Tool CaT
stdout:
YES(?,O(n^1))
Problem:
f(s(x)) -> s(s(f(p(s(x)))))
f(0()) -> 0()
p(s(x)) -> x
Proof:
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {4,3}
transitions:
01() -> 21*
s1(5) -> 6*
s1(19) -> 20*
s1(9) -> 10*
s1(8) -> 9*
f1(7) -> 8*
p1(6) -> 7*
f0(2) -> 3*
f0(1) -> 3*
s0(2) -> 1*
s0(1) -> 1*
p0(2) -> 4*
p0(1) -> 4*
00() -> 2*
1 -> 4,19
2 -> 4,5
5 -> 7*
10 -> 8,3
19 -> 7*
20 -> 6*
21 -> 8,3
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:
{ f(s(x)) -> s(s(f(p(s(x)))))
, f(0()) -> 0()
, p(s(x)) -> x}
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:
{ f(s(x)) -> s(s(f(p(s(x)))))
, f(0()) -> 0()
, p(s(x)) -> x}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ f_0(2) -> 1
, f_0(4) -> 1
, f_1(7) -> 6
, s_0(2) -> 2
, s_0(2) -> 3
, s_0(2) -> 7
, s_0(4) -> 2
, s_0(4) -> 3
, s_0(4) -> 7
, s_1(2) -> 8
, s_1(4) -> 8
, s_1(5) -> 1
, s_1(5) -> 6
, s_1(6) -> 5
, p_0(2) -> 3
, p_0(4) -> 3
, p_1(8) -> 7
, 0_0() -> 3
, 0_0() -> 4
, 0_0() -> 7
, 0_1() -> 1
, 0_1() -> 6}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:
{ f(s(x)) -> s(s(f(p(s(x)))))
, f(0()) -> 0()
, p(s(x)) -> x}
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:
{ f(s(x)) -> s(s(f(p(s(x)))))
, f(0()) -> 0()
, p(s(x)) -> x}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ f_0(2) -> 1
, f_1(5) -> 4
, s_0(2) -> 1
, s_0(2) -> 2
, s_0(2) -> 5
, s_1(2) -> 6
, s_1(3) -> 1
, s_1(3) -> 4
, s_1(4) -> 3
, p_0(2) -> 1
, p_1(6) -> 5
, 0_0() -> 1
, 0_0() -> 2
, 0_0() -> 5
, 0_1() -> 1
, 0_1() -> 4}