Tool CaT
stdout:
YES(?,O(n^1))
Problem:
q(0(x1)) -> p(p(s(s(0(s(s(s(s(x1)))))))))
q(s(x1)) -> p(p(s(s(s(s(s(s(r(p(p(s(s(x1)))))))))))))
r(0(x1)) -> p(s(p(s(0(p(p(p(s(s(s(x1)))))))))))
r(s(x1)) -> p(s(p(s(s(q(p(s(p(s(x1))))))))))
p(p(s(x1))) -> p(x1)
p(s(x1)) -> x1
p(0(x1)) -> 0(s(s(s(x1))))
Proof:
Bounds Processor:
bound: 2
enrichment: match
automaton:
final states: {5,4,3}
transitions:
01(10) -> 11*
01(78) -> 79*
01(58) -> 59*
s1(65) -> 66*
s1(35) -> 36*
s1(12) -> 13*
s1(7) -> 8*
s1(59) -> 60*
s1(34) -> 35*
s1(9) -> 10*
s1(61) -> 62*
s1(36) -> 37*
s1(11) -> 12*
s1(6) -> 7*
s1(68) -> 69*
s1(33) -> 34*
s1(28) -> 29*
s1(8) -> 9*
p1(60) -> 61*
p1(55) -> 56*
p1(30) -> 31*
p1(62) -> 63*
p1(57) -> 58*
p1(64) -> 65*
p1(14) -> 15*
p1(66) -> 67*
p1(56) -> 57*
p1(31) -> 32*
p1(13) -> 14*
q1(67) -> 68*
r1(32) -> 33*
p2(80) -> 81*
p2(86) -> 87*
p2(88) -> 89*
q0(2) -> 3*
q0(1) -> 3*
00(2) -> 1*
00(1) -> 1*
p0(2) -> 5*
p0(1) -> 5*
s0(2) -> 2*
s0(1) -> 2*
r0(2) -> 4*
r0(1) -> 4*
1 -> 5,28
2 -> 5,6
6 -> 87,65
7 -> 89,57,31,86,64
8 -> 56,88,30
9 -> 78,55
11 -> 81,15
12 -> 14,80
15 -> 68,3
28 -> 87,65
29 -> 7*
37 -> 11*
59 -> 61*
61 -> 63*
63 -> 33,4
65 -> 67*
69 -> 59*
79 -> 5*
81 -> 15,3
87 -> 58,32
89 -> 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:
{ q(0(x1)) -> p(p(s(s(0(s(s(s(s(x1)))))))))
, q(s(x1)) -> p(p(s(s(s(s(s(s(r(p(p(s(s(x1)))))))))))))
, r(0(x1)) -> p(s(p(s(0(p(p(p(s(s(s(x1)))))))))))
, r(s(x1)) -> p(s(p(s(s(q(p(s(p(s(x1))))))))))
, p(p(s(x1))) -> p(x1)
, p(s(x1)) -> x1
, p(0(x1)) -> 0(s(s(s(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:
{ q(0(x1)) -> p(p(s(s(0(s(s(s(s(x1)))))))))
, q(s(x1)) -> p(p(s(s(s(s(s(s(r(p(p(s(s(x1)))))))))))))
, r(0(x1)) -> p(s(p(s(0(p(p(p(s(s(s(x1)))))))))))
, r(s(x1)) -> p(s(p(s(s(q(p(s(p(s(x1))))))))))
, p(p(s(x1))) -> p(x1)
, p(s(x1)) -> x1
, p(0(x1)) -> 0(s(s(s(x1))))}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ q_0(2) -> 1
, q_1(24) -> 14
, q_1(24) -> 23
, 0_0(2) -> 1
, 0_0(2) -> 2
, 0_0(2) -> 15
, 0_0(2) -> 20
, 0_0(2) -> 24
, 0_0(2) -> 26
, 0_1(7) -> 1
, 0_1(7) -> 6
, 0_1(7) -> 14
, 0_1(7) -> 23
, 0_1(8) -> 1
, 0_1(20) -> 1
, 0_1(20) -> 14
, 0_1(20) -> 17
, 0_1(20) -> 19
, 0_1(20) -> 23
, 0_2(27) -> 14
, p_0(2) -> 1
, p_1(3) -> 1
, p_1(3) -> 14
, p_1(3) -> 23
, p_1(4) -> 3
, p_1(8) -> 22
, p_1(9) -> 16
, p_1(10) -> 24
, p_1(10) -> 26
, p_1(16) -> 15
, p_1(18) -> 1
, p_1(18) -> 14
, p_1(18) -> 17
, p_1(18) -> 23
, p_1(19) -> 14
, p_1(21) -> 20
, p_1(22) -> 21
, p_1(25) -> 24
, p_2(5) -> 1
, p_2(5) -> 14
, p_2(5) -> 23
, p_2(9) -> 21
, p_2(10) -> 15
, p_2(10) -> 20
, s_0(2) -> 1
, s_0(2) -> 2
, s_0(2) -> 15
, s_0(2) -> 20
, s_0(2) -> 24
, s_0(2) -> 26
, s_1(2) -> 10
, s_1(2) -> 16
, s_1(2) -> 21
, s_1(5) -> 4
, s_1(6) -> 3
, s_1(6) -> 5
, s_1(8) -> 7
, s_1(9) -> 8
, s_1(10) -> 9
, s_1(10) -> 22
, s_1(11) -> 1
, s_1(11) -> 6
, s_1(11) -> 14
, s_1(11) -> 23
, s_1(12) -> 11
, s_1(13) -> 12
, s_1(14) -> 13
, s_1(17) -> 3
, s_1(19) -> 18
, s_1(23) -> 1
, s_1(23) -> 14
, s_1(23) -> 17
, s_1(23) -> 19
, s_1(23) -> 23
, s_1(26) -> 25
, s_2(20) -> 29
, s_2(28) -> 27
, s_2(29) -> 28
, r_0(2) -> 1
, r_1(15) -> 14}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:
{ q(0(x1)) -> p(p(s(s(0(s(s(s(s(x1)))))))))
, q(s(x1)) -> p(p(s(s(s(s(s(s(r(p(p(s(s(x1)))))))))))))
, r(0(x1)) -> p(s(p(s(0(p(p(p(s(s(s(x1)))))))))))
, r(s(x1)) -> p(s(p(s(s(q(p(s(p(s(x1))))))))))
, p(p(s(x1))) -> p(x1)
, p(s(x1)) -> x1
, p(0(x1)) -> 0(s(s(s(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:
{ q(0(x1)) -> p(p(s(s(0(s(s(s(s(x1)))))))))
, q(s(x1)) -> p(p(s(s(s(s(s(s(r(p(p(s(s(x1)))))))))))))
, r(0(x1)) -> p(s(p(s(0(p(p(p(s(s(s(x1)))))))))))
, r(s(x1)) -> p(s(p(s(s(q(p(s(p(s(x1))))))))))
, p(p(s(x1))) -> p(x1)
, p(s(x1)) -> x1
, p(0(x1)) -> 0(s(s(s(x1))))}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ q_0(2) -> 1
, q_1(24) -> 14
, q_1(24) -> 23
, 0_0(2) -> 1
, 0_0(2) -> 2
, 0_0(2) -> 15
, 0_0(2) -> 20
, 0_0(2) -> 24
, 0_0(2) -> 26
, 0_1(7) -> 1
, 0_1(7) -> 6
, 0_1(7) -> 14
, 0_1(7) -> 23
, 0_1(8) -> 1
, 0_1(20) -> 1
, 0_1(20) -> 14
, 0_1(20) -> 17
, 0_1(20) -> 19
, 0_1(20) -> 23
, 0_2(27) -> 14
, p_0(2) -> 1
, p_1(3) -> 1
, p_1(3) -> 14
, p_1(3) -> 23
, p_1(4) -> 3
, p_1(8) -> 22
, p_1(9) -> 16
, p_1(10) -> 24
, p_1(10) -> 26
, p_1(16) -> 15
, p_1(18) -> 1
, p_1(18) -> 14
, p_1(18) -> 17
, p_1(18) -> 23
, p_1(19) -> 14
, p_1(21) -> 20
, p_1(22) -> 21
, p_1(25) -> 24
, p_2(5) -> 1
, p_2(5) -> 14
, p_2(5) -> 23
, p_2(9) -> 21
, p_2(10) -> 15
, p_2(10) -> 20
, s_0(2) -> 1
, s_0(2) -> 2
, s_0(2) -> 15
, s_0(2) -> 20
, s_0(2) -> 24
, s_0(2) -> 26
, s_1(2) -> 10
, s_1(2) -> 16
, s_1(2) -> 21
, s_1(5) -> 4
, s_1(6) -> 3
, s_1(6) -> 5
, s_1(8) -> 7
, s_1(9) -> 8
, s_1(10) -> 9
, s_1(10) -> 22
, s_1(11) -> 1
, s_1(11) -> 6
, s_1(11) -> 14
, s_1(11) -> 23
, s_1(12) -> 11
, s_1(13) -> 12
, s_1(14) -> 13
, s_1(17) -> 3
, s_1(19) -> 18
, s_1(23) -> 1
, s_1(23) -> 14
, s_1(23) -> 17
, s_1(23) -> 19
, s_1(23) -> 23
, s_1(26) -> 25
, s_2(20) -> 29
, s_2(28) -> 27
, s_2(29) -> 28
, r_0(2) -> 1
, r_1(15) -> 14}