WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: dbl(0(),y) -> y dbl(S(0()),S(0())) -> S(S(S(S(0())))) unsafe(0()) -> 0() unsafe(S(x)) -> dbl(unsafe(x),0()) - Signature: {dbl/2,unsafe/1} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {dbl,unsafe} and constructors {0,S} + Applied Processor: NaturalPI {shape = Linear, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a polynomial interpretation of kind constructor-based(linear): The following argument positions are considered usable: uargs(dbl) = {1} Following symbols are considered usable: {dbl,unsafe} TcT has computed the following interpretation: p(0) = 2 p(S) = 3 + x1 p(dbl) = 5 + x1 + x2 p(unsafe) = 1 + 5*x1 Following rules are strictly oriented: dbl(0(),y) = 7 + y > y = y dbl(S(0()),S(0())) = 15 > 14 = S(S(S(S(0())))) unsafe(0()) = 11 > 2 = 0() unsafe(S(x)) = 16 + 5*x > 8 + 5*x = dbl(unsafe(x),0()) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))