Problem Transformed CSR 04 ExProp7 Luc06 L

Tool Bounds

Execution Time	3.0183077e-2ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 ExProp7 Luc06 L

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  p(s(X)) -> X
     , f(s(0())) -> f(p(s(0())))
     , f(0()) -> cons(0())}
  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:
  {  0_0() -> 1
   , 0_1() -> 2
   , 0_1() -> 4
   , 0_2() -> 5
   , f_0(1) -> 1
   , f_1(2) -> 1
   , cons_0(1) -> 1
   , cons_1(4) -> 1
   , cons_2(5) -> 1
   , s_0(1) -> 1
   , s_1(4) -> 3
   , p_0(1) -> 1
   , p_1(3) -> 2}

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

Tool CDI

Execution Time	3.763498ms
Answer	MAYBE
Input	Transformed CSR 04 ExProp7 Luc06 L

stdout:

MAYBE

Statistics:
Number of monomials: 319
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	1.574882ms
Answer	YES(?,O(n^3))
Input	Transformed CSR 04 ExProp7 Luc06 L

stdout:

YES(?,O(n^3))

We consider the following Problem:

  Strict Trs:
    {  p(s(X)) -> X
     , f(s(0())) -> f(p(s(0())))
     , f(0()) -> cons(0())}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^3))

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

Hurray, we answered YES(?,O(n^3))

Tool IDA

Execution Time	3.447937ms
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 ExProp7 Luc06 L

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  p(s(X)) -> X
     , f(s(0())) -> f(p(s(0())))
     , f(0()) -> cons(0())}
  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:
   0() = [0]
         [2]
         [0]
   f(x1) = [1 0 2] x1 + [1]
           [0 0 0]      [0]
           [0 0 0]      [0]
   cons(x1) = [1 0 0] x1 + [0]
              [0 0 0]      [0]
              [0 0 0]      [0]
   s(x1) = [1 0 0] x1 + [0]
           [0 0 1]      [0]
           [0 1 0]      [2]
   p(x1) = [1 0 0] x1 + [1]
           [0 0 1]      [0]
           [0 1 0]      [0]

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

Tool TRI

Execution Time	60.029205ms
Answer	TIMEOUT
Input	Transformed CSR 04 ExProp7 Luc06 L

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  p(s(X)) -> X
     , f(s(0())) -> f(p(s(0())))
     , f(0()) -> cons(0())}
  StartTerms: all
  Strategy: none

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool TRI2

Execution Time	0.27548313ms
Answer	MAYBE
Input	Transformed CSR 04 ExProp7 Luc06 L

stdout:

MAYBE

We consider the following Problem:

  Strict Trs:
    {  p(s(X)) -> X
     , f(s(0())) -> f(p(s(0())))
     , f(0()) -> cons(0())}
  StartTerms: all
  Strategy: none

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..