Problem Various 04 27

Tool Bounds

Execution Time	4.955578e-2ms
Answer	YES(?,O(n^1))
Input	Various 04 27

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs: {g(x, a(), b()) -> g(b(), b(), a())}
  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() -> 4
   , b_0() -> 1
   , b_1() -> 2
   , b_1() -> 3
   , g_0(1, 1, 1) -> 1
   , g_1(2, 3, 4) -> 1}

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

Tool CDI

Execution Time	0.27730584ms
Answer	YES(?,O(n^2))
Input	Various 04 27

stdout:

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

This TRS is terminating using the deltarestricted interpretation
a(delta) =  + 0 + 0*delta
b(delta) =  + 2 + 0*delta
g(delta, X2, X1, X0) =  + 1*X0 + 0*X1 + 1*X2 + 0 + 3*X0*delta + 2*X1*delta + 0*X2*delta + 0*delta
g_tau_1(delta) = delta/(1 + 0 * delta)
g_tau_2(delta) = delta/(0 + 2 * delta)
g_tau_3(delta) = delta/(1 + 3 * delta)

Time: 0.239494 seconds
Statistics:
Number of monomials: 97
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.32285905ms
Answer	YES(?,O(n^2))
Input	Various 04 27

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   a() = [0]
         [2]
   b() = [0]
         [0]
   g(x1, x2, x3) = [1 0] x1 + [1 2] x2 + [1 0] x3 + [0]
                   [0 0]      [0 0]      [0 0]      [1]

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

Tool IDA

Execution Time	0.3396709ms
Answer	YES(?,O(n^1))
Input	Various 04 27

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs: {g(x, a(), b()) -> g(b(), b(), 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:
   a() = [0]
         [2]
   b() = [0]
         [0]
   g(x1, x2, x3) = [1 0] x1 + [1 2] x2 + [1 0] x3 + [0]
                   [0 0]      [0 0]      [0 0]      [1]

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

Tool TRI

Execution Time	0.12286091ms
Answer	YES(?,O(n^1))
Input	Various 04 27

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   a() = [0]
         [0]
   b() = [0]
         [2]
   g(x1, x2, x3) = [1 0] x1 + [1 0] x2 + [1 1] x3 + [2]
                   [0 0]      [0 0]      [0 0]      [1]

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

Tool TRI2

Execution Time	9.489083e-2ms
Answer	YES(?,O(n^1))
Input	Various 04 27

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   a() = [0]
         [0]
   b() = [0]
         [1]
   g(x1, x2, x3) = [1 0] x1 + [1 0] x2 + [1 1] x3 + [3]
                   [0 0]      [0 0]      [0 0]      [1]

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