(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
h(f(x), y) → f(g(x, y))
g(x, y) → h(x, y)
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Polynomial interpretation [POLO]:
POL(f(x1)) = 2 + x1
POL(g(x1, x2)) = 1 + 2·x1 + x2
POL(h(x1, x2)) = 2·x1 + x2
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
h(f(x), y) → f(g(x, y))
g(x, y) → h(x, y)
(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) YES