BEST_CASE(Omega(n^2),?) Solution: --------- "0" :: [] -(0)-> "c"(0, 0) "append" :: ["b"(1, 0) x "b"(0, 0)] -(1)-> "b"(0, 0) "bubble" :: ["b"(0, 2)] -(0)-> "d"(0, 1) "bubble'" :: ["a"(12, 0) x "c"(0, 0) x "c"(0, 0) x "b"(8, 2)] -(7)-> "d"(0, 1) "bubble''" :: ["c"(0, 0) x "d"(4, 1)] -(0)-> "d"(0, 1) "bubblesort" :: ["b"(0, 2)] -(1)-> "b"(0, 0) "bubblesort'" :: ["d"(0, 1)] -(0)-> "b"(0, 0) "dd" :: ["c"(0, 0) x "b"(1, 0)] -(1)-> "b"(1, 0) "dd" :: ["c"(0, 0) x "b"(4, 2)] -(2)-> "b"(0, 2) "dd" :: ["c"(0, 0) x "b"(8, 2)] -(6)-> "b"(4, 2) "dd" :: ["c"(0, 0) x "b"(0, 0)] -(0)-> "b"(0, 0) "dd" :: ["c"(0, 0) x "b"(5, 2)] -(3)-> "b"(1, 2) "false" :: [] -(0)-> "a"(12, 0) "false" :: [] -(0)-> "a"(2, 15) "false" :: [] -(0)-> "a"(2, 3) "lt" :: ["c"(0, 0) x "c"(0, 0)] -(1)-> "a"(12, 15) "nil" :: [] -(0)-> "b"(1, 0) "nil" :: [] -(0)-> "b"(4, 2) "nil" :: [] -(0)-> "b"(0, 2) "nil" :: [] -(0)-> "b"(0, 0) "pair" :: ["b"(5, 2) x "c"(0, 0)] -(5)-> "d"(4, 1) "pair" :: ["b"(1, 2) x "c"(0, 0)] -(1)-> "d"(0, 1) "s" :: ["c"(0, 0)] -(0)-> "c"(0, 0) "true" :: [] -(0)-> "a"(12, 0) "true" :: [] -(0)-> "a"(2, 1) Cost Free Signatures: --------------------- "0" :: [] -(0)-> "c"_cf(0, 0) "append" :: ["b"_cf(0, 0) x "b"_cf(0, 0)] -(0)-> "b"_cf(0, 0) "append" :: ["b"_cf(1, 0) x "b"_cf(1, 0)] -(0)-> "b"_cf(1, 0) "bubble" :: ["b"_cf(0, 0)] -(0)-> "d"_cf(0, 0) "bubble" :: ["b"_cf(4, 0)] -(0)-> "d"_cf(4, 0) "bubble" :: ["b"_cf(1, 0)] -(0)-> "d"_cf(1, 0) "bubble'" :: ["a"_cf(0, 15) x "c"_cf(0, 0) x "c"_cf(0, 0) x "b"_cf(0, 0)] -(0)-> "d"_cf(0, 0) "bubble'" :: ["a"_cf(8, 4) x "c"_cf(0, 0) x "c"_cf(0, 0) x "b"_cf(4, 0)] -(8)-> "d"_cf(4, 0) "bubble'" :: ["a"_cf(4, 4) x "c"_cf(0, 0) x "c"_cf(0, 0) x "b"_cf(4, 0)] -(8)-> "d"_cf(4, 0) "bubble'" :: ["a"_cf(0, 0) x "c"_cf(0, 0) x "c"_cf(0, 0) x "b"_cf(0, 0)] -(0)-> "d"_cf(0, 0) "bubble'" :: ["a"_cf(4, 4) x "c"_cf(0, 0) x "c"_cf(0, 0) x "b"_cf(1, 0)] -(2)-> "d"_cf(1, 0) "bubble''" :: ["c"_cf(0, 0) x "d"_cf(0, 0)] -(0)-> "d"_cf(0, 0) "bubble''" :: ["c"_cf(0, 0) x "d"_cf(4, 0)] -(4)-> "d"_cf(4, 0) "bubble''" :: ["c"_cf(0, 0) x "d"_cf(1, 0)] -(1)-> "d"_cf(1, 0) "bubblesort" :: ["b"_cf(0, 0)] -(0)-> "b"_cf(0, 0) "bubblesort" :: ["b"_cf(1, 0)] -(0)-> "b"_cf(1, 0) "bubblesort'" :: ["d"_cf(0, 0)] -(0)-> "b"_cf(0, 0) "bubblesort'" :: ["d"_cf(1, 0)] -(0)-> "b"_cf(1, 0) "dd" :: ["c"_cf(0, 0) x "b"_cf(0, 0)] -(0)-> "b"_cf(0, 0) "dd" :: ["c"_cf(0, 0) x "b"_cf(4, 0)] -(4)-> "b"_cf(4, 0) "dd" :: ["c"_cf(0, 0) x "b"_cf(1, 0)] -(1)-> "b"_cf(1, 0) "false" :: [] -(0)-> "a"_cf(0, 0) "false" :: [] -(0)-> "a"_cf(0, 15) "false" :: [] -(0)-> "a"_cf(0, 1) "false" :: [] -(0)-> "a"_cf(8, 4) "false" :: [] -(0)-> "a"_cf(3, 0) "false" :: [] -(0)-> "a"_cf(4, 4) "lt" :: ["c"_cf(0, 0) x "c"_cf(0, 0)] -(0)-> "a"_cf(0, 0) "lt" :: ["c"_cf(0, 0) x "c"_cf(0, 0)] -(0)-> "a"_cf(0, 10) "lt" :: ["c"_cf(0, 0) x "c"_cf(0, 0)] -(0)-> "a"_cf(0, 9) "lt" :: ["c"_cf(0, 0) x "c"_cf(0, 0)] -(0)-> "a"_cf(5, 1) "lt" :: ["c"_cf(0, 0) x "c"_cf(0, 0)] -(0)-> "a"_cf(1, 1) "nil" :: [] -(0)-> "b"_cf(0, 0) "nil" :: [] -(0)-> "b"_cf(4, 0) "nil" :: [] -(0)-> "b"_cf(1, 0) "pair" :: ["b"_cf(0, 0) x "c"_cf(0, 0)] -(0)-> "d"_cf(0, 0) "pair" :: ["b"_cf(4, 0) x "c"_cf(0, 0)] -(4)-> "d"_cf(4, 0) "pair" :: ["b"_cf(1, 0) x "c"_cf(0, 0)] -(1)-> "d"_cf(1, 0) "s" :: ["c"_cf(0, 0)] -(0)-> "c"_cf(0, 0) "true" :: [] -(0)-> "a"_cf(0, 0) "true" :: [] -(0)-> "a"_cf(0, 15) "true" :: [] -(0)-> "a"_cf(0, 1) "true" :: [] -(0)-> "a"_cf(8, 4) "true" :: [] -(0)-> "a"_cf(4, 4) Base Constructors: ------------------ "\"0\"_c" :: [] -(0)-> "c"(1, 0) "\"0\"_c" :: [] -(0)-> "c"(0, 1) "\"dd\"_b" :: ["c"(0, 0) x "b"(1, 0)] -(1)-> "b"(1, 0) "\"dd\"_b" :: ["c"(0, 0) x "b"(2, 1)] -(1)-> "b"(0, 1) "\"false\"_a" :: [] -(0)-> "a"(1, 0) "\"false\"_a" :: [] -(0)-> "a"(0, 1) "\"nil\"_b" :: [] -(0)-> "b"(1, 0) "\"nil\"_b" :: [] -(0)-> "b"(0, 1) "\"pair\"_d" :: ["b"(1, 0) x "c"(0, 0)] -(1)-> "d"(1, 0) "\"pair\"_d" :: ["b"(1, 2) x "c"(0, 0)] -(1)-> "d"(0, 1) "\"s\"_c" :: ["c"(1, 0)] -(1)-> "c"(1, 0) "\"s\"_c" :: ["c"(0, 4)] -(1)-> "c"(0, 1) "\"true\"_a" :: [] -(0)-> "a"(1, 0) "\"true\"_a" :: [] -(0)-> "a"(0, 1)