Problem Endrullis 06 direct

Tool Bounds

Execution Time	7.023811e-2ms
Answer	YES(?,O(n^1))
Input	Endrullis 06 direct

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  h(c(s(x), c(s(0()), y)), z) -> h(y, c(s(0()), c(x, z)))
     , h(x, c(y, z)) -> h(c(s(y), x), z)}
  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:
  {  c_0(1, 1) -> 1
   , c_1(1, 1) -> 4
   , c_1(1, 2) -> 4
   , c_1(3, 2) -> 2
   , c_1(3, 4) -> 2
   , c_1(7, 1) -> 6
   , c_1(7, 6) -> 6
   , c_1(7, 10) -> 6
   , c_2(9, 1) -> 8
   , c_2(9, 6) -> 8
   , c_2(9, 8) -> 8
   , c_2(9, 10) -> 8
   , c_2(11, 8) -> 10
   , h_0(1, 1) -> 1
   , h_1(1, 2) -> 1
   , h_1(6, 1) -> 1
   , h_1(6, 2) -> 1
   , h_1(8, 2) -> 1
   , h_1(10, 2) -> 1
   , h_2(8, 2) -> 1
   , h_2(8, 4) -> 1
   , h_2(10, 1) -> 1
   , h_2(10, 2) -> 1
   , s_0(1) -> 1
   , s_1(1) -> 7
   , s_1(5) -> 3
   , s_2(1) -> 11
   , s_2(3) -> 9
   , 0_0() -> 1
   , 0_1() -> 5}

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

Tool CDI

Execution Time	60.039616ms
Answer	TIMEOUT
Input	Endrullis 06 direct

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	9.281966ms
Answer	YES(?,O(n^3))
Input	Endrullis 06 direct

stdout:

YES(?,O(n^3))

We consider the following Problem:

  Strict Trs:
    {  h(c(s(x), c(s(0()), y)), z) -> h(y, c(s(0()), c(x, z)))
     , h(x, c(y, z)) -> h(c(s(y), x), z)}
  StartTerms: all
  Strategy: none

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

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

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

Tool IDA

Execution Time	11.502682ms
Answer	YES(?,O(n^2))
Input	Endrullis 06 direct

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  h(c(s(x), c(s(0()), y)), z) -> h(y, c(s(0()), c(x, z)))
     , h(x, c(y, z)) -> h(c(s(y), x), z)}
  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:
   c(x1, x2) = [1 0 3] x1 + [1 0 0] x2 + [0]
               [0 1 0]      [0 1 0]      [0]
               [0 0 0]      [0 0 1]      [2]
   h(x1, x2) = [1 1 0] x1 + [1 0 2] x2 + [0]
               [0 0 0]      [0 0 0]      [0]
               [0 0 0]      [0 0 0]      [0]
   s(x1) = [1 0 0] x1 + [0]
           [0 0 3]      [0]
           [0 0 0]      [0]
   0() = [0]
         [0]
         [3]

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

Tool TRI

Execution Time	1.1127229ms
Answer	YES(?,O(n^1))
Input	Endrullis 06 direct

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  h(c(s(x), c(s(0()), y)), z) -> h(y, c(s(0()), c(x, z)))
     , h(x, c(y, z)) -> h(c(s(y), x), z)}
  StartTerms: all
  Strategy: none

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

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

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

Tool TRI2

Execution Time	1.4855142ms
Answer	MAYBE
Input	Endrullis 06 direct

stdout:

MAYBE

We consider the following Problem:

  Strict Trs:
    {  h(c(s(x), c(s(0()), y)), z) -> h(y, c(s(0()), c(x, z)))
     , h(x, c(y, z)) -> h(c(s(y), x), z)}
  StartTerms: all
  Strategy: none

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..