(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
bin(x, 0) → s(0)
bin(0, s(y)) → 0
bin(s(x), s(y)) → +(bin(x, s(y)), bin(x, y))
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Lexicographic Path Order [LPO].
Precedence:
bin2 > s1 > +2
0 > s1 > +2
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
bin(x, 0) → s(0)
bin(0, s(y)) → 0
bin(s(x), s(y)) → +(bin(x, s(y)), bin(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) TRUE