* Step 1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
add(0(),X) -> X
add(s(),Y) -> s()
from(X) -> cons(X)
fst(0(),Z) -> nil()
fst(s(),cons(Y)) -> cons(Y)
len(cons(X)) -> s()
len(nil()) -> 0()
- Signature:
{add/2,from/1,fst/2,len/1} / {0/0,cons/1,nil/0,s/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {add,from,fst,len} and constructors {0,cons,nil,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_0() -> 1
0_0() -> 2
0_1() -> 1
add_0(2,2) -> 1
cons_0(2) -> 1
cons_0(2) -> 2
cons_1(2) -> 1
from_0(2) -> 1
fst_0(2,2) -> 1
len_0(2) -> 1
nil_0() -> 1
nil_0() -> 2
nil_1() -> 1
s_0() -> 1
s_0() -> 2
s_1() -> 1
2 -> 1
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
add(0(),X) -> X
add(s(),Y) -> s()
from(X) -> cons(X)
fst(0(),Z) -> nil()
fst(s(),cons(Y)) -> cons(Y)
len(cons(X)) -> s()
len(nil()) -> 0()
- Signature:
{add/2,from/1,fst/2,len/1} / {0/0,cons/1,nil/0,s/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {add,from,fst,len} and constructors {0,cons,nil,s}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).
WORST_CASE(?,O(n^1))