* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
2ndsneg(0(),Z) -> rnil()
2ndsneg(s(N),cons(X,cons(Y,Z))) -> rcons(negrecip(Y),2ndspos(N,Z))
2ndspos(0(),Z) -> rnil()
2ndspos(s(N),cons(X,cons(Y,Z))) -> rcons(posrecip(Y),2ndsneg(N,Z))
from(X) -> cons(X,from(s(X)))
pi(X) -> 2ndspos(X,from(0()))
plus(0(),Y) -> Y
plus(s(X),Y) -> s(plus(X,Y))
square(X) -> times(X,X)
times(0(),Y) -> 0()
times(s(X),Y) -> plus(Y,times(X,Y))
- Signature:
{2ndsneg/2,2ndspos/2,from/1,pi/1,plus/2,square/1,times/2} / {0/0,cons/2,negrecip/1,posrecip/1,rcons/2,rnil/0
,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {2ndsneg,2ndspos,from,pi,plus,square
,times} and constructors {0,cons,negrecip,posrecip,rcons,rnil,s}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
2ndsneg(0(),Z) -> rnil()
2ndsneg(s(N),cons(X,cons(Y,Z))) -> rcons(negrecip(Y),2ndspos(N,Z))
2ndspos(0(),Z) -> rnil()
2ndspos(s(N),cons(X,cons(Y,Z))) -> rcons(posrecip(Y),2ndsneg(N,Z))
from(X) -> cons(X,from(s(X)))
pi(X) -> 2ndspos(X,from(0()))
plus(0(),Y) -> Y
plus(s(X),Y) -> s(plus(X,Y))
square(X) -> times(X,X)
times(0(),Y) -> 0()
times(s(X),Y) -> plus(Y,times(X,Y))
- Signature:
{2ndsneg/2,2ndspos/2,from/1,pi/1,plus/2,square/1,times/2} / {0/0,cons/2,negrecip/1,posrecip/1,rcons/2,rnil/0
,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {2ndsneg,2ndspos,from,pi,plus,square
,times} and constructors {0,cons,negrecip,posrecip,rcons,rnil,s}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
plus(x,y){x -> s(x)} =
plus(s(x),y) ->^+ s(plus(x,y))
= C[plus(x,y) = plus(x,y){}]
WORST_CASE(Omega(n^1),?)