Problem ICFP 2010 264370

Tool Bounds

Execution Time	5.5842876e-2ms
Answer	YES(?,O(n^1))
Input	ICFP 2010 264370

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  0(5(4(1(3(2(x1)))))) -> 0(5(4(3(1(2(x1))))))
     , 0(5(3(1(2(4(x1)))))) -> 0(1(5(3(2(4(x1))))))
     , 0(5(2(4(1(3(x1)))))) -> 0(1(5(2(4(3(x1))))))
     , 0(5(1(2(4(3(x1)))))) -> 0(5(2(1(4(3(x1))))))
     , 0(1(2(3(4(x1))))) -> 0(2(1(3(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) -> 10
   , 4_1(4) -> 3
   , 4_1(12) -> 11
   , 3_0(1) -> 1
   , 3_1(1) -> 12
   , 3_1(5) -> 4
   , 3_1(9) -> 8
   , 3_1(10) -> 15
   , 2_0(1) -> 1
   , 2_1(1) -> 6
   , 2_1(10) -> 9
   , 2_1(11) -> 8
   , 2_1(13) -> 3
   , 2_1(14) -> 2
   , 1_0(1) -> 1
   , 1_1(6) -> 5
   , 1_1(7) -> 2
   , 1_1(11) -> 13
   , 1_1(15) -> 14
   , 0_0(1) -> 1
   , 0_1(2) -> 1
   , 5_0(1) -> 1
   , 5_1(3) -> 2
   , 5_1(8) -> 7}

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

Tool CDI

Execution Time	60.03899ms
Answer	TIMEOUT
Input	ICFP 2010 264370

stdout:

TIMEOUT

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

Tool EDA

Execution Time	39.370426ms
Answer	YES(?,O(n^2))
Input	ICFP 2010 264370

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

Tool IDA

Execution Time	59.50315ms
Answer	YES(?,O(n^2))
Input	ICFP 2010 264370

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

Tool TRI

Execution Time	1.476049ms
Answer	YES(?,O(n^2))
Input	ICFP 2010 264370

stdout:

YES(?,O(n^2))

We consider the following Problem:

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

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

Tool TRI2

Execution Time	2.015495ms
Answer	YES(?,O(n^1))
Input	ICFP 2010 264370

stdout:

YES(?,O(n^1))

We consider the following Problem:

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

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

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

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