Problem Transformed CSR 04 Ex6 GM04 iGM

Tool Bounds

Execution Time	8.840394e-2ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex6 GM04 iGM

stdout:

YES(?,O(n^1))

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(f(X)) -> active(f(X))
     , mark(c()) -> active(c())
     , active(f(g(X))) -> mark(g(X))
     , active(c()) -> mark(f(g(c())))}
  StartTerms: all
  Strategy: none

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

Proof:
  The problem is match-bounded by 5.
  The enriched problem is compatible with the following automaton:
  {  c_0() -> 1
   , c_1() -> 1
   , c_2() -> 4
   , c_3() -> 6
   , active_0(1) -> 1
   , active_1(1) -> 1
   , active_2(1) -> 1
   , active_2(2) -> 1
   , active_2(4) -> 1
   , active_3(2) -> 1
   , active_3(3) -> 1
   , active_3(5) -> 1
   , active_4(5) -> 1
   , active_4(9) -> 1
   , active_4(10) -> 1
   , active_5(11) -> 1
   , g_0(1) -> 1
   , g_1(1) -> 1
   , g_1(1) -> 2
   , g_1(1) -> 5
   , g_1(1) -> 9
   , g_1(2) -> 1
   , g_1(3) -> 1
   , g_1(4) -> 1
   , g_1(5) -> 1
   , g_1(6) -> 1
   , g_1(9) -> 1
   , g_1(10) -> 1
   , g_1(11) -> 1
   , g_2(1) -> 1
   , g_2(1) -> 2
   , g_2(1) -> 5
   , g_2(1) -> 9
   , g_2(2) -> 1
   , g_2(2) -> 2
   , g_2(2) -> 5
   , g_2(2) -> 9
   , g_2(3) -> 1
   , g_2(3) -> 2
   , g_2(3) -> 5
   , g_2(3) -> 9
   , g_2(4) -> 1
   , g_2(4) -> 2
   , g_2(4) -> 3
   , g_2(4) -> 5
   , g_2(4) -> 9
   , g_2(5) -> 1
   , g_2(5) -> 2
   , g_2(5) -> 5
   , g_2(5) -> 9
   , g_2(6) -> 2
   , g_2(9) -> 1
   , g_2(9) -> 2
   , g_2(9) -> 5
   , g_2(9) -> 9
   , g_2(10) -> 1
   , g_2(10) -> 2
   , g_2(10) -> 5
   , g_2(10) -> 9
   , g_2(11) -> 1
   , g_2(11) -> 2
   , g_2(11) -> 5
   , g_2(11) -> 9
   , g_3(1) -> 1
   , g_3(1) -> 2
   , g_3(1) -> 5
   , g_3(1) -> 9
   , g_3(2) -> 1
   , g_3(2) -> 2
   , g_3(2) -> 5
   , g_3(2) -> 9
   , g_3(3) -> 1
   , g_3(3) -> 2
   , g_3(3) -> 5
   , g_3(3) -> 9
   , g_3(4) -> 1
   , g_3(4) -> 2
   , g_3(4) -> 5
   , g_3(4) -> 9
   , g_3(5) -> 1
   , g_3(5) -> 2
   , g_3(5) -> 5
   , g_3(5) -> 9
   , g_3(6) -> 3
   , g_3(9) -> 1
   , g_3(9) -> 2
   , g_3(9) -> 5
   , g_3(9) -> 9
   , g_3(10) -> 1
   , g_3(10) -> 2
   , g_3(10) -> 5
   , g_3(10) -> 9
   , g_3(11) -> 1
   , g_3(11) -> 2
   , g_3(11) -> 5
   , g_3(11) -> 9
   , g_4(1) -> 9
   , g_4(2) -> 1
   , g_4(2) -> 2
   , g_4(2) -> 5
   , g_4(2) -> 9
   , g_4(3) -> 1
   , g_4(3) -> 2
   , g_4(3) -> 5
   , g_4(3) -> 9
   , g_4(4) -> 5
   , g_4(5) -> 1
   , g_4(5) -> 2
   , g_4(5) -> 5
   , g_4(5) -> 9
   , g_4(6) -> 10
   , g_4(9) -> 1
   , g_4(9) -> 2
   , g_4(9) -> 5
   , g_4(9) -> 9
   , g_4(10) -> 1
   , g_4(10) -> 2
   , g_4(10) -> 5
   , g_4(10) -> 9
   , g_4(11) -> 1
   , g_4(11) -> 2
   , g_4(11) -> 5
   , g_4(11) -> 9
   , g_5(5) -> 9
   , g_5(6) -> 11
   , g_5(9) -> 9
   , g_5(10) -> 9
   , g_5(11) -> 9
   , f_0(1) -> 1
   , f_1(1) -> 1
   , f_1(2) -> 1
   , f_1(3) -> 1
   , f_1(4) -> 1
   , f_1(5) -> 1
   , f_1(9) -> 1
   , f_1(10) -> 1
   , f_1(11) -> 1
   , f_2(1) -> 1
   , f_2(2) -> 1
   , f_2(3) -> 1
   , f_2(3) -> 2
   , f_2(4) -> 1
   , f_2(5) -> 1
   , f_2(9) -> 1
   , f_2(10) -> 1
   , f_2(11) -> 1
   , f_3(1) -> 1
   , f_3(2) -> 1
   , f_3(3) -> 1
   , f_3(3) -> 2
   , f_3(4) -> 1
   , f_3(5) -> 1
   , f_3(9) -> 1
   , f_3(10) -> 1
   , f_3(11) -> 1
   , f_4(2) -> 1
   , f_4(3) -> 1
   , f_4(3) -> 5
   , f_4(5) -> 1
   , f_4(9) -> 1
   , f_4(10) -> 1
   , f_4(11) -> 1
   , mark_0(1) -> 1
   , mark_1(1) -> 1
   , mark_2(2) -> 1
   , mark_3(2) -> 1
   , mark_3(3) -> 1
   , mark_3(5) -> 1
   , mark_4(10) -> 1}

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

Tool CDI

Execution Time	12.347486ms
Answer	MAYBE
Input	Transformed CSR 04 Ex6 GM04 iGM

stdout:

MAYBE

Statistics:
Number of monomials: 743
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.595448ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex6 GM04 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(f(X)) -> active(f(X))
     , mark(c()) -> active(c())
     , active(f(g(X))) -> mark(g(X))
     , active(c()) -> mark(f(g(c())))}
  StartTerms: all
  Strategy: none

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

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

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

Tool IDA

Execution Time	1.0262461ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex6 GM04 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(f(X)) -> active(f(X))
     , mark(c()) -> active(c())
     , active(f(g(X))) -> mark(g(X))
     , active(c()) -> mark(f(g(c())))}
  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:
   c() = [0]
         [3]
   active(x1) = [1 3] x1 + [0]
                [0 1]      [2]
   g(x1) = [1 1] x1 + [0]
           [0 0]      [0]
   f(x1) = [1 1] x1 + [0]
           [0 0]      [1]
   mark(x1) = [1 3] x1 + [1]
              [0 1]      [3]

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

Tool TRI

Execution Time	0.25416803ms
Answer	YES(?,O(n^2))
Input	Transformed CSR 04 Ex6 GM04 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(f(X)) -> active(f(X))
     , mark(c()) -> active(c())
     , active(f(g(X))) -> mark(g(X))
     , active(c()) -> mark(f(g(c())))}
  StartTerms: all
  Strategy: none

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

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

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

Tool TRI2

Execution Time	0.24945998ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex6 GM04 iGM