* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: append(cons(y(),ys),x) -> cons(y(),append(ys,x)) append(nil(),x) -> cons(x,nil()) elem(node(l,x,r)) -> x if(false(),false(),n,m,xs,ys) -> listify(m,xs) if(false(),true(),n,m,xs,ys) -> listify(n,ys) if(true(),b,n,m,xs,ys) -> xs isEmpty(empty()) -> true() isEmpty(node(l,x,r)) -> false() left(empty()) -> empty() left(node(l,x,r)) -> l listify(n,xs) -> if(isEmpty(n) ,isEmpty(left(n)) ,right(n) ,node(left(left(n)),elem(left(n)),node(right(left(n)),elem(n),right(n))) ,xs ,append(xs,n)) right(empty()) -> empty() right(node(l,x,r)) -> r toList(n) -> listify(n,nil()) - Signature: {append/2,elem/1,if/6,isEmpty/1,left/1,listify/2,right/1,toList/1} / {cons/2,empty/0,false/0,nil/0,node/3 ,true/0,y/0} - Obligation: innermost runtime complexity wrt. defined symbols {append,elem,if,isEmpty,left,listify,right ,toList} and constructors {cons,empty,false,nil,node,true,y} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: append(cons(y(),ys),x) -> cons(y(),append(ys,x)) append(nil(),x) -> cons(x,nil()) elem(node(l,x,r)) -> x if(false(),false(),n,m,xs,ys) -> listify(m,xs) if(false(),true(),n,m,xs,ys) -> listify(n,ys) if(true(),b,n,m,xs,ys) -> xs isEmpty(empty()) -> true() isEmpty(node(l,x,r)) -> false() left(empty()) -> empty() left(node(l,x,r)) -> l listify(n,xs) -> if(isEmpty(n) ,isEmpty(left(n)) ,right(n) ,node(left(left(n)),elem(left(n)),node(right(left(n)),elem(n),right(n))) ,xs ,append(xs,n)) right(empty()) -> empty() right(node(l,x,r)) -> r toList(n) -> listify(n,nil()) - Signature: {append/2,elem/1,if/6,isEmpty/1,left/1,listify/2,right/1,toList/1} / {cons/2,empty/0,false/0,nil/0,node/3 ,true/0,y/0} - Obligation: innermost runtime complexity wrt. defined symbols {append,elem,if,isEmpty,left,listify,right ,toList} and constructors {cons,empty,false,nil,node,true,y} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: append(x,y){x -> cons(y(),x)} = append(cons(y(),x),y) ->^+ cons(y(),append(x,y)) = C[append(x,y) = append(x,y){}] WORST_CASE(Omega(n^1),?)