Problem Endrullis 06 quadruple1

Tool Bounds

Execution Time	2.9744148e-2ms
Answer	YES(?,O(n^1))
Input	Endrullis 06 quadruple1

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {p(p(b(a(x0)), x1), p(x2, x3)) ->
     p(p(x3, a(x2)), p(b(a(x1)), b(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(1) -> 6
   , a_1(1) -> 7
   , a_1(2) -> 8
   , a_1(4) -> 9
   , a_1(7) -> 6
   , a_1(9) -> 6
   , b_0(1) -> 1
   , b_1(1) -> 5
   , b_1(6) -> 4
   , p_0(1, 1) -> 1
   , p_1(1, 7) -> 2
   , p_1(2, 3) -> 1
   , p_1(3, 8) -> 2
   , p_1(4, 5) -> 3
   , p_1(5, 9) -> 2}

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

Tool CDI

Execution Time	60.039192ms
Answer	TIMEOUT
Input	Endrullis 06 quadruple1

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	60.02824ms
Answer	TIMEOUT
Input	Endrullis 06 quadruple1

stdout:

TIMEOUT

We consider the following Problem:

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

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool IDA

Execution Time	60.02931ms
Answer	TIMEOUT
Input	Endrullis 06 quadruple1

stdout:

Tool TRI

Execution Time	12.753093ms
Answer	YES(?,O(n^3))
Input	Endrullis 06 quadruple1

stdout:

YES(?,O(n^3))

We consider the following Problem:

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

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

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

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

Tool TRI2

Execution Time	1.935149ms
Answer	MAYBE
Input	Endrullis 06 quadruple1

stdout:

MAYBE

We consider the following Problem:

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

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..