Problem Der95 04

Tool Bounds

Execution Time	60.022713ms
Answer	TIMEOUT
Input	Der95 04

stdout:

TIMEOUT

We consider the following Problem:

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

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	9.6097946e-2ms
Answer	YES(?,O(n^2))
Input	Der95 04

stdout:

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

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

Time: 0.058733 seconds
Statistics:
Number of monomials: 81
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	8.855295e-2ms
Answer	YES(?,O(n^1))
Input	Der95 04

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   f(x1) = [1] x1 + [3]
   g(x1) = [1] x1 + [2]

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

Tool IDA

Execution Time	0.17649102ms
Answer	YES(?,O(n^1))
Input	Der95 04

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  g(g(x)) -> f(x)
     , f(f(x)) -> g(f(x))}
  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) = [1] x1 + [3]
   g(x1) = [1] x1 + [2]

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

Tool TRI

Execution Time	6.853008e-2ms
Answer	YES(?,O(n^1))
Input	Der95 04

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

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

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

Tool TRI2

Execution Time	5.863309e-2ms
Answer	YES(?,O(n^1))
Input	Der95 04

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

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

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