Problem SK90 4.39

Tool Bounds

Execution Time	2.4378061e-2ms
Answer	MAYBE
Input	SK90 4.39

stdout:

MAYBE

We consider the following Problem:

  Strict Trs: {*(x, *(minus(y), y)) -> *(minus(*(y, y)), x)}
  StartTerms: all
  Strategy: none

Certificate: MAYBE

Proof:
  None of the processors succeeded.

  Details of failed attempt(s):
  -----------------------------
    1) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason:
         match-boundness of the problem could not be verified.

    2) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason:
         match-boundness of the problem could not be verified.


Arrrr..

Tool CDI

Execution Time	3.383665ms
Answer	YES(?,O(n^2))
Input	SK90 4.39

stdout:

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

This TRS is terminating using the deltarestricted interpretation
minus(delta, X0) = + 1*X0 + 2 + 0*X0*delta + 0*delta
*(delta, X1, X0) = + 1*X0 + 1*X1 + 0 + 2*X0*delta + 2*X1*delta + 0*delta
minus_tau_1(delta) = delta/(1 + 0 * delta)
*_tau_1(delta) = delta/(1 + 2 * delta)
*_tau_2(delta) = delta/(1 + 2 * delta)

Time: 3.343096 seconds
Statistics:
Number of monomials: 456
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.45553803ms
Answer	YES(?,O(n^2))
Input	SK90 4.39

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs: {*(x, *(minus(y), y)) -> *(minus(*(y, y)), x)}
  StartTerms: all
  Strategy: none

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

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

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

Tool IDA

Execution Time	0.49836397ms
Answer	YES(?,O(n^2))
Input	SK90 4.39

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

Tool TRI

Execution Time	0.12921691ms
Answer	YES(?,O(n^2))
Input	SK90 4.39

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs: {*(x, *(minus(y), y)) -> *(minus(*(y, y)), x)}
  StartTerms: all
  Strategy: none

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

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

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

Tool TRI2

Execution Time	0.11980295ms
Answer	YES(?,O(n^2))
Input	SK90 4.39

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs: {*(x, *(minus(y), y)) -> *(minus(*(y, y)), x)}
  StartTerms: all
  Strategy: none

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

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

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