Problem Zantema 04 z002

Tool Bounds

Execution Time	4.9036026e-2ms
Answer	YES(?,O(n^1))
Input	Zantema 04 z002

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  a(a(x1)) -> a(c(b(a(x1))))
     , b(x1) -> c(c(x1))
     , b(c(a(x1))) -> a(b(a(b(x1))))}
  StartTerms: all
  Strategy: none

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

Proof:
  The problem is match-bounded by 3.
  The enriched problem is compatible with the following automaton:
  {  a_0(1) -> 1
   , a_1(1) -> 4
   , a_1(2) -> 1
   , a_1(2) -> 4
   , a_1(2) -> 8
   , a_1(8) -> 7
   , a_2(2) -> 11
   , a_2(9) -> 4
   , a_2(9) -> 7
   , c_0(1) -> 1
   , c_1(1) -> 5
   , c_1(3) -> 2
   , c_1(5) -> 1
   , c_2(1) -> 12
   , c_2(2) -> 12
   , c_2(4) -> 6
   , c_2(6) -> 3
   , c_2(7) -> 13
   , c_2(10) -> 9
   , c_2(12) -> 8
   , c_2(13) -> 2
   , c_3(11) -> 14
   , c_3(14) -> 10
   , b_0(1) -> 1
   , b_1(1) -> 8
   , b_1(2) -> 8
   , b_1(4) -> 3
   , b_1(7) -> 2
   , b_2(11) -> 10}

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

Tool CDI

Execution Time	45.18441ms
Answer	MAYBE
Input	Zantema 04 z002

stdout:

MAYBE

Statistics:
Number of monomials: 1445
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	6.718238ms
Answer	YES(?,O(n^3))
Input	Zantema 04 z002

stdout:

YES(?,O(n^3))

We consider the following Problem:

  Strict Trs:
    {  a(a(x1)) -> a(c(b(a(x1))))
     , b(x1) -> c(c(x1))
     , b(c(a(x1))) -> a(b(a(b(x1))))}
  StartTerms: all
  Strategy: none

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

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

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

Tool IDA

Execution Time	8.741125ms
Answer	YES(?,O(n^3))
Input	Zantema 04 z002

stdout:

YES(?,O(n^3))

We consider the following Problem:

  Strict Trs:
    {  a(a(x1)) -> a(c(b(a(x1))))
     , b(x1) -> c(c(x1))
     , b(c(a(x1))) -> a(b(a(b(x1))))}
  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:
   a(x1) = [1 3 1] x1 + [0]
           [0 0 0]      [0]
           [0 0 0]      [2]
   c(x1) = [1 0 0] x1 + [0]
           [0 0 1]      [0]
           [0 0 0]      [0]
   b(x1) = [1 2 0] x1 + [1]
           [0 0 0]      [0]
           [0 1 0]      [0]

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

Tool TRI

Execution Time	3.0603762ms
Answer	YES(?,O(n^2))
Input	Zantema 04 z002

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  a(a(x1)) -> a(c(b(a(x1))))
     , b(x1) -> c(c(x1))
     , b(c(a(x1))) -> a(b(a(b(x1))))}
  StartTerms: all
  Strategy: none

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

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

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

Tool TRI2

Execution Time	0.19171095ms
Answer	MAYBE
Input	Zantema 04 z002

stdout:

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a(a(x1)) -> a(c(b(a(x1))))
     , b(x1) -> c(c(x1))
     , b(c(a(x1))) -> a(b(a(b(x1))))}
  StartTerms: all
  Strategy: none

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..