Problem Bouchare 06 02

Tool Bounds

Execution Time	60.040295ms
Answer	TIMEOUT
Input	Bouchare 06 02

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  a(a(x1)) -> b(b(b(x1)))
     , b(b(b(x1))) -> b(a(b(x1)))
     , a(b(a(x1))) -> b(a(x1))}
  StartTerms: all
  Strategy: none

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	2.457212ms
Answer	MAYBE
Input	Bouchare 06 02

stdout:

MAYBE

Statistics:
Number of monomials: 378
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.44275594ms
Answer	YES(?,O(n^2))
Input	Bouchare 06 02

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  a(a(x1)) -> b(b(b(x1)))
     , b(b(b(x1))) -> b(a(b(x1)))
     , a(b(a(x1))) -> b(a(x1))}
  StartTerms: all
  Strategy: none

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

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

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

Tool IDA

Execution Time	0.577013ms
Answer	YES(?,O(n^2))
Input	Bouchare 06 02

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  a(a(x1)) -> b(b(b(x1)))
     , b(b(b(x1))) -> b(a(b(x1)))
     , a(b(a(x1))) -> b(a(x1))}
  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:
   a(x1) = [1 3] x1 + [1]
           [0 0]      [3]
   b(x1) = [1 0] x1 + [3]
           [0 0]      [0]

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

Tool TRI

Execution Time	0.16785407ms
Answer	YES(?,O(n^1))
Input	Bouchare 06 02

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  a(a(x1)) -> b(b(b(x1)))
     , b(b(b(x1))) -> b(a(b(x1)))
     , a(b(a(x1))) -> b(a(x1))}
  StartTerms: all
  Strategy: none

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

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

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

Tool TRI2

Execution Time	0.15009403ms
Answer	YES(?,O(n^1))
Input	Bouchare 06 02

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  a(a(x1)) -> b(b(b(x1)))
     , b(b(b(x1))) -> b(a(b(x1)))
     , a(b(a(x1))) -> b(a(x1))}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   a(x1) = [1 3] x1 + [1]
           [0 0]      [3]
   b(x1) = [1 0] x1 + [3]
           [0 0]      [0]

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