Problem ICFP 2010 264405

Tool Bounds

Execution Time6.252909e-2ms
Answer
YES(?,O(n^1))
InputICFP 2010 264405

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  0(5(2(3(1(4(x1)))))) -> 0(1(5(2(3(4(x1))))))
     , 0(5(1(2(3(4(x1)))))) -> 5(0(2(3(1(4(x1))))))
     , 0(5(1(2(3(4(x1)))))) -> 0(5(2(1(3(4(x1))))))
     , 0(5(1(2(3(4(x1)))))) -> 0(1(2(5(3(4(x1))))))
     , 0(1(2(3(4(x1))))) -> 0(2(3(1(4(x1)))))}
  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:
  {  4_0(1) -> 1
   , 4_1(1) -> 6
   , 3_0(1) -> 1
   , 3_1(6) -> 5
   , 3_1(10) -> 9
   , 2_0(1) -> 1
   , 2_1(5) -> 4
   , 2_1(9) -> 8
   , 2_1(12) -> 11
   , 2_1(13) -> 3
   , 1_0(1) -> 1
   , 1_1(3) -> 2
   , 1_1(5) -> 12
   , 1_1(6) -> 10
   , 0_0(1) -> 1
   , 0_1(2) -> 1
   , 0_1(8) -> 1
   , 0_1(8) -> 7
   , 5_0(1) -> 1
   , 5_1(4) -> 3
   , 5_1(5) -> 13
   , 5_1(7) -> 1
   , 5_1(11) -> 2}

Hurray, we answered YES(?,O(n^1))

Tool CDI

Execution Time60.040726ms
Answer
TIMEOUT
InputICFP 2010 264405

stdout:

TIMEOUT

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

Tool EDA

Execution Time24.685965ms
Answer
YES(?,O(n^2))
InputICFP 2010 264405

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  0(5(2(3(1(4(x1)))))) -> 0(1(5(2(3(4(x1))))))
     , 0(5(1(2(3(4(x1)))))) -> 5(0(2(3(1(4(x1))))))
     , 0(5(1(2(3(4(x1)))))) -> 0(5(2(1(3(4(x1))))))
     , 0(5(1(2(3(4(x1)))))) -> 0(1(2(5(3(4(x1))))))
     , 0(1(2(3(4(x1))))) -> 0(2(3(1(4(x1)))))}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^2))

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   4(x1) = [1 0] x1 + [0]
           [0 0]      [0]
   3(x1) = [1 1] x1 + [0]
           [0 0]      [2]
   2(x1) = [1 1] x1 + [0]
           [0 0]      [0]
   1(x1) = [1 0] x1 + [0]
           [0 0]      [1]
   0(x1) = [1 2] x1 + [0]
           [0 0]      [1]
   5(x1) = [1 0] x1 + [1]
           [0 0]      [1]

Hurray, we answered YES(?,O(n^2))

Tool IDA

Execution Time37.482376ms
Answer
YES(?,O(n^2))
InputICFP 2010 264405

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  0(5(2(3(1(4(x1)))))) -> 0(1(5(2(3(4(x1))))))
     , 0(5(1(2(3(4(x1)))))) -> 5(0(2(3(1(4(x1))))))
     , 0(5(1(2(3(4(x1)))))) -> 0(5(2(1(3(4(x1))))))
     , 0(5(1(2(3(4(x1)))))) -> 0(1(2(5(3(4(x1))))))
     , 0(1(2(3(4(x1))))) -> 0(2(3(1(4(x1)))))}
  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:
   4(x1) = [1 0] x1 + [0]
           [0 0]      [2]
   3(x1) = [1 2] x1 + [0]
           [0 0]      [1]
   2(x1) = [1 0] x1 + [0]
           [0 1]      [3]
   1(x1) = [1 2] x1 + [0]
           [0 1]      [0]
   0(x1) = [1 0] x1 + [0]
           [0 0]      [0]
   5(x1) = [1 0] x1 + [0]
           [0 0]      [0]

Hurray, we answered YES(?,O(n^2))

Tool TRI

Execution Time1.4118829ms
Answer
YES(?,O(n^2))
InputICFP 2010 264405

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  0(5(2(3(1(4(x1)))))) -> 0(1(5(2(3(4(x1))))))
     , 0(5(1(2(3(4(x1)))))) -> 5(0(2(3(1(4(x1))))))
     , 0(5(1(2(3(4(x1)))))) -> 0(5(2(1(3(4(x1))))))
     , 0(5(1(2(3(4(x1)))))) -> 0(1(2(5(3(4(x1))))))
     , 0(1(2(3(4(x1))))) -> 0(2(3(1(4(x1)))))}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^2))

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   4(x1) = [1 0] x1 + [0]
           [0 0]      [1]
   3(x1) = [1 0] x1 + [0]
           [0 1]      [0]
   2(x1) = [1 1] x1 + [0]
           [0 0]      [0]
   1(x1) = [1 0] x1 + [0]
           [0 0]      [0]
   0(x1) = [1 2] x1 + [0]
           [0 1]      [0]
   5(x1) = [1 0] x1 + [0]
           [0 0]      [2]

Hurray, we answered YES(?,O(n^2))

Tool TRI2

Execution Time1.475599ms
Answer
YES(?,O(n^1))
InputICFP 2010 264405

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  0(5(2(3(1(4(x1)))))) -> 0(1(5(2(3(4(x1))))))
     , 0(5(1(2(3(4(x1)))))) -> 5(0(2(3(1(4(x1))))))
     , 0(5(1(2(3(4(x1)))))) -> 0(5(2(1(3(4(x1))))))
     , 0(5(1(2(3(4(x1)))))) -> 0(1(2(5(3(4(x1))))))
     , 0(1(2(3(4(x1))))) -> 0(2(3(1(4(x1)))))}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^1))

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   4(x1) = [1 0] x1 + [0]
           [0 0]      [0]
   3(x1) = [1 1] x1 + [0]
           [0 0]      [0]
   2(x1) = [1 0] x1 + [0]
           [0 0]      [3]
   1(x1) = [1 3] x1 + [0]
           [0 0]      [1]
   0(x1) = [1 0] x1 + [0]
           [0 0]      [0]
   5(x1) = [1 1] x1 + [0]
           [0 0]      [0]

Hurray, we answered YES(?,O(n^1))