Problem SK90 2.54

Tool Bounds

Execution Time	60.026623ms
Answer	TIMEOUT
Input	SK90 2.54

stdout:

TIMEOUT

We consider the following Problem:

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

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	9.8899126e-2ms
Answer	YES(?,O(n^2))
Input	SK90 2.54

stdout:

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

This TRS is terminating using the deltarestricted interpretation
g(delta, X0) =  + 1*X0 + 2 + 0*X0*delta + 0*delta
a(delta) =  + 3 + 0*delta
f(delta, X1, X0) =  + 1*X0 + 1*X1 + 1 + 1*X0*delta + 0*X1*delta + 0*delta
g_tau_1(delta) = delta/(1 + 0 * delta)
f_tau_1(delta) = delta/(1 + 0 * delta)
f_tau_2(delta) = delta/(1 + 1 * delta)

Time: 0.057721 seconds
Statistics:
Number of monomials: 87
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.20599294ms
Answer	YES(?,O(n^2))
Input	SK90 2.54

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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

Tool IDA

Execution Time	0.31409907ms
Answer	YES(?,O(n^2))
Input	SK90 2.54

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  f(x, g(y)) -> f(g(x), y)
     , f(x, a()) -> 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:
   a() = [3]
         [3]
   f(x1, x2) = [1 0] x1 + [1 1] x2 + [1]
               [0 1]      [0 1]      [0]
   g(x1) = [1 0] x1 + [0]
           [0 1]      [3]

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

Tool TRI

Execution Time	7.855606e-2ms
Answer	YES(?,O(n^2))
Input	SK90 2.54

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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

Tool TRI2

Execution Time	6.154704e-2ms
Answer	YES(?,O(n^2))
Input	SK90 2.54

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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