* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
div(plus(x,y),z) -> plus(div(x,z),div(y,z))
div(s(x),s(y)) -> s(div(minus(x,y),s(y)))
minus(x,0()) -> x
minus(x,plus(y,z)) -> minus(minus(x,y),z)
minus(0(),y) -> 0()
minus(s(x),s(y)) -> minus(p(s(x)),p(s(y)))
p(0()) -> s(s(0()))
p(s(s(x))) -> s(p(s(x)))
plus(0(),y) -> y
plus(s(x),y) -> s(plus(y,minus(s(x),s(0()))))
- Signature:
{div/2,minus/2,p/1,plus/2} / {0/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {div,minus,p,plus} and constructors {0,s}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
div(plus(x,y),z) -> plus(div(x,z),div(y,z))
div(s(x),s(y)) -> s(div(minus(x,y),s(y)))
minus(x,0()) -> x
minus(x,plus(y,z)) -> minus(minus(x,y),z)
minus(0(),y) -> 0()
minus(s(x),s(y)) -> minus(p(s(x)),p(s(y)))
p(0()) -> s(s(0()))
p(s(s(x))) -> s(p(s(x)))
plus(0(),y) -> y
plus(s(x),y) -> s(plus(y,minus(s(x),s(0()))))
- Signature:
{div/2,minus/2,p/1,plus/2} / {0/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {div,minus,p,plus} 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),?)