* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: del(x,cons(y,xs)) -> if(eq(x,y),x,y,xs) del(x,nil()) -> nil() eq(0(),0()) -> true() eq(0(),s(y)) -> false() eq(s(x),0()) -> false() eq(s(x),s(y)) -> eq(x,y) if(false(),x,y,xs) -> cons(y,del(x,xs)) if(true(),x,y,xs) -> xs last(cons(x,cons(y,xs))) -> last(cons(y,xs)) last(cons(x,nil())) -> x last(nil()) -> 0() reverse(cons(x,xs)) -> cons(last(cons(x,xs)),reverse(del(last(cons(x,xs)),cons(x,xs)))) reverse(nil()) -> nil() - Signature: {del/2,eq/2,if/4,last/1,reverse/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {del,eq,if,last,reverse} and constructors {0,cons,false ,nil,s,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: del(x,cons(y,xs)) -> if(eq(x,y),x,y,xs) del(x,nil()) -> nil() eq(0(),0()) -> true() eq(0(),s(y)) -> false() eq(s(x),0()) -> false() eq(s(x),s(y)) -> eq(x,y) if(false(),x,y,xs) -> cons(y,del(x,xs)) if(true(),x,y,xs) -> xs last(cons(x,cons(y,xs))) -> last(cons(y,xs)) last(cons(x,nil())) -> x last(nil()) -> 0() reverse(cons(x,xs)) -> cons(last(cons(x,xs)),reverse(del(last(cons(x,xs)),cons(x,xs)))) reverse(nil()) -> nil() - Signature: {del/2,eq/2,if/4,last/1,reverse/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {del,eq,if,last,reverse} and constructors {0,cons,false ,nil,s,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: eq(x,y){x -> s(x),y -> s(y)} = eq(s(x),s(y)) ->^+ eq(x,y) = C[eq(x,y) = eq(x,y){}] WORST_CASE(Omega(n^1),?)