Problem ICFP 2010 45720

Tool CaT

Execution TimeUnknown
Answer
YES(?,O(n^1))
InputICFP 2010 45720

stdout:

YES(?,O(n^1))

Problem:
 0(1(0(x1))) -> 0(2(3(1(3(0(x1))))))
 0(2(1(x1))) -> 3(1(3(0(2(x1)))))
 0(2(1(x1))) -> 0(2(3(3(1(3(x1))))))
 0(2(1(x1))) -> 0(4(3(1(3(2(2(x1)))))))
 0(2(1(x1))) -> 0(2(3(2(2(1(3(2(x1))))))))
 1(0(0(x1))) -> 2(3(1(3(0(0(x1))))))
 0(0(2(0(x1)))) -> 0(0(4(4(3(2(0(x1)))))))
 0(1(2(1(x1)))) -> 0(3(1(3(1(3(2(x1)))))))
 0(1(3(5(x1)))) -> 0(5(4(4(3(1(4(x1)))))))
 0(1(3(5(x1)))) -> 3(5(4(3(1(3(2(0(x1))))))))
 0(1(5(1(x1)))) -> 5(3(1(3(0(1(x1))))))
 0(2(1(4(x1)))) -> 0(3(2(2(1(4(x1))))))
 0(2(1(4(x1)))) -> 3(2(1(0(4(3(x1))))))
 0(2(2(1(x1)))) -> 3(2(0(2(3(1(x1))))))
 0(2(2(5(x1)))) -> 3(1(3(2(2(0(4(5(x1))))))))
 0(2(4(4(x1)))) -> 3(2(0(4(4(5(4(x1)))))))
 0(2(4(5(x1)))) -> 3(2(0(4(5(x1)))))
 0(3(3(4(x1)))) -> 5(4(3(2(3(0(x1))))))
 0(3(5(1(x1)))) -> 5(4(3(2(2(0(1(x1)))))))
 1(0(2(4(x1)))) -> 2(3(0(3(1(4(x1))))))
 1(1(2(5(x1)))) -> 1(3(2(2(1(5(x1))))))
 0(0(0(3(4(x1))))) -> 0(0(4(4(5(2(3(0(x1))))))))
 0(0(1(1(5(x1))))) -> 5(0(3(1(3(1(0(5(x1))))))))
 0(1(2(2(4(x1))))) -> 4(3(2(1(2(3(0(x1)))))))
 0(1(5(1(4(x1))))) -> 5(3(1(0(4(3(1(x1)))))))
 0(2(2(0(1(x1))))) -> 0(4(3(0(2(3(2(1(x1))))))))
 0(2(2(2(5(x1))))) -> 3(2(2(5(4(3(2(0(x1))))))))
 0(2(2(5(0(x1))))) -> 3(2(2(0(5(2(3(0(x1))))))))
 0(3(4(1(4(x1))))) -> 2(3(3(1(0(5(4(4(x1))))))))
 0(4(1(3(4(x1))))) -> 3(1(3(0(4(4(5(x1)))))))
 0(4(2(2(4(x1))))) -> 3(2(2(0(4(4(x1))))))
 0(4(2(4(1(x1))))) -> 3(1(0(4(4(3(2(x1)))))))
 0(5(2(1(5(x1))))) -> 5(4(5(2(3(1(0(x1)))))))
 1(0(2(2(4(x1))))) -> 2(2(0(4(3(1(4(x1)))))))
 1(0(2(2(4(x1))))) -> 2(3(3(2(1(0(4(3(x1))))))))
 1(2(2(0(1(x1))))) -> 4(3(2(1(0(2(3(1(x1))))))))
 1(2(3(5(0(x1))))) -> 5(2(3(1(3(0(x1))))))
 1(2(4(3(5(x1))))) -> 5(4(3(1(3(2(x1))))))
 0(0(1(3(3(5(x1)))))) -> 0(3(2(3(0(1(5(x1)))))))
 0(0(2(2(3(0(x1)))))) -> 0(2(3(0(3(2(0(x1)))))))
 0(0(2(2(5(1(x1)))))) -> 0(3(0(2(3(2(1(5(x1))))))))
 0(0(3(5(3(0(x1)))))) -> 0(5(0(3(1(3(3(0(x1))))))))
 0(0(4(0(5(1(x1)))))) -> 0(0(4(0(4(3(1(5(x1))))))))
 0(0(4(1(3(0(x1)))))) -> 0(0(3(2(3(0(1(4(x1))))))))
 0(1(0(3(4(5(x1)))))) -> 3(1(0(4(3(5(0(4(x1))))))))
 0(1(4(0(2(5(x1)))))) -> 0(5(2(0(4(4(1(x1)))))))
 0(1(5(3(4(0(x1)))))) -> 0(4(4(2(0(3(1(5(x1))))))))
 0(2(1(5(3(5(x1)))))) -> 3(2(1(3(5(1(5(0(x1))))))))
 0(3(5(2(4(1(x1)))))) -> 0(0(5(4(3(2(1(x1)))))))
 0(5(0(1(5(4(x1)))))) -> 3(1(3(0(0(5(4(5(x1))))))))
 0(5(1(1(3(4(x1)))))) -> 4(1(0(4(5(4(3(1(x1))))))))
 0(5(3(4(1(4(x1)))))) -> 5(4(0(4(3(1(3(x1)))))))
 0(5(3(4(1(5(x1)))))) -> 0(3(2(1(0(5(4(5(x1))))))))
 0(5(5(0(1(5(x1)))))) -> 0(5(5(3(2(1(5(0(x1))))))))
 1(0(2(4(0(5(x1)))))) -> 1(4(0(3(2(3(0(5(x1))))))))
 1(1(4(0(1(0(x1)))))) -> 0(3(1(3(1(4(1(0(x1))))))))
 1(2(1(0(2(1(x1)))))) -> 1(1(3(2(0(2(1(x1)))))))
 1(2(4(0(3(4(x1)))))) -> 3(2(0(4(3(3(1(4(x1))))))))
 1(2(4(3(3(0(x1)))))) -> 4(0(2(3(3(1(3(0(x1))))))))
 1(2(4(3(3(5(x1)))))) -> 3(2(3(2(5(4(3(1(x1))))))))
 1(2(4(3(4(5(x1)))))) -> 3(1(3(2(4(5(4(x1)))))))
 1(2(4(5(1(0(x1)))))) -> 0(4(2(1(3(1(5(x1)))))))
 1(2(4(5(3(4(x1)))))) -> 4(3(2(2(1(3(5(4(x1))))))))
 1(2(5(5(3(0(x1)))))) -> 5(2(3(3(1(3(5(0(x1))))))))
 0(0(2(4(5(3(5(x1))))))) -> 2(0(5(4(3(5(3(0(x1))))))))
 0(1(0(5(3(5(1(x1))))))) -> 1(0(0(5(5(3(1(3(x1))))))))
 0(1(2(2(5(2(0(x1))))))) -> 5(1(0(3(2(2(2(0(x1))))))))
 0(2(1(5(4(0(1(x1))))))) -> 0(0(5(1(2(3(1(4(x1))))))))
 0(2(3(4(1(1(4(x1))))))) -> 3(1(0(4(4(1(2(0(x1))))))))
 0(2(4(1(1(5(1(x1))))))) -> 3(1(0(5(4(1(1(2(x1))))))))
 0(2(5(0(4(0(1(x1))))))) -> 0(5(1(0(4(3(2(0(x1))))))))
 0(2(5(5(3(5(1(x1))))))) -> 0(5(5(1(5(5(3(2(x1))))))))
 0(4(0(3(5(2(0(x1))))))) -> 0(4(0(4(5(3(2(0(x1))))))))
 0(4(1(1(4(1(5(x1))))))) -> 0(4(3(1(4(1(1(5(x1))))))))
 0(4(1(4(0(3(5(x1))))))) -> 3(1(5(0(0(4(3(4(x1))))))))
 0(5(1(3(4(2(4(x1))))))) -> 5(4(4(0(3(1(5(2(x1))))))))
 1(0(3(3(3(4(0(x1))))))) -> 0(3(0(3(3(1(4(5(x1))))))))
 1(0(3(4(4(3(5(x1))))))) -> 5(4(3(1(3(0(2(4(x1))))))))
 1(2(0(4(1(3(5(x1))))))) -> 5(4(2(3(1(4(1(0(x1))))))))
 1(2(4(0(5(3(5(x1))))))) -> 5(1(3(2(3(5(0(4(x1))))))))

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {6,5}
   transitions:
    41(187) -> 188*
    41(57) -> 58*
    41(47) -> 48*
    41(17) -> 18*
    41(139) -> 140*
    41(59) -> 60*
    41(44) -> 45*
    41(71) -> 72*
    41(51) -> 52*
    41(46) -> 47*
    41(108) -> 109*
    41(115) -> 116*
    41(95) -> 96*
    31(70) -> 71*
    31(65) -> 66*
    31(182) -> 183*
    31(142) -> 143*
    31(112) -> 113*
    31(144) -> 145*
    31(114) -> 115*
    31(94) -> 95*
    31(186) -> 187*
    31(21) -> 22*
    31(168) -> 169*
    31(138) -> 139*
    31(68) -> 69*
    31(23) -> 24*
    21(20) -> 21*
    21(167) -> 168*
    21(127) -> 128*
    21(97) -> 98*
    21(184) -> 185*
    21(129) -> 130*
    21(69) -> 70*
    21(49) -> 50*
    21(19) -> 20*
    21(141) -> 142*
    21(111) -> 112*
    21(143) -> 144*
    21(93) -> 94*
    21(185) -> 186*
    21(135) -> 136*
    11(157) -> 158*
    11(137) -> 138*
    11(22) -> 23*
    11(169) -> 170*
    11(159) -> 160*
    11(183) -> 184*
    11(113) -> 114*
    11(165) -> 166*
    51(45) -> 46*
    51(25) -> 26*
    51(72) -> 73*
    51(116) -> 117*
    51(96) -> 97*
    51(31) -> 32*
    51(16) -> 17*
    51(33) -> 34*
    51(140) -> 141*
    01(85) -> 86*
    01(67) -> 68*
    01(109) -> 110*
    01(91) -> 92*
    01(83) -> 84*
    01(48) -> 49*
    01(18) -> 19*
    00(2) -> 5*
    00(4) -> 5*
    00(1) -> 5*
    00(3) -> 5*
    10(2) -> 6*
    10(4) -> 6*
    10(1) -> 6*
    10(3) -> 6*
    20(2) -> 1*
    20(4) -> 1*
    20(1) -> 1*
    20(3) -> 1*
    30(2) -> 2*
    30(4) -> 2*
    30(1) -> 2*
    30(3) -> 2*
    40(2) -> 3*
    40(4) -> 3*
    40(1) -> 3*
    40(3) -> 3*
    50(2) -> 4*
    50(4) -> 4*
    50(1) -> 4*
    50(3) -> 4*
    1 -> 159,129,85,57,31
    2 -> 137,111,67,44,16
    3 -> 165,135,91,59,33
    4 -> 157,127,83,51,25
    20 -> 65*
    24 -> 86,68,93,5
    26 -> 17*
    32 -> 17*
    34 -> 17*
    45 -> 108*
    46 -> 182*
    47 -> 167*
    50 -> 23*
    52 -> 45*
    58 -> 45*
    60 -> 45*
    66 -> 92,86,68,93,5
    68 -> 93*
    73 -> 68,93,5
    84 -> 68*
    86 -> 68*
    92 -> 68*
    98 -> 19*
    110 -> 97*
    117 -> 160,138,6
    128 -> 112*
    130 -> 112*
    136 -> 112*
    145 -> 160,138,6
    158 -> 138*
    160 -> 138*
    166 -> 138*
    170 -> 144*
    188 -> 160,138,6
  problem:
   
  Qed

Tool IRC1

Execution TimeUnknown
Answer
MAYBE
InputICFP 2010 45720

stdout:

MAYBE

Tool IRC2

Execution TimeUnknown
Answer
YES(?,O(n^1))
InputICFP 2010 45720

stdout:

YES(?,O(n^1))

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           YES(?,O(n^1))
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  0(1(0(x1))) -> 0(2(3(1(3(0(x1))))))
     , 0(2(1(x1))) -> 3(1(3(0(2(x1)))))
     , 0(2(1(x1))) -> 0(2(3(3(1(3(x1))))))
     , 0(2(1(x1))) -> 0(4(3(1(3(2(2(x1)))))))
     , 0(2(1(x1))) -> 0(2(3(2(2(1(3(2(x1))))))))
     , 1(0(0(x1))) -> 2(3(1(3(0(0(x1))))))
     , 0(0(2(0(x1)))) -> 0(0(4(4(3(2(0(x1)))))))
     , 0(1(2(1(x1)))) -> 0(3(1(3(1(3(2(x1)))))))
     , 0(1(3(5(x1)))) -> 0(5(4(4(3(1(4(x1)))))))
     , 0(1(3(5(x1)))) -> 3(5(4(3(1(3(2(0(x1))))))))
     , 0(1(5(1(x1)))) -> 5(3(1(3(0(1(x1))))))
     , 0(2(1(4(x1)))) -> 0(3(2(2(1(4(x1))))))
     , 0(2(1(4(x1)))) -> 3(2(1(0(4(3(x1))))))
     , 0(2(2(1(x1)))) -> 3(2(0(2(3(1(x1))))))
     , 0(2(2(5(x1)))) -> 3(1(3(2(2(0(4(5(x1))))))))
     , 0(2(4(4(x1)))) -> 3(2(0(4(4(5(4(x1)))))))
     , 0(2(4(5(x1)))) -> 3(2(0(4(5(x1)))))
     , 0(3(3(4(x1)))) -> 5(4(3(2(3(0(x1))))))
     , 0(3(5(1(x1)))) -> 5(4(3(2(2(0(1(x1)))))))
     , 1(0(2(4(x1)))) -> 2(3(0(3(1(4(x1))))))
     , 1(1(2(5(x1)))) -> 1(3(2(2(1(5(x1))))))
     , 0(0(0(3(4(x1))))) -> 0(0(4(4(5(2(3(0(x1))))))))
     , 0(0(1(1(5(x1))))) -> 5(0(3(1(3(1(0(5(x1))))))))
     , 0(1(2(2(4(x1))))) -> 4(3(2(1(2(3(0(x1)))))))
     , 0(1(5(1(4(x1))))) -> 5(3(1(0(4(3(1(x1)))))))
     , 0(2(2(0(1(x1))))) -> 0(4(3(0(2(3(2(1(x1))))))))
     , 0(2(2(2(5(x1))))) -> 3(2(2(5(4(3(2(0(x1))))))))
     , 0(2(2(5(0(x1))))) -> 3(2(2(0(5(2(3(0(x1))))))))
     , 0(3(4(1(4(x1))))) -> 2(3(3(1(0(5(4(4(x1))))))))
     , 0(4(1(3(4(x1))))) -> 3(1(3(0(4(4(5(x1)))))))
     , 0(4(2(2(4(x1))))) -> 3(2(2(0(4(4(x1))))))
     , 0(4(2(4(1(x1))))) -> 3(1(0(4(4(3(2(x1)))))))
     , 0(5(2(1(5(x1))))) -> 5(4(5(2(3(1(0(x1)))))))
     , 1(0(2(2(4(x1))))) -> 2(2(0(4(3(1(4(x1)))))))
     , 1(0(2(2(4(x1))))) -> 2(3(3(2(1(0(4(3(x1))))))))
     , 1(2(2(0(1(x1))))) -> 4(3(2(1(0(2(3(1(x1))))))))
     , 1(2(3(5(0(x1))))) -> 5(2(3(1(3(0(x1))))))
     , 1(2(4(3(5(x1))))) -> 5(4(3(1(3(2(x1))))))
     , 0(0(1(3(3(5(x1)))))) -> 0(3(2(3(0(1(5(x1)))))))
     , 0(0(2(2(3(0(x1)))))) -> 0(2(3(0(3(2(0(x1)))))))
     , 0(0(2(2(5(1(x1)))))) -> 0(3(0(2(3(2(1(5(x1))))))))
     , 0(0(3(5(3(0(x1)))))) -> 0(5(0(3(1(3(3(0(x1))))))))
     , 0(0(4(0(5(1(x1)))))) -> 0(0(4(0(4(3(1(5(x1))))))))
     , 0(0(4(1(3(0(x1)))))) -> 0(0(3(2(3(0(1(4(x1))))))))
     , 0(1(0(3(4(5(x1)))))) -> 3(1(0(4(3(5(0(4(x1))))))))
     , 0(1(4(0(2(5(x1)))))) -> 0(5(2(0(4(4(1(x1)))))))
     , 0(1(5(3(4(0(x1)))))) -> 0(4(4(2(0(3(1(5(x1))))))))
     , 0(2(1(5(3(5(x1)))))) -> 3(2(1(3(5(1(5(0(x1))))))))
     , 0(3(5(2(4(1(x1)))))) -> 0(0(5(4(3(2(1(x1)))))))
     , 0(5(0(1(5(4(x1)))))) -> 3(1(3(0(0(5(4(5(x1))))))))
     , 0(5(1(1(3(4(x1)))))) -> 4(1(0(4(5(4(3(1(x1))))))))
     , 0(5(3(4(1(4(x1)))))) -> 5(4(0(4(3(1(3(x1)))))))
     , 0(5(3(4(1(5(x1)))))) -> 0(3(2(1(0(5(4(5(x1))))))))
     , 0(5(5(0(1(5(x1)))))) -> 0(5(5(3(2(1(5(0(x1))))))))
     , 1(0(2(4(0(5(x1)))))) -> 1(4(0(3(2(3(0(5(x1))))))))
     , 1(1(4(0(1(0(x1)))))) -> 0(3(1(3(1(4(1(0(x1))))))))
     , 1(2(1(0(2(1(x1)))))) -> 1(1(3(2(0(2(1(x1)))))))
     , 1(2(4(0(3(4(x1)))))) -> 3(2(0(4(3(3(1(4(x1))))))))
     , 1(2(4(3(3(0(x1)))))) -> 4(0(2(3(3(1(3(0(x1))))))))
     , 1(2(4(3(3(5(x1)))))) -> 3(2(3(2(5(4(3(1(x1))))))))
     , 1(2(4(3(4(5(x1)))))) -> 3(1(3(2(4(5(4(x1)))))))
     , 1(2(4(5(1(0(x1)))))) -> 0(4(2(1(3(1(5(x1)))))))
     , 1(2(4(5(3(4(x1)))))) -> 4(3(2(2(1(3(5(4(x1))))))))
     , 1(2(5(5(3(0(x1)))))) -> 5(2(3(3(1(3(5(0(x1))))))))
     , 0(0(2(4(5(3(5(x1))))))) -> 2(0(5(4(3(5(3(0(x1))))))))
     , 0(1(0(5(3(5(1(x1))))))) -> 1(0(0(5(5(3(1(3(x1))))))))
     , 0(1(2(2(5(2(0(x1))))))) -> 5(1(0(3(2(2(2(0(x1))))))))
     , 0(2(1(5(4(0(1(x1))))))) -> 0(0(5(1(2(3(1(4(x1))))))))
     , 0(2(3(4(1(1(4(x1))))))) -> 3(1(0(4(4(1(2(0(x1))))))))
     , 0(2(4(1(1(5(1(x1))))))) -> 3(1(0(5(4(1(1(2(x1))))))))
     , 0(2(5(0(4(0(1(x1))))))) -> 0(5(1(0(4(3(2(0(x1))))))))
     , 0(2(5(5(3(5(1(x1))))))) -> 0(5(5(1(5(5(3(2(x1))))))))
     , 0(4(0(3(5(2(0(x1))))))) -> 0(4(0(4(5(3(2(0(x1))))))))
     , 0(4(1(1(4(1(5(x1))))))) -> 0(4(3(1(4(1(1(5(x1))))))))
     , 0(4(1(4(0(3(5(x1))))))) -> 3(1(5(0(0(4(3(4(x1))))))))
     , 0(5(1(3(4(2(4(x1))))))) -> 5(4(4(0(3(1(5(2(x1))))))))
     , 1(0(3(3(3(4(0(x1))))))) -> 0(3(0(3(3(1(4(5(x1))))))))
     , 1(0(3(4(4(3(5(x1))))))) -> 5(4(3(1(3(0(2(4(x1))))))))
     , 1(2(0(4(1(3(5(x1))))))) -> 5(4(2(3(1(4(1(0(x1))))))))
     , 1(2(4(0(5(3(5(x1))))))) -> 5(1(3(2(3(5(0(4(x1))))))))}

Proof Output:    
  'Bounds with minimal-enrichment and initial automaton 'match'' proved the best result:
  
  Details:
  --------
    'Bounds with minimal-enrichment and initial automaton 'match'' succeeded with the following output:
     'Bounds with minimal-enrichment and initial automaton 'match''
     --------------------------------------------------------------
     Answer:           YES(?,O(n^1))
     Input Problem:    innermost runtime-complexity with respect to
       Rules:
         {  0(1(0(x1))) -> 0(2(3(1(3(0(x1))))))
          , 0(2(1(x1))) -> 3(1(3(0(2(x1)))))
          , 0(2(1(x1))) -> 0(2(3(3(1(3(x1))))))
          , 0(2(1(x1))) -> 0(4(3(1(3(2(2(x1)))))))
          , 0(2(1(x1))) -> 0(2(3(2(2(1(3(2(x1))))))))
          , 1(0(0(x1))) -> 2(3(1(3(0(0(x1))))))
          , 0(0(2(0(x1)))) -> 0(0(4(4(3(2(0(x1)))))))
          , 0(1(2(1(x1)))) -> 0(3(1(3(1(3(2(x1)))))))
          , 0(1(3(5(x1)))) -> 0(5(4(4(3(1(4(x1)))))))
          , 0(1(3(5(x1)))) -> 3(5(4(3(1(3(2(0(x1))))))))
          , 0(1(5(1(x1)))) -> 5(3(1(3(0(1(x1))))))
          , 0(2(1(4(x1)))) -> 0(3(2(2(1(4(x1))))))
          , 0(2(1(4(x1)))) -> 3(2(1(0(4(3(x1))))))
          , 0(2(2(1(x1)))) -> 3(2(0(2(3(1(x1))))))
          , 0(2(2(5(x1)))) -> 3(1(3(2(2(0(4(5(x1))))))))
          , 0(2(4(4(x1)))) -> 3(2(0(4(4(5(4(x1)))))))
          , 0(2(4(5(x1)))) -> 3(2(0(4(5(x1)))))
          , 0(3(3(4(x1)))) -> 5(4(3(2(3(0(x1))))))
          , 0(3(5(1(x1)))) -> 5(4(3(2(2(0(1(x1)))))))
          , 1(0(2(4(x1)))) -> 2(3(0(3(1(4(x1))))))
          , 1(1(2(5(x1)))) -> 1(3(2(2(1(5(x1))))))
          , 0(0(0(3(4(x1))))) -> 0(0(4(4(5(2(3(0(x1))))))))
          , 0(0(1(1(5(x1))))) -> 5(0(3(1(3(1(0(5(x1))))))))
          , 0(1(2(2(4(x1))))) -> 4(3(2(1(2(3(0(x1)))))))
          , 0(1(5(1(4(x1))))) -> 5(3(1(0(4(3(1(x1)))))))
          , 0(2(2(0(1(x1))))) -> 0(4(3(0(2(3(2(1(x1))))))))
          , 0(2(2(2(5(x1))))) -> 3(2(2(5(4(3(2(0(x1))))))))
          , 0(2(2(5(0(x1))))) -> 3(2(2(0(5(2(3(0(x1))))))))
          , 0(3(4(1(4(x1))))) -> 2(3(3(1(0(5(4(4(x1))))))))
          , 0(4(1(3(4(x1))))) -> 3(1(3(0(4(4(5(x1)))))))
          , 0(4(2(2(4(x1))))) -> 3(2(2(0(4(4(x1))))))
          , 0(4(2(4(1(x1))))) -> 3(1(0(4(4(3(2(x1)))))))
          , 0(5(2(1(5(x1))))) -> 5(4(5(2(3(1(0(x1)))))))
          , 1(0(2(2(4(x1))))) -> 2(2(0(4(3(1(4(x1)))))))
          , 1(0(2(2(4(x1))))) -> 2(3(3(2(1(0(4(3(x1))))))))
          , 1(2(2(0(1(x1))))) -> 4(3(2(1(0(2(3(1(x1))))))))
          , 1(2(3(5(0(x1))))) -> 5(2(3(1(3(0(x1))))))
          , 1(2(4(3(5(x1))))) -> 5(4(3(1(3(2(x1))))))
          , 0(0(1(3(3(5(x1)))))) -> 0(3(2(3(0(1(5(x1)))))))
          , 0(0(2(2(3(0(x1)))))) -> 0(2(3(0(3(2(0(x1)))))))
          , 0(0(2(2(5(1(x1)))))) -> 0(3(0(2(3(2(1(5(x1))))))))
          , 0(0(3(5(3(0(x1)))))) -> 0(5(0(3(1(3(3(0(x1))))))))
          , 0(0(4(0(5(1(x1)))))) -> 0(0(4(0(4(3(1(5(x1))))))))
          , 0(0(4(1(3(0(x1)))))) -> 0(0(3(2(3(0(1(4(x1))))))))
          , 0(1(0(3(4(5(x1)))))) -> 3(1(0(4(3(5(0(4(x1))))))))
          , 0(1(4(0(2(5(x1)))))) -> 0(5(2(0(4(4(1(x1)))))))
          , 0(1(5(3(4(0(x1)))))) -> 0(4(4(2(0(3(1(5(x1))))))))
          , 0(2(1(5(3(5(x1)))))) -> 3(2(1(3(5(1(5(0(x1))))))))
          , 0(3(5(2(4(1(x1)))))) -> 0(0(5(4(3(2(1(x1)))))))
          , 0(5(0(1(5(4(x1)))))) -> 3(1(3(0(0(5(4(5(x1))))))))
          , 0(5(1(1(3(4(x1)))))) -> 4(1(0(4(5(4(3(1(x1))))))))
          , 0(5(3(4(1(4(x1)))))) -> 5(4(0(4(3(1(3(x1)))))))
          , 0(5(3(4(1(5(x1)))))) -> 0(3(2(1(0(5(4(5(x1))))))))
          , 0(5(5(0(1(5(x1)))))) -> 0(5(5(3(2(1(5(0(x1))))))))
          , 1(0(2(4(0(5(x1)))))) -> 1(4(0(3(2(3(0(5(x1))))))))
          , 1(1(4(0(1(0(x1)))))) -> 0(3(1(3(1(4(1(0(x1))))))))
          , 1(2(1(0(2(1(x1)))))) -> 1(1(3(2(0(2(1(x1)))))))
          , 1(2(4(0(3(4(x1)))))) -> 3(2(0(4(3(3(1(4(x1))))))))
          , 1(2(4(3(3(0(x1)))))) -> 4(0(2(3(3(1(3(0(x1))))))))
          , 1(2(4(3(3(5(x1)))))) -> 3(2(3(2(5(4(3(1(x1))))))))
          , 1(2(4(3(4(5(x1)))))) -> 3(1(3(2(4(5(4(x1)))))))
          , 1(2(4(5(1(0(x1)))))) -> 0(4(2(1(3(1(5(x1)))))))
          , 1(2(4(5(3(4(x1)))))) -> 4(3(2(2(1(3(5(4(x1))))))))
          , 1(2(5(5(3(0(x1)))))) -> 5(2(3(3(1(3(5(0(x1))))))))
          , 0(0(2(4(5(3(5(x1))))))) -> 2(0(5(4(3(5(3(0(x1))))))))
          , 0(1(0(5(3(5(1(x1))))))) -> 1(0(0(5(5(3(1(3(x1))))))))
          , 0(1(2(2(5(2(0(x1))))))) -> 5(1(0(3(2(2(2(0(x1))))))))
          , 0(2(1(5(4(0(1(x1))))))) -> 0(0(5(1(2(3(1(4(x1))))))))
          , 0(2(3(4(1(1(4(x1))))))) -> 3(1(0(4(4(1(2(0(x1))))))))
          , 0(2(4(1(1(5(1(x1))))))) -> 3(1(0(5(4(1(1(2(x1))))))))
          , 0(2(5(0(4(0(1(x1))))))) -> 0(5(1(0(4(3(2(0(x1))))))))
          , 0(2(5(5(3(5(1(x1))))))) -> 0(5(5(1(5(5(3(2(x1))))))))
          , 0(4(0(3(5(2(0(x1))))))) -> 0(4(0(4(5(3(2(0(x1))))))))
          , 0(4(1(1(4(1(5(x1))))))) -> 0(4(3(1(4(1(1(5(x1))))))))
          , 0(4(1(4(0(3(5(x1))))))) -> 3(1(5(0(0(4(3(4(x1))))))))
          , 0(5(1(3(4(2(4(x1))))))) -> 5(4(4(0(3(1(5(2(x1))))))))
          , 1(0(3(3(3(4(0(x1))))))) -> 0(3(0(3(3(1(4(5(x1))))))))
          , 1(0(3(4(4(3(5(x1))))))) -> 5(4(3(1(3(0(2(4(x1))))))))
          , 1(2(0(4(1(3(5(x1))))))) -> 5(4(2(3(1(4(1(0(x1))))))))
          , 1(2(4(0(5(3(5(x1))))))) -> 5(1(3(2(3(5(0(4(x1))))))))}
     
     Proof Output:    
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  0_0(2) -> 1
        , 0_1(2) -> 19
        , 0_1(8) -> 7
        , 0_1(11) -> 10
        , 0_1(30) -> 20
        , 1_0(2) -> 1
        , 1_1(2) -> 39
        , 1_1(4) -> 3
        , 1_1(31) -> 17
        , 1_1(49) -> 48
        , 2_0(2) -> 2
        , 2_1(2) -> 32
        , 2_1(6) -> 5
        , 2_1(7) -> 6
        , 2_1(10) -> 3
        , 2_1(12) -> 5
        , 2_1(18) -> 17
        , 2_1(19) -> 24
        , 2_1(20) -> 7
        , 2_1(34) -> 33
        , 2_1(47) -> 46
        , 2_1(48) -> 47
        , 3_0(2) -> 2
        , 3_1(3) -> 1
        , 3_1(3) -> 19
        , 3_1(3) -> 39
        , 3_1(5) -> 4
        , 3_1(6) -> 1
        , 3_1(6) -> 19
        , 3_1(6) -> 39
        , 3_1(13) -> 49
        , 3_1(17) -> 16
        , 3_1(19) -> 18
        , 3_1(24) -> 23
        , 3_1(32) -> 31
        , 3_1(33) -> 7
        , 3_1(39) -> 38
        , 3_1(46) -> 45
        , 4_0(2) -> 2
        , 4_1(2) -> 14
        , 4_1(9) -> 8
        , 4_1(12) -> 11
        , 4_1(13) -> 12
        , 4_1(14) -> 30
        , 4_1(16) -> 15
        , 4_1(23) -> 22
        , 4_1(38) -> 37
        , 4_1(45) -> 1
        , 4_1(45) -> 39
        , 5_0(2) -> 2
        , 5_1(2) -> 9
        , 5_1(14) -> 13
        , 5_1(15) -> 1
        , 5_1(15) -> 19
        , 5_1(15) -> 39
        , 5_1(22) -> 20
        , 5_1(37) -> 34}

Tool RC1

Execution TimeUnknown
Answer
MAYBE
InputICFP 2010 45720

stdout:

MAYBE

Tool RC2

Execution TimeUnknown
Answer
YES(?,O(n^1))
InputICFP 2010 45720

stdout:

YES(?,O(n^1))

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           YES(?,O(n^1))
Input Problem:    runtime-complexity with respect to
  Rules:
    {  0(1(0(x1))) -> 0(2(3(1(3(0(x1))))))
     , 0(2(1(x1))) -> 3(1(3(0(2(x1)))))
     , 0(2(1(x1))) -> 0(2(3(3(1(3(x1))))))
     , 0(2(1(x1))) -> 0(4(3(1(3(2(2(x1)))))))
     , 0(2(1(x1))) -> 0(2(3(2(2(1(3(2(x1))))))))
     , 1(0(0(x1))) -> 2(3(1(3(0(0(x1))))))
     , 0(0(2(0(x1)))) -> 0(0(4(4(3(2(0(x1)))))))
     , 0(1(2(1(x1)))) -> 0(3(1(3(1(3(2(x1)))))))
     , 0(1(3(5(x1)))) -> 0(5(4(4(3(1(4(x1)))))))
     , 0(1(3(5(x1)))) -> 3(5(4(3(1(3(2(0(x1))))))))
     , 0(1(5(1(x1)))) -> 5(3(1(3(0(1(x1))))))
     , 0(2(1(4(x1)))) -> 0(3(2(2(1(4(x1))))))
     , 0(2(1(4(x1)))) -> 3(2(1(0(4(3(x1))))))
     , 0(2(2(1(x1)))) -> 3(2(0(2(3(1(x1))))))
     , 0(2(2(5(x1)))) -> 3(1(3(2(2(0(4(5(x1))))))))
     , 0(2(4(4(x1)))) -> 3(2(0(4(4(5(4(x1)))))))
     , 0(2(4(5(x1)))) -> 3(2(0(4(5(x1)))))
     , 0(3(3(4(x1)))) -> 5(4(3(2(3(0(x1))))))
     , 0(3(5(1(x1)))) -> 5(4(3(2(2(0(1(x1)))))))
     , 1(0(2(4(x1)))) -> 2(3(0(3(1(4(x1))))))
     , 1(1(2(5(x1)))) -> 1(3(2(2(1(5(x1))))))
     , 0(0(0(3(4(x1))))) -> 0(0(4(4(5(2(3(0(x1))))))))
     , 0(0(1(1(5(x1))))) -> 5(0(3(1(3(1(0(5(x1))))))))
     , 0(1(2(2(4(x1))))) -> 4(3(2(1(2(3(0(x1)))))))
     , 0(1(5(1(4(x1))))) -> 5(3(1(0(4(3(1(x1)))))))
     , 0(2(2(0(1(x1))))) -> 0(4(3(0(2(3(2(1(x1))))))))
     , 0(2(2(2(5(x1))))) -> 3(2(2(5(4(3(2(0(x1))))))))
     , 0(2(2(5(0(x1))))) -> 3(2(2(0(5(2(3(0(x1))))))))
     , 0(3(4(1(4(x1))))) -> 2(3(3(1(0(5(4(4(x1))))))))
     , 0(4(1(3(4(x1))))) -> 3(1(3(0(4(4(5(x1)))))))
     , 0(4(2(2(4(x1))))) -> 3(2(2(0(4(4(x1))))))
     , 0(4(2(4(1(x1))))) -> 3(1(0(4(4(3(2(x1)))))))
     , 0(5(2(1(5(x1))))) -> 5(4(5(2(3(1(0(x1)))))))
     , 1(0(2(2(4(x1))))) -> 2(2(0(4(3(1(4(x1)))))))
     , 1(0(2(2(4(x1))))) -> 2(3(3(2(1(0(4(3(x1))))))))
     , 1(2(2(0(1(x1))))) -> 4(3(2(1(0(2(3(1(x1))))))))
     , 1(2(3(5(0(x1))))) -> 5(2(3(1(3(0(x1))))))
     , 1(2(4(3(5(x1))))) -> 5(4(3(1(3(2(x1))))))
     , 0(0(1(3(3(5(x1)))))) -> 0(3(2(3(0(1(5(x1)))))))
     , 0(0(2(2(3(0(x1)))))) -> 0(2(3(0(3(2(0(x1)))))))
     , 0(0(2(2(5(1(x1)))))) -> 0(3(0(2(3(2(1(5(x1))))))))
     , 0(0(3(5(3(0(x1)))))) -> 0(5(0(3(1(3(3(0(x1))))))))
     , 0(0(4(0(5(1(x1)))))) -> 0(0(4(0(4(3(1(5(x1))))))))
     , 0(0(4(1(3(0(x1)))))) -> 0(0(3(2(3(0(1(4(x1))))))))
     , 0(1(0(3(4(5(x1)))))) -> 3(1(0(4(3(5(0(4(x1))))))))
     , 0(1(4(0(2(5(x1)))))) -> 0(5(2(0(4(4(1(x1)))))))
     , 0(1(5(3(4(0(x1)))))) -> 0(4(4(2(0(3(1(5(x1))))))))
     , 0(2(1(5(3(5(x1)))))) -> 3(2(1(3(5(1(5(0(x1))))))))
     , 0(3(5(2(4(1(x1)))))) -> 0(0(5(4(3(2(1(x1)))))))
     , 0(5(0(1(5(4(x1)))))) -> 3(1(3(0(0(5(4(5(x1))))))))
     , 0(5(1(1(3(4(x1)))))) -> 4(1(0(4(5(4(3(1(x1))))))))
     , 0(5(3(4(1(4(x1)))))) -> 5(4(0(4(3(1(3(x1)))))))
     , 0(5(3(4(1(5(x1)))))) -> 0(3(2(1(0(5(4(5(x1))))))))
     , 0(5(5(0(1(5(x1)))))) -> 0(5(5(3(2(1(5(0(x1))))))))
     , 1(0(2(4(0(5(x1)))))) -> 1(4(0(3(2(3(0(5(x1))))))))
     , 1(1(4(0(1(0(x1)))))) -> 0(3(1(3(1(4(1(0(x1))))))))
     , 1(2(1(0(2(1(x1)))))) -> 1(1(3(2(0(2(1(x1)))))))
     , 1(2(4(0(3(4(x1)))))) -> 3(2(0(4(3(3(1(4(x1))))))))
     , 1(2(4(3(3(0(x1)))))) -> 4(0(2(3(3(1(3(0(x1))))))))
     , 1(2(4(3(3(5(x1)))))) -> 3(2(3(2(5(4(3(1(x1))))))))
     , 1(2(4(3(4(5(x1)))))) -> 3(1(3(2(4(5(4(x1)))))))
     , 1(2(4(5(1(0(x1)))))) -> 0(4(2(1(3(1(5(x1)))))))
     , 1(2(4(5(3(4(x1)))))) -> 4(3(2(2(1(3(5(4(x1))))))))
     , 1(2(5(5(3(0(x1)))))) -> 5(2(3(3(1(3(5(0(x1))))))))
     , 0(0(2(4(5(3(5(x1))))))) -> 2(0(5(4(3(5(3(0(x1))))))))
     , 0(1(0(5(3(5(1(x1))))))) -> 1(0(0(5(5(3(1(3(x1))))))))
     , 0(1(2(2(5(2(0(x1))))))) -> 5(1(0(3(2(2(2(0(x1))))))))
     , 0(2(1(5(4(0(1(x1))))))) -> 0(0(5(1(2(3(1(4(x1))))))))
     , 0(2(3(4(1(1(4(x1))))))) -> 3(1(0(4(4(1(2(0(x1))))))))
     , 0(2(4(1(1(5(1(x1))))))) -> 3(1(0(5(4(1(1(2(x1))))))))
     , 0(2(5(0(4(0(1(x1))))))) -> 0(5(1(0(4(3(2(0(x1))))))))
     , 0(2(5(5(3(5(1(x1))))))) -> 0(5(5(1(5(5(3(2(x1))))))))
     , 0(4(0(3(5(2(0(x1))))))) -> 0(4(0(4(5(3(2(0(x1))))))))
     , 0(4(1(1(4(1(5(x1))))))) -> 0(4(3(1(4(1(1(5(x1))))))))
     , 0(4(1(4(0(3(5(x1))))))) -> 3(1(5(0(0(4(3(4(x1))))))))
     , 0(5(1(3(4(2(4(x1))))))) -> 5(4(4(0(3(1(5(2(x1))))))))
     , 1(0(3(3(3(4(0(x1))))))) -> 0(3(0(3(3(1(4(5(x1))))))))
     , 1(0(3(4(4(3(5(x1))))))) -> 5(4(3(1(3(0(2(4(x1))))))))
     , 1(2(0(4(1(3(5(x1))))))) -> 5(4(2(3(1(4(1(0(x1))))))))
     , 1(2(4(0(5(3(5(x1))))))) -> 5(1(3(2(3(5(0(4(x1))))))))}

Proof Output:    
  'Bounds with minimal-enrichment and initial automaton 'match'' proved the best result:
  
  Details:
  --------
    'Bounds with minimal-enrichment and initial automaton 'match'' succeeded with the following output:
     'Bounds with minimal-enrichment and initial automaton 'match''
     --------------------------------------------------------------
     Answer:           YES(?,O(n^1))
     Input Problem:    runtime-complexity with respect to
       Rules:
         {  0(1(0(x1))) -> 0(2(3(1(3(0(x1))))))
          , 0(2(1(x1))) -> 3(1(3(0(2(x1)))))
          , 0(2(1(x1))) -> 0(2(3(3(1(3(x1))))))
          , 0(2(1(x1))) -> 0(4(3(1(3(2(2(x1)))))))
          , 0(2(1(x1))) -> 0(2(3(2(2(1(3(2(x1))))))))
          , 1(0(0(x1))) -> 2(3(1(3(0(0(x1))))))
          , 0(0(2(0(x1)))) -> 0(0(4(4(3(2(0(x1)))))))
          , 0(1(2(1(x1)))) -> 0(3(1(3(1(3(2(x1)))))))
          , 0(1(3(5(x1)))) -> 0(5(4(4(3(1(4(x1)))))))
          , 0(1(3(5(x1)))) -> 3(5(4(3(1(3(2(0(x1))))))))
          , 0(1(5(1(x1)))) -> 5(3(1(3(0(1(x1))))))
          , 0(2(1(4(x1)))) -> 0(3(2(2(1(4(x1))))))
          , 0(2(1(4(x1)))) -> 3(2(1(0(4(3(x1))))))
          , 0(2(2(1(x1)))) -> 3(2(0(2(3(1(x1))))))
          , 0(2(2(5(x1)))) -> 3(1(3(2(2(0(4(5(x1))))))))
          , 0(2(4(4(x1)))) -> 3(2(0(4(4(5(4(x1)))))))
          , 0(2(4(5(x1)))) -> 3(2(0(4(5(x1)))))
          , 0(3(3(4(x1)))) -> 5(4(3(2(3(0(x1))))))
          , 0(3(5(1(x1)))) -> 5(4(3(2(2(0(1(x1)))))))
          , 1(0(2(4(x1)))) -> 2(3(0(3(1(4(x1))))))
          , 1(1(2(5(x1)))) -> 1(3(2(2(1(5(x1))))))
          , 0(0(0(3(4(x1))))) -> 0(0(4(4(5(2(3(0(x1))))))))
          , 0(0(1(1(5(x1))))) -> 5(0(3(1(3(1(0(5(x1))))))))
          , 0(1(2(2(4(x1))))) -> 4(3(2(1(2(3(0(x1)))))))
          , 0(1(5(1(4(x1))))) -> 5(3(1(0(4(3(1(x1)))))))
          , 0(2(2(0(1(x1))))) -> 0(4(3(0(2(3(2(1(x1))))))))
          , 0(2(2(2(5(x1))))) -> 3(2(2(5(4(3(2(0(x1))))))))
          , 0(2(2(5(0(x1))))) -> 3(2(2(0(5(2(3(0(x1))))))))
          , 0(3(4(1(4(x1))))) -> 2(3(3(1(0(5(4(4(x1))))))))
          , 0(4(1(3(4(x1))))) -> 3(1(3(0(4(4(5(x1)))))))
          , 0(4(2(2(4(x1))))) -> 3(2(2(0(4(4(x1))))))
          , 0(4(2(4(1(x1))))) -> 3(1(0(4(4(3(2(x1)))))))
          , 0(5(2(1(5(x1))))) -> 5(4(5(2(3(1(0(x1)))))))
          , 1(0(2(2(4(x1))))) -> 2(2(0(4(3(1(4(x1)))))))
          , 1(0(2(2(4(x1))))) -> 2(3(3(2(1(0(4(3(x1))))))))
          , 1(2(2(0(1(x1))))) -> 4(3(2(1(0(2(3(1(x1))))))))
          , 1(2(3(5(0(x1))))) -> 5(2(3(1(3(0(x1))))))
          , 1(2(4(3(5(x1))))) -> 5(4(3(1(3(2(x1))))))
          , 0(0(1(3(3(5(x1)))))) -> 0(3(2(3(0(1(5(x1)))))))
          , 0(0(2(2(3(0(x1)))))) -> 0(2(3(0(3(2(0(x1)))))))
          , 0(0(2(2(5(1(x1)))))) -> 0(3(0(2(3(2(1(5(x1))))))))
          , 0(0(3(5(3(0(x1)))))) -> 0(5(0(3(1(3(3(0(x1))))))))
          , 0(0(4(0(5(1(x1)))))) -> 0(0(4(0(4(3(1(5(x1))))))))
          , 0(0(4(1(3(0(x1)))))) -> 0(0(3(2(3(0(1(4(x1))))))))
          , 0(1(0(3(4(5(x1)))))) -> 3(1(0(4(3(5(0(4(x1))))))))
          , 0(1(4(0(2(5(x1)))))) -> 0(5(2(0(4(4(1(x1)))))))
          , 0(1(5(3(4(0(x1)))))) -> 0(4(4(2(0(3(1(5(x1))))))))
          , 0(2(1(5(3(5(x1)))))) -> 3(2(1(3(5(1(5(0(x1))))))))
          , 0(3(5(2(4(1(x1)))))) -> 0(0(5(4(3(2(1(x1)))))))
          , 0(5(0(1(5(4(x1)))))) -> 3(1(3(0(0(5(4(5(x1))))))))
          , 0(5(1(1(3(4(x1)))))) -> 4(1(0(4(5(4(3(1(x1))))))))
          , 0(5(3(4(1(4(x1)))))) -> 5(4(0(4(3(1(3(x1)))))))
          , 0(5(3(4(1(5(x1)))))) -> 0(3(2(1(0(5(4(5(x1))))))))
          , 0(5(5(0(1(5(x1)))))) -> 0(5(5(3(2(1(5(0(x1))))))))
          , 1(0(2(4(0(5(x1)))))) -> 1(4(0(3(2(3(0(5(x1))))))))
          , 1(1(4(0(1(0(x1)))))) -> 0(3(1(3(1(4(1(0(x1))))))))
          , 1(2(1(0(2(1(x1)))))) -> 1(1(3(2(0(2(1(x1)))))))
          , 1(2(4(0(3(4(x1)))))) -> 3(2(0(4(3(3(1(4(x1))))))))
          , 1(2(4(3(3(0(x1)))))) -> 4(0(2(3(3(1(3(0(x1))))))))
          , 1(2(4(3(3(5(x1)))))) -> 3(2(3(2(5(4(3(1(x1))))))))
          , 1(2(4(3(4(5(x1)))))) -> 3(1(3(2(4(5(4(x1)))))))
          , 1(2(4(5(1(0(x1)))))) -> 0(4(2(1(3(1(5(x1)))))))
          , 1(2(4(5(3(4(x1)))))) -> 4(3(2(2(1(3(5(4(x1))))))))
          , 1(2(5(5(3(0(x1)))))) -> 5(2(3(3(1(3(5(0(x1))))))))
          , 0(0(2(4(5(3(5(x1))))))) -> 2(0(5(4(3(5(3(0(x1))))))))
          , 0(1(0(5(3(5(1(x1))))))) -> 1(0(0(5(5(3(1(3(x1))))))))
          , 0(1(2(2(5(2(0(x1))))))) -> 5(1(0(3(2(2(2(0(x1))))))))
          , 0(2(1(5(4(0(1(x1))))))) -> 0(0(5(1(2(3(1(4(x1))))))))
          , 0(2(3(4(1(1(4(x1))))))) -> 3(1(0(4(4(1(2(0(x1))))))))
          , 0(2(4(1(1(5(1(x1))))))) -> 3(1(0(5(4(1(1(2(x1))))))))
          , 0(2(5(0(4(0(1(x1))))))) -> 0(5(1(0(4(3(2(0(x1))))))))
          , 0(2(5(5(3(5(1(x1))))))) -> 0(5(5(1(5(5(3(2(x1))))))))
          , 0(4(0(3(5(2(0(x1))))))) -> 0(4(0(4(5(3(2(0(x1))))))))
          , 0(4(1(1(4(1(5(x1))))))) -> 0(4(3(1(4(1(1(5(x1))))))))
          , 0(4(1(4(0(3(5(x1))))))) -> 3(1(5(0(0(4(3(4(x1))))))))
          , 0(5(1(3(4(2(4(x1))))))) -> 5(4(4(0(3(1(5(2(x1))))))))
          , 1(0(3(3(3(4(0(x1))))))) -> 0(3(0(3(3(1(4(5(x1))))))))
          , 1(0(3(4(4(3(5(x1))))))) -> 5(4(3(1(3(0(2(4(x1))))))))
          , 1(2(0(4(1(3(5(x1))))))) -> 5(4(2(3(1(4(1(0(x1))))))))
          , 1(2(4(0(5(3(5(x1))))))) -> 5(1(3(2(3(5(0(4(x1))))))))}
     
     Proof Output:    
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  0_0(2) -> 1
        , 0_1(2) -> 19
        , 0_1(8) -> 7
        , 0_1(11) -> 10
        , 0_1(30) -> 20
        , 1_0(2) -> 1
        , 1_1(2) -> 39
        , 1_1(4) -> 3
        , 1_1(31) -> 17
        , 1_1(49) -> 48
        , 2_0(2) -> 2
        , 2_1(2) -> 32
        , 2_1(6) -> 5
        , 2_1(7) -> 6
        , 2_1(10) -> 3
        , 2_1(12) -> 5
        , 2_1(18) -> 17
        , 2_1(19) -> 24
        , 2_1(20) -> 7
        , 2_1(34) -> 33
        , 2_1(47) -> 46
        , 2_1(48) -> 47
        , 3_0(2) -> 2
        , 3_1(3) -> 1
        , 3_1(3) -> 19
        , 3_1(3) -> 39
        , 3_1(5) -> 4
        , 3_1(6) -> 1
        , 3_1(6) -> 19
        , 3_1(6) -> 39
        , 3_1(13) -> 49
        , 3_1(17) -> 16
        , 3_1(19) -> 18
        , 3_1(24) -> 23
        , 3_1(32) -> 31
        , 3_1(33) -> 7
        , 3_1(39) -> 38
        , 3_1(46) -> 45
        , 4_0(2) -> 2
        , 4_1(2) -> 14
        , 4_1(9) -> 8
        , 4_1(12) -> 11
        , 4_1(13) -> 12
        , 4_1(14) -> 30
        , 4_1(16) -> 15
        , 4_1(23) -> 22
        , 4_1(38) -> 37
        , 4_1(45) -> 1
        , 4_1(45) -> 39
        , 5_0(2) -> 2
        , 5_1(2) -> 9
        , 5_1(14) -> 13
        , 5_1(15) -> 1
        , 5_1(15) -> 19
        , 5_1(15) -> 39
        , 5_1(22) -> 20
        , 5_1(37) -> 34}