Problem SK90 2.60

Tool Bounds

Execution Time	4.2124987e-2ms
Answer	YES(?,O(n^1))
Input	SK90 2.60

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {f(g(f(a()), h(a(), f(a())))) ->
     f(h(g(f(a()), a()), g(f(a()), f(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() -> 9
   , a_1() -> 10
   , a_1() -> 13
   , a_1() -> 14
   , f_0(1) -> 2
   , f_0(2) -> 2
   , f_0(3) -> 2
   , f_0(4) -> 2
   , f_1(5) -> 2
   , f_1(10) -> 8
   , f_1(13) -> 11
   , f_1(14) -> 12
   , h_0(1, 1) -> 3
   , h_0(1, 2) -> 3
   , h_0(1, 3) -> 3
   , h_0(1, 4) -> 3
   , h_0(2, 1) -> 3
   , h_0(2, 2) -> 3
   , h_0(2, 3) -> 3
   , h_0(2, 4) -> 3
   , h_0(3, 1) -> 3
   , h_0(3, 2) -> 3
   , h_0(3, 3) -> 3
   , h_0(3, 4) -> 3
   , h_0(4, 1) -> 3
   , h_0(4, 2) -> 3
   , h_0(4, 3) -> 3
   , h_0(4, 4) -> 3
   , h_1(6, 7) -> 5
   , g_0(1, 1) -> 4
   , g_0(1, 2) -> 4
   , g_0(1, 3) -> 4
   , g_0(1, 4) -> 4
   , g_0(2, 1) -> 4
   , g_0(2, 2) -> 4
   , g_0(2, 3) -> 4
   , g_0(2, 4) -> 4
   , g_0(3, 1) -> 4
   , g_0(3, 2) -> 4
   , g_0(3, 3) -> 4
   , g_0(3, 4) -> 4
   , g_0(4, 1) -> 4
   , g_0(4, 2) -> 4
   , g_0(4, 3) -> 4
   , g_0(4, 4) -> 4
   , g_1(8, 9) -> 6
   , g_1(11, 12) -> 7}

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

Tool CDI

Execution Time	60.038002ms
Answer	TIMEOUT
Input	SK90 2.60

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	2.377734ms
Answer	YES(?,O(n^2))
Input	SK90 2.60

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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

Tool IDA

Execution Time	2.769451ms
Answer	YES(?,O(n^2))
Input	SK90 2.60

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {f(g(f(a()), h(a(), f(a())))) ->
     f(h(g(f(a()), a()), g(f(a()), f(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) = [1 3] x1 + [0]
           [0 1]      [2]
   h(x1, x2) = [1 0] x1 + [1 1] x2 + [0]
               [0 0]      [0 0]      [0]
   g(x1, x2) = [1 0] x1 + [1 1] x2 + [0]
               [0 1]      [0 0]      [0]

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

Tool TRI

Execution Time	0.548692ms
Answer	YES(?,O(n^2))
Input	SK90 2.60

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   a() = [0]
         [1]
   f(x1) = [1 1] x1 + [0]
           [0 1]      [0]
   h(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
               [0 0]      [0 0]      [3]
   g(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
               [0 1]      [0 1]      [3]

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

Tool TRI2

Execution Time	0.59772706ms
Answer	YES(?,O(n^2))
Input	SK90 2.60

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   a() = [0]
         [1]
   f(x1) = [1 1] x1 + [0]
           [0 1]      [3]
   h(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
               [0 0]      [0 0]      [0]
   g(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
               [0 1]      [0 0]      [3]

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