Certification Problem
Input (TPDB Runtime_Complexity_Innermost_Rewriting/SK90/2.54)
The rewrite relation of the following TRS is considered.
|
f(x,a) |
→ |
x |
(1) |
|
f(x,g(y)) |
→ |
f(g(x),y) |
(2) |
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}
-
transitions:
|
a0
|
→ |
0 |
|
g0(0) |
→ |
0 |
|
f0(0,0) |
→ |
1 |
|
g1(0) |
→ |
2 |
|
f1(2,0) |
→ |
1 |
|
g1(2) |
→ |
2 |
| 0 |
→ |
1 |
| 2 |
→ |
1 |