Problem HirokawaMiddeldorp 04 t011

Tool Bounds

Execution Time	60.08344ms
Answer	TIMEOUT
Input	HirokawaMiddeldorp 04 t011

stdout:

TIMEOUT

We consider the following Problem:

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

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	0.14948201ms
Answer	YES(?,O(n^2))
Input	HirokawaMiddeldorp 04 t011

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 + 3*X1*delta + 0*delta
h(delta, X1, X0) =  + 0*X0 + 1*X1 + 0 + 1*X0*delta + 3*X1*delta + 2*delta
f(delta, X0) =  + 1*X0 + 1 + 0*X0*delta + 0*delta
g_tau_1(delta) = delta/(1 + 3 * delta)
g_tau_2(delta) = delta/(0 + 1 * delta)
h_tau_1(delta) = delta/(1 + 3 * delta)
h_tau_2(delta) = delta/(0 + 1 * delta)
f_tau_1(delta) = delta/(1 + 0 * delta)

Time: 0.109752 seconds
Statistics:
Number of monomials: 137
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.23614216ms
Answer	YES(?,O(n^2))
Input	HirokawaMiddeldorp 04 t011

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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

Tool IDA

Execution Time	0.46494293ms
Answer	YES(?,O(n^2))
Input	HirokawaMiddeldorp 04 t011

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  h(x, y) -> g(x, f(y))
     , g(f(x), y) -> f(h(x, y))}
  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:
   f(x1) = [1 0] x1 + [0]
           [0 1]      [2]
   g(x1, x2) = [1 1] x1 + [1 0] x2 + [0]
               [0 1]      [0 0]      [2]
   h(x1, x2) = [1 1] x1 + [1 0] x2 + [1]
               [0 1]      [0 0]      [2]

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

Tool TRI

Execution Time	0.11220193ms
Answer	YES(?,O(n^2))
Input	HirokawaMiddeldorp 04 t011

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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

Tool TRI2

Execution Time	7.544398e-2ms
Answer	YES(?,O(n^2))
Input	HirokawaMiddeldorp 04 t011

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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