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