* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: cond1(true(),x) -> cond2(even(x),x) cond2(false(),x) -> cond1(neq(x,0()),p(x)) cond2(true(),x) -> cond1(neq(x,0()),div2(x)) div2(0()) -> 0() div2(s(0())) -> 0() div2(s(s(x))) -> s(div2(x)) even(0()) -> true() even(s(0())) -> false() even(s(s(x))) -> even(x) neq(0(),0()) -> false() neq(0(),s(x)) -> true() neq(s(x),0()) -> true() neq(s(x),s(y())) -> neq(x,y()) p(0()) -> 0() p(s(x)) -> x - Signature: {cond1/2,cond2/2,div2/1,even/1,neq/2,p/1} / {0/0,false/0,s/1,true/0,y/0} - Obligation: innermost runtime complexity wrt. defined symbols {cond1,cond2,div2,even,neq,p} and constructors {0,false,s ,true,y} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: cond1(true(),x) -> cond2(even(x),x) cond2(false(),x) -> cond1(neq(x,0()),p(x)) cond2(true(),x) -> cond1(neq(x,0()),div2(x)) div2(0()) -> 0() div2(s(0())) -> 0() div2(s(s(x))) -> s(div2(x)) even(0()) -> true() even(s(0())) -> false() even(s(s(x))) -> even(x) neq(0(),0()) -> false() neq(0(),s(x)) -> true() neq(s(x),0()) -> true() neq(s(x),s(y())) -> neq(x,y()) p(0()) -> 0() p(s(x)) -> x - Signature: {cond1/2,cond2/2,div2/1,even/1,neq/2,p/1} / {0/0,false/0,s/1,true/0,y/0} - Obligation: innermost runtime complexity wrt. defined symbols {cond1,cond2,div2,even,neq,p} and constructors {0,false,s ,true,y} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: div2(x){x -> s(s(x))} = div2(s(s(x))) ->^+ s(div2(x)) = C[div2(x) = div2(x){}] WORST_CASE(Omega(n^1),?)