Problem Transformed CSR 04 Ex18 Luc06 iGM

Tool Bounds

Execution Time	60.03505ms
Answer	TIMEOUT
Input	Transformed CSR 04 Ex18 Luc06 iGM

stdout:

TIMEOUT

We consider the following Problem:

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

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	60.040154ms
Answer	TIMEOUT
Input	Transformed CSR 04 Ex18 Luc06 iGM

stdout:

TIMEOUT

Statistics:
Number of monomials: 0
Last formula building started for bound 0
Last SAT solving started for bound 0

Tool EDA

Execution Time	0.89458513ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex18 Luc06 iGM

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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

Tool IDA

Execution Time	1.3657851ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex18 Luc06 iGM

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

Tool TRI

Execution Time	0.3465762ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex18 Luc06 iGM

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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

Tool TRI2

Execution Time	0.32523203ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex18 Luc06 iGM

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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