* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: and(x,false()) -> false() and(false(),x) -> false() and(true(),true()) -> true() cond(true(),x) -> cond(and(even(x),gr(x,0())),p(x)) even(0()) -> true() even(s(0())) -> false() even(s(s(x))) -> even(x) gr(0(),x) -> false() gr(s(x),0()) -> true() gr(s(x),s(y())) -> gr(x,y()) p(0()) -> 0() p(s(x)) -> x - Signature: {and/2,cond/2,even/1,gr/2,p/1} / {0/0,false/0,s/1,true/0,y/0} - Obligation: innermost runtime complexity wrt. defined symbols {and,cond,even,gr,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: and(x,false()) -> false() and(false(),x) -> false() and(true(),true()) -> true() cond(true(),x) -> cond(and(even(x),gr(x,0())),p(x)) even(0()) -> true() even(s(0())) -> false() even(s(s(x))) -> even(x) gr(0(),x) -> false() gr(s(x),0()) -> true() gr(s(x),s(y())) -> gr(x,y()) p(0()) -> 0() p(s(x)) -> x - Signature: {and/2,cond/2,even/1,gr/2,p/1} / {0/0,false/0,s/1,true/0,y/0} - Obligation: innermost runtime complexity wrt. defined symbols {and,cond,even,gr,p} and constructors {0,false,s,true,y} + 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),?)