Problem SK90 4.52

Tool Bounds

Execution Time	60.03326ms
Answer	TIMEOUT
Input	SK90 4.52

stdout:

TIMEOUT

We consider the following Problem:

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

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	2.4172342ms
Answer	MAYBE
Input	SK90 4.52

stdout:

MAYBE

Statistics:
Number of monomials: 826
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.54632187ms
Answer	YES(?,O(n^2))
Input	SK90 4.52

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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

Tool IDA

Execution Time	0.74781513ms
Answer	YES(?,O(n^2))
Input	SK90 4.52

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

Tool TRI

Execution Time	0.286124ms
Answer	YES(?,O(n^2))
Input	SK90 4.52

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   a() = [2]
         [1]
   s(x1) = [1 1] x1 + [2]
           [0 1]      [0]
   f(x1, x2) = [1 1] x1 + [1 1] x2 + [2]
               [0 1]      [0 1]      [3]
   g(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
               [0 1]      [0 1]      [3]

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

Tool TRI2

Execution Time	0.23552203ms
Answer	YES(?,O(n^2))
Input	SK90 4.52

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   a() = [2]
         [1]
   s(x1) = [1 1] x1 + [2]
           [0 1]      [0]
   f(x1, x2) = [1 1] x1 + [1 1] x2 + [2]
               [0 1]      [0 1]      [3]
   g(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
               [0 1]      [0 1]      [3]

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