Problem SK90 4.45

Tool Bounds

Execution Time	2.7706861e-2ms
Answer	YES(?,O(n^1))
Input	SK90 4.45

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

Proof:
  The problem is match-bounded by 2.
  The enriched problem is compatible with the following automaton:
  {  f_0(1, 1) -> 1
   , f_1(1, 1) -> 1
   , a_0() -> 1
   , a_1() -> 1
   , a_2() -> 1
   , g_0(1) -> 1}

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

Tool CDI

Execution Time	4.515481e-2ms
Answer	YES(?,O(n^2))
Input	SK90 4.45

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 + 2*X0*delta + 1*delta
f(delta, X1, X0) =  + 0*X0 + 0*X1 + 0 + 2*X0*delta + 2*X1*delta + 1*delta
a(delta) =  + 0 + 0*delta
g_tau_1(delta) = delta/(0 + 2 * delta)
f_tau_1(delta) = delta/(0 + 2 * delta)
f_tau_2(delta) = delta/(0 + 2 * delta)

Time: 0.007597 seconds
Statistics:
Number of monomials: 42
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	8.6652994e-2ms
Answer	YES(?,O(n^1))
Input	SK90 4.45

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   f(x1, x2) = [1] x1 + [1] x2 + [3]
   a() = [2]
   g(x1) = [1] x1 + [3]

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

Tool IDA

Execution Time	0.10117102ms
Answer	YES(?,O(n^1))
Input	SK90 4.45

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

Proof:
  We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
  Interpretation Functions:
   f(x1, x2) = [1] x1 + [1] x2 + [3]
   a() = [2]
   g(x1) = [1] x1 + [3]

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

Tool TRI

Execution Time	3.7683964e-2ms
Answer	YES(?,O(n^1))
Input	SK90 4.45

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

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

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

Tool TRI2

Execution Time	4.7571898e-2ms
Answer	YES(?,O(n^2))
Input	SK90 4.45

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

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

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