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