Tool LMPO
Execution Time | 0.038 |
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Answer | YES(?,ELEMENTARY) |
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Input | SK90 4.25 |
---|
stdout:
YES(?,ELEMENTARY)
We consider the following Problem:
Strict Trs:
{ rev(a()) -> a()
, rev(b()) -> b()
, rev(++(x, y)) -> ++(rev(y), rev(x))
, rev(++(x, x)) -> rev(x)}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,ELEMENTARY)
Proof:
The input was oriented with the instance of
Lightweight Multiset Path Order () as induced by the safe mapping
safe(rev) = {}, safe(a) = {}, safe(b) = {}, safe(++) = {1, 2}
and precedence
empty .
Following symbols are considered recursive:
{rev}
The recursion depth is 1 .
For your convenience, here are the oriented rules in predicative
notation (possibly applying argument filtering):
Strict DPs: {}
Weak DPs : {}
Strict Trs:
{ rev(a();) -> a()
, rev(b();) -> b()
, rev(++(; x, y);) -> ++(; rev(y;), rev(x;))
, rev(++(; x, x);) -> rev(x;)}
Weak Trs : {}
Hurray, we answered YES(?,ELEMENTARY)
Tool MPO
Execution Time | 0.058 |
---|
Answer | YES(?,PRIMREC) |
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Input | SK90 4.25 |
---|
stdout:
YES(?,PRIMREC)
We consider the following Problem:
Strict Trs:
{ rev(a()) -> a()
, rev(b()) -> b()
, rev(++(x, y)) -> ++(rev(y), rev(x))
, rev(++(x, x)) -> rev(x)}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,PRIMREC)
Proof:
The input was oriented with the instance of
'multiset path orders' as induced by the precedence
rev > ++ .
Hurray, we answered YES(?,PRIMREC)
Tool POP*
stdout:
MAYBE
We consider the following Problem:
Strict Trs:
{ rev(a()) -> a()
, rev(b()) -> b()
, rev(++(x, y)) -> ++(rev(y), rev(x))
, rev(++(x, x)) -> rev(x)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Tool POP* (PS)
stdout:
MAYBE
We consider the following Problem:
Strict Trs:
{ rev(a()) -> a()
, rev(b()) -> b()
, rev(++(x, y)) -> ++(rev(y), rev(x))
, rev(++(x, x)) -> rev(x)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Tool Small POP*
stdout:
MAYBE
We consider the following Problem:
Strict Trs:
{ rev(a()) -> a()
, rev(b()) -> b()
, rev(++(x, y)) -> ++(rev(y), rev(x))
, rev(++(x, x)) -> rev(x)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Tool Small POP* (PS)
stdout:
MAYBE
We consider the following Problem:
Strict Trs:
{ rev(a()) -> a()
, rev(b()) -> b()
, rev(++(x, y)) -> ++(rev(y), rev(x))
, rev(++(x, x)) -> rev(x)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..