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