* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: add(0(),X) -> X add(s(X),Y) -> s(add(X,Y)) and(false(),Y) -> false() and(true(),X) -> X first(0(),X) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z)) from(X) -> cons(X,from(s(X))) if(false(),X,Y) -> Y if(true(),X,Y) -> X - Signature: {add/2,and/2,first/2,from/1,if/3} / {0/0,cons/2,false/0,nil/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {add,and,first,from,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: add(0(),X) -> X add(s(X),Y) -> s(add(X,Y)) and(false(),Y) -> false() and(true(),X) -> X first(0(),X) -> nil() first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z)) from(X) -> cons(X,from(s(X))) if(false(),X,Y) -> Y if(true(),X,Y) -> X - Signature: {add/2,and/2,first/2,from/1,if/3} / {0/0,cons/2,false/0,nil/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {add,and,first,from,if} and constructors {0,cons,false,nil ,s,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: add(x,y){x -> s(x)} = add(s(x),y) ->^+ s(add(x,y)) = C[add(x,y) = add(x,y){}] WORST_CASE(Omega(n^1),?)