Problem AG01 3.37

Tool Bounds

Execution Time	6.0949087e-2ms
Answer	YES(?,O(n^1))
Input	AG01 3.37

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  evenodd(s(x), s(0())) -> evenodd(x, 0())
     , evenodd(0(), s(0())) -> false()
     , evenodd(x, 0()) -> not(evenodd(x, s(0())))
     , not(false()) -> true()
     , not(true()) -> false()}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^1))

Proof:
  The problem is match-bounded by 3.
  The enriched problem is compatible with the following automaton:
  {  true_0() -> 1
   , true_1() -> 1
   , true_2() -> 1
   , true_2() -> 3
   , true_2() -> 5
   , true_3() -> 1
   , true_3() -> 3
   , true_3() -> 5
   , not_0(1) -> 1
   , not_1(3) -> 1
   , not_2(5) -> 1
   , not_2(5) -> 3
   , not_2(5) -> 5
   , false_0() -> 1
   , false_1() -> 1
   , false_1() -> 3
   , false_1() -> 5
   , false_2() -> 1
   , false_3() -> 1
   , false_3() -> 3
   , false_3() -> 5
   , 0_0() -> 1
   , 0_1() -> 2
   , 0_2() -> 7
   , evenodd_0(1, 1) -> 1
   , evenodd_1(1, 2) -> 1
   , evenodd_1(1, 2) -> 3
   , evenodd_1(1, 2) -> 5
   , evenodd_1(1, 4) -> 3
   , evenodd_2(1, 6) -> 5
   , s_0(1) -> 1
   , s_1(2) -> 4
   , s_2(7) -> 6}

Hurray, we answered YES(?,O(n^1))

Tool CDI

Execution Time	48.649017ms
Answer	MAYBE
Input	AG01 3.37

stdout:

MAYBE

Statistics:
Number of monomials: 650
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	2.043027ms
Answer	YES(?,O(n^3))
Input	AG01 3.37

stdout:

YES(?,O(n^3))

We consider the following Problem:

  Strict Trs:
    {  evenodd(s(x), s(0())) -> evenodd(x, 0())
     , evenodd(0(), s(0())) -> false()
     , evenodd(x, 0()) -> not(evenodd(x, s(0())))
     , not(false()) -> true()
     , not(true()) -> false()}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^3))

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   true() = [0]
            [0]
            [0]
   not(x1) = [1 0 0] x1 + [1]
             [0 0 0]      [0]
             [0 0 0]      [0]
   false() = [0]
             [0]
             [0]
   0() = [0]
         [0]
         [2]
   evenodd(x1, x2) = [1 2 0] x1 + [1 0 2] x2 + [0]
                     [0 0 0]      [0 1 2]      [0]
                     [0 0 0]      [0 0 0]      [0]
   s(x1) = [1 2 0] x1 + [1]
           [0 0 1]      [2]
           [0 0 0]      [0]

Hurray, we answered YES(?,O(n^3))

Tool IDA

Execution Time	4.008928ms
Answer	YES(?,O(n^2))
Input	AG01 3.37

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  evenodd(s(x), s(0())) -> evenodd(x, 0())
     , evenodd(0(), s(0())) -> false()
     , evenodd(x, 0()) -> not(evenodd(x, s(0())))
     , not(false()) -> true()
     , not(true()) -> false()}
  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:
   true() = [0]
            [0]
            [0]
   not(x1) = [1 0 0] x1 + [2]
             [0 0 0]      [0]
             [0 0 0]      [0]
   false() = [0]
             [0]
             [0]
   0() = [0]
         [2]
         [1]
   evenodd(x1, x2) = [1 0 3] x1 + [1 2 0] x2 + [0]
                     [0 0 2]      [0 1 0]      [2]
                     [0 0 0]      [0 0 0]      [0]
   s(x1) = [1 0 0] x1 + [0]
           [0 0 0]      [0]
           [0 0 1]      [3]

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

Tool TRI

Execution Time	0.57444215ms
Answer	YES(?,O(n^2))
Input	AG01 3.37

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  evenodd(s(x), s(0())) -> evenodd(x, 0())
     , evenodd(0(), s(0())) -> false()
     , evenodd(x, 0()) -> not(evenodd(x, s(0())))
     , not(false()) -> true()
     , not(true()) -> false()}
  StartTerms: all
  Strategy: none

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

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

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

Tool TRI2

Execution Time	0.24655795ms
Answer	MAYBE
Input	AG01 3.37

stdout:

MAYBE

We consider the following Problem:

  Strict Trs:
    {  evenodd(s(x), s(0())) -> evenodd(x, 0())
     , evenodd(0(), s(0())) -> false()
     , evenodd(x, 0()) -> not(evenodd(x, s(0())))
     , not(false()) -> true()
     , not(true()) -> false()}
  StartTerms: all
  Strategy: none

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..