Problem Zantema 05 jw50

Tool Bounds

Execution Time	2.9846907e-2ms
Answer	YES(?,O(n^1))
Input	Zantema 05 jw50

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

Proof:
  The problem is match-bounded by 1.
  The enriched problem is compatible with the following automaton:
  {  a_0() -> 1
   , a_1() -> 5
   , a_1() -> 6
   , a_1() -> 7
   , f_0(1, 1) -> 2
   , f_0(1, 2) -> 2
   , f_0(2, 1) -> 2
   , f_0(2, 2) -> 2
   , f_1(1, 3) -> 2
   , f_1(2, 3) -> 2
   , f_1(3, 3) -> 2
   , f_1(4, 5) -> 3
   , f_1(6, 7) -> 4}

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

Tool CDI

Execution Time	60.039837ms
Answer	TIMEOUT
Input	Zantema 05 jw50

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	4.126423ms
Answer	YES(?,O(n^3))
Input	Zantema 05 jw50

stdout:

YES(?,O(n^3))

We consider the following Problem:

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

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

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

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

Tool IDA

Execution Time	5.3346887ms
Answer	YES(?,O(n^1))
Input	Zantema 05 jw50

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

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

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

Tool TRI

Execution Time	0.7454281ms
Answer	YES(?,O(n^2))
Input	Zantema 05 jw50

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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

Tool TRI2

Execution Time	0.8805659ms
Answer	MAYBE
Input	Zantema 05 jw50

stdout:

MAYBE

We consider the following Problem:

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

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..