Tool CaT
stdout:
YES(?,O(n^1))
Problem:
3(1(x1)) -> 4(1(x1))
5(9(x1)) -> 2(6(5(x1)))
3(5(x1)) -> 8(9(7(x1)))
9(x1) -> 3(2(3(x1)))
8(4(x1)) -> 6(x1)
2(6(x1)) -> 4(3(x1))
3(8(x1)) -> 3(2(7(x1)))
9(x1) -> 5(0(2(x1)))
8(8(4(x1))) -> 1(9(x1))
7(1(x1)) -> 6(9(x1))
3(9(x1)) -> 9(3(x1))
7(5(x1)) -> 1(0(x1))
Proof:
Bounds Processor:
bound: 2
enrichment: match
automaton:
final states: {10,9,8,7,6,5}
transitions:
61(59) -> 60*
61(61) -> 62*
61(51) -> 52*
61(53) -> 54*
61(105) -> 106*
91(107) -> 108*
91(104) -> 105*
91(113) -> 114*
91(115) -> 116*
51(87) -> 88*
01(86) -> 87*
21(85) -> 86*
21(97) -> 98*
21(89) -> 90*
21(34) -> 35*
21(95) -> 96*
41(75) -> 76*
41(15) -> 16*
41(77) -> 78*
41(67) -> 68*
41(69) -> 70*
31(45) -> 46*
31(35) -> 36*
31(37) -> 38*
31(43) -> 44*
31(33) -> 34*
11(25) -> 26*
11(17) -> 18*
11(14) -> 15*
11(23) -> 24*
52(151) -> 152*
52(143) -> 144*
02(142) -> 143*
02(150) -> 151*
22(159) -> 160*
22(149) -> 150*
22(124) -> 125*
22(141) -> 142*
22(153) -> 154*
22(128) -> 129*
30(2) -> 5*
30(4) -> 5*
30(1) -> 5*
30(3) -> 5*
32(137) -> 138*
32(127) -> 128*
32(129) -> 130*
32(123) -> 124*
32(135) -> 136*
32(125) -> 126*
10(2) -> 1*
10(4) -> 1*
10(1) -> 1*
10(3) -> 1*
40(2) -> 2*
40(4) -> 2*
40(1) -> 2*
40(3) -> 2*
50(2) -> 6*
50(4) -> 6*
50(1) -> 6*
50(3) -> 6*
90(2) -> 7*
90(4) -> 7*
90(1) -> 7*
90(3) -> 7*
20(2) -> 9*
20(4) -> 9*
20(1) -> 9*
20(3) -> 9*
60(2) -> 3*
60(4) -> 3*
60(1) -> 3*
60(3) -> 3*
80(2) -> 8*
80(4) -> 8*
80(1) -> 8*
80(3) -> 8*
70(2) -> 10*
70(4) -> 10*
70(1) -> 10*
70(3) -> 10*
00(2) -> 4*
00(4) -> 4*
00(1) -> 4*
00(3) -> 4*
1 -> 113,89,59,37,23
2 -> 104,97,51,45,14
3 -> 115,85,61,33,25
4 -> 107,95,53,43,17
16 -> 124,38,75,34,77,5
18 -> 15*
24 -> 15*
26 -> 15*
34 -> 77*
36 -> 7*
38 -> 75,34
44 -> 69,34
46 -> 67,34
52 -> 8*
54 -> 8*
60 -> 8*
62 -> 8*
68 -> 150,86,9
70 -> 150,86,9
76 -> 150,86,9
78 -> 150,86,9
88 -> 7*
90 -> 86*
96 -> 86*
98 -> 86*
104 -> 153,135
106 -> 10*
107 -> 159,137
108 -> 105*
113 -> 141,123
114 -> 105*
115 -> 149,127
116 -> 105*
126 -> 108,114
130 -> 116*
136 -> 124*
138 -> 124*
144 -> 108,114
152 -> 116*
154 -> 142*
160 -> 142*
problem:
QedTool IRC1
stdout:
YES(?,O(n^1))
Tool IRC2
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:
{ 3(1(x1)) -> 4(1(x1))
, 5(9(x1)) -> 2(6(5(x1)))
, 3(5(x1)) -> 8(9(7(x1)))
, 9(x1) -> 3(2(3(x1)))
, 8(4(x1)) -> 6(x1)
, 2(6(x1)) -> 4(3(x1))
, 3(8(x1)) -> 3(2(7(x1)))
, 9(x1) -> 5(0(2(x1)))
, 8(8(4(x1))) -> 1(9(x1))
, 7(1(x1)) -> 6(9(x1))
, 3(9(x1)) -> 9(3(x1))
, 7(5(x1)) -> 1(0(x1))}
Proof Output:
'Bounds with perSymbol-enrichment and initial automaton 'match'' proved the best result:
Details:
--------
'Bounds with perSymbol-enrichment and initial automaton 'match'' succeeded with the following output:
'Bounds with perSymbol-enrichment and initial automaton 'match''
----------------------------------------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost runtime-complexity with respect to
Rules:
{ 3(1(x1)) -> 4(1(x1))
, 5(9(x1)) -> 2(6(5(x1)))
, 3(5(x1)) -> 8(9(7(x1)))
, 9(x1) -> 3(2(3(x1)))
, 8(4(x1)) -> 6(x1)
, 2(6(x1)) -> 4(3(x1))
, 3(8(x1)) -> 3(2(7(x1)))
, 9(x1) -> 5(0(2(x1)))
, 8(8(4(x1))) -> 1(9(x1))
, 7(1(x1)) -> 6(9(x1))
, 3(9(x1)) -> 9(3(x1))
, 7(5(x1)) -> 1(0(x1))}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ 3_0(2) -> 1
, 3_0(3) -> 1
, 3_0(7) -> 1
, 3_0(10) -> 1
, 3_1(2) -> 13
, 3_1(3) -> 13
, 3_1(7) -> 13
, 3_1(10) -> 13
, 3_1(12) -> 5
, 3_2(2) -> 18
, 3_2(3) -> 18
, 3_2(7) -> 18
, 3_2(10) -> 18
, 3_2(17) -> 16
, 1_0(2) -> 2
, 1_0(3) -> 2
, 1_0(7) -> 2
, 1_0(10) -> 2
, 1_1(2) -> 11
, 1_1(3) -> 11
, 1_1(7) -> 11
, 1_1(10) -> 11
, 4_0(2) -> 3
, 4_0(3) -> 3
, 4_0(7) -> 3
, 4_0(10) -> 3
, 4_1(11) -> 1
, 4_1(11) -> 13
, 4_1(11) -> 18
, 4_1(13) -> 6
, 4_1(13) -> 15
, 4_1(13) -> 20
, 5_0(2) -> 4
, 5_0(3) -> 4
, 5_0(7) -> 4
, 5_0(10) -> 4
, 5_1(14) -> 5
, 5_2(19) -> 16
, 9_0(2) -> 5
, 9_0(3) -> 5
, 9_0(7) -> 5
, 9_0(10) -> 5
, 9_1(2) -> 16
, 9_1(3) -> 16
, 9_1(7) -> 16
, 9_1(10) -> 16
, 2_0(2) -> 6
, 2_0(3) -> 6
, 2_0(7) -> 6
, 2_0(10) -> 6
, 2_1(2) -> 15
, 2_1(3) -> 15
, 2_1(7) -> 15
, 2_1(10) -> 15
, 2_1(13) -> 12
, 2_2(2) -> 20
, 2_2(3) -> 20
, 2_2(7) -> 20
, 2_2(10) -> 20
, 2_2(18) -> 17
, 6_0(2) -> 7
, 6_0(3) -> 7
, 6_0(7) -> 7
, 6_0(10) -> 7
, 6_1(2) -> 8
, 6_1(3) -> 8
, 6_1(7) -> 8
, 6_1(10) -> 8
, 6_1(16) -> 9
, 8_0(2) -> 8
, 8_0(3) -> 8
, 8_0(7) -> 8
, 8_0(10) -> 8
, 7_0(2) -> 9
, 7_0(3) -> 9
, 7_0(7) -> 9
, 7_0(10) -> 9
, 0_0(2) -> 10
, 0_0(3) -> 10
, 0_0(7) -> 10
, 0_0(10) -> 10
, 0_1(15) -> 14
, 0_2(20) -> 19}Tool RC1
stdout:
YES(?,O(n^1))
Tool RC2
stdout:
YES(?,O(n^1))
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: YES(?,O(n^1))
Input Problem: runtime-complexity with respect to
Rules:
{ 3(1(x1)) -> 4(1(x1))
, 5(9(x1)) -> 2(6(5(x1)))
, 3(5(x1)) -> 8(9(7(x1)))
, 9(x1) -> 3(2(3(x1)))
, 8(4(x1)) -> 6(x1)
, 2(6(x1)) -> 4(3(x1))
, 3(8(x1)) -> 3(2(7(x1)))
, 9(x1) -> 5(0(2(x1)))
, 8(8(4(x1))) -> 1(9(x1))
, 7(1(x1)) -> 6(9(x1))
, 3(9(x1)) -> 9(3(x1))
, 7(5(x1)) -> 1(0(x1))}
Proof Output:
'Bounds with perSymbol-enrichment and initial automaton 'match'' proved the best result:
Details:
--------
'Bounds with perSymbol-enrichment and initial automaton 'match'' succeeded with the following output:
'Bounds with perSymbol-enrichment and initial automaton 'match''
----------------------------------------------------------------
Answer: YES(?,O(n^1))
Input Problem: runtime-complexity with respect to
Rules:
{ 3(1(x1)) -> 4(1(x1))
, 5(9(x1)) -> 2(6(5(x1)))
, 3(5(x1)) -> 8(9(7(x1)))
, 9(x1) -> 3(2(3(x1)))
, 8(4(x1)) -> 6(x1)
, 2(6(x1)) -> 4(3(x1))
, 3(8(x1)) -> 3(2(7(x1)))
, 9(x1) -> 5(0(2(x1)))
, 8(8(4(x1))) -> 1(9(x1))
, 7(1(x1)) -> 6(9(x1))
, 3(9(x1)) -> 9(3(x1))
, 7(5(x1)) -> 1(0(x1))}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ 3_0(2) -> 1
, 3_0(3) -> 1
, 3_0(7) -> 1
, 3_0(10) -> 1
, 3_1(2) -> 13
, 3_1(3) -> 13
, 3_1(7) -> 13
, 3_1(10) -> 13
, 3_1(12) -> 5
, 3_2(2) -> 18
, 3_2(3) -> 18
, 3_2(7) -> 18
, 3_2(10) -> 18
, 3_2(17) -> 16
, 1_0(2) -> 2
, 1_0(3) -> 2
, 1_0(7) -> 2
, 1_0(10) -> 2
, 1_1(2) -> 11
, 1_1(3) -> 11
, 1_1(7) -> 11
, 1_1(10) -> 11
, 4_0(2) -> 3
, 4_0(3) -> 3
, 4_0(7) -> 3
, 4_0(10) -> 3
, 4_1(11) -> 1
, 4_1(11) -> 13
, 4_1(11) -> 18
, 4_1(13) -> 6
, 4_1(13) -> 15
, 4_1(13) -> 20
, 5_0(2) -> 4
, 5_0(3) -> 4
, 5_0(7) -> 4
, 5_0(10) -> 4
, 5_1(14) -> 5
, 5_2(19) -> 16
, 9_0(2) -> 5
, 9_0(3) -> 5
, 9_0(7) -> 5
, 9_0(10) -> 5
, 9_1(2) -> 16
, 9_1(3) -> 16
, 9_1(7) -> 16
, 9_1(10) -> 16
, 2_0(2) -> 6
, 2_0(3) -> 6
, 2_0(7) -> 6
, 2_0(10) -> 6
, 2_1(2) -> 15
, 2_1(3) -> 15
, 2_1(7) -> 15
, 2_1(10) -> 15
, 2_1(13) -> 12
, 2_2(2) -> 20
, 2_2(3) -> 20
, 2_2(7) -> 20
, 2_2(10) -> 20
, 2_2(18) -> 17
, 6_0(2) -> 7
, 6_0(3) -> 7
, 6_0(7) -> 7
, 6_0(10) -> 7
, 6_1(2) -> 8
, 6_1(3) -> 8
, 6_1(7) -> 8
, 6_1(10) -> 8
, 6_1(16) -> 9
, 8_0(2) -> 8
, 8_0(3) -> 8
, 8_0(7) -> 8
, 8_0(10) -> 8
, 7_0(2) -> 9
, 7_0(3) -> 9
, 7_0(7) -> 9
, 7_0(10) -> 9
, 0_0(2) -> 10
, 0_0(3) -> 10
, 0_0(7) -> 10
, 0_0(10) -> 10
, 0_1(15) -> 14
, 0_2(20) -> 19}