Tool LMPO
Execution Time | 0.066 |
---|
Answer | YES(?,ELEMENTARY) |
---|
Input | SK90 2.17 |
---|
stdout:
YES(?,ELEMENTARY)
We consider the following Problem:
Strict Trs:
{ sum(0()) -> 0()
, sum(s(x)) -> +(sum(x), s(x))
, sum1(0()) -> 0()
, sum1(s(x)) -> s(+(sum1(x), +(x, 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(sum1) = {}
and precedence
empty .
Following symbols are considered recursive:
{sum, sum1}
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);) -> +(; sum(x;), s(; x))
, sum1(0();) -> 0()
, sum1(s(; x);) -> s(; +(; sum1(x;), +(; x, x)))}
Weak Trs : {}
Hurray, we answered YES(?,ELEMENTARY)
Tool MPO
Execution Time | 0.040 |
---|
Answer | YES(?,PRIMREC) |
---|
Input | SK90 2.17 |
---|
stdout:
YES(?,PRIMREC)
We consider the following Problem:
Strict Trs:
{ sum(0()) -> 0()
, sum(s(x)) -> +(sum(x), s(x))
, sum1(0()) -> 0()
, sum1(s(x)) -> s(+(sum1(x), +(x, 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 > +, sum1 > s, sum1 > + .
Hurray, we answered YES(?,PRIMREC)
Tool POP*
Execution Time | 0.049 |
---|
Answer | YES(?,POLY) |
---|
Input | SK90 2.17 |
---|
stdout:
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ sum(0()) -> 0()
, sum(s(x)) -> +(sum(x), s(x))
, sum1(0()) -> 0()
, sum1(s(x)) -> s(+(sum1(x), +(x, 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(sum1) = {}
and precedence
empty .
Following symbols are considered recursive:
{sum, sum1}
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);) -> +(; sum(x;), s(; x))
, sum1(0();) -> 0()
, sum1(s(; x);) -> s(; +(; sum1(x;), +(; x, x)))}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
Tool POP* (PS)
Execution Time | 0.033 |
---|
Answer | YES(?,POLY) |
---|
Input | SK90 2.17 |
---|
stdout:
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ sum(0()) -> 0()
, sum(s(x)) -> +(sum(x), s(x))
, sum1(0()) -> 0()
, sum1(s(x)) -> s(+(sum1(x), +(x, 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(sum1) = {}
and precedence
empty .
Following symbols are considered recursive:
{sum, sum1}
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);) -> +(; sum(x;), s(; x))
, sum1(0();) -> 0()
, sum1(s(; x);) -> s(; +(; sum1(x;), +(; x, x)))}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
Tool Small POP*
Execution Time | 0.045 |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.17 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ sum(0()) -> 0()
, sum(s(x)) -> +(sum(x), s(x))
, sum1(0()) -> 0()
, sum1(s(x)) -> s(+(sum1(x), +(x, 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(sum1) = {}
and precedence
empty .
Following symbols are considered recursive:
{sum, sum1}
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);) -> +(; sum(x;), s(; x))
, sum1(0();) -> 0()
, sum1(s(; x);) -> s(; +(; sum1(x;), +(; x, x)))}
Weak Trs : {}
Hurray, we answered YES(?,O(n^1))
Tool Small POP* (PS)
Execution Time | 0.053 |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.17 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ sum(0()) -> 0()
, sum(s(x)) -> +(sum(x), s(x))
, sum1(0()) -> 0()
, sum1(s(x)) -> s(+(sum1(x), +(x, 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) as induced by the safe mapping
safe(sum) = {}, safe(0) = {}, safe(s) = {1}, safe(+) = {1, 2},
safe(sum1) = {}
and precedence
empty .
Following symbols are considered recursive:
{sum, sum1}
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);) -> +(; sum(x;), s(; x))
, sum1(0();) -> 0()
, sum1(s(; x);) -> s(; +(; sum1(x;), +(; x, x)))}
Weak Trs : {}
Hurray, we answered YES(?,O(n^1))