Problem SK90 4.12

Tool Bounds

Execution Time	60.030247ms
Answer	TIMEOUT
Input	SK90 4.12

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  +(s(x), s(y)) -> s(+(s(x), +(y, 0())))
     , +(s(x), 0()) -> s(x)
     , +(0(), y) -> y}
  StartTerms: all
  Strategy: none

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	60.04483ms
Answer	TIMEOUT
Input	SK90 4.12

stdout:

TIMEOUT

Statistics:
Number of monomials: 2181
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.63898516ms
Answer	YES(?,O(n^2))
Input	SK90 4.12

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  +(s(x), s(y)) -> s(+(s(x), +(y, 0())))
     , +(s(x), 0()) -> s(x)
     , +(0(), y) -> y}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   0() = [0]
         [0]
   +(x1, x2) = [1 0] x1 + [1 3] x2 + [1]
               [0 1]      [0 1]      [0]
   s(x1) = [1 0] x1 + [0]
           [0 1]      [3]

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

Tool IDA

Execution Time	0.6846261ms
Answer	YES(?,O(n^2))
Input	SK90 4.12

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  +(s(x), s(y)) -> s(+(s(x), +(y, 0())))
     , +(s(x), 0()) -> s(x)
     , +(0(), y) -> y}
  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:
   0() = [1]
         [0]
   +(x1, x2) = [1 0] x1 + [1 1] x2 + [0]
               [0 1]      [0 1]      [0]
   s(x1) = [1 0] x1 + [0]
           [0 1]      [2]

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

Tool TRI

Execution Time	0.22419691ms
Answer	YES(?,O(n^2))
Input	SK90 4.12

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  +(s(x), s(y)) -> s(+(s(x), +(y, 0())))
     , +(s(x), 0()) -> s(x)
     , +(0(), y) -> y}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   0() = [0]
         [0]
   +(x1, x2) = [1 0] x1 + [1 1] x2 + [1]
               [0 1]      [0 1]      [0]
   s(x1) = [1 0] x1 + [1]
           [0 1]      [2]

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

Tool TRI2

Execution Time	0.23202491ms
Answer	YES(?,O(n^2))
Input	SK90 4.12

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  +(s(x), s(y)) -> s(+(s(x), +(y, 0())))
     , +(s(x), 0()) -> s(x)
     , +(0(), y) -> y}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   0() = [2]
         [0]
   +(x1, x2) = [1 0] x1 + [1 3] x2 + [0]
               [0 1]      [0 1]      [0]
   s(x1) = [1 0] x1 + [2]
           [0 1]      [2]

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