Tool CaT
stdout:
YES(?,O(n^1))
Problem:
b(c(a(x1))) -> a(b(a(b(c(x1)))))
b(x1) -> c(c(x1))
c(d(x1)) -> a(b(c(a(x1))))
a(a(x1)) -> a(c(b(a(x1))))
Proof:
Bounds Processor:
bound: 3
enrichment: match
automaton:
final states: {4,3,2}
transitions:
a1(14) -> 15*
a1(11) -> 12*
b1(13) -> 14*
c1(12) -> 13*
c1(9) -> 10*
c1(8) -> 9*
c2(27) -> 28*
c2(34) -> 35*
c2(56) -> 57*
c2(33) -> 34*
a2(57) -> 58*
a2(29) -> 30*
a2(31) -> 32*
b0(1) -> 2*
b2(55) -> 56*
b2(30) -> 31*
b2(28) -> 29*
c0(1) -> 3*
c3(60) -> 61*
c3(40) -> 41*
c3(59) -> 60*
c3(49) -> 50*
c3(39) -> 40*
c3(48) -> 49*
a0(1) -> 4*
d0(1) -> 1*
1 -> 11,8
10 -> 2*
11 -> 27*
13 -> 33*
15 -> 28,9,3
28 -> 39*
30 -> 48*
32 -> 55,14
35 -> 14*
41 -> 29*
50 -> 31*
55 -> 59*
58 -> 15,3,9
61 -> 56*
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:
{ b(c(a(x1))) -> a(b(a(b(c(x1)))))
, b(x1) -> c(c(x1))
, c(d(x1)) -> a(b(c(a(x1))))
, a(a(x1)) -> a(c(b(a(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:
{ b(c(a(x1))) -> a(b(a(b(c(x1)))))
, b(x1) -> c(c(x1))
, c(d(x1)) -> a(b(c(a(x1))))
, a(a(x1)) -> a(c(b(a(x1))))}
Proof Output:
The problem is match-bounded by 3.
The enriched problem is compatible with the following automaton:
{ b_0(2) -> 1
, b_1(5) -> 4
, b_2(4) -> 15
, b_2(8) -> 7
, b_2(10) -> 9
, c_0(2) -> 1
, c_1(2) -> 3
, c_1(3) -> 1
, c_1(6) -> 5
, c_2(2) -> 10
, c_2(5) -> 11
, c_2(11) -> 4
, c_2(15) -> 14
, c_3(4) -> 16
, c_3(8) -> 12
, c_3(10) -> 13
, c_3(12) -> 7
, c_3(13) -> 9
, c_3(16) -> 15
, a_0(2) -> 1
, a_1(2) -> 6
, a_1(4) -> 1
, a_1(4) -> 3
, a_1(4) -> 10
, a_2(7) -> 4
, a_2(9) -> 8
, a_2(14) -> 1
, a_2(14) -> 3
, a_2(14) -> 10
, d_0(2) -> 2}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:
{ b(c(a(x1))) -> a(b(a(b(c(x1)))))
, b(x1) -> c(c(x1))
, c(d(x1)) -> a(b(c(a(x1))))
, a(a(x1)) -> a(c(b(a(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:
{ b(c(a(x1))) -> a(b(a(b(c(x1)))))
, b(x1) -> c(c(x1))
, c(d(x1)) -> a(b(c(a(x1))))
, a(a(x1)) -> a(c(b(a(x1))))}
Proof Output:
The problem is match-bounded by 3.
The enriched problem is compatible with the following automaton:
{ b_0(4) -> 1
, b_1(7) -> 6
, b_2(6) -> 17
, b_2(10) -> 9
, b_2(12) -> 11
, c_0(4) -> 2
, c_1(4) -> 5
, c_1(5) -> 1
, c_1(8) -> 7
, c_2(4) -> 12
, c_2(7) -> 13
, c_2(13) -> 6
, c_2(17) -> 16
, c_3(6) -> 18
, c_3(10) -> 14
, c_3(12) -> 15
, c_3(14) -> 9
, c_3(15) -> 11
, c_3(18) -> 17
, a_0(4) -> 3
, a_1(4) -> 8
, a_1(6) -> 2
, a_1(6) -> 5
, a_1(6) -> 12
, a_2(9) -> 6
, a_2(11) -> 10
, a_2(16) -> 2
, a_2(16) -> 5
, a_2(16) -> 12
, d_0(4) -> 4}