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