LMPO
Execution Time (secs) | 0.035 |
Answer | YES(?,ELEMENTARY) |
Input | SK90 2.20 |
YES(?,ELEMENTARY)
We consider the following Problem:
Strict Trs:
{ sum(0()) -> 0()
, sum(s(x)) -> +(sqr(s(x)), sum(x))
, sqr(x) -> *(x, x)
, sum(s(x)) -> +(*(s(x), s(x)), sum(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(sum) = {}, safe(0) = {}, safe(s) = {1}, safe(+) = {1, 2},
safe(sqr) = {}, safe(*) = {1, 2}
and precedence
sum > sqr .
Following symbols are considered recursive:
{sum, sqr}
The recursion depth is 2 .
For your convenience, here are the oriented rules in predicative
notation (possibly applying argument filtering):
Strict DPs: {}
Weak DPs : {}
Strict Trs:
{ sum(0();) -> 0()
, sum(s(; x);) -> +(; sqr(s(; x);), sum(x;))
, sqr(x;) -> *(; x, x)
, sum(s(; x);) -> +(; *(; s(; x), s(; x)), sum(x;))}
Weak Trs : {}
Hurray, we answered YES(?,ELEMENTARY)
MPO
Execution Time (secs) | 0.046 |
Answer | YES(?,PRIMREC) |
Input | SK90 2.20 |
YES(?,PRIMREC)
We consider the following Problem:
Strict Trs:
{ sum(0()) -> 0()
, sum(s(x)) -> +(sqr(s(x)), sum(x))
, sqr(x) -> *(x, x)
, sum(s(x)) -> +(*(s(x), s(x)), sum(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
sum > +, sum > sqr, sum > *, sqr > * .
Hurray, we answered YES(?,PRIMREC)
POP*
Execution Time (secs) | 0.034 |
Answer | YES(?,POLY) |
Input | SK90 2.20 |
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ sum(0()) -> 0()
, sum(s(x)) -> +(sqr(s(x)), sum(x))
, sqr(x) -> *(x, x)
, sum(s(x)) -> +(*(s(x), s(x)), sum(x))}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,POLY)
Proof:
The input was oriented with the instance of
Polynomial Path Order () as induced by the safe mapping
safe(sum) = {}, safe(0) = {}, safe(s) = {1}, safe(+) = {1, 2},
safe(sqr) = {}, safe(*) = {1, 2}
and precedence
sum > sqr .
Following symbols are considered recursive:
{sum}
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:
{ sum(0();) -> 0()
, sum(s(; x);) -> +(; sqr(s(; x);), sum(x;))
, sqr(x;) -> *(; x, x)
, sum(s(; x);) -> +(; *(; s(; x), s(; x)), sum(x;))}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
POP* (PS)
Execution Time (secs) | 0.040 |
Answer | YES(?,POLY) |
Input | SK90 2.20 |
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ sum(0()) -> 0()
, sum(s(x)) -> +(sqr(s(x)), sum(x))
, sqr(x) -> *(x, x)
, sum(s(x)) -> +(*(s(x), s(x)), sum(x))}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,POLY)
Proof:
The input was oriented with the instance of
Polynomial Path Order (PS) as induced by the safe mapping
safe(sum) = {}, safe(0) = {}, safe(s) = {1}, safe(+) = {1, 2},
safe(sqr) = {}, safe(*) = {1, 2}
and precedence
sum > sqr .
Following symbols are considered recursive:
{sum}
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:
{ sum(0();) -> 0()
, sum(s(; x);) -> +(; sqr(s(; x);), sum(x;))
, sqr(x;) -> *(; x, x)
, sum(s(; x);) -> +(; *(; s(; x), s(; x)), sum(x;))}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
Small POP*
Execution Time (secs) | 0.042 |
Answer | YES(?,O(n^1)) |
Input | SK90 2.20 |
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ sum(0()) -> 0()
, sum(s(x)) -> +(sqr(s(x)), sum(x))
, sqr(x) -> *(x, x)
, sum(s(x)) -> +(*(s(x), s(x)), sum(x))}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(n^1))
Proof:
The input was oriented with the instance of
Small Polynomial Path Order (WSC) as induced by the safe mapping
safe(sum) = {}, safe(0) = {}, safe(s) = {1}, safe(+) = {1, 2},
safe(sqr) = {1}, safe(*) = {1, 2}
and precedence
sum > sqr .
Following symbols are considered recursive:
{sum}
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:
{ sum(0();) -> 0()
, sum(s(; x);) -> +(; sqr(; s(; x)), sum(x;))
, sqr(; x) -> *(; x, x)
, sum(s(; x);) -> +(; *(; s(; x), s(; x)), sum(x;))}
Weak Trs : {}
Hurray, we answered YES(?,O(n^1))
Small POP* (PS)
Execution Time (secs) | 0.068 |
Answer | YES(?,O(n^1)) |
Input | SK90 2.20 |
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ sum(0()) -> 0()
, sum(s(x)) -> +(sqr(s(x)), sum(x))
, sqr(x) -> *(x, x)
, sum(s(x)) -> +(*(s(x), s(x)), sum(x))}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(n^1))
Proof:
The input was oriented with the instance of
Small Polynomial Path Order (WSC,
PS,
Nat 1-bounded) as induced by the safe mapping
safe(sum) = {}, safe(0) = {}, safe(s) = {1}, safe(+) = {1, 2},
safe(sqr) = {1}, safe(*) = {1, 2}
and precedence
sum > sqr .
Following symbols are considered recursive:
{sum}
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:
{ sum(0();) -> 0()
, sum(s(; x);) -> +(; sqr(; s(; x)), sum(x;))
, sqr(; x) -> *(; x, x)
, sum(s(; x);) -> +(; *(; s(; x), s(; x)), sum(x;))}
Weak Trs : {}
Hurray, we answered YES(?,O(n^1))