Tool CaT
stdout:
YES(?,O(n^1))
Problem:
0(1(2(2(x1)))) -> 0(1(0(2(2(x1)))))
0(1(2(2(x1)))) -> 0(1(2(3(2(x1)))))
0(1(2(2(x1)))) -> 0(2(2(1(3(x1)))))
0(1(2(2(x1)))) -> 1(0(3(2(2(x1)))))
0(1(2(2(x1)))) -> 1(2(0(3(2(x1)))))
0(1(2(2(x1)))) -> 1(3(0(2(2(x1)))))
0(1(2(2(x1)))) -> 1(3(2(0(2(x1)))))
0(1(2(2(x1)))) -> 0(1(0(4(2(2(x1))))))
0(1(2(2(x1)))) -> 0(2(1(3(2(3(x1))))))
0(1(2(2(x1)))) -> 1(2(1(0(4(2(x1))))))
0(1(2(2(x1)))) -> 1(5(0(4(2(2(x1))))))
0(1(2(2(x1)))) -> 2(0(3(1(3(2(x1))))))
0(1(2(2(x1)))) -> 2(1(1(0(4(2(x1))))))
0(1(2(2(x1)))) -> 2(1(3(0(2(0(x1))))))
0(1(2(2(x1)))) -> 2(1(3(3(2(0(x1))))))
0(1(2(2(x1)))) -> 2(1(5(3(0(2(x1))))))
0(1(2(2(x1)))) -> 2(2(1(3(0(5(x1))))))
0(1(2(2(x1)))) -> 2(4(1(3(2(0(x1))))))
0(1(4(5(x1)))) -> 1(5(0(4(1(x1)))))
0(1(4(5(x1)))) -> 5(0(4(1(5(x1)))))
0(1(4(5(x1)))) -> 5(4(1(5(0(x1)))))
0(1(4(5(x1)))) -> 1(1(5(0(4(1(x1))))))
0(1(4(5(x1)))) -> 5(4(1(5(5(0(x1))))))
5(1(2(2(x1)))) -> 1(0(2(2(5(x1)))))
5(1(2(2(x1)))) -> 1(3(5(2(2(x1)))))
5(1(2(2(x1)))) -> 1(5(2(3(2(x1)))))
5(1(2(2(x1)))) -> 1(5(0(2(2(3(x1))))))
5(1(2(2(x1)))) -> 2(1(0(3(2(5(x1))))))
5(1(2(2(x1)))) -> 3(1(3(5(2(2(x1))))))
5(1(2(2(x1)))) -> 4(1(3(2(2(5(x1))))))
5(1(2(2(x1)))) -> 5(1(0(4(2(2(x1))))))
5(1(2(2(x1)))) -> 5(1(2(0(4(2(x1))))))
0(1(1(4(5(x1))))) -> 3(1(0(4(1(5(x1))))))
0(1(2(2(2(x1))))) -> 1(0(2(2(5(2(x1))))))
0(1(2(2(5(x1))))) -> 1(5(0(4(2(2(x1))))))
0(1(2(4(5(x1))))) -> 2(5(1(0(4(5(x1))))))
0(1(4(5(2(x1))))) -> 1(0(4(2(0(5(x1))))))
0(1(4(5(5(x1))))) -> 5(0(4(0(1(5(x1))))))
0(1(5(4(5(x1))))) -> 1(5(0(4(1(5(x1))))))
0(5(1(2(2(x1))))) -> 0(1(3(2(5(2(x1))))))
3(3(1(2(2(x1))))) -> 1(3(2(0(3(2(x1))))))
3(4(4(0(5(x1))))) -> 3(5(4(5(0(4(x1))))))
5(0(1(2(2(x1))))) -> 1(3(2(0(5(2(x1))))))
5(1(2(2(5(x1))))) -> 1(5(2(3(2(5(x1))))))
5(2(1(2(2(x1))))) -> 2(1(3(5(2(2(x1))))))
5(2(4(0(5(x1))))) -> 0(4(2(5(5(5(x1))))))
5(2(4(0(5(x1))))) -> 0(4(5(4(2(5(x1))))))
Proof:
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {6,5,4}
transitions:
21(60) -> 61*
21(35) -> 36*
21(117) -> 118*
21(77) -> 78*
21(7) -> 8*
21(221) -> 222*
21(211) -> 212*
21(166) -> 167*
21(36) -> 37*
21(31) -> 32*
21(223) -> 224*
21(21) -> 22*
21(188) -> 189*
21(183) -> 184*
21(143) -> 144*
21(23) -> 24*
21(220) -> 221*
21(8) -> 9*
21(165) -> 166*
21(105) -> 106*
11(10) -> 11*
11(187) -> 188*
11(162) -> 163*
11(142) -> 143*
11(107) -> 108*
11(102) -> 103*
11(57) -> 58*
11(79) -> 80*
11(34) -> 35*
11(91) -> 92*
11(168) -> 169*
11(200) -> 201*
31(55) -> 56*
31(45) -> 46*
31(30) -> 31*
31(227) -> 228*
31(197) -> 198*
31(67) -> 68*
31(47) -> 48*
31(199) -> 200*
31(179) -> 180*
31(129) -> 130*
31(119) -> 120*
31(141) -> 142*
31(136) -> 137*
31(103) -> 104*
31(78) -> 79*
31(33) -> 34*
31(185) -> 186*
51(137) -> 138*
51(219) -> 220*
51(209) -> 210*
51(139) -> 140*
51(178) -> 179*
51(153) -> 154*
51(93) -> 94*
51(155) -> 156*
01(167) -> 168*
01(127) -> 128*
01(104) -> 105*
01(69) -> 70*
01(59) -> 60*
01(9) -> 10*
01(186) -> 187*
01(121) -> 122*
01(116) -> 117*
01(56) -> 57*
01(11) -> 12*
01(118) -> 119*
01(140) -> 141*
01(90) -> 91*
41(75) -> 76*
41(89) -> 90*
41(201) -> 202*
41(163) -> 164*
00(2) -> 4*
00(1) -> 4*
00(3) -> 4*
10(2) -> 1*
10(1) -> 1*
10(3) -> 1*
20(2) -> 2*
20(1) -> 2*
20(3) -> 2*
30(2) -> 6*
30(1) -> 6*
30(3) -> 6*
40(2) -> 3*
40(1) -> 3*
40(3) -> 3*
50(2) -> 5*
50(1) -> 5*
50(3) -> 5*
1 -> 153,121,45,21
2 -> 139,116,33,7
3 -> 155,127,47,23
8 -> 219,89,69,30
9 -> 178,75,55
10 -> 93,67
11 -> 209*
12 -> 122,4
22 -> 8*
24 -> 8*
31 -> 102,59
32 -> 10*
34 -> 77*
37 -> 11*
46 -> 34*
48 -> 34*
58 -> 154,165,122,5,4
61 -> 57*
68 -> 57*
70 -> 136,31
76 -> 9*
78 -> 183*
80 -> 36*
91 -> 211*
92 -> 107,60
94 -> 57*
106 -> 122,4
108 -> 105*
118 -> 129*
120 -> 107*
122 -> 117*
128 -> 117*
130 -> 162,119
138 -> 107*
140 -> 165*
144 -> 105*
154 -> 140*
156 -> 140*
164 -> 105*
166 -> 220,140,185
167 -> 199*
169 -> 154,165,223,197,5
180 -> 168*
184 -> 9*
189 -> 154,165,5
198 -> 154,165,5
202 -> 154,165,5
210 -> 154,165,5
212 -> 10*
221 -> 227*
222 -> 56*
224 -> 5*
228 -> 57*
problem:
QedTool IRC1
stdout:
MAYBE
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:
{ 0(1(2(2(x1)))) -> 0(1(0(2(2(x1)))))
, 0(1(2(2(x1)))) -> 0(1(2(3(2(x1)))))
, 0(1(2(2(x1)))) -> 0(2(2(1(3(x1)))))
, 0(1(2(2(x1)))) -> 1(0(3(2(2(x1)))))
, 0(1(2(2(x1)))) -> 1(2(0(3(2(x1)))))
, 0(1(2(2(x1)))) -> 1(3(0(2(2(x1)))))
, 0(1(2(2(x1)))) -> 1(3(2(0(2(x1)))))
, 0(1(2(2(x1)))) -> 0(1(0(4(2(2(x1))))))
, 0(1(2(2(x1)))) -> 0(2(1(3(2(3(x1))))))
, 0(1(2(2(x1)))) -> 1(2(1(0(4(2(x1))))))
, 0(1(2(2(x1)))) -> 1(5(0(4(2(2(x1))))))
, 0(1(2(2(x1)))) -> 2(0(3(1(3(2(x1))))))
, 0(1(2(2(x1)))) -> 2(1(1(0(4(2(x1))))))
, 0(1(2(2(x1)))) -> 2(1(3(0(2(0(x1))))))
, 0(1(2(2(x1)))) -> 2(1(3(3(2(0(x1))))))
, 0(1(2(2(x1)))) -> 2(1(5(3(0(2(x1))))))
, 0(1(2(2(x1)))) -> 2(2(1(3(0(5(x1))))))
, 0(1(2(2(x1)))) -> 2(4(1(3(2(0(x1))))))
, 0(1(4(5(x1)))) -> 1(5(0(4(1(x1)))))
, 0(1(4(5(x1)))) -> 5(0(4(1(5(x1)))))
, 0(1(4(5(x1)))) -> 5(4(1(5(0(x1)))))
, 0(1(4(5(x1)))) -> 1(1(5(0(4(1(x1))))))
, 0(1(4(5(x1)))) -> 5(4(1(5(5(0(x1))))))
, 5(1(2(2(x1)))) -> 1(0(2(2(5(x1)))))
, 5(1(2(2(x1)))) -> 1(3(5(2(2(x1)))))
, 5(1(2(2(x1)))) -> 1(5(2(3(2(x1)))))
, 5(1(2(2(x1)))) -> 1(5(0(2(2(3(x1))))))
, 5(1(2(2(x1)))) -> 2(1(0(3(2(5(x1))))))
, 5(1(2(2(x1)))) -> 3(1(3(5(2(2(x1))))))
, 5(1(2(2(x1)))) -> 4(1(3(2(2(5(x1))))))
, 5(1(2(2(x1)))) -> 5(1(0(4(2(2(x1))))))
, 5(1(2(2(x1)))) -> 5(1(2(0(4(2(x1))))))
, 0(1(1(4(5(x1))))) -> 3(1(0(4(1(5(x1))))))
, 0(1(2(2(2(x1))))) -> 1(0(2(2(5(2(x1))))))
, 0(1(2(2(5(x1))))) -> 1(5(0(4(2(2(x1))))))
, 0(1(2(4(5(x1))))) -> 2(5(1(0(4(5(x1))))))
, 0(1(4(5(2(x1))))) -> 1(0(4(2(0(5(x1))))))
, 0(1(4(5(5(x1))))) -> 5(0(4(0(1(5(x1))))))
, 0(1(5(4(5(x1))))) -> 1(5(0(4(1(5(x1))))))
, 0(5(1(2(2(x1))))) -> 0(1(3(2(5(2(x1))))))
, 3(3(1(2(2(x1))))) -> 1(3(2(0(3(2(x1))))))
, 3(4(4(0(5(x1))))) -> 3(5(4(5(0(4(x1))))))
, 5(0(1(2(2(x1))))) -> 1(3(2(0(5(2(x1))))))
, 5(1(2(2(5(x1))))) -> 1(5(2(3(2(5(x1))))))
, 5(2(1(2(2(x1))))) -> 2(1(3(5(2(2(x1))))))
, 5(2(4(0(5(x1))))) -> 0(4(2(5(5(5(x1))))))
, 5(2(4(0(5(x1))))) -> 0(4(5(4(2(5(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(2(2(x1)))) -> 0(1(0(2(2(x1)))))
, 0(1(2(2(x1)))) -> 0(1(2(3(2(x1)))))
, 0(1(2(2(x1)))) -> 0(2(2(1(3(x1)))))
, 0(1(2(2(x1)))) -> 1(0(3(2(2(x1)))))
, 0(1(2(2(x1)))) -> 1(2(0(3(2(x1)))))
, 0(1(2(2(x1)))) -> 1(3(0(2(2(x1)))))
, 0(1(2(2(x1)))) -> 1(3(2(0(2(x1)))))
, 0(1(2(2(x1)))) -> 0(1(0(4(2(2(x1))))))
, 0(1(2(2(x1)))) -> 0(2(1(3(2(3(x1))))))
, 0(1(2(2(x1)))) -> 1(2(1(0(4(2(x1))))))
, 0(1(2(2(x1)))) -> 1(5(0(4(2(2(x1))))))
, 0(1(2(2(x1)))) -> 2(0(3(1(3(2(x1))))))
, 0(1(2(2(x1)))) -> 2(1(1(0(4(2(x1))))))
, 0(1(2(2(x1)))) -> 2(1(3(0(2(0(x1))))))
, 0(1(2(2(x1)))) -> 2(1(3(3(2(0(x1))))))
, 0(1(2(2(x1)))) -> 2(1(5(3(0(2(x1))))))
, 0(1(2(2(x1)))) -> 2(2(1(3(0(5(x1))))))
, 0(1(2(2(x1)))) -> 2(4(1(3(2(0(x1))))))
, 0(1(4(5(x1)))) -> 1(5(0(4(1(x1)))))
, 0(1(4(5(x1)))) -> 5(0(4(1(5(x1)))))
, 0(1(4(5(x1)))) -> 5(4(1(5(0(x1)))))
, 0(1(4(5(x1)))) -> 1(1(5(0(4(1(x1))))))
, 0(1(4(5(x1)))) -> 5(4(1(5(5(0(x1))))))
, 5(1(2(2(x1)))) -> 1(0(2(2(5(x1)))))
, 5(1(2(2(x1)))) -> 1(3(5(2(2(x1)))))
, 5(1(2(2(x1)))) -> 1(5(2(3(2(x1)))))
, 5(1(2(2(x1)))) -> 1(5(0(2(2(3(x1))))))
, 5(1(2(2(x1)))) -> 2(1(0(3(2(5(x1))))))
, 5(1(2(2(x1)))) -> 3(1(3(5(2(2(x1))))))
, 5(1(2(2(x1)))) -> 4(1(3(2(2(5(x1))))))
, 5(1(2(2(x1)))) -> 5(1(0(4(2(2(x1))))))
, 5(1(2(2(x1)))) -> 5(1(2(0(4(2(x1))))))
, 0(1(1(4(5(x1))))) -> 3(1(0(4(1(5(x1))))))
, 0(1(2(2(2(x1))))) -> 1(0(2(2(5(2(x1))))))
, 0(1(2(2(5(x1))))) -> 1(5(0(4(2(2(x1))))))
, 0(1(2(4(5(x1))))) -> 2(5(1(0(4(5(x1))))))
, 0(1(4(5(2(x1))))) -> 1(0(4(2(0(5(x1))))))
, 0(1(4(5(5(x1))))) -> 5(0(4(0(1(5(x1))))))
, 0(1(5(4(5(x1))))) -> 1(5(0(4(1(5(x1))))))
, 0(5(1(2(2(x1))))) -> 0(1(3(2(5(2(x1))))))
, 3(3(1(2(2(x1))))) -> 1(3(2(0(3(2(x1))))))
, 3(4(4(0(5(x1))))) -> 3(5(4(5(0(4(x1))))))
, 5(0(1(2(2(x1))))) -> 1(3(2(0(5(2(x1))))))
, 5(1(2(2(5(x1))))) -> 1(5(2(3(2(5(x1))))))
, 5(2(1(2(2(x1))))) -> 2(1(3(5(2(2(x1))))))
, 5(2(4(0(5(x1))))) -> 0(4(2(5(5(5(x1))))))
, 5(2(4(0(5(x1))))) -> 0(4(5(4(2(5(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) -> 23
, 0_1(3) -> 1
, 0_1(3) -> 23
, 0_1(5) -> 4
, 0_1(6) -> 7
, 0_1(7) -> 13
, 0_1(12) -> 11
, 0_1(17) -> 16
, 0_1(19) -> 18
, 0_1(20) -> 27
, 0_1(22) -> 21
, 0_1(28) -> 27
, 1_0(2) -> 2
, 1_1(4) -> 3
, 1_1(7) -> 20
, 1_1(10) -> 9
, 1_1(11) -> 1
, 1_1(11) -> 23
, 1_1(11) -> 28
, 1_1(13) -> 18
, 1_1(14) -> 8
, 1_1(16) -> 13
, 1_1(21) -> 29
, 1_1(26) -> 25
, 1_1(32) -> 31
, 2_0(2) -> 2
, 2_1(2) -> 6
, 2_1(6) -> 5
, 2_1(7) -> 4
, 2_1(8) -> 3
, 2_1(9) -> 8
, 2_1(10) -> 15
, 2_1(13) -> 11
, 2_1(15) -> 5
, 2_1(16) -> 4
, 2_1(18) -> 1
, 2_1(18) -> 23
, 2_1(18) -> 28
, 2_1(23) -> 22
, 2_1(25) -> 18
, 2_1(28) -> 1
, 2_1(28) -> 28
, 2_1(28) -> 30
, 2_1(30) -> 12
, 3_0(2) -> 1
, 3_1(2) -> 10
, 3_1(4) -> 11
, 3_1(5) -> 12
, 3_1(6) -> 7
, 3_1(7) -> 24
, 3_1(12) -> 32
, 3_1(15) -> 14
, 3_1(20) -> 19
, 3_1(21) -> 13
, 3_1(22) -> 21
, 3_1(27) -> 26
, 3_1(28) -> 1
, 3_1(28) -> 28
, 3_1(30) -> 7
, 4_0(2) -> 2
, 4_1(5) -> 5
, 4_1(6) -> 17
, 4_1(29) -> 18
, 4_1(31) -> 1
, 4_1(31) -> 28
, 5_0(2) -> 1
, 5_1(2) -> 28
, 5_1(3) -> 1
, 5_1(3) -> 28
, 5_1(4) -> 11
, 5_1(5) -> 4
, 5_1(6) -> 28
, 5_1(24) -> 13}Tool RC1
stdout:
MAYBE
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:
{ 0(1(2(2(x1)))) -> 0(1(0(2(2(x1)))))
, 0(1(2(2(x1)))) -> 0(1(2(3(2(x1)))))
, 0(1(2(2(x1)))) -> 0(2(2(1(3(x1)))))
, 0(1(2(2(x1)))) -> 1(0(3(2(2(x1)))))
, 0(1(2(2(x1)))) -> 1(2(0(3(2(x1)))))
, 0(1(2(2(x1)))) -> 1(3(0(2(2(x1)))))
, 0(1(2(2(x1)))) -> 1(3(2(0(2(x1)))))
, 0(1(2(2(x1)))) -> 0(1(0(4(2(2(x1))))))
, 0(1(2(2(x1)))) -> 0(2(1(3(2(3(x1))))))
, 0(1(2(2(x1)))) -> 1(2(1(0(4(2(x1))))))
, 0(1(2(2(x1)))) -> 1(5(0(4(2(2(x1))))))
, 0(1(2(2(x1)))) -> 2(0(3(1(3(2(x1))))))
, 0(1(2(2(x1)))) -> 2(1(1(0(4(2(x1))))))
, 0(1(2(2(x1)))) -> 2(1(3(0(2(0(x1))))))
, 0(1(2(2(x1)))) -> 2(1(3(3(2(0(x1))))))
, 0(1(2(2(x1)))) -> 2(1(5(3(0(2(x1))))))
, 0(1(2(2(x1)))) -> 2(2(1(3(0(5(x1))))))
, 0(1(2(2(x1)))) -> 2(4(1(3(2(0(x1))))))
, 0(1(4(5(x1)))) -> 1(5(0(4(1(x1)))))
, 0(1(4(5(x1)))) -> 5(0(4(1(5(x1)))))
, 0(1(4(5(x1)))) -> 5(4(1(5(0(x1)))))
, 0(1(4(5(x1)))) -> 1(1(5(0(4(1(x1))))))
, 0(1(4(5(x1)))) -> 5(4(1(5(5(0(x1))))))
, 5(1(2(2(x1)))) -> 1(0(2(2(5(x1)))))
, 5(1(2(2(x1)))) -> 1(3(5(2(2(x1)))))
, 5(1(2(2(x1)))) -> 1(5(2(3(2(x1)))))
, 5(1(2(2(x1)))) -> 1(5(0(2(2(3(x1))))))
, 5(1(2(2(x1)))) -> 2(1(0(3(2(5(x1))))))
, 5(1(2(2(x1)))) -> 3(1(3(5(2(2(x1))))))
, 5(1(2(2(x1)))) -> 4(1(3(2(2(5(x1))))))
, 5(1(2(2(x1)))) -> 5(1(0(4(2(2(x1))))))
, 5(1(2(2(x1)))) -> 5(1(2(0(4(2(x1))))))
, 0(1(1(4(5(x1))))) -> 3(1(0(4(1(5(x1))))))
, 0(1(2(2(2(x1))))) -> 1(0(2(2(5(2(x1))))))
, 0(1(2(2(5(x1))))) -> 1(5(0(4(2(2(x1))))))
, 0(1(2(4(5(x1))))) -> 2(5(1(0(4(5(x1))))))
, 0(1(4(5(2(x1))))) -> 1(0(4(2(0(5(x1))))))
, 0(1(4(5(5(x1))))) -> 5(0(4(0(1(5(x1))))))
, 0(1(5(4(5(x1))))) -> 1(5(0(4(1(5(x1))))))
, 0(5(1(2(2(x1))))) -> 0(1(3(2(5(2(x1))))))
, 3(3(1(2(2(x1))))) -> 1(3(2(0(3(2(x1))))))
, 3(4(4(0(5(x1))))) -> 3(5(4(5(0(4(x1))))))
, 5(0(1(2(2(x1))))) -> 1(3(2(0(5(2(x1))))))
, 5(1(2(2(5(x1))))) -> 1(5(2(3(2(5(x1))))))
, 5(2(1(2(2(x1))))) -> 2(1(3(5(2(2(x1))))))
, 5(2(4(0(5(x1))))) -> 0(4(2(5(5(5(x1))))))
, 5(2(4(0(5(x1))))) -> 0(4(5(4(2(5(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(2(2(x1)))) -> 0(1(0(2(2(x1)))))
, 0(1(2(2(x1)))) -> 0(1(2(3(2(x1)))))
, 0(1(2(2(x1)))) -> 0(2(2(1(3(x1)))))
, 0(1(2(2(x1)))) -> 1(0(3(2(2(x1)))))
, 0(1(2(2(x1)))) -> 1(2(0(3(2(x1)))))
, 0(1(2(2(x1)))) -> 1(3(0(2(2(x1)))))
, 0(1(2(2(x1)))) -> 1(3(2(0(2(x1)))))
, 0(1(2(2(x1)))) -> 0(1(0(4(2(2(x1))))))
, 0(1(2(2(x1)))) -> 0(2(1(3(2(3(x1))))))
, 0(1(2(2(x1)))) -> 1(2(1(0(4(2(x1))))))
, 0(1(2(2(x1)))) -> 1(5(0(4(2(2(x1))))))
, 0(1(2(2(x1)))) -> 2(0(3(1(3(2(x1))))))
, 0(1(2(2(x1)))) -> 2(1(1(0(4(2(x1))))))
, 0(1(2(2(x1)))) -> 2(1(3(0(2(0(x1))))))
, 0(1(2(2(x1)))) -> 2(1(3(3(2(0(x1))))))
, 0(1(2(2(x1)))) -> 2(1(5(3(0(2(x1))))))
, 0(1(2(2(x1)))) -> 2(2(1(3(0(5(x1))))))
, 0(1(2(2(x1)))) -> 2(4(1(3(2(0(x1))))))
, 0(1(4(5(x1)))) -> 1(5(0(4(1(x1)))))
, 0(1(4(5(x1)))) -> 5(0(4(1(5(x1)))))
, 0(1(4(5(x1)))) -> 5(4(1(5(0(x1)))))
, 0(1(4(5(x1)))) -> 1(1(5(0(4(1(x1))))))
, 0(1(4(5(x1)))) -> 5(4(1(5(5(0(x1))))))
, 5(1(2(2(x1)))) -> 1(0(2(2(5(x1)))))
, 5(1(2(2(x1)))) -> 1(3(5(2(2(x1)))))
, 5(1(2(2(x1)))) -> 1(5(2(3(2(x1)))))
, 5(1(2(2(x1)))) -> 1(5(0(2(2(3(x1))))))
, 5(1(2(2(x1)))) -> 2(1(0(3(2(5(x1))))))
, 5(1(2(2(x1)))) -> 3(1(3(5(2(2(x1))))))
, 5(1(2(2(x1)))) -> 4(1(3(2(2(5(x1))))))
, 5(1(2(2(x1)))) -> 5(1(0(4(2(2(x1))))))
, 5(1(2(2(x1)))) -> 5(1(2(0(4(2(x1))))))
, 0(1(1(4(5(x1))))) -> 3(1(0(4(1(5(x1))))))
, 0(1(2(2(2(x1))))) -> 1(0(2(2(5(2(x1))))))
, 0(1(2(2(5(x1))))) -> 1(5(0(4(2(2(x1))))))
, 0(1(2(4(5(x1))))) -> 2(5(1(0(4(5(x1))))))
, 0(1(4(5(2(x1))))) -> 1(0(4(2(0(5(x1))))))
, 0(1(4(5(5(x1))))) -> 5(0(4(0(1(5(x1))))))
, 0(1(5(4(5(x1))))) -> 1(5(0(4(1(5(x1))))))
, 0(5(1(2(2(x1))))) -> 0(1(3(2(5(2(x1))))))
, 3(3(1(2(2(x1))))) -> 1(3(2(0(3(2(x1))))))
, 3(4(4(0(5(x1))))) -> 3(5(4(5(0(4(x1))))))
, 5(0(1(2(2(x1))))) -> 1(3(2(0(5(2(x1))))))
, 5(1(2(2(5(x1))))) -> 1(5(2(3(2(5(x1))))))
, 5(2(1(2(2(x1))))) -> 2(1(3(5(2(2(x1))))))
, 5(2(4(0(5(x1))))) -> 0(4(2(5(5(5(x1))))))
, 5(2(4(0(5(x1))))) -> 0(4(5(4(2(5(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) -> 23
, 0_1(3) -> 1
, 0_1(3) -> 23
, 0_1(5) -> 4
, 0_1(6) -> 7
, 0_1(7) -> 13
, 0_1(12) -> 11
, 0_1(17) -> 16
, 0_1(19) -> 18
, 0_1(20) -> 27
, 0_1(22) -> 21
, 0_1(28) -> 27
, 1_0(2) -> 2
, 1_1(4) -> 3
, 1_1(7) -> 20
, 1_1(10) -> 9
, 1_1(11) -> 1
, 1_1(11) -> 23
, 1_1(11) -> 28
, 1_1(13) -> 18
, 1_1(14) -> 8
, 1_1(16) -> 13
, 1_1(21) -> 29
, 1_1(26) -> 25
, 1_1(32) -> 31
, 2_0(2) -> 2
, 2_1(2) -> 6
, 2_1(6) -> 5
, 2_1(7) -> 4
, 2_1(8) -> 3
, 2_1(9) -> 8
, 2_1(10) -> 15
, 2_1(13) -> 11
, 2_1(15) -> 5
, 2_1(16) -> 4
, 2_1(18) -> 1
, 2_1(18) -> 23
, 2_1(18) -> 28
, 2_1(23) -> 22
, 2_1(25) -> 18
, 2_1(28) -> 1
, 2_1(28) -> 28
, 2_1(28) -> 30
, 2_1(30) -> 12
, 3_0(2) -> 1
, 3_1(2) -> 10
, 3_1(4) -> 11
, 3_1(5) -> 12
, 3_1(6) -> 7
, 3_1(7) -> 24
, 3_1(12) -> 32
, 3_1(15) -> 14
, 3_1(20) -> 19
, 3_1(21) -> 13
, 3_1(22) -> 21
, 3_1(27) -> 26
, 3_1(28) -> 1
, 3_1(28) -> 28
, 3_1(30) -> 7
, 4_0(2) -> 2
, 4_1(5) -> 5
, 4_1(6) -> 17
, 4_1(29) -> 18
, 4_1(31) -> 1
, 4_1(31) -> 28
, 5_0(2) -> 1
, 5_1(2) -> 28
, 5_1(3) -> 1
, 5_1(3) -> 28
, 5_1(4) -> 11
, 5_1(5) -> 4
, 5_1(6) -> 28
, 5_1(24) -> 13}