LMPO
Execution Time (secs) | 0.061 |
Answer | YES(?,ELEMENTARY) |
Input | SK90 2.18 |
YES(?,ELEMENTARY)
We consider the following Problem:
Strict Trs:
{ sum(0()) -> 0()
, sum(s(x)) -> +(sum(x), s(x))
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))}
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}
and precedence
sum > + .
Following symbols are considered recursive:
{sum, +}
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);) -> +(s(; x); sum(x;))
, +(0(); x) -> x
, +(s(; y); x) -> s(; +(y; x))}
Weak Trs : {}
Hurray, we answered YES(?,ELEMENTARY)
MPO
Execution Time (secs) | 0.038 |
Answer | YES(?,PRIMREC) |
Input | SK90 2.18 |
YES(?,PRIMREC)
We consider the following Problem:
Strict Trs:
{ sum(0()) -> 0()
, sum(s(x)) -> +(sum(x), s(x))
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))}
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 > +, + > s .
Hurray, we answered YES(?,PRIMREC)
POP*
Execution Time (secs) | 0.056 |
Answer | YES(?,POLY) |
Input | SK90 2.18 |
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ sum(0()) -> 0()
, sum(s(x)) -> +(sum(x), s(x))
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))}
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}
and precedence
sum > + .
Following symbols are considered recursive:
{sum, +}
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);) -> +(s(; x); sum(x;))
, +(0(); x) -> x
, +(s(; y); x) -> s(; +(y; x))}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
POP* (PS)
Execution Time (secs) | 0.030 |
Answer | YES(?,POLY) |
Input | SK90 2.18 |
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ sum(0()) -> 0()
, sum(s(x)) -> +(sum(x), s(x))
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))}
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}
and precedence
sum > + .
Following symbols are considered recursive:
{sum, +}
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);) -> +(s(; x); sum(x;))
, +(0(); x) -> x
, +(s(; y); x) -> s(; +(y; x))}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
Small POP*
Execution Time (secs) | 0.058 |
Answer | YES(?,O(n^2)) |
Input | SK90 2.18 |
YES(?,O(n^2))
We consider the following Problem:
Strict Trs:
{ sum(0()) -> 0()
, sum(s(x)) -> +(sum(x), s(x))
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(n^2))
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}
and precedence
sum > + .
Following symbols are considered recursive:
{sum, +}
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);) -> +(s(; x); sum(x;))
, +(0(); x) -> x
, +(s(; y); x) -> s(; +(y; x))}
Weak Trs : {}
Hurray, we answered YES(?,O(n^2))
Small POP* (PS)
Execution Time (secs) | 0.060 |
Answer | YES(?,O(n^2)) |
Input | SK90 2.18 |
YES(?,O(n^2))
We consider the following Problem:
Strict Trs:
{ sum(0()) -> 0()
, sum(s(x)) -> +(sum(x), s(x))
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(n^2))
Proof:
The input was oriented with the instance of
Small Polynomial Path Order (WSC,
PS) as induced by the safe mapping
safe(sum) = {}, safe(0) = {}, safe(s) = {1}, safe(+) = {1}
and precedence
sum > + .
Following symbols are considered recursive:
{sum, +}
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);) -> +(s(; x); sum(x;))
, +(0(); x) -> x
, +(s(; y); x) -> s(; +(y; x))}
Weak Trs : {}
Hurray, we answered YES(?,O(n^2))