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