Problem Zantema 04 z025

Tool Bounds

Execution Time	60.03431ms
Answer	TIMEOUT
Input	Zantema 04 z025

stdout:

TIMEOUT

We consider the following Problem:

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

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	17.06007ms
Answer	MAYBE
Input	Zantema 04 z025

stdout:

MAYBE

Statistics:
Number of monomials: 952
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	6.86456ms
Answer	YES(?,O(n^3))
Input	Zantema 04 z025

stdout:

YES(?,O(n^3))

We consider the following Problem:

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

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

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

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

Tool IDA

Execution Time	35.81545ms
Answer	MAYBE
Input	Zantema 04 z025

stdout:

MAYBE

We consider the following Problem:

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

Certificate: MAYBE

Proof:
  None of the processors succeeded.

  Details of failed attempt(s):
  -----------------------------
    1) 'matrix-interpretation of dimension 3' failed due to the following reason:
         The input cannot be shown compatible

    2) 'matrix-interpretation of dimension 3' failed due to the following reason:
         The input cannot be shown compatible

    3) 'matrix-interpretation of dimension 3' failed due to the following reason:
         The input cannot be shown compatible

    4) 'matrix-interpretation of dimension 2' failed due to the following reason:
         The input cannot be shown compatible

    5) 'matrix-interpretation of dimension 2' failed due to the following reason:
         The input cannot be shown compatible

    6) 'matrix-interpretation of dimension 1' failed due to the following reason:
         The input cannot be shown compatible


Arrrr..

Tool TRI

Execution Time	2.809682ms
Answer	YES(?,O(n^2))
Input	Zantema 04 z025

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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

Tool TRI2

Execution Time	0.28530002ms
Answer	YES(?,O(n^2))
Input	Zantema 04 z025

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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