* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
cond(true(),x,y) -> s(minus(x,s(y)))
equal(0(),0()) -> true()
equal(0(),s(y)) -> false()
equal(s(x),0()) -> false()
equal(s(x),s(y)) -> equal(x,y)
min(u,0()) -> 0()
min(0(),v) -> 0()
min(s(u),s(v)) -> s(min(u,v))
minus(x,y) -> cond(equal(min(x,y),y),x,y)
- Signature:
{cond/3,equal/2,min/2,minus/2} / {0/0,false/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {cond,equal,min,minus} and constructors {0,false,s,true}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
cond(true(),x,y) -> s(minus(x,s(y)))
equal(0(),0()) -> true()
equal(0(),s(y)) -> false()
equal(s(x),0()) -> false()
equal(s(x),s(y)) -> equal(x,y)
min(u,0()) -> 0()
min(0(),v) -> 0()
min(s(u),s(v)) -> s(min(u,v))
minus(x,y) -> cond(equal(min(x,y),y),x,y)
- Signature:
{cond/3,equal/2,min/2,minus/2} / {0/0,false/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {cond,equal,min,minus} and constructors {0,false,s,true}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
equal(x,y){x -> s(x),y -> s(y)} =
equal(s(x),s(y)) ->^+ equal(x,y)
= C[equal(x,y) = equal(x,y){}]
WORST_CASE(Omega(n^1),?)