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