* Step 1: Sum WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
add0(0(),x2) -> x2
add0(S(x),x2) -> +(S(0()),add0(x2,x))
- Weak TRS:
+(x,S(0())) -> S(x)
+(S(0()),y) -> S(y)
- Signature:
{+/2,add0/2} / {0/0,S/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {+,add0} and constructors {0,S}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
add0(0(),x2) -> x2
add0(S(x),x2) -> +(S(0()),add0(x2,x))
- Weak TRS:
+(x,S(0())) -> S(x)
+(S(0()),y) -> S(y)
- Signature:
{+/2,add0/2} / {0/0,S/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {+,add0} and constructors {0,S}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 1.
The enriched problem is compatible with follwoing automaton.
+_0(2,2) -> 1
+_1(3,4) -> 1
+_1(3,4) -> 4
0_0() -> 1
0_0() -> 2
0_0() -> 4
0_1() -> 5
S_0(2) -> 1
S_0(2) -> 2
S_0(2) -> 4
S_1(3) -> 1
S_1(3) -> 4
S_1(4) -> 1
S_1(4) -> 4
S_1(5) -> 3
add0_0(2,2) -> 1
add0_1(2,2) -> 4
2 -> 1
2 -> 4
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
+(x,S(0())) -> S(x)
+(S(0()),y) -> S(y)
add0(0(),x2) -> x2
add0(S(x),x2) -> +(S(0()),add0(x2,x))
- Signature:
{+/2,add0/2} / {0/0,S/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {+,add0} and constructors {0,S}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).
WORST_CASE(?,O(n^1))