Tool CaT
stdout:
YES(?,O(n^1))
Problem:
rev(ls) -> r1(ls,empty())
r1(empty(),a) -> a
r1(cons(x,k),a) -> r1(k,cons(x,a))
Proof:
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {4,3}
transitions:
r11(1,10) -> 4*
r11(2,5) -> 3*
r11(2,7) -> 4*
r11(1,5) -> 3*
r11(1,7) -> 4*
r11(2,10) -> 4*
cons1(1,2) -> 7*
cons1(1,10) -> 7*
cons1(2,1) -> 7*
cons1(2,5) -> 5*
cons1(2,7) -> 7*
cons1(1,1) -> 7*
cons1(1,5) -> 5*
cons1(1,7) -> 7*
cons1(2,2) -> 10*
cons1(2,10) -> 7*
empty1() -> 5*
rev0(2) -> 3*
rev0(1) -> 3*
r10(1,2) -> 4*
r10(2,1) -> 4*
r10(1,1) -> 4*
r10(2,2) -> 4*
empty0() -> 1*
cons0(1,2) -> 2*
cons0(2,1) -> 2*
cons0(1,1) -> 2*
cons0(2,2) -> 2*
1 -> 4*
2 -> 4*
5 -> 3*
7 -> 4*
10 -> 4*
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:
{ rev(ls) -> r1(ls, empty())
, r1(empty(), a) -> a
, r1(cons(x, k), a) -> r1(k, cons(x, a))}
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:
{ rev(ls) -> r1(ls, empty())
, r1(empty(), a) -> a
, r1(cons(x, k), a) -> r1(k, cons(x, a))}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ rev_0(2) -> 1
, r1_0(2, 2) -> 1
, r1_1(2, 3) -> 1
, empty_0() -> 1
, empty_0() -> 2
, empty_1() -> 1
, empty_1() -> 3
, cons_0(2, 2) -> 1
, cons_0(2, 2) -> 2
, cons_1(2, 2) -> 1
, cons_1(2, 2) -> 3
, cons_1(2, 3) -> 1
, cons_1(2, 3) -> 3}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:
{ rev(ls) -> r1(ls, empty())
, r1(empty(), a) -> a
, r1(cons(x, k), a) -> r1(k, cons(x, a))}
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:
{ rev(ls) -> r1(ls, empty())
, r1(empty(), a) -> a
, r1(cons(x, k), a) -> r1(k, cons(x, a))}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ rev_0(2) -> 1
, r1_0(2, 2) -> 1
, r1_1(2, 3) -> 1
, empty_0() -> 1
, empty_0() -> 2
, empty_1() -> 1
, empty_1() -> 3
, cons_0(2, 2) -> 1
, cons_0(2, 2) -> 2
, cons_1(2, 2) -> 1
, cons_1(2, 2) -> 3
, cons_1(2, 3) -> 1
, cons_1(2, 3) -> 3}