Problem SK90 2.01

Tool Bounds

Execution Time	60.035645ms
Answer	TIMEOUT
Input	SK90 2.01

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  +(+(x, y), i(y)) -> x
     , +(+(x, i(y)), y) -> x
     , +(x, +(y, z)) -> +(+(x, y), z)
     , i(+(x, y)) -> +(i(x), i(y))
     , +(x, i(x)) -> 0()
     , +(i(x), x) -> 0()
     , i(i(x)) -> x
     , +(x, 0()) -> x
     , +(0(), y) -> y
     , i(0()) -> 0()}
  StartTerms: all
  Strategy: none

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	0.6194198ms
Answer	MAYBE
Input	SK90 2.01

stdout:

MAYBE

Statistics:
Number of monomials: 489
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.47707415ms
Answer	YES(?,O(n^2))
Input	SK90 2.01

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  +(+(x, y), i(y)) -> x
     , +(+(x, i(y)), y) -> x
     , +(x, +(y, z)) -> +(+(x, y), z)
     , i(+(x, y)) -> +(i(x), i(y))
     , +(x, i(x)) -> 0()
     , +(i(x), x) -> 0()
     , i(i(x)) -> x
     , +(x, 0()) -> x
     , +(0(), y) -> y
     , i(0()) -> 0()}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   0() = [1]
         [0]
   i(x1) = [1 3] x1 + [2]
           [0 1]      [0]
   +(x1, x2) = [1 0] x1 + [1 2] x2 + [0]
               [0 1]      [0 1]      [2]

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

Tool IDA

Execution Time	0.6038351ms
Answer	YES(?,O(n^2))
Input	SK90 2.01

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  +(+(x, y), i(y)) -> x
     , +(+(x, i(y)), y) -> x
     , +(x, +(y, z)) -> +(+(x, y), z)
     , i(+(x, y)) -> +(i(x), i(y))
     , +(x, i(x)) -> 0()
     , +(i(x), x) -> 0()
     , i(i(x)) -> x
     , +(x, 0()) -> x
     , +(0(), y) -> y
     , i(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]
   i(x1) = [1 1] x1 + [1]
           [0 1]      [0]
   +(x1, x2) = [1 0] x1 + [1 3] x2 + [2]
               [0 1]      [0 1]      [3]

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

Tool TRI

Execution Time	0.23949409ms
Answer	YES(?,O(n^2))
Input	SK90 2.01

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  +(+(x, y), i(y)) -> x
     , +(+(x, i(y)), y) -> x
     , +(x, +(y, z)) -> +(+(x, y), z)
     , i(+(x, y)) -> +(i(x), i(y))
     , +(x, i(x)) -> 0()
     , +(i(x), x) -> 0()
     , i(i(x)) -> x
     , +(x, 0()) -> x
     , +(0(), y) -> y
     , i(0()) -> 0()}
  StartTerms: all
  Strategy: none

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

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

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

Tool TRI2

Execution Time	0.20179296ms
Answer	YES(?,O(n^2))
Input	SK90 2.01

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  +(+(x, y), i(y)) -> x
     , +(+(x, i(y)), y) -> x
     , +(x, +(y, z)) -> +(+(x, y), z)
     , i(+(x, y)) -> +(i(x), i(y))
     , +(x, i(x)) -> 0()
     , +(i(x), x) -> 0()
     , i(i(x)) -> x
     , +(x, 0()) -> x
     , +(0(), y) -> y
     , i(0()) -> 0()}
  StartTerms: all
  Strategy: none

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

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

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