Problem SK90 4.29

Tool Bounds

Execution Time	60.035656ms
Answer	TIMEOUT
Input	SK90 4.29

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  merge(++(x, y), ++(u(), v())) -> ++(u(), merge(++(x, y), v()))
     , merge(++(x, y), ++(u(), v())) -> ++(x, merge(y, ++(u(), v())))
     , merge(nil(), y) -> y
     , merge(x, nil()) -> x}
  StartTerms: all
  Strategy: none

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	60.0439ms
Answer	TIMEOUT
Input	SK90 4.29

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	0.7831671ms
Answer	YES(?,O(n^2))
Input	SK90 4.29

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  merge(++(x, y), ++(u(), v())) -> ++(u(), merge(++(x, y), v()))
     , merge(++(x, y), ++(u(), v())) -> ++(x, merge(y, ++(u(), v())))
     , merge(nil(), y) -> y
     , merge(x, nil()) -> x}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   nil() = [0]
           [0]
   merge(x1, x2) = [1 1] x1 + [1 1] x2 + [2]
                   [0 1]      [0 1]      [0]
   ++(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                [0 0]      [0 1]      [2]
   u() = [0]
         [0]
   v() = [0]
         [0]

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

Tool IDA

Execution Time	0.920161ms
Answer	YES(?,O(n^2))
Input	SK90 4.29

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  merge(++(x, y), ++(u(), v())) -> ++(u(), merge(++(x, y), v()))
     , merge(++(x, y), ++(u(), v())) -> ++(x, merge(y, ++(u(), v())))
     , merge(nil(), y) -> y
     , merge(x, nil()) -> 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:
   nil() = [0]
           [0]
   merge(x1, x2) = [1 1] x1 + [1 1] x2 + [2]
                   [0 1]      [0 1]      [0]
   ++(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                [0 0]      [0 1]      [2]
   u() = [0]
         [0]
   v() = [0]
         [0]

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

Tool TRI

Execution Time	0.33004403ms
Answer	YES(?,O(n^2))
Input	SK90 4.29

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  merge(++(x, y), ++(u(), v())) -> ++(u(), merge(++(x, y), v()))
     , merge(++(x, y), ++(u(), v())) -> ++(x, merge(y, ++(u(), v())))
     , merge(nil(), y) -> y
     , merge(x, nil()) -> x}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   nil() = [2]
           [0]
   merge(x1, x2) = [1 1] x1 + [1 2] x2 + [0]
                   [0 1]      [0 1]      [0]
   ++(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                [0 1]      [0 1]      [1]
   u() = [0]
         [1]
   v() = [0]
         [0]

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

Tool TRI2

Execution Time	0.33684206ms
Answer	YES(?,O(n^2))
Input	SK90 4.29

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  merge(++(x, y), ++(u(), v())) -> ++(u(), merge(++(x, y), v()))
     , merge(++(x, y), ++(u(), v())) -> ++(x, merge(y, ++(u(), v())))
     , merge(nil(), y) -> y
     , merge(x, nil()) -> x}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   nil() = [0]
           [0]
   merge(x1, x2) = [1 2] x1 + [1 1] x2 + [3]
                   [0 1]      [0 1]      [0]
   ++(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                [0 1]      [0 1]      [2]
   u() = [0]
         [3]
   v() = [2]
         [2]

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