Tool CaT
stdout:
YES(?,O(n^1))
Problem:
c(c(c(y))) -> c(c(a(y,0())))
c(a(a(0(),x),y)) -> a(c(c(c(0()))),y)
c(y) -> y
Proof:
Bounds Processor:
bound: 2
enrichment: match
automaton:
final states: {3}
transitions:
a1(11,2) -> 3*
a1(11,1) -> 3*
c1(10) -> 11*
c1(9) -> 10*
c1(8) -> 9*
01() -> 8*
c2(17) -> 11*
c2(16) -> 17*
c0(2) -> 3*
c0(1) -> 3*
a2(8,15) -> 16*
a0(1,2) -> 1*
a0(2,1) -> 1*
a0(1,1) -> 1*
a0(2,2) -> 1*
02() -> 15*
00() -> 2*
1 -> 3*
2 -> 3*
8 -> 9*
9 -> 10*
10 -> 11*
16 -> 17*
17 -> 11*
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:
{ c(c(c(y))) -> c(c(a(y, 0())))
, c(a(a(0(), x), y)) -> a(c(c(c(0()))), y)
, c(y) -> y}
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:
{ c(c(c(y))) -> c(c(a(y, 0())))
, c(a(a(0(), x), y)) -> a(c(c(c(0()))), y)
, c(y) -> y}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ c_0(2) -> 1
, c_1(4) -> 3
, c_1(5) -> 3
, c_1(5) -> 4
, c_1(6) -> 3
, c_1(6) -> 4
, c_1(6) -> 5
, c_2(7) -> 3
, c_2(8) -> 3
, c_2(8) -> 7
, a_0(2, 2) -> 1
, a_0(2, 2) -> 2
, a_1(3, 2) -> 1
, a_2(6, 9) -> 3
, a_2(6, 9) -> 7
, a_2(6, 9) -> 8
, 0_0() -> 1
, 0_0() -> 2
, 0_1() -> 3
, 0_1() -> 4
, 0_1() -> 5
, 0_1() -> 6
, 0_2() -> 9}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:
{ c(c(c(y))) -> c(c(a(y, 0())))
, c(a(a(0(), x), y)) -> a(c(c(c(0()))), y)
, c(y) -> y}
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:
{ c(c(c(y))) -> c(c(a(y, 0())))
, c(a(a(0(), x), y)) -> a(c(c(c(0()))), y)
, c(y) -> y}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ c_0(2) -> 1
, c_1(4) -> 3
, c_1(5) -> 3
, c_1(5) -> 4
, c_1(6) -> 3
, c_1(6) -> 4
, c_1(6) -> 5
, c_2(7) -> 3
, c_2(8) -> 3
, c_2(8) -> 7
, a_0(2, 2) -> 1
, a_0(2, 2) -> 2
, a_1(3, 2) -> 1
, a_2(6, 9) -> 3
, a_2(6, 9) -> 7
, a_2(6, 9) -> 8
, 0_0() -> 1
, 0_0() -> 2
, 0_1() -> 3
, 0_1() -> 4
, 0_1() -> 5
, 0_1() -> 6
, 0_2() -> 9}