Problem SK90 4.46

Tool Bounds

Execution Time	4.9230814e-2ms
Answer	YES(?,O(n^1))
Input	SK90 4.46

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

Proof:
  The problem is match-bounded by 1.
  The enriched problem is compatible with the following automaton:
  {  a_0() -> 1
   , a_1() -> 5
   , f_0(1) -> 2
   , f_0(2) -> 2
   , f_0(3) -> 2
   , f_0(4) -> 2
   , f_1(6) -> 2
   , b_0() -> 3
   , b_1() -> 6
   , g_0(1) -> 4
   , g_0(2) -> 4
   , g_0(3) -> 4
   , g_0(4) -> 4
   , g_1(5) -> 4}

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

Tool CDI

Execution Time	5.6874037e-2ms
Answer	YES(?,O(n^2))
Input	SK90 4.46

stdout:

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

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

Time: 0.018071 seconds
Statistics:
Number of monomials: 30
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.24799204ms
Answer	YES(?,O(n^2))
Input	SK90 4.46

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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

Tool IDA

Execution Time	0.2584741ms
Answer	YES(?,O(n^2))
Input	SK90 4.46

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

Tool TRI

Execution Time	9.9509e-2ms
Answer	YES(?,O(n^2))
Input	SK90 4.46

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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

Tool TRI2

Execution Time	7.023096e-2ms
Answer	YES(?,O(n^2))
Input	SK90 4.46

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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