Problem SK90 2.33

Tool Bounds

Execution Time	60.02835ms
Answer	TIMEOUT
Input	SK90 2.33

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  not(or(x, y)) -> and(not(x), not(y))
     , not(and(x, y)) -> or(not(x), not(y))
     , not(not(x)) -> x
     , and(x, x) -> x
     , or(x, x) -> x}
  StartTerms: all
  Strategy: none

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	0.795367ms
Answer	MAYBE
Input	SK90 2.33

stdout:

MAYBE

Statistics:
Number of monomials: 423
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.34388494ms
Answer	YES(?,O(n^2))
Input	SK90 2.33

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  not(or(x, y)) -> and(not(x), not(y))
     , not(and(x, y)) -> or(not(x), not(y))
     , not(not(x)) -> x
     , and(x, x) -> x
     , or(x, x) -> x}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^2))

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   or(x1, x2) = [1 0] x1 + [1 0] x2 + [1]
                [0 1]      [0 1]      [3]
   and(x1, x2) = [1 0] x1 + [1 0] x2 + [1]
                 [0 1]      [0 1]      [3]
   not(x1) = [1 1] x1 + [1]
             [0 1]      [0]

Hurray, we answered YES(?,O(n^2))

Tool IDA

Execution Time	0.6900959ms
Answer	YES(?,O(n^2))
Input	SK90 2.33

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  not(or(x, y)) -> and(not(x), not(y))
     , not(and(x, y)) -> or(not(x), not(y))
     , not(not(x)) -> x
     , and(x, x) -> x
     , or(x, x) -> x}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^2))

Proof:
  We have the following EDA-non-satisfying and IDA(2)-non-satisfying matrix interpretation:
  Interpretation Functions:
   or(x1, x2) = [1 0] x1 + [1 0] x2 + [1]
                [0 1]      [0 1]      [3]
   and(x1, x2) = [1 0] x1 + [1 0] x2 + [1]
                 [0 1]      [0 1]      [3]
   not(x1) = [1 1] x1 + [2]
             [0 1]      [0]

Hurray, we answered YES(?,O(n^2))

Tool TRI

Execution Time	0.15747094ms
Answer	YES(?,O(n^2))
Input	SK90 2.33

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  not(or(x, y)) -> and(not(x), not(y))
     , not(and(x, y)) -> or(not(x), not(y))
     , not(not(x)) -> x
     , and(x, x) -> x
     , or(x, x) -> x}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^2))

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   or(x1, x2) = [1 0] x1 + [1 0] x2 + [1]
                [0 1]      [0 1]      [3]
   and(x1, x2) = [1 0] x1 + [1 0] x2 + [1]
                 [0 1]      [0 1]      [3]
   not(x1) = [1 1] x1 + [2]
             [0 1]      [0]

Hurray, we answered YES(?,O(n^2))

Tool TRI2

Execution Time	0.14113116ms
Answer	YES(?,O(n^2))
Input	SK90 2.33

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  not(or(x, y)) -> and(not(x), not(y))
     , not(and(x, y)) -> or(not(x), not(y))
     , not(not(x)) -> x
     , and(x, x) -> x
     , or(x, x) -> x}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^2))

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   or(x1, x2) = [1 2] x1 + [1 2] x2 + [2]
                [0 1]      [0 1]      [1]
   and(x1, x2) = [1 2] x1 + [1 2] x2 + [2]
                 [0 1]      [0 1]      [1]
   not(x1) = [1 2] x1 + [1]
             [0 1]      [0]

Hurray, we answered YES(?,O(n^2))