Certification Problem
Input (TPDB Runtime_Complexity_Innermost_Rewriting/Mixed_TRS/jones1)
The rewrite relation of the following TRS is considered.
|
rev(ls) |
→ |
r1(ls,empty) |
(1) |
|
r1(empty,a) |
→ |
a |
(2) |
|
r1(cons(x,k),a) |
→ |
r1(k,cons(x,a)) |
(3) |
The evaluation strategy is innermost.Property / Task
Determine bounds on the runtime complexity.Answer / Result
An upperbound for the complexity is O(n).Proof (by AProVE @ termCOMP 2023)
1 Bounds
The given TRS is
match-(raise)-bounded by 1.
This is shown by the following automaton.
-
final states:
{0, 1, 2}
-
transitions:
|
empty0
|
→ |
0 |
|
cons0(0,0) |
→ |
0 |
|
rev0(0) |
→ |
1 |
|
r10(0,0) |
→ |
2 |
|
empty1
|
→ |
3 |
|
r11(0,3) |
→ |
1 |
|
cons1(0,0) |
→ |
4 |
|
r11(0,4) |
→ |
2 |
|
cons1(0,3) |
→ |
4 |
|
r11(0,4) |
→ |
1 |
|
cons1(0,4) |
→ |
4 |
| 0 |
→ |
2 |
| 3 |
→ |
1 |
| 4 |
→ |
2 |
| 4 |
→ |
1 |