Certification Problem
Input (TPDB Runtime_Complexity_Innermost_Rewriting/Mixed_TRS/jones4)
The rewrite relation of the following TRS is considered.
|
p(m,n,s(r)) |
→ |
p(m,r,n) |
(1) |
|
p(m,s(n),0) |
→ |
p(0,n,m) |
(2) |
|
p(m,0,0) |
→ |
m |
(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}
-
transitions:
|
s0(0) |
→ |
0 |
|
00
|
→ |
0 |
|
p0(0,0,0) |
→ |
1 |
|
p1(0,0,0) |
→ |
1 |
|
01
|
→ |
2 |
|
p1(2,0,0) |
→ |
1 |
|
p1(2,0,2) |
→ |
1 |
| 0 |
→ |
1 |
| 2 |
→ |
1 |