Problem Various 04 07

Tool Bounds

Execution Time	3.0030966e-2ms
Answer	YES(?,O(n^1))
Input	Various 04 07

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

Proof:
  The problem is match-bounded by 1.
  The enriched problem is compatible with the following automaton:
  {  f_0(1, 1) -> 1
   , h_0(1, 1) -> 1
   , h_1(1, 1) -> 1}

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

Tool CDI

Execution Time	4.1845083e-2ms
Answer	YES(?,O(n^2))
Input	Various 04 07

stdout:

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

This TRS is terminating using the deltarestricted interpretation
f(delta, X1, X0) = + 1*X0 + 1*X1 + 3 + 0*X0*delta + 0*X1*delta + 2*delta
h(delta, X1, X0) = + 1*X0 + 1*X1 + 2 + 0*X0*delta + 0*X1*delta + 1*delta
f_tau_1(delta) = delta/(1 + 0 * delta)
f_tau_2(delta) = delta/(1 + 0 * delta)
h_tau_1(delta) = delta/(1 + 0 * delta)
h_tau_2(delta) = delta/(1 + 0 * delta)

Time: 0.002277 seconds
Statistics:
Number of monomials: 72
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	7.918501e-2ms
Answer	YES(?,O(n^1))
Input	Various 04 07

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

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

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

Tool IDA

Execution Time	0.14745688ms
Answer	YES(?,O(n^1))
Input	Various 04 07

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

Tool TRI

Execution Time	6.831908e-2ms
Answer	YES(?,O(n^1))
Input	Various 04 07

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

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

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

Tool TRI2

Execution Time	4.1654825e-2ms
Answer	YES(?,O(n^2))
Input	Various 04 07

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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