* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
fac(0(),x) -> x
fac(s(x),y) -> fac(p(s(x)),times(s(x),y))
factorial(x) -> fac(x,s(0()))
p(s(0())) -> 0()
p(s(s(x))) -> s(p(s(x)))
plus(0(),x) -> x
plus(s(x),y) -> s(plus(p(s(x)),y))
times(0(),y) -> 0()
times(s(x),y) -> plus(y,times(p(s(x)),y))
- Signature:
{fac/2,factorial/1,p/1,plus/2,times/2} / {0/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {fac,factorial,p,plus,times} and constructors {0,s}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
fac(0(),x) -> x
fac(s(x),y) -> fac(p(s(x)),times(s(x),y))
factorial(x) -> fac(x,s(0()))
p(s(0())) -> 0()
p(s(s(x))) -> s(p(s(x)))
plus(0(),x) -> x
plus(s(x),y) -> s(plus(p(s(x)),y))
times(0(),y) -> 0()
times(s(x),y) -> plus(y,times(p(s(x)),y))
- Signature:
{fac/2,factorial/1,p/1,plus/2,times/2} / {0/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {fac,factorial,p,plus,times} and constructors {0,s}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
p(s(x)){x -> s(x)} =
p(s(s(x))) ->^+ s(p(s(x)))
= C[p(s(x)) = p(s(x)){}]
WORST_CASE(Omega(n^1),?)