Problem HirokawaMiddeldorp 04 t006

Tool Bounds

Execution Time	2.2392988e-2ms
Answer	MAYBE
Input	HirokawaMiddeldorp 04 t006

stdout:

MAYBE

We consider the following Problem:

  Strict Trs: {f(g(x, y), f(y, y)) -> f(g(y, x), y)}
  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	0.10939908ms
Answer	YES(?,O(n^2))
Input	HirokawaMiddeldorp 04 t006

stdout:

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

This TRS is terminating using the deltarestricted interpretation
g(delta, X1, X0) = + 0*X0 + 1*X1 + 0 + 1*X0*delta + 0*X1*delta + 0*delta
f(delta, X1, X0) = + 0*X0 + 0*X1 + 0 + 1*X0*delta + 1*X1*delta + 2*delta
g_tau_1(delta) = delta/(1 + 0 * delta)
g_tau_2(delta) = delta/(0 + 1 * delta)
f_tau_1(delta) = delta/(0 + 1 * delta)
f_tau_2(delta) = delta/(0 + 1 * delta)

Time: 0.069845 seconds
Statistics:
Number of monomials: 146
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.11483908ms
Answer	YES(?,O(n^1))
Input	HirokawaMiddeldorp 04 t006

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

Certificate: YES(?,O(n^1))

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

Hurray, we answered YES(?,O(n^1))

Tool IDA

Execution Time	0.19439292ms
Answer	YES(?,O(n^1))
Input	HirokawaMiddeldorp 04 t006

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

Certificate: YES(?,O(n^1))

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

Hurray, we answered YES(?,O(n^1))

Tool TRI

Execution Time	4.791689e-2ms
Answer	YES(?,O(n^1))
Input	HirokawaMiddeldorp 04 t006

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

Certificate: YES(?,O(n^1))

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

Hurray, we answered YES(?,O(n^1))

Tool TRI2

Execution Time	7.388401e-2ms
Answer	YES(?,O(n^1))
Input	HirokawaMiddeldorp 04 t006

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

Certificate: YES(?,O(n^1))

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

Hurray, we answered YES(?,O(n^1))