Problem SK90 4.25

Tool Bounds

Execution Time	60.034466ms
Answer	TIMEOUT
Input	SK90 4.25

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  rev(++(x, x)) -> rev(x)
     , rev(++(x, y)) -> ++(rev(y), rev(x))
     , rev(b()) -> b()
     , rev(a()) -> a()}
  StartTerms: all
  Strategy: none

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	0.4219458ms
Answer	YES(?,O(n^2))
Input	SK90 4.25

stdout:

YES(?,O(n^2))
QUADRATIC upper bound on the derivational complexity

This TRS is terminating using the deltarestricted interpretation
++(delta, X1, X0) =  + 1*X0 + 1*X1 + 1 + 0*X0*delta + 0*X1*delta + 3*delta
b(delta) =  + 1 + 0*delta
rev(delta, X0) =  + 1*X0 + 0 + 2*X0*delta + 0*delta
a(delta) =  + 2 + 0*delta
++_tau_1(delta) = delta/(1 + 0 * delta)
++_tau_2(delta) = delta/(1 + 0 * delta)
rev_tau_1(delta) = delta/(1 + 2 * delta)

Time: 0.381396 seconds
Statistics:
Number of monomials: 227
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.29933286ms
Answer	YES(?,O(n^2))
Input	SK90 4.25

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  rev(++(x, x)) -> rev(x)
     , rev(++(x, y)) -> ++(rev(y), rev(x))
     , rev(b()) -> b()
     , rev(a()) -> a()}
  StartTerms: all
  Strategy: none

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

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

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

Tool IDA

Execution Time	0.49151897ms
Answer	YES(?,O(n^2))
Input	SK90 4.25

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

Tool TRI

Execution Time	0.11783695ms
Answer	YES(?,O(n^2))
Input	SK90 4.25

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  rev(++(x, x)) -> rev(x)
     , rev(++(x, y)) -> ++(rev(y), rev(x))
     , rev(b()) -> b()
     , rev(a()) -> a()}
  StartTerms: all
  Strategy: none

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

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

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

Tool TRI2

Execution Time	9.634113e-2ms
Answer	YES(?,O(n^2))
Input	SK90 4.25

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  rev(++(x, x)) -> rev(x)
     , rev(++(x, y)) -> ++(rev(y), rev(x))
     , rev(b()) -> b()
     , rev(a()) -> a()}
  StartTerms: all
  Strategy: none

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

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

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