Problem AG01 3.51

Tool Bounds

Execution Time	3.85139e-2ms
Answer	YES(?,O(n^1))
Input	AG01 3.51

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  g(h(x)) -> g(x)
     , g(c(1())) -> g(d(h(0())))
     , g(c(h(0()))) -> g(d(1()))
     , g(d(x)) -> x
     , g(c(x)) -> x
     , f(f(x)) -> f(d(f(x)))
     , f(f(x)) -> f(c(f(x)))}
  StartTerms: all
  Strategy: none

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

Proof:
  The problem is match-bounded by 2.
  The enriched problem is compatible with the following automaton:
  {  f_0(1) -> 1
   , f_1(1) -> 5
   , f_1(4) -> 1
   , f_1(4) -> 5
   , f_2(4) -> 7
   , f_2(6) -> 5
   , c_0(1) -> 1
   , c_1(5) -> 4
   , c_2(7) -> 6
   , d_0(1) -> 1
   , d_1(2) -> 1
   , d_1(5) -> 4
   , d_2(7) -> 6
   , g_0(1) -> 1
   , g_1(1) -> 1
   , g_1(3) -> 1
   , g_2(3) -> 1
   , 0_0() -> 1
   , 0_1() -> 3
   , h_0(1) -> 1
   , h_1(3) -> 1
   , h_1(3) -> 2
   , 1_0() -> 1
   , 1_1() -> 1
   , 1_1() -> 2}

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

Tool CDI

Execution Time	14.99015ms
Answer	MAYBE
Input	AG01 3.51

stdout:

MAYBE

Statistics:
Number of monomials: 1105
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	4.4336753ms
Answer	YES(?,O(n^3))
Input	AG01 3.51

stdout:

YES(?,O(n^3))

We consider the following Problem:

  Strict Trs:
    {  g(h(x)) -> g(x)
     , g(c(1())) -> g(d(h(0())))
     , g(c(h(0()))) -> g(d(1()))
     , g(d(x)) -> x
     , g(c(x)) -> x
     , f(f(x)) -> f(d(f(x)))
     , f(f(x)) -> f(c(f(x)))}
  StartTerms: all
  Strategy: none

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

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

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

Tool IDA

Execution Time	7.076066ms
Answer	YES(?,O(n^3))
Input	AG01 3.51

stdout:

YES(?,O(n^3))

We consider the following Problem:

  Strict Trs:
    {  g(h(x)) -> g(x)
     , g(c(1())) -> g(d(h(0())))
     , g(c(h(0()))) -> g(d(1()))
     , g(d(x)) -> x
     , g(c(x)) -> x
     , f(f(x)) -> f(d(f(x)))
     , f(f(x)) -> f(c(f(x)))}
  StartTerms: all
  Strategy: none

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

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

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

Tool TRI

Execution Time	11.35996ms
Answer	MAYBE
Input	AG01 3.51

stdout:

MAYBE

We consider the following Problem:

  Strict Trs:
    {  g(h(x)) -> g(x)
     , g(c(1())) -> g(d(h(0())))
     , g(c(h(0()))) -> g(d(1()))
     , g(d(x)) -> x
     , g(c(x)) -> x
     , f(f(x)) -> f(d(f(x)))
     , f(f(x)) -> f(c(f(x)))}
  StartTerms: all
  Strategy: none

Certificate: MAYBE

Proof:
  None of the processors succeeded.

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

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

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

    4) 'matrix-interpretation of dimension 3' 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 TRI2

Execution Time	0.3005929ms
Answer	MAYBE
Input	AG01 3.51