Problem SK90 4.16

Tool Bounds

Execution Time	6.426406e-2ms
Answer	YES(?,O(n^1))
Input	SK90 4.16

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  f(+(x, y)) -> *(f(x), f(y))
     , f(+(x, s(0()))) -> +(s(s(0())), f(x))
     , f(s(0())) -> *(s(s(0())), f(0()))
     , f(s(0())) -> s(s(0()))
     , f(0()) -> s(0())}
  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:
  {  0_0() -> 1
   , 0_1() -> 10
   , 0_2() -> 12
   , 0_3() -> 17
   , f_0(1) -> 2
   , f_0(2) -> 2
   , f_0(3) -> 2
   , f_0(4) -> 2
   , f_0(5) -> 2
   , f_1(1) -> 6
   , f_1(1) -> 7
   , f_1(2) -> 7
   , f_1(3) -> 7
   , f_1(4) -> 7
   , f_1(5) -> 7
   , f_1(6) -> 7
   , f_1(7) -> 7
   , f_1(8) -> 6
   , f_1(10) -> 11
   , f_2(6) -> 14
   , f_2(7) -> 14
   , f_2(8) -> 13
   , f_2(12) -> 16
   , f_2(13) -> 14
   , f_2(15) -> 13
   , f_3(13) -> 19
   , f_3(15) -> 18
   , s_0(1) -> 3
   , s_0(2) -> 3
   , s_0(3) -> 3
   , s_0(4) -> 3
   , s_0(5) -> 3
   , s_1(9) -> 2
   , s_1(9) -> 7
   , s_1(9) -> 8
   , s_1(10) -> 2
   , s_1(10) -> 6
   , s_1(10) -> 7
   , s_1(10) -> 9
   , s_2(11) -> 7
   , s_2(11) -> 14
   , s_2(11) -> 15
   , s_2(12) -> 11
   , s_3(17) -> 16
   , *_0(1, 1) -> 4
   , *_0(1, 2) -> 4
   , *_0(1, 3) -> 4
   , *_0(1, 4) -> 4
   , *_0(1, 5) -> 4
   , *_0(2, 1) -> 4
   , *_0(2, 2) -> 4
   , *_0(2, 3) -> 4
   , *_0(2, 4) -> 4
   , *_0(2, 5) -> 4
   , *_0(3, 1) -> 4
   , *_0(3, 2) -> 4
   , *_0(3, 3) -> 4
   , *_0(3, 4) -> 4
   , *_0(3, 5) -> 4
   , *_0(4, 1) -> 4
   , *_0(4, 2) -> 4
   , *_0(4, 3) -> 4
   , *_0(4, 4) -> 4
   , *_0(4, 5) -> 4
   , *_0(5, 1) -> 4
   , *_0(5, 2) -> 4
   , *_0(5, 3) -> 4
   , *_0(5, 4) -> 4
   , *_0(5, 5) -> 4
   , *_1(6, 7) -> 2
   , *_1(7, 7) -> 2
   , *_1(7, 7) -> 7
   , *_1(8, 11) -> 2
   , *_1(8, 11) -> 7
   , *_2(13, 14) -> 7
   , *_2(13, 14) -> 14
   , *_2(15, 16) -> 7
   , *_2(15, 16) -> 14
   , *_3(18, 19) -> 14
   , +_0(1, 1) -> 5
   , +_0(1, 2) -> 5
   , +_0(1, 3) -> 5
   , +_0(1, 4) -> 5
   , +_0(1, 5) -> 5
   , +_0(2, 1) -> 5
   , +_0(2, 2) -> 5
   , +_0(2, 3) -> 5
   , +_0(2, 4) -> 5
   , +_0(2, 5) -> 5
   , +_0(3, 1) -> 5
   , +_0(3, 2) -> 5
   , +_0(3, 3) -> 5
   , +_0(3, 4) -> 5
   , +_0(3, 5) -> 5
   , +_0(4, 1) -> 5
   , +_0(4, 2) -> 5
   , +_0(4, 3) -> 5
   , +_0(4, 4) -> 5
   , +_0(4, 5) -> 5
   , +_0(5, 1) -> 5
   , +_0(5, 2) -> 5
   , +_0(5, 3) -> 5
   , +_0(5, 4) -> 5
   , +_0(5, 5) -> 5
   , +_1(8, 6) -> 2
   , +_1(8, 7) -> 2
   , +_1(8, 7) -> 7
   , +_2(15, 13) -> 7
   , +_2(15, 13) -> 14}

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

Tool CDI

Execution Time	60.041946ms
Answer	TIMEOUT
Input	SK90 4.16

stdout:

TIMEOUT

Statistics:
Number of monomials: 11729
Last formula building started for bound 3
Last SAT solving started for bound 0

Tool EDA

Execution Time	0.8836112ms
Answer	YES(?,O(n^2))
Input	SK90 4.16

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  f(+(x, y)) -> *(f(x), f(y))
     , f(+(x, s(0()))) -> +(s(s(0())), f(x))
     , f(s(0())) -> *(s(s(0())), f(0()))
     , f(s(0())) -> s(s(0()))
     , f(0()) -> s(0())}
  StartTerms: all
  Strategy: none

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

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   0() = [0]
         [1]
   f(x1) = [1 3] x1 + [0]
           [0 1]      [3]
   s(x1) = [1 0] x1 + [0]
           [0 0]      [3]
   *(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
               [0 0]      [0 0]      [0]
   +(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
               [0 1]      [0 1]      [1]

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

Tool IDA

Execution Time	1.2109959ms
Answer	YES(?,O(n^2))
Input	SK90 4.16

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  f(+(x, y)) -> *(f(x), f(y))
     , f(+(x, s(0()))) -> +(s(s(0())), f(x))
     , f(s(0())) -> *(s(s(0())), f(0()))
     , f(s(0())) -> s(s(0()))
     , f(0()) -> s(0())}
  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:
   0() = [0]
         [1]
   f(x1) = [1 1] x1 + [0]
           [0 1]      [1]
   s(x1) = [1 0] x1 + [0]
           [0 0]      [2]
   *(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
               [0 0]      [0 0]      [0]
   +(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
               [0 1]      [0 1]      [2]

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

Tool TRI

Execution Time	0.38330102ms
Answer	YES(?,O(n^2))
Input	SK90 4.16

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  f(+(x, y)) -> *(f(x), f(y))
     , f(+(x, s(0()))) -> +(s(s(0())), f(x))
     , f(s(0())) -> *(s(s(0())), f(0()))
     , f(s(0())) -> s(s(0()))
     , f(0()) -> s(0())}
  StartTerms: all
  Strategy: none

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

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

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

Tool TRI2

Execution Time	0.35093403ms
Answer	YES(?,O(n^2))
Input	SK90 4.16

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  f(+(x, y)) -> *(f(x), f(y))
     , f(+(x, s(0()))) -> +(s(s(0())), f(x))
     , f(s(0())) -> *(s(s(0())), f(0()))
     , f(s(0())) -> s(s(0()))
     , f(0()) -> s(0())}
  StartTerms: all
  Strategy: none

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

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

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