Problem Rubio 04 mfp95

Tool Bounds

Execution Time	5.4591894e-2ms
Answer	YES(?,O(n^1))
Input	Rubio 04 mfp95

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs: {f(s(X), Y) -> h(s(f(h(Y), X)))}
  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:
  {  s_0(1) -> 1
   , s_1(3) -> 2
   , f_0(1, 1) -> 1
   , f_1(4, 1) -> 3
   , h_0(1) -> 1
   , h_1(1) -> 4
   , h_1(2) -> 1}

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

Tool CDI

Execution Time	7.413358ms
Answer	YES(?,O(n^2))
Input	Rubio 04 mfp95

stdout:

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

This TRS is terminating using the deltarestricted interpretation
f(delta, X1, X0) =  + 1*X0 + 1*X1 + 0 + 2*X0*delta + 2*X1*delta + 0*delta
s(delta, X0) =  + 1*X0 + 2 + 0*X0*delta + 0*delta
h(delta, X0) =  + 1*X0 + 0 + 0*X0*delta + 0*delta
f_tau_1(delta) = delta/(1 + 2 * delta)
f_tau_2(delta) = delta/(1 + 2 * delta)
s_tau_1(delta) = delta/(1 + 0 * delta)
h_tau_1(delta) = delta/(1 + 0 * delta)

Time: 7.375977 seconds
Statistics:
Number of monomials: 586
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.50326705ms
Answer	YES(?,O(n^2))
Input	Rubio 04 mfp95

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs: {f(s(X), Y) -> h(s(f(h(Y), X)))}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   s(x1) = [1 0] x1 + [0]
           [0 0]      [2]
   f(x1, x2) = [1 2] x1 + [1 0] x2 + [0]
               [0 0]      [0 0]      [0]
   h(x1) = [1 0] x1 + [0]
           [0 0]      [0]

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

Tool IDA

Execution Time	0.64156985ms
Answer	YES(?,O(n^2))
Input	Rubio 04 mfp95

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs: {f(s(X), Y) -> h(s(f(h(Y), X)))}
  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:
   s(x1) = [1 1] x1 + [0]
           [0 0]      [2]
   f(x1, x2) = [1 3] x1 + [1 1] x2 + [2]
               [0 0]      [0 0]      [0]
   h(x1) = [1 1] x1 + [0]
           [0 0]      [0]

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

Tool TRI

Execution Time	0.13759303ms
Answer	YES(?,O(n^1))
Input	Rubio 04 mfp95

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs: {f(s(X), Y) -> h(s(f(h(Y), X)))}
  StartTerms: all
  Strategy: none

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

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

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

Tool TRI2

Execution Time	0.13115788ms
Answer	YES(?,O(n^2))
Input	Rubio 04 mfp95

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs: {f(s(X), Y) -> h(s(f(h(Y), X)))}
  StartTerms: all
  Strategy: none

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

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

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