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