Problem HirokawaMiddeldorp 04 t008

Tool Bounds

Execution Time	60.032738ms
Answer	TIMEOUT
Input	HirokawaMiddeldorp 04 t008

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  log(s(x)) -> s(log(half(s(x))))
     , s(log(0())) -> s(0())
     , half(s(s(x))) -> s(half(x))
     , half(s(0())) -> 0()
     , half(0()) -> 0()}
  StartTerms: all
  Strategy: none

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	56.689796ms
Answer	MAYBE
Input	HirokawaMiddeldorp 04 t008

stdout:

MAYBE

Statistics:
Number of monomials: 642
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	4.402508ms
Answer	YES(?,O(n^3))
Input	HirokawaMiddeldorp 04 t008

stdout:

YES(?,O(n^3))

We consider the following Problem:

  Strict Trs:
    {  log(s(x)) -> s(log(half(s(x))))
     , s(log(0())) -> s(0())
     , half(s(s(x))) -> s(half(x))
     , half(s(0())) -> 0()
     , half(0()) -> 0()}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   0() = [1]
         [1]
         [1]
   half(x1) = [1 0 0] x1 + [1]
              [0 1 0]      [0]
              [0 1 0]      [0]
   s(x1) = [1 0 0] x1 + [1]
           [0 1 0]      [1]
           [0 1 0]      [2]
   log(x1) = [1 0 3] x1 + [0]
             [0 0 1]      [0]
             [0 1 0]      [2]

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

Tool IDA

Execution Time	6.0414276ms
Answer	YES(?,O(n^2))
Input	HirokawaMiddeldorp 04 t008

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  log(s(x)) -> s(log(half(s(x))))
     , s(log(0())) -> s(0())
     , half(s(s(x))) -> s(half(x))
     , half(s(0())) -> 0()
     , half(0()) -> 0()}
  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:
   0() = [0]
         [0]
         [0]
   half(x1) = [1 0 0] x1 + [1]
              [0 1 0]      [0]
              [0 1 0]      [0]
   s(x1) = [1 0 0] x1 + [1]
           [0 1 0]      [1]
           [0 1 0]      [2]
   log(x1) = [1 0 3] x1 + [1]
             [0 0 1]      [1]
             [0 0 1]      [2]

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

Tool TRI

Execution Time	60.026695ms
Answer	TIMEOUT
Input	HirokawaMiddeldorp 04 t008

stdout:

Tool TRI2

Execution Time	0.23631692ms
Answer	MAYBE
Input	HirokawaMiddeldorp 04 t008

stdout:

MAYBE

We consider the following Problem:

  Strict Trs:
    {  log(s(x)) -> s(log(half(s(x))))
     , s(log(0())) -> s(0())
     , half(s(s(x))) -> s(half(x))
     , half(s(0())) -> 0()
     , half(0()) -> 0()}
  StartTerms: all
  Strategy: none

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..