(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
average(s(x), y) → average(x, s(y))
average(x, s(s(s(y)))) → s(average(s(x), y))
average(0, 0) → 0
average(0, s(0)) → 0
average(0, s(s(0))) → s(0)
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Knuth-Bendix order [KBO] with precedence:
average2 > s1 > 0
and weight map:
0=1
s_1=1
average_2=0
The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
average(s(x), y) → average(x, s(y))
average(x, s(s(s(y)))) → s(average(s(x), y))
average(0, 0) → 0
average(0, s(0)) → 0
average(0, s(s(0))) → s(0)
(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