* Step 1: Sum WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
f(0()) -> cons(0())
f(s(0())) -> f(p(s(0())))
p(s(X)) -> X
- Signature:
{f/1,p/1} / {0/0,cons/1,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f,p} and constructors {0,cons,s}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
f(0()) -> cons(0())
f(s(0())) -> f(p(s(0())))
p(s(X)) -> X
- Signature:
{f/1,p/1} / {0/0,cons/1,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f,p} and constructors {0,cons,s}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 2.
The enriched problem is compatible with follwoing automaton.
0_0() -> 1
0_0() -> 2
0_1() -> 3
0_1() -> 4
0_2() -> 6
cons_0(2) -> 1
cons_0(2) -> 2
cons_1(3) -> 1
cons_2(6) -> 1
f_0(2) -> 1
f_1(4) -> 1
p_0(2) -> 1
p_1(5) -> 4
s_0(2) -> 1
s_0(2) -> 2
s_1(3) -> 5
2 -> 1
3 -> 4
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
f(0()) -> cons(0())
f(s(0())) -> f(p(s(0())))
p(s(X)) -> X
- Signature:
{f/1,p/1} / {0/0,cons/1,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f,p} and constructors {0,cons,s}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).
WORST_CASE(?,O(n^1))