Problem Various 04 23

Tool Bounds

Execution Time	60.032578ms
Answer	TIMEOUT
Input	Various 04 23

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  g(f(x, y), 0()) -> f(g(x, 0()), g(y, 0()))
     , g(s(x), y) -> g(f(x, y), 0())
     , g(x, s(y)) -> g(f(x, y), 0())
     , g(0(), f(x, x)) -> x}
  StartTerms: all
  Strategy: none

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	44.956436ms
Answer	MAYBE
Input	Various 04 23

stdout:

MAYBE

Statistics:
Number of monomials: 2045
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.47390008ms
Answer	YES(?,O(n^2))
Input	Various 04 23

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  g(f(x, y), 0()) -> f(g(x, 0()), g(y, 0()))
     , g(s(x), y) -> g(f(x, y), 0())
     , g(x, s(y)) -> g(f(x, y), 0())
     , g(0(), f(x, x)) -> x}
  StartTerms: all
  Strategy: none

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

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

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

Tool IDA

Execution Time	0.90449286ms
Answer	YES(?,O(n^2))
Input	Various 04 23

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  g(f(x, y), 0()) -> f(g(x, 0()), g(y, 0()))
     , g(s(x), y) -> g(f(x, y), 0())
     , g(x, s(y)) -> g(f(x, y), 0())
     , g(0(), f(x, x)) -> x}
  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]
   f(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
               [0 1]      [0 1]      [1]
   g(x1, x2) = [1 1] x1 + [1 2] x2 + [0]
               [0 1]      [0 1]      [0]
   s(x1) = [1 0] x1 + [0]
           [0 1]      [2]

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

Tool TRI

Execution Time	0.22352386ms
Answer	YES(?,O(n^2))
Input	Various 04 23

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  g(f(x, y), 0()) -> f(g(x, 0()), g(y, 0()))
     , g(s(x), y) -> g(f(x, y), 0())
     , g(x, s(y)) -> g(f(x, y), 0())
     , g(0(), f(x, x)) -> x}
  StartTerms: all
  Strategy: none

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

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

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

Tool TRI2

Execution Time	0.17915201ms
Answer	YES(?,O(n^2))
Input	Various 04 23

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  g(f(x, y), 0()) -> f(g(x, 0()), g(y, 0()))
     , g(s(x), y) -> g(f(x, y), 0())
     , g(x, s(y)) -> g(f(x, y), 0())
     , g(0(), f(x, x)) -> x}
  StartTerms: all
  Strategy: none

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

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

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