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