LMPO
Execution Time (secs) | 0.052 |
Answer | YES(?,ELEMENTARY) |
Input | SK90 2.30 |
YES(?,ELEMENTARY)
We consider the following Problem:
Strict Trs:
{ not(x) -> xor(x, true())
, implies(x, y) -> xor(and(x, y), xor(x, true()))
, or(x, y) -> xor(and(x, y), xor(x, y))
, =(x, y) -> xor(x, xor(y, true()))}
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(not) = {1}, safe(xor) = {1, 2}, safe(true) = {},
safe(implies) = {1, 2}, safe(and) = {1, 2}, safe(or) = {1},
safe(=) = {2}
and precedence
empty .
Following symbols are considered recursive:
{}
The recursion depth is 0 .
For your convenience, here are the oriented rules in predicative
notation (possibly applying argument filtering):
Strict DPs: {}
Weak DPs : {}
Strict Trs:
{ not(; x) -> xor(; x, true())
, implies(; x, y) -> xor(; and(; x, y), xor(; x, true()))
, or(y; x) -> xor(; and(; x, y), xor(; x, y))
, =(x; y) -> xor(; x, xor(; y, true()))}
Weak Trs : {}
Hurray, we answered YES(?,ELEMENTARY)
MPO
Execution Time (secs) | 0.088 |
Answer | YES(?,PRIMREC) |
Input | SK90 2.30 |
YES(?,PRIMREC)
We consider the following Problem:
Strict Trs:
{ not(x) -> xor(x, true())
, implies(x, y) -> xor(and(x, y), xor(x, true()))
, or(x, y) -> xor(and(x, y), xor(x, y))
, =(x, y) -> xor(x, xor(y, true()))}
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
not > xor, not > true, implies > xor, implies > true,
implies > and, or > xor, or > and, = > xor, = > true .
Hurray, we answered YES(?,PRIMREC)
POP*
Execution Time (secs) | 0.045 |
Answer | YES(?,POLY) |
Input | SK90 2.30 |
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ not(x) -> xor(x, true())
, implies(x, y) -> xor(and(x, y), xor(x, true()))
, or(x, y) -> xor(and(x, y), xor(x, y))
, =(x, y) -> xor(x, xor(y, true()))}
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(not) = {1}, safe(xor) = {1, 2}, safe(true) = {},
safe(implies) = {2}, safe(and) = {1, 2}, safe(or) = {1},
safe(=) = {2}
and precedence
empty .
Following symbols are considered recursive:
{}
The recursion depth is 0 .
For your convenience, here are the oriented rules in predicative
notation (possibly applying argument filtering):
Strict DPs: {}
Weak DPs : {}
Strict Trs:
{ not(; x) -> xor(; x, true())
, implies(x; y) -> xor(; and(; x, y), xor(; x, true()))
, or(y; x) -> xor(; and(; x, y), xor(; x, y))
, =(x; y) -> xor(; x, xor(; y, true()))}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
POP* (PS)
Execution Time (secs) | 0.051 |
Answer | YES(?,POLY) |
Input | SK90 2.30 |
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ not(x) -> xor(x, true())
, implies(x, y) -> xor(and(x, y), xor(x, true()))
, or(x, y) -> xor(and(x, y), xor(x, y))
, =(x, y) -> xor(x, xor(y, true()))}
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(not) = {1}, safe(xor) = {1, 2}, safe(true) = {},
safe(implies) = {2}, safe(and) = {1, 2}, safe(or) = {1},
safe(=) = {2}
and precedence
empty .
Following symbols are considered recursive:
{}
The recursion depth is 0 .
For your convenience, here are the oriented rules in predicative
notation (possibly applying argument filtering):
Strict DPs: {}
Weak DPs : {}
Strict Trs:
{ not(; x) -> xor(; x, true())
, implies(x; y) -> xor(; and(; x, y), xor(; x, true()))
, or(y; x) -> xor(; and(; x, y), xor(; x, y))
, =(x; y) -> xor(; x, xor(; y, true()))}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
Small POP*
Execution Time (secs) | 0.080 |
Answer | YES(?,O(1)) |
Input | SK90 2.30 |
YES(?,O(1))
We consider the following Problem:
Strict Trs:
{ not(x) -> xor(x, true())
, implies(x, y) -> xor(and(x, y), xor(x, true()))
, or(x, y) -> xor(and(x, y), xor(x, y))
, =(x, y) -> xor(x, xor(y, true()))}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(1))
Proof:
The input was oriented with the instance of
Small Polynomial Path Order (WSC) as induced by the safe mapping
safe(not) = {1}, safe(xor) = {1, 2}, safe(true) = {},
safe(implies) = {1, 2}, safe(and) = {1, 2}, safe(or) = {2},
safe(=) = {1}
and precedence
empty .
Following symbols are considered recursive:
{}
The recursion depth is 0 .
For your convenience, here are the oriented rules in predicative
notation (possibly applying argument filtering):
Strict DPs: {}
Weak DPs : {}
Strict Trs:
{ not(; x) -> xor(; x, true())
, implies(; x, y) -> xor(; and(; x, y), xor(; x, true()))
, or(x; y) -> xor(; and(; x, y), xor(; x, y))
, =(y; x) -> xor(; x, xor(; y, true()))}
Weak Trs : {}
Hurray, we answered YES(?,O(1))
Small POP* (PS)
Execution Time (secs) | 0.096 |
Answer | YES(?,O(1)) |
Input | SK90 2.30 |
YES(?,O(1))
We consider the following Problem:
Strict Trs:
{ not(x) -> xor(x, true())
, implies(x, y) -> xor(and(x, y), xor(x, true()))
, or(x, y) -> xor(and(x, y), xor(x, y))
, =(x, y) -> xor(x, xor(y, true()))}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(1))
Proof:
The input was oriented with the instance of
Small Polynomial Path Order (WSC,
PS) as induced by the safe mapping
safe(not) = {1}, safe(xor) = {1, 2}, safe(true) = {},
safe(implies) = {1, 2}, safe(and) = {1, 2}, safe(or) = {2},
safe(=) = {1}
and precedence
empty .
Following symbols are considered recursive:
{}
The recursion depth is 0 .
For your convenience, here are the oriented rules in predicative
notation (possibly applying argument filtering):
Strict DPs: {}
Weak DPs : {}
Strict Trs:
{ not(; x) -> xor(; x, true())
, implies(; x, y) -> xor(; and(; x, y), xor(; x, true()))
, or(x; y) -> xor(; and(; x, y), xor(; x, y))
, =(y; x) -> xor(; x, xor(; y, true()))}
Weak Trs : {}
Hurray, we answered YES(?,O(1))