Problem Endrullis 06 quadruple2

Tool Bounds

Execution Time	3.2571077e-2ms
Answer	YES(?,O(n^1))
Input	Endrullis 06 quadruple2

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {p(p(b(a(x0)), x1), p(x2, x3)) ->
     p(p(b(x2), a(a(b(x1)))), p(x3, x0))}
  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) -> 1
   , a_1(6) -> 5
   , a_1(7) -> 6
   , b_0(1) -> 1
   , b_1(1) -> 4
   , b_1(1) -> 7
   , b_1(2) -> 4
   , b_1(3) -> 4
   , b_1(5) -> 7
   , p_0(1, 1) -> 1
   , p_1(1, 1) -> 3
   , p_1(2, 3) -> 1
   , p_1(2, 3) -> 3
   , p_1(3, 1) -> 3
   , p_1(4, 5) -> 2}

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

Tool CDI

Execution Time	60.040836ms
Answer	TIMEOUT
Input	Endrullis 06 quadruple2

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	15.674141ms
Answer	YES(?,O(n^3))
Input	Endrullis 06 quadruple2

stdout:

YES(?,O(n^3))

We consider the following Problem:

  Strict Trs:
    {p(p(b(a(x0)), x1), p(x2, x3)) ->
     p(p(b(x2), a(a(b(x1)))), p(x3, x0))}
  StartTerms: all
  Strategy: none

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

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

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

Tool IDA

Execution Time	25.181433ms
Answer	YES(?,O(n^2))
Input	Endrullis 06 quadruple2

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {p(p(b(a(x0)), x1), p(x2, x3)) ->
     p(p(b(x2), a(a(b(x1)))), p(x3, x0))}
  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(x1) = [1 0 2] x1 + [0]
           [0 1 0]      [2]
           [0 0 0]      [0]
   b(x1) = [1 0 0] x1 + [0]
           [0 1 0]      [0]
           [0 0 0]      [0]
   p(x1, x2) = [1 2 0] x1 + [1 0 2] x2 + [0]
               [0 0 0]      [0 0 0]      [0]
               [0 0 0]      [0 1 0]      [0]

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

Tool TRI

Execution Time	0.9805629ms
Answer	YES(?,O(n^2))
Input	Endrullis 06 quadruple2

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {p(p(b(a(x0)), x1), p(x2, x3)) ->
     p(p(b(x2), a(a(b(x1)))), p(x3, x0))}
  StartTerms: all
  Strategy: none

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

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

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

Tool TRI2

Execution Time	1.0870821ms
Answer	MAYBE
Input	Endrullis 06 quadruple2

stdout:

MAYBE

We consider the following Problem:

  Strict Trs:
    {p(p(b(a(x0)), x1), p(x2, x3)) ->
     p(p(b(x2), a(a(b(x1)))), p(x3, x0))}
  StartTerms: all
  Strategy: none

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..