Tool CaT
stdout:
YES(?,O(n^1))
Problem:
a(b(c(x1))) -> a(a(b(x1)))
a(b(c(x1))) -> b(c(b(c(x1))))
a(b(c(x1))) -> c(b(c(a(x1))))
Proof:
Bounds Processor:
bound: 3
enrichment: match
automaton:
final states: {3}
transitions:
c3(187) -> 188*
c3(182) -> 183*
c3(172) -> 173*
c3(147) -> 148*
c3(139) -> 140*
c3(141) -> 142*
c3(185) -> 186*
c3(170) -> 171*
c3(145) -> 146*
c1(31) -> 32*
c1(16) -> 17*
c1(33) -> 34*
c1(28) -> 29*
c1(18) -> 19*
b3(162) -> 163*
b3(142) -> 143*
b3(186) -> 187*
b3(171) -> 172*
b3(166) -> 167*
b3(146) -> 147*
b3(126) -> 127*
b3(173) -> 174*
b3(140) -> 141*
b1(32) -> 33*
b1(17) -> 18*
b1(19) -> 20*
b1(14) -> 15*
b1(4) -> 5*
a3(127) -> 128*
a3(184) -> 185*
a3(164) -> 165*
a3(144) -> 145*
a3(196) -> 197*
a3(163) -> 164*
a3(128) -> 129*
a1(30) -> 31*
a1(5) -> 6*
a1(42) -> 43*
a1(6) -> 7*
c2(65) -> 66*
c2(97) -> 98*
c2(52) -> 53*
c2(109) -> 110*
c2(54) -> 55*
c2(111) -> 112*
c2(86) -> 87*
c2(63) -> 64*
c2(100) -> 101*
c2(95) -> 96*
a0(2) -> 3*
a0(1) -> 3*
b2(55) -> 56*
b2(84) -> 85*
b2(74) -> 75*
b2(64) -> 65*
b2(44) -> 45*
b2(96) -> 97*
b2(76) -> 77*
b2(98) -> 99*
b2(53) -> 54*
b2(130) -> 131*
b2(110) -> 111*
b0(2) -> 1*
b0(1) -> 1*
a2(45) -> 46*
a2(77) -> 78*
a2(62) -> 63*
a2(156) -> 157*
a2(106) -> 107*
a2(46) -> 47*
a2(108) -> 109*
a2(120) -> 121*
c0(2) -> 2*
c0(1) -> 2*
1 -> 42,28,14
2 -> 30,16,4
7 -> 78,109,62,6,43,3
15 -> 5*
16 -> 120,100,84
18 -> 62,52,44
20 -> 78,109,62,6,43,3
28 -> 108,95,76
29 -> 17*
34 -> 78,109,62,6,43,3
43 -> 31*
47 -> 7,6,3,43,31
52 -> 144,139,126
54 -> 196,182,166,106,74
56 -> 86,7,6,3,43,31
63 -> 145*
66 -> 7,6,3,43,31
75 -> 45*
78 -> 62*
85 -> 77*
86 -> 184,170,162,156,130
87 -> 55*
99 -> 63*
101 -> 96*
107 -> 63*
112 -> 63*
121 -> 109*
129 -> 197,185,107,63
131 -> 45*
143 -> 197,185,107,63
148 -> 197,185,107,63
157 -> 63*
165 -> 185,157
167 -> 163*
174 -> 185,157
183 -> 171*
188 -> 185,157
197 -> 185*
problem:
QedTool IRC1
stdout:
MAYBE
Tool IRC2
stdout:
TIMEOUT
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: TIMEOUT
Input Problem: innermost runtime-complexity with respect to
Rules:
{ a(b(c(x1))) -> a(a(b(x1)))
, a(b(c(x1))) -> b(c(b(c(x1))))
, a(b(c(x1))) -> c(b(c(a(x1))))}
Proof Output:
Computation stopped due to timeout after 60.0 secondsTool RC1
stdout:
MAYBE
Tool RC2
stdout:
TIMEOUT
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: TIMEOUT
Input Problem: runtime-complexity with respect to
Rules:
{ a(b(c(x1))) -> a(a(b(x1)))
, a(b(c(x1))) -> b(c(b(c(x1))))
, a(b(c(x1))) -> c(b(c(a(x1))))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds