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