Problem Zantema 05 jw44

Tool Bounds

Execution Time	60.029682ms
Answer	TIMEOUT
Input	Zantema 05 jw44

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {f(a(), f(f(a(), x), a())) -> f(f(a(), f(a(), x)), a())}
  StartTerms: all
  Strategy: none

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	60.03831ms
Answer	TIMEOUT
Input	Zantema 05 jw44

stdout:

TIMEOUT

Statistics:
Number of monomials: 0
Last formula building started for bound 0
Last SAT solving started for bound 0

Tool EDA

Execution Time	0.58235ms
Answer	YES(?,O(n^2))
Input	Zantema 05 jw44

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {f(a(), f(f(a(), x), a())) -> f(f(a(), f(a(), x)), a())}
  StartTerms: all
  Strategy: none

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

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

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

Tool IDA

Execution Time	0.74640894ms
Answer	YES(?,O(n^2))
Input	Zantema 05 jw44

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

Tool TRI

Execution Time	0.23112702ms
Answer	YES(?,O(n^2))
Input	Zantema 05 jw44

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {f(a(), f(f(a(), x), a())) -> f(f(a(), f(a(), x)), a())}
  StartTerms: all
  Strategy: none

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

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

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

Tool TRI2

Execution Time	0.23874688ms
Answer	YES(?,O(n^2))
Input	Zantema 05 jw44

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {f(a(), f(f(a(), x), a())) -> f(f(a(), f(a(), x)), a())}
  StartTerms: all
  Strategy: none

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

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

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