* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: if(false(),b,x,y) -> logZeroError() if(true(),false(),x,s(y)) -> y if(true(),true(),x,y) -> logIter(x,y) inc(0()) -> s(0()) inc(s(x)) -> s(inc(x)) le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) log(x) -> logIter(x,0()) logIter(x,y) -> if(le(s(0()),x),le(s(s(0())),x),quot(x,s(s(0()))),inc(y)) minus(x,0()) -> x minus(s(x),s(y)) -> minus(x,y) quot(0(),s(y)) -> 0() quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) - Signature: {if/4,inc/1,le/2,log/1,logIter/2,minus/2,quot/2} / {0/0,false/0,logZeroError/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {if,inc,le,log,logIter,minus,quot} and constructors {0 ,false,logZeroError,s,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: if(false(),b,x,y) -> logZeroError() if(true(),false(),x,s(y)) -> y if(true(),true(),x,y) -> logIter(x,y) inc(0()) -> s(0()) inc(s(x)) -> s(inc(x)) le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) log(x) -> logIter(x,0()) logIter(x,y) -> if(le(s(0()),x),le(s(s(0())),x),quot(x,s(s(0()))),inc(y)) minus(x,0()) -> x minus(s(x),s(y)) -> minus(x,y) quot(0(),s(y)) -> 0() quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) - Signature: {if/4,inc/1,le/2,log/1,logIter/2,minus/2,quot/2} / {0/0,false/0,logZeroError/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {if,inc,le,log,logIter,minus,quot} and constructors {0 ,false,logZeroError,s,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: inc(x){x -> s(x)} = inc(s(x)) ->^+ s(inc(x)) = C[inc(x) = inc(x){}] WORST_CASE(Omega(n^1),?)