* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: and(x,false()) -> false() and(false(),x) -> false() and(true(),true()) -> true() cond1(true(),x,y) -> cond2(gr(x,y),x,y) cond2(false(),x,y) -> cond4(gr(y,0()),x,y) cond2(true(),x,y) -> cond3(gr(x,0()),x,y) cond3(false(),x,y) -> cond1(and(gr(x,0()),gr(y,0())),x,y) cond3(true(),x,y) -> cond3(gr(x,0()),p(x),y) cond4(false(),x,y) -> cond1(and(gr(x,0()),gr(y,0())),x,y) cond4(true(),x,y) -> cond4(gr(y,0()),x,p(y)) 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,cond1/3,cond2/3,cond3/3,cond4/3,gr/2,p/1} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {and,cond1,cond2,cond3,cond4,gr,p} 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: and(x,false()) -> false() and(false(),x) -> false() and(true(),true()) -> true() cond1(true(),x,y) -> cond2(gr(x,y),x,y) cond2(false(),x,y) -> cond4(gr(y,0()),x,y) cond2(true(),x,y) -> cond3(gr(x,0()),x,y) cond3(false(),x,y) -> cond1(and(gr(x,0()),gr(y,0())),x,y) cond3(true(),x,y) -> cond3(gr(x,0()),p(x),y) cond4(false(),x,y) -> cond1(and(gr(x,0()),gr(y,0())),x,y) cond4(true(),x,y) -> cond4(gr(y,0()),x,p(y)) 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,cond1/3,cond2/3,cond3/3,cond4/3,gr/2,p/1} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {and,cond1,cond2,cond3,cond4,gr,p} and constructors {0 ,false,s,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: gr(x,y){x -> s(x),y -> s(y)} = gr(s(x),s(y)) ->^+ gr(x,y) = C[gr(x,y) = gr(x,y){}] WORST_CASE(Omega(n^1),?)