LMPO
Execution Time (secs) | 0.044 |
Answer | YES(?,ELEMENTARY) |
Input | SK90 2.13 |
YES(?,ELEMENTARY)
We consider the following Problem:
Strict Trs:
{ double(0()) -> 0()
, double(s(x)) -> s(s(double(x)))
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))
, +(s(x), y) -> s(+(x, y))
, double(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(double) = {}, safe(0) = {}, safe(s) = {1}, safe(+) = {}
and precedence
double > + .
Following symbols are considered recursive:
{double, +}
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:
{ double(0();) -> 0()
, double(s(; x);) -> s(; s(; double(x;)))
, +(x, 0();) -> x
, +(x, s(; y);) -> s(; +(x, y;))
, +(s(; x), y;) -> s(; +(x, y;))
, double(x;) -> +(x, x;)}
Weak Trs : {}
Hurray, we answered YES(?,ELEMENTARY)
MPO
Execution Time (secs) | 0.075 |
Answer | YES(?,PRIMREC) |
Input | SK90 2.13 |
YES(?,PRIMREC)
We consider the following Problem:
Strict Trs:
{ double(0()) -> 0()
, double(s(x)) -> s(s(double(x)))
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))
, +(s(x), y) -> s(+(x, y))
, double(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
double > s, double > +, + > s .
Hurray, we answered YES(?,PRIMREC)
POP*
Execution Time (secs) | 0.065 |
Answer | YES(?,POLY) |
Input | SK90 2.13 |
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ double(0()) -> 0()
, double(s(x)) -> s(s(double(x)))
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))
, +(s(x), y) -> s(+(x, y))
, double(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(double) = {}, safe(0) = {}, safe(s) = {1}, safe(+) = {}
and precedence
double > + .
Following symbols are considered recursive:
{double, +}
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:
{ double(0();) -> 0()
, double(s(; x);) -> s(; s(; double(x;)))
, +(x, 0();) -> x
, +(x, s(; y);) -> s(; +(x, y;))
, +(s(; x), y;) -> s(; +(x, y;))
, double(x;) -> +(x, x;)}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
POP* (PS)
Execution Time (secs) | 0.046 |
Answer | YES(?,POLY) |
Input | SK90 2.13 |
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ double(0()) -> 0()
, double(s(x)) -> s(s(double(x)))
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))
, +(s(x), y) -> s(+(x, y))
, double(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(double) = {}, safe(0) = {}, safe(s) = {1}, safe(+) = {}
and precedence
double > + .
Following symbols are considered recursive:
{double, +}
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:
{ double(0();) -> 0()
, double(s(; x);) -> s(; s(; double(x;)))
, +(x, 0();) -> x
, +(x, s(; y);) -> s(; +(x, y;))
, +(s(; x), y;) -> s(; +(x, y;))
, double(x;) -> +(x, x;)}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
Small POP*
Execution Time (secs) | 0.077 |
Answer | YES(?,O(n^2)) |
Input | SK90 2.13 |
YES(?,O(n^2))
We consider the following Problem:
Strict Trs:
{ double(0()) -> 0()
, double(s(x)) -> s(s(double(x)))
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))
, +(s(x), y) -> s(+(x, y))
, double(x) -> +(x, x)}
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(double) = {}, safe(0) = {}, safe(s) = {1}, safe(+) = {}
and precedence
double > + .
Following symbols are considered recursive:
{double, +}
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:
{ double(0();) -> 0()
, double(s(; x);) -> s(; s(; double(x;)))
, +(x, 0();) -> x
, +(x, s(; y);) -> s(; +(x, y;))
, +(s(; x), y;) -> s(; +(x, y;))
, double(x;) -> +(x, x;)}
Weak Trs : {}
Hurray, we answered YES(?,O(n^2))
Small POP* (PS)
Execution Time (secs) | 0.070 |
Answer | YES(?,O(n^2)) |
Input | SK90 2.13 |
YES(?,O(n^2))
We consider the following Problem:
Strict Trs:
{ double(0()) -> 0()
, double(s(x)) -> s(s(double(x)))
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))
, +(s(x), y) -> s(+(x, y))
, double(x) -> +(x, x)}
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(double) = {}, safe(0) = {}, safe(s) = {1}, safe(+) = {}
and precedence
double > + .
Following symbols are considered recursive:
{double, +}
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:
{ double(0();) -> 0()
, double(s(; x);) -> s(; s(; double(x;)))
, +(x, 0();) -> x
, +(x, s(; y);) -> s(; +(x, y;))
, +(s(; x), y;) -> s(; +(x, y;))
, double(x;) -> +(x, x;)}
Weak Trs : {}
Hurray, we answered YES(?,O(n^2))