Problem Rubio 04 mfp90b

Tool Bounds

Execution Time	2.9088974e-2ms
Answer	YES(?,O(n^1))
Input	Rubio 04 mfp90b

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

Proof:
  The problem is match-bounded by 3.
  The enriched problem is compatible with the following automaton:
  {  a_0() -> 1
   , a_1() -> 2
   , a_2() -> 5
   , c_0() -> 1
   , c_1() -> 3
   , c_2() -> 4
   , c_3() -> 6
   , g_0(1) -> 1
   , g_1(3) -> 1
   , g_2(4) -> 2
   , g_3(6) -> 5
   , b_0() -> 1
   , b_1() -> 1
   , f_0(1, 1) -> 1
   , f_1(2, 1) -> 1
   , f_1(2, 3) -> 1
   , f_1(2, 4) -> 1
   , f_2(5, 4) -> 1}

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

Tool CDI

Execution Time	0.12703204ms
Answer	YES(?,O(n^2))
Input	Rubio 04 mfp90b

stdout:

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

This TRS is terminating using the deltarestricted interpretation
f(delta, X1, X0) =  + 0*X0 + 1*X1 + 0 + 1*X0*delta + 0*X1*delta + 0*delta
b(delta) =  + 0 + 2*delta
a(delta) =  + 0 + 3*delta
c(delta) =  + 0 + 0*delta
g(delta, X0) =  + 0*X0 + 0 + 1*X0*delta + 2*delta
f_tau_1(delta) = delta/(1 + 0 * delta)
f_tau_2(delta) = delta/(0 + 1 * delta)
g_tau_1(delta) = delta/(0 + 1 * delta)

Time: 0.087698 seconds
Statistics:
Number of monomials: 94
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.14251304ms
Answer	YES(?,O(n^1))
Input	Rubio 04 mfp90b

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   a() = [3]
   c() = [0]
   g(x1) = [1] x1 + [2]
   b() = [2]
   f(x1, x2) = [1] x1 + [1] x2 + [0]

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

Tool IDA

Execution Time	0.13388896ms
Answer	YES(?,O(n^1))
Input	Rubio 04 mfp90b

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  f(g(X), b()) -> f(a(), X)
     , g(a()) -> b()
     , a() -> g(c())}
  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() = [3]
   c() = [0]
   g(x1) = [1] x1 + [2]
   b() = [2]
   f(x1, x2) = [1] x1 + [1] x2 + [0]

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

Tool TRI

Execution Time	7.753205e-2ms
Answer	YES(?,O(n^1))
Input	Rubio 04 mfp90b

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

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

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

Tool TRI2

Execution Time	7.4662924e-2ms
Answer	YES(?,O(n^1))
Input	Rubio 04 mfp90b

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

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

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