WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: merge(x,nil()) -> x merge(++(x,y),++(u(),v())) -> ++(x,merge(y,++(u(),v()))) merge(++(x,y),++(u(),v())) -> ++(u(),merge(++(x,y),v())) merge(nil(),y) -> y - Signature: {merge/2} / {++/2,nil/0,u/0,v/0} - Obligation: innermost runtime complexity wrt. defined symbols {merge} and constructors {++,nil,u,v} + 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(++) = {2} Following symbols are considered usable: {merge} TcT has computed the following interpretation: p(++) = 2 + x2 p(merge) = 4 + 6*x1 + 4*x2 p(nil) = 0 p(u) = 4 p(v) = 0 Following rules are strictly oriented: merge(x,nil()) = 4 + 6*x > x = x merge(++(x,y),++(u(),v())) = 24 + 6*y > 14 + 6*y = ++(x,merge(y,++(u(),v()))) merge(++(x,y),++(u(),v())) = 24 + 6*y > 18 + 6*y = ++(u(),merge(++(x,y),v())) merge(nil(),y) = 4 + 4*y > y = y Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))