Problem HirokawaMiddeldorp 04 t010

Tool Bounds

Execution Time	60.026894ms
Answer	TIMEOUT
Input	HirokawaMiddeldorp 04 t010

stdout:

TIMEOUT

We consider the following Problem:

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

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	0.16237783ms
Answer	YES(?,O(n^2))
Input	HirokawaMiddeldorp 04 t010

stdout:

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

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

Time: 0.122428 seconds
Statistics:
Number of monomials: 75
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.27186704ms
Answer	YES(?,O(n^2))
Input	HirokawaMiddeldorp 04 t010

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   b() = [3]
         [3]
   g(x1) = [1 2] x1 + [0]
           [0 0]      [0]
   f(x1) = [1 1] x1 + [2]
           [0 0]      [0]
   a() = [2]
         [1]

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

Tool IDA

Execution Time	0.3441348ms
Answer	YES(?,O(n^2))
Input	HirokawaMiddeldorp 04 t010

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  b() -> a()
     , f(a()) -> g(a())
     , g(b()) -> f(b())}
  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:
   b() = [3]
         [3]
   g(x1) = [1 2] x1 + [0]
           [0 0]      [0]
   f(x1) = [1 1] x1 + [2]
           [0 0]      [0]
   a() = [2]
         [1]

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

Tool TRI

Execution Time	0.11538005ms
Answer	YES(?,O(n^2))
Input	HirokawaMiddeldorp 04 t010

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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

Tool TRI2

Execution Time	5.9781075e-2ms
Answer	YES(?,O(n^2))
Input	HirokawaMiddeldorp 04 t010

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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