Problem SK90 2.06

Tool Bounds

Execution Time	60.032284ms
Answer	TIMEOUT
Input	SK90 2.06

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  +(*(x, y), +(*(x, z), u)) -> +(*(x, +(y, z)), u)
     , +(*(x, y), +(x, z)) -> *(x, +(y, z))
     , +(x, +(y, z)) -> +(+(x, y), z)}
  StartTerms: all
  Strategy: none

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	4.119065ms
Answer	MAYBE
Input	SK90 2.06

stdout:

MAYBE

Statistics:
Number of monomials: 783
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.5950639ms
Answer	YES(?,O(n^2))
Input	SK90 2.06

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  +(*(x, y), +(*(x, z), u)) -> +(*(x, +(y, z)), u)
     , +(*(x, y), +(x, z)) -> *(x, +(y, z))
     , +(x, +(y, z)) -> +(+(x, y), z)}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   +(x1, x2) = [1 0] x1 + [1 2] x2 + [1]
               [0 1]      [0 1]      [3]
   *(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
               [0 0]      [0 1]      [2]

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

Tool IDA

Execution Time	0.80751705ms
Answer	YES(?,O(n^2))
Input	SK90 2.06

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  +(*(x, y), +(*(x, z), u)) -> +(*(x, +(y, z)), u)
     , +(*(x, y), +(x, z)) -> *(x, +(y, z))
     , +(x, +(y, z)) -> +(+(x, y), z)}
  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:
   +(x1, x2) = [1 0] x1 + [1 2] x2 + [1]
               [0 1]      [0 1]      [3]
   *(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
               [0 0]      [0 1]      [2]

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

Tool TRI

Execution Time	0.23644018ms
Answer	YES(?,O(n^2))
Input	SK90 2.06

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  +(*(x, y), +(*(x, z), u)) -> +(*(x, +(y, z)), u)
     , +(*(x, y), +(x, z)) -> *(x, +(y, z))
     , +(x, +(y, z)) -> +(+(x, y), z)}
  StartTerms: all
  Strategy: none

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

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

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

Tool TRI2

Execution Time	0.22542119ms
Answer	YES(?,O(n^2))
Input	SK90 2.06

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  +(*(x, y), +(*(x, z), u)) -> +(*(x, +(y, z)), u)
     , +(*(x, y), +(x, z)) -> *(x, +(y, z))
     , +(x, +(y, z)) -> +(+(x, y), z)}
  StartTerms: all
  Strategy: none

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

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

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