LMPO
Execution Time (secs) | 0.036 |
Answer | YES(?,ELEMENTARY) |
Input | SK90 2.11 |
YES(?,ELEMENTARY)
We consider the following Problem:
Strict Trs:
{ +(0(), y) -> y
, +(s(x), y) -> s(+(x, y))
, -(0(), y) -> 0()
, -(x, 0()) -> x
, -(s(x), s(y)) -> -(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(+) = {}, safe(0) = {}, safe(s) = {1}, safe(-) = {}
and precedence
empty .
Following symbols are considered recursive:
{+, -}
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:
{ +(0(), y;) -> y
, +(s(; x), y;) -> s(; +(x, y;))
, -(0(), y;) -> 0()
, -(x, 0();) -> x
, -(s(; x), s(; y);) -> -(x, y;)}
Weak Trs : {}
Hurray, we answered YES(?,ELEMENTARY)
MPO
Execution Time (secs) | 0.045 |
Answer | YES(?,PRIMREC) |
Input | SK90 2.11 |
YES(?,PRIMREC)
We consider the following Problem:
Strict Trs:
{ +(0(), y) -> y
, +(s(x), y) -> s(+(x, y))
, -(0(), y) -> 0()
, -(x, 0()) -> x
, -(s(x), s(y)) -> -(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
+ > s .
Hurray, we answered YES(?,PRIMREC)
POP*
Execution Time (secs) | 0.031 |
Answer | YES(?,POLY) |
Input | SK90 2.11 |
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ +(0(), y) -> y
, +(s(x), y) -> s(+(x, y))
, -(0(), y) -> 0()
, -(x, 0()) -> x
, -(s(x), s(y)) -> -(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(+) = {}, safe(0) = {}, safe(s) = {1}, safe(-) = {}
and precedence
empty .
Following symbols are considered recursive:
{+, -}
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:
{ +(0(), y;) -> y
, +(s(; x), y;) -> s(; +(x, y;))
, -(0(), y;) -> 0()
, -(x, 0();) -> x
, -(s(; x), s(; y);) -> -(x, y;)}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
POP* (PS)
Execution Time (secs) | 0.035 |
Answer | YES(?,POLY) |
Input | SK90 2.11 |
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ +(0(), y) -> y
, +(s(x), y) -> s(+(x, y))
, -(0(), y) -> 0()
, -(x, 0()) -> x
, -(s(x), s(y)) -> -(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(+) = {2}, safe(0) = {}, safe(s) = {1}, safe(-) = {}
and precedence
empty .
Following symbols are considered recursive:
{+, -}
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:
{ +(0(); y) -> y
, +(s(; x); y) -> s(; +(x; y))
, -(0(), y;) -> 0()
, -(x, 0();) -> x
, -(s(; x), s(; y);) -> -(x, y;)}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
Small POP*
Execution Time (secs) | 0.055 |
Answer | YES(?,O(n^1)) |
Input | SK90 2.11 |
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ +(0(), y) -> y
, +(s(x), y) -> s(+(x, y))
, -(0(), y) -> 0()
, -(x, 0()) -> x
, -(s(x), s(y)) -> -(x, y)}
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(+) = {2}, safe(0) = {}, safe(s) = {1}, safe(-) = {1}
and precedence
empty .
Following symbols are considered recursive:
{+, -}
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:
{ +(0(); y) -> y
, +(s(; x); y) -> s(; +(x; y))
, -(y; 0()) -> 0()
, -(0(); x) -> x
, -(s(; y); s(; x)) -> -(y; x)}
Weak Trs : {}
Hurray, we answered YES(?,O(n^1))
Small POP* (PS)
Execution Time (secs) | 0.048 |
Answer | YES(?,O(n^1)) |
Input | SK90 2.11 |
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ +(0(), y) -> y
, +(s(x), y) -> s(+(x, y))
, -(0(), y) -> 0()
, -(x, 0()) -> x
, -(s(x), s(y)) -> -(x, y)}
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(+) = {2}, safe(0) = {}, safe(s) = {1}, safe(-) = {2}
and precedence
empty .
Following symbols are considered recursive:
{+, -}
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:
{ +(0(); y) -> y
, +(s(; x); y) -> s(; +(x; y))
, -(0(); y) -> 0()
, -(x; 0()) -> x
, -(s(; x); s(; y)) -> -(x; y)}
Weak Trs : {}
Hurray, we answered YES(?,O(n^1))