Tool CaT
stdout:
YES(?,O(n^1))
Problem:
0(*(x1)) -> *(1(x1))
1(*(x1)) -> 0(#(x1))
#(0(x1)) -> 0(#(x1))
#(1(x1)) -> 1(#(x1))
#($(x1)) -> *($(x1))
#(#(x1)) -> #(x1)
#(*(x1)) -> *(x1)
Proof:
Bounds Processor:
bound: 2
enrichment: match
automaton:
final states: {5,4,3}
transitions:
*1(42) -> 43*
*1(27) -> 28*
*1(7) -> 8*
*1(36) -> 37*
$1(34) -> 35*
$1(26) -> 27*
01(17) -> 18*
#1(24) -> 25*
#1(16) -> 17*
11(14) -> 15*
11(6) -> 7*
*2(48) -> 49*
00(2) -> 3*
00(1) -> 3*
12(50) -> 51*
12(47) -> 48*
12(56) -> 57*
*0(2) -> 1*
*0(1) -> 1*
10(2) -> 4*
10(1) -> 4*
#0(2) -> 5*
#0(1) -> 5*
$0(2) -> 2*
$0(1) -> 2*
1 -> 42,34,24,14
2 -> 36,26,16,6
8 -> 3*
15 -> 7*
18 -> 48,15,7,4
25 -> 17*
27 -> 50*
28 -> 17,5
35 -> 27*
36 -> 56*
37 -> 25,17,5
42 -> 47*
43 -> 25,17,5
49 -> 18,4,15
51 -> 48*
57 -> 48*
problem:
QedTool IRC1
stdout:
YES(?,O(n^1))
Tool IRC2
stdout:
YES(?,O(n^1))
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost runtime-complexity with respect to
Rules:
{ 0(*(x1)) -> *(1(x1))
, 1(*(x1)) -> 0(#(x1))
, #(0(x1)) -> 0(#(x1))
, #(1(x1)) -> 1(#(x1))
, #($(x1)) -> *($(x1))
, #(#(x1)) -> #(x1)
, #(*(x1)) -> *(x1)}
Proof Output:
'Bounds with perSymbol-enrichment and initial automaton 'match'' proved the best result:
Details:
--------
'Bounds with perSymbol-enrichment and initial automaton 'match'' succeeded with the following output:
'Bounds with perSymbol-enrichment and initial automaton 'match''
----------------------------------------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost runtime-complexity with respect to
Rules:
{ 0(*(x1)) -> *(1(x1))
, 1(*(x1)) -> 0(#(x1))
, #(0(x1)) -> 0(#(x1))
, #(1(x1)) -> 1(#(x1))
, #($(x1)) -> *($(x1))
, #(#(x1)) -> #(x1)
, #(*(x1)) -> *(x1)}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ 0_0(2) -> 1
, 0_0(5) -> 1
, 0_1(7) -> 3
, 0_1(7) -> 6
, 0_1(7) -> 9
, *_0(2) -> 2
, *_0(5) -> 2
, *_1(2) -> 4
, *_1(2) -> 7
, *_1(5) -> 4
, *_1(5) -> 7
, *_1(6) -> 1
, *_1(8) -> 4
, *_1(8) -> 7
, *_2(9) -> 3
, *_2(9) -> 6
, *_2(9) -> 9
, 1_0(2) -> 3
, 1_0(5) -> 3
, 1_1(2) -> 6
, 1_1(5) -> 6
, 1_2(2) -> 9
, 1_2(5) -> 9
, 1_2(8) -> 9
, #_0(2) -> 4
, #_0(5) -> 4
, #_1(2) -> 7
, #_1(5) -> 7
, $_0(2) -> 5
, $_0(5) -> 5
, $_1(2) -> 8
, $_1(5) -> 8}Tool RC1
stdout:
YES(?,O(n^1))
Tool RC2
stdout:
YES(?,O(n^1))
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: YES(?,O(n^1))
Input Problem: runtime-complexity with respect to
Rules:
{ 0(*(x1)) -> *(1(x1))
, 1(*(x1)) -> 0(#(x1))
, #(0(x1)) -> 0(#(x1))
, #(1(x1)) -> 1(#(x1))
, #($(x1)) -> *($(x1))
, #(#(x1)) -> #(x1)
, #(*(x1)) -> *(x1)}
Proof Output:
'Bounds with perSymbol-enrichment and initial automaton 'match'' proved the best result:
Details:
--------
'Bounds with perSymbol-enrichment and initial automaton 'match'' succeeded with the following output:
'Bounds with perSymbol-enrichment and initial automaton 'match''
----------------------------------------------------------------
Answer: YES(?,O(n^1))
Input Problem: runtime-complexity with respect to
Rules:
{ 0(*(x1)) -> *(1(x1))
, 1(*(x1)) -> 0(#(x1))
, #(0(x1)) -> 0(#(x1))
, #(1(x1)) -> 1(#(x1))
, #($(x1)) -> *($(x1))
, #(#(x1)) -> #(x1)
, #(*(x1)) -> *(x1)}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ 0_0(2) -> 1
, 0_0(5) -> 1
, 0_1(7) -> 3
, 0_1(7) -> 6
, 0_1(7) -> 9
, *_0(2) -> 2
, *_0(5) -> 2
, *_1(2) -> 4
, *_1(2) -> 7
, *_1(5) -> 4
, *_1(5) -> 7
, *_1(6) -> 1
, *_1(8) -> 4
, *_1(8) -> 7
, *_2(9) -> 3
, *_2(9) -> 6
, *_2(9) -> 9
, 1_0(2) -> 3
, 1_0(5) -> 3
, 1_1(2) -> 6
, 1_1(5) -> 6
, 1_2(2) -> 9
, 1_2(5) -> 9
, 1_2(8) -> 9
, #_0(2) -> 4
, #_0(5) -> 4
, #_1(2) -> 7
, #_1(5) -> 7
, $_0(2) -> 5
, $_0(5) -> 5
, $_1(2) -> 8
, $_1(5) -> 8}