → g(c)
g(a) → b
f(g(X), b) → f(a, X)
(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