Problem SK90 2.38

Tool Bounds

Execution Time	60.02988ms
Answer	TIMEOUT
Input	SK90 2.38

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  ++(++(x, y), z) -> ++(x, ++(y, z))
     , ++(.(x, y), z) -> .(x, ++(y, z))
     , ++(x, nil()) -> x
     , ++(nil(), y) -> y}
  StartTerms: all
  Strategy: none

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	0.15406394ms
Answer	MAYBE
Input	SK90 2.38

stdout:

MAYBE

Statistics:
Number of monomials: 180
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.348536ms
Answer	YES(?,O(n^2))
Input	SK90 2.38

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  ++(++(x, y), z) -> ++(x, ++(y, z))
     , ++(.(x, y), z) -> .(x, ++(y, z))
     , ++(x, nil()) -> x
     , ++(nil(), y) -> y}
  StartTerms: all
  Strategy: none

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

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

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

Tool IDA

Execution Time	0.48014283ms
Answer	YES(?,O(n^2))
Input	SK90 2.38

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  ++(++(x, y), z) -> ++(x, ++(y, z))
     , ++(.(x, y), z) -> .(x, ++(y, z))
     , ++(x, nil()) -> x
     , ++(nil(), y) -> y}
  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() = [1]
           [0]
   ++(x1, x2) = [1 2] x1 + [1 0] x2 + [0]
                [0 1]      [0 1]      [2]
   .(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
               [0 0]      [0 1]      [2]

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

Tool TRI

Execution Time	0.15026307ms
Answer	YES(?,O(n^2))
Input	SK90 2.38

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  ++(++(x, y), z) -> ++(x, ++(y, z))
     , ++(.(x, y), z) -> .(x, ++(y, z))
     , ++(x, nil()) -> x
     , ++(nil(), y) -> y}
  StartTerms: all
  Strategy: none

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

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

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

Tool TRI2

Execution Time	0.11423898ms
Answer	YES(?,O(n^2))
Input	SK90 2.38

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  ++(++(x, y), z) -> ++(x, ++(y, z))
     , ++(.(x, y), z) -> .(x, ++(y, z))
     , ++(x, nil()) -> x
     , ++(nil(), y) -> y}
  StartTerms: all
  Strategy: none

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

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

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