Problem TCT 09 ma9

Tool Bounds

Execution Time	6.2235117e-2ms
Answer	YES(?,O(n^1))
Input	TCT 09 ma9

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  g(s(s(x))) -> f(x)
     , g(s(0())) -> s(0())
     , g(0()) -> s(0())
     , f(s(x)) -> g(s(s(x)))
     , f(0()) -> s(0())}
  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:
  {  0_0() -> 1
   , 0_1() -> 2
   , 0_2() -> 7
   , 0_3() -> 10
   , 0_4() -> 11
   , 0_5() -> 12
   , f_0(1) -> 1
   , f_1(1) -> 1
   , f_1(2) -> 1
   , f_1(7) -> 1
   , f_1(10) -> 1
   , f_1(11) -> 1
   , f_1(12) -> 1
   , f_2(1) -> 1
   , f_2(2) -> 1
   , f_2(7) -> 1
   , f_2(10) -> 1
   , f_2(11) -> 1
   , f_2(12) -> 1
   , f_3(2) -> 1
   , f_3(7) -> 1
   , f_3(10) -> 1
   , f_3(11) -> 1
   , f_3(12) -> 1
   , f_4(7) -> 1
   , f_4(10) -> 1
   , f_4(11) -> 1
   , f_4(12) -> 1
   , s_0(1) -> 1
   , s_1(1) -> 4
   , s_1(2) -> 1
   , s_1(4) -> 3
   , s_1(7) -> 1
   , s_1(10) -> 1
   , s_1(11) -> 1
   , s_1(12) -> 1
   , s_2(1) -> 5
   , s_2(2) -> 6
   , s_2(6) -> 5
   , s_2(7) -> 1
   , s_2(10) -> 1
   , s_2(11) -> 1
   , s_2(12) -> 1
   , s_3(1) -> 8
   , s_3(7) -> 9
   , s_3(9) -> 8
   , s_3(10) -> 1
   , s_3(11) -> 1
   , s_3(12) -> 1
   , s_4(11) -> 1
   , s_5(12) -> 1
   , g_0(1) -> 1
   , g_1(3) -> 1
   , g_1(4) -> 1
   , g_2(5) -> 1
   , g_3(8) -> 1}

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

Tool CDI

Execution Time	1.3661199ms
Answer	YES(?,O(n^2))
Input	TCT 09 ma9

stdout:

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

This TRS is terminating using the deltarestricted interpretation
g(delta, X0) =  + 1*X0 + 2 + 0*X0*delta + 1*delta
f(delta, X0) =  + 0*X0 + 3 + 2*X0*delta + 2*delta
0(delta) =  + 0 + 0*delta
s(delta, X0) =  + 0*X0 + 1 + 2*X0*delta + 0*delta
g_tau_1(delta) = delta/(1 + 0 * delta)
f_tau_1(delta) = delta/(0 + 2 * delta)
s_tau_1(delta) = delta/(0 + 2 * delta)

Time: 1.328848 seconds
Statistics:
Number of monomials: 360
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.4769261ms
Answer	YES(?,O(n^2))
Input	TCT 09 ma9

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  g(s(s(x))) -> f(x)
     , g(s(0())) -> s(0())
     , g(0()) -> s(0())
     , f(s(x)) -> g(s(s(x)))
     , f(0()) -> s(0())}
  StartTerms: all
  Strategy: none

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

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

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

Tool IDA

Execution Time	0.497715ms
Answer	YES(?,O(n^2))
Input	TCT 09 ma9

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

Tool TRI

Execution Time	0.17298818ms
Answer	YES(?,O(n^1))
Input	TCT 09 ma9

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  g(s(s(x))) -> f(x)
     , g(s(0())) -> s(0())
     , g(0()) -> s(0())
     , f(s(x)) -> g(s(s(x)))
     , f(0()) -> s(0())}
  StartTerms: all
  Strategy: none

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

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

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

Tool TRI2

Execution Time	0.14396381ms
Answer	YES(?,O(n^1))
Input	TCT 09 ma9

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  g(s(s(x))) -> f(x)
     , g(s(0())) -> s(0())
     , g(0()) -> s(0())
     , f(s(x)) -> g(s(s(x)))
     , f(0()) -> s(0())}
  StartTerms: all
  Strategy: none

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

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

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