YES(?,O(n^1)) * Step 1: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb0_in(v_1,v_n,v_x_0,v_x_1) True (1,1) 1. eval_start_bb0_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_0(v_1,v_n,v_x_0,v_x_1) True (?,1) 2. eval_start_0(v_1,v_n,v_x_0,v_x_1) -> eval_start_1(v_1,v_n,v_x_0,v_x_1) True (?,1) 3. eval_start_1(v_1,v_n,v_x_0,v_x_1) -> eval_start_2(v_1,v_n,v_x_0,v_x_1) True (?,1) 4. eval_start_2(v_1,v_n,v_x_0,v_x_1) -> eval_start_3(v_1,v_n,v_x_0,v_x_1) True (?,1) 5. eval_start_3(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb1_in(v_1,v_n,0,v_x_1) True (?,1) 6. eval_start_bb1_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb2_in(v_1,v_n,v_x_0,v_x_1) [v_x_0 >= 0 && -1 + v_n >= v_x_0] (?,1) 7. eval_start_bb1_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,v_x_0) [v_x_0 >= 0 && v_x_0 >= v_n] (?,1) 8. eval_start_bb2_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_4(v_1,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] (?,1) 9. eval_start_4(v_1,v_n,v_x_0,v_x_1) -> eval_start_5(nondef_0,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] (?,1) 10. eval_start_5(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,v_x_0) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0 && -1 + v_1 >= 0] (?,1) 11. eval_start_5(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb3_in(v_1,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0 && 0 >= v_1] (?,1) 12. eval_start_bb3_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb1_in(v_1,v_n,1 + v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 (?,1) && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1*v_1 + v_x_0 >= 0 && -1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1*v_1 >= 0] 13. eval_start_bb4_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb5_in(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_1] (?,1) 14. eval_start_bb4_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb6_in(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && v_x_0 >= 0 && v_x_1 >= v_n] (?,1) 15. eval_start_bb5_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,1 + v_x_1) [-1 + v_n + -1*v_x_1 >= 0 (?,1) && v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && -1 + v_n + v_x_1 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] 16. eval_start_bb6_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_stop(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && -1*v_n + v_x_1 >= 0 && v_x_0 >= 0] (?,1) Signature: {(eval_start_0,4) ;(eval_start_1,4) ;(eval_start_2,4) ;(eval_start_3,4) ;(eval_start_4,4) ;(eval_start_5,4) ;(eval_start_bb0_in,4) ;(eval_start_bb1_in,4) ;(eval_start_bb2_in,4) ;(eval_start_bb3_in,4) ;(eval_start_bb4_in,4) ;(eval_start_bb5_in,4) ;(eval_start_bb6_in,4) ;(eval_start_start,4) ;(eval_start_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8},7->{13,14},8->{9},9->{10,11},10->{13,14},11->{12} ,12->{6,7},13->{15},14->{16},15->{13,14},16->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(7,13),(10,14)] * Step 2: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb0_in(v_1,v_n,v_x_0,v_x_1) True (1,1) 1. eval_start_bb0_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_0(v_1,v_n,v_x_0,v_x_1) True (?,1) 2. eval_start_0(v_1,v_n,v_x_0,v_x_1) -> eval_start_1(v_1,v_n,v_x_0,v_x_1) True (?,1) 3. eval_start_1(v_1,v_n,v_x_0,v_x_1) -> eval_start_2(v_1,v_n,v_x_0,v_x_1) True (?,1) 4. eval_start_2(v_1,v_n,v_x_0,v_x_1) -> eval_start_3(v_1,v_n,v_x_0,v_x_1) True (?,1) 5. eval_start_3(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb1_in(v_1,v_n,0,v_x_1) True (?,1) 6. eval_start_bb1_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb2_in(v_1,v_n,v_x_0,v_x_1) [v_x_0 >= 0 && -1 + v_n >= v_x_0] (?,1) 7. eval_start_bb1_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,v_x_0) [v_x_0 >= 0 && v_x_0 >= v_n] (?,1) 8. eval_start_bb2_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_4(v_1,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] (?,1) 9. eval_start_4(v_1,v_n,v_x_0,v_x_1) -> eval_start_5(nondef_0,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] (?,1) 10. eval_start_5(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,v_x_0) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0 && -1 + v_1 >= 0] (?,1) 11. eval_start_5(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb3_in(v_1,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0 && 0 >= v_1] (?,1) 12. eval_start_bb3_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb1_in(v_1,v_n,1 + v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 (?,1) && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1*v_1 + v_x_0 >= 0 && -1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1*v_1 >= 0] 13. eval_start_bb4_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb5_in(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_1] (?,1) 14. eval_start_bb4_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb6_in(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && v_x_0 >= 0 && v_x_1 >= v_n] (?,1) 15. eval_start_bb5_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,1 + v_x_1) [-1 + v_n + -1*v_x_1 >= 0 (?,1) && v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && -1 + v_n + v_x_1 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] 16. eval_start_bb6_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_stop(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && -1*v_n + v_x_1 >= 0 && v_x_0 >= 0] (?,1) Signature: {(eval_start_0,4) ;(eval_start_1,4) ;(eval_start_2,4) ;(eval_start_3,4) ;(eval_start_4,4) ;(eval_start_5,4) ;(eval_start_bb0_in,4) ;(eval_start_bb1_in,4) ;(eval_start_bb2_in,4) ;(eval_start_bb3_in,4) ;(eval_start_bb4_in,4) ;(eval_start_bb5_in,4) ;(eval_start_bb6_in,4) ;(eval_start_start,4) ;(eval_start_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8},7->{14},8->{9},9->{10,11},10->{13},11->{12},12->{6,7} ,13->{15},14->{16},15->{13,14},16->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 3: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb0_in(v_1,v_n,v_x_0,v_x_1) True (1,1) 1. eval_start_bb0_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_0(v_1,v_n,v_x_0,v_x_1) True (1,1) 2. eval_start_0(v_1,v_n,v_x_0,v_x_1) -> eval_start_1(v_1,v_n,v_x_0,v_x_1) True (1,1) 3. eval_start_1(v_1,v_n,v_x_0,v_x_1) -> eval_start_2(v_1,v_n,v_x_0,v_x_1) True (1,1) 4. eval_start_2(v_1,v_n,v_x_0,v_x_1) -> eval_start_3(v_1,v_n,v_x_0,v_x_1) True (1,1) 5. eval_start_3(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb1_in(v_1,v_n,0,v_x_1) True (1,1) 6. eval_start_bb1_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb2_in(v_1,v_n,v_x_0,v_x_1) [v_x_0 >= 0 && -1 + v_n >= v_x_0] (?,1) 7. eval_start_bb1_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,v_x_0) [v_x_0 >= 0 && v_x_0 >= v_n] (1,1) 8. eval_start_bb2_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_4(v_1,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] (?,1) 9. eval_start_4(v_1,v_n,v_x_0,v_x_1) -> eval_start_5(nondef_0,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] (?,1) 10. eval_start_5(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,v_x_0) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0 && -1 + v_1 >= 0] (1,1) 11. eval_start_5(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb3_in(v_1,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0 && 0 >= v_1] (?,1) 12. eval_start_bb3_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb1_in(v_1,v_n,1 + v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 (?,1) && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1*v_1 + v_x_0 >= 0 && -1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1*v_1 >= 0] 13. eval_start_bb4_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb5_in(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_1] (?,1) 14. eval_start_bb4_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb6_in(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && v_x_0 >= 0 && v_x_1 >= v_n] (1,1) 15. eval_start_bb5_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,1 + v_x_1) [-1 + v_n + -1*v_x_1 >= 0 (?,1) && v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && -1 + v_n + v_x_1 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] 16. eval_start_bb6_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_stop(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && -1*v_n + v_x_1 >= 0 && v_x_0 >= 0] (1,1) Signature: {(eval_start_0,4) ;(eval_start_1,4) ;(eval_start_2,4) ;(eval_start_3,4) ;(eval_start_4,4) ;(eval_start_5,4) ;(eval_start_bb0_in,4) ;(eval_start_bb1_in,4) ;(eval_start_bb2_in,4) ;(eval_start_bb3_in,4) ;(eval_start_bb4_in,4) ;(eval_start_bb5_in,4) ;(eval_start_bb6_in,4) ;(eval_start_start,4) ;(eval_start_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8},7->{14},8->{9},9->{10,11},10->{13},11->{12},12->{6,7} ,13->{15},14->{16},15->{13,14},16->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval_start_0) = x2 p(eval_start_1) = x2 p(eval_start_2) = x2 p(eval_start_3) = x2 p(eval_start_4) = x2 p(eval_start_5) = x2 p(eval_start_bb0_in) = x2 p(eval_start_bb1_in) = x2 p(eval_start_bb2_in) = x2 p(eval_start_bb3_in) = x2 p(eval_start_bb4_in) = x2 + -1*x4 p(eval_start_bb5_in) = x2 + -1*x4 p(eval_start_bb6_in) = x2 + -1*x4 p(eval_start_start) = x2 p(eval_start_stop) = x2 + -1*x4 Following rules are strictly oriented: [-1 + v_n + -1*v_x_1 >= 0 ==> && v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && -1 + v_n + v_x_1 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] eval_start_bb5_in(v_1,v_n,v_x_0,v_x_1) = v_n + -1*v_x_1 > -1 + v_n + -1*v_x_1 = eval_start_bb4_in(v_1,v_n,v_x_0,1 + v_x_1) Following rules are weakly oriented: True ==> eval_start_start(v_1,v_n,v_x_0,v_x_1) = v_n >= v_n = eval_start_bb0_in(v_1,v_n,v_x_0,v_x_1) True ==> eval_start_bb0_in(v_1,v_n,v_x_0,v_x_1) = v_n >= v_n = eval_start_0(v_1,v_n,v_x_0,v_x_1) True ==> eval_start_0(v_1,v_n,v_x_0,v_x_1) = v_n >= v_n = eval_start_1(v_1,v_n,v_x_0,v_x_1) True ==> eval_start_1(v_1,v_n,v_x_0,v_x_1) = v_n >= v_n = eval_start_2(v_1,v_n,v_x_0,v_x_1) True ==> eval_start_2(v_1,v_n,v_x_0,v_x_1) = v_n >= v_n = eval_start_3(v_1,v_n,v_x_0,v_x_1) True ==> eval_start_3(v_1,v_n,v_x_0,v_x_1) = v_n >= v_n = eval_start_bb1_in(v_1,v_n,0,v_x_1) [v_x_0 >= 0 && -1 + v_n >= v_x_0] ==> eval_start_bb1_in(v_1,v_n,v_x_0,v_x_1) = v_n >= v_n = eval_start_bb2_in(v_1,v_n,v_x_0,v_x_1) [v_x_0 >= 0 && v_x_0 >= v_n] ==> eval_start_bb1_in(v_1,v_n,v_x_0,v_x_1) = v_n >= v_n + -1*v_x_0 = eval_start_bb4_in(v_1,v_n,v_x_0,v_x_0) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] ==> eval_start_bb2_in(v_1,v_n,v_x_0,v_x_1) = v_n >= v_n = eval_start_4(v_1,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] ==> eval_start_4(v_1,v_n,v_x_0,v_x_1) = v_n >= v_n = eval_start_5(nondef_0,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0 && -1 + v_1 >= 0] ==> eval_start_5(v_1,v_n,v_x_0,v_x_1) = v_n >= v_n + -1*v_x_0 = eval_start_bb4_in(v_1,v_n,v_x_0,v_x_0) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0 && 0 >= v_1] ==> eval_start_5(v_1,v_n,v_x_0,v_x_1) = v_n >= v_n = eval_start_bb3_in(v_1,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 ==> && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1*v_1 + v_x_0 >= 0 && -1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1*v_1 >= 0] eval_start_bb3_in(v_1,v_n,v_x_0,v_x_1) = v_n >= v_n = eval_start_bb1_in(v_1,v_n,1 + v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_1] ==> eval_start_bb4_in(v_1,v_n,v_x_0,v_x_1) = v_n + -1*v_x_1 >= v_n + -1*v_x_1 = eval_start_bb5_in(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && v_x_0 >= 0 && v_x_1 >= v_n] ==> eval_start_bb4_in(v_1,v_n,v_x_0,v_x_1) = v_n + -1*v_x_1 >= v_n + -1*v_x_1 = eval_start_bb6_in(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && -1*v_n + v_x_1 >= 0 && v_x_0 >= 0] ==> eval_start_bb6_in(v_1,v_n,v_x_0,v_x_1) = v_n + -1*v_x_1 >= v_n + -1*v_x_1 = eval_start_stop(v_1,v_n,v_x_0,v_x_1) * Step 4: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb0_in(v_1,v_n,v_x_0,v_x_1) True (1,1) 1. eval_start_bb0_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_0(v_1,v_n,v_x_0,v_x_1) True (1,1) 2. eval_start_0(v_1,v_n,v_x_0,v_x_1) -> eval_start_1(v_1,v_n,v_x_0,v_x_1) True (1,1) 3. eval_start_1(v_1,v_n,v_x_0,v_x_1) -> eval_start_2(v_1,v_n,v_x_0,v_x_1) True (1,1) 4. eval_start_2(v_1,v_n,v_x_0,v_x_1) -> eval_start_3(v_1,v_n,v_x_0,v_x_1) True (1,1) 5. eval_start_3(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb1_in(v_1,v_n,0,v_x_1) True (1,1) 6. eval_start_bb1_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb2_in(v_1,v_n,v_x_0,v_x_1) [v_x_0 >= 0 && -1 + v_n >= v_x_0] (?,1) 7. eval_start_bb1_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,v_x_0) [v_x_0 >= 0 && v_x_0 >= v_n] (1,1) 8. eval_start_bb2_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_4(v_1,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] (?,1) 9. eval_start_4(v_1,v_n,v_x_0,v_x_1) -> eval_start_5(nondef_0,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] (?,1) 10. eval_start_5(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,v_x_0) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0 && -1 + v_1 >= 0] (1,1) 11. eval_start_5(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb3_in(v_1,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0 && 0 >= v_1] (?,1) 12. eval_start_bb3_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb1_in(v_1,v_n,1 + v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 (?,1) && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1*v_1 + v_x_0 >= 0 && -1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1*v_1 >= 0] 13. eval_start_bb4_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb5_in(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_1] (?,1) 14. eval_start_bb4_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb6_in(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && v_x_0 >= 0 && v_x_1 >= v_n] (1,1) 15. eval_start_bb5_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,1 + v_x_1) [-1 + v_n + -1*v_x_1 >= 0 (v_n,1) && v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && -1 + v_n + v_x_1 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] 16. eval_start_bb6_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_stop(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && -1*v_n + v_x_1 >= 0 && v_x_0 >= 0] (1,1) Signature: {(eval_start_0,4) ;(eval_start_1,4) ;(eval_start_2,4) ;(eval_start_3,4) ;(eval_start_4,4) ;(eval_start_5,4) ;(eval_start_bb0_in,4) ;(eval_start_bb1_in,4) ;(eval_start_bb2_in,4) ;(eval_start_bb3_in,4) ;(eval_start_bb4_in,4) ;(eval_start_bb5_in,4) ;(eval_start_bb6_in,4) ;(eval_start_start,4) ;(eval_start_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8},7->{14},8->{9},9->{10,11},10->{13},11->{12},12->{6,7} ,13->{15},14->{16},15->{13,14},16->{}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 5: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb0_in(v_1,v_n,v_x_0,v_x_1) True (1,1) 1. eval_start_bb0_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_0(v_1,v_n,v_x_0,v_x_1) True (1,1) 2. eval_start_0(v_1,v_n,v_x_0,v_x_1) -> eval_start_1(v_1,v_n,v_x_0,v_x_1) True (1,1) 3. eval_start_1(v_1,v_n,v_x_0,v_x_1) -> eval_start_2(v_1,v_n,v_x_0,v_x_1) True (1,1) 4. eval_start_2(v_1,v_n,v_x_0,v_x_1) -> eval_start_3(v_1,v_n,v_x_0,v_x_1) True (1,1) 5. eval_start_3(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb1_in(v_1,v_n,0,v_x_1) True (1,1) 6. eval_start_bb1_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb2_in(v_1,v_n,v_x_0,v_x_1) [v_x_0 >= 0 && -1 + v_n >= v_x_0] (?,1) 7. eval_start_bb1_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,v_x_0) [v_x_0 >= 0 && v_x_0 >= v_n] (1,1) 8. eval_start_bb2_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_4(v_1,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] (?,1) 9. eval_start_4(v_1,v_n,v_x_0,v_x_1) -> eval_start_5(nondef_0,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] (?,1) 10. eval_start_5(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,v_x_0) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0 && -1 + v_1 >= 0] (1,1) 11. eval_start_5(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb3_in(v_1,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0 && 0 >= v_1] (?,1) 12. eval_start_bb3_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb1_in(v_1,v_n,1 + v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 (?,1) && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1*v_1 + v_x_0 >= 0 && -1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1*v_1 >= 0] 13. eval_start_bb4_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb5_in(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_1] (1 + v_n,1) 14. eval_start_bb4_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb6_in(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && v_x_0 >= 0 && v_x_1 >= v_n] (1,1) 15. eval_start_bb5_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,1 + v_x_1) [-1 + v_n + -1*v_x_1 >= 0 (v_n,1) && v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && -1 + v_n + v_x_1 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] 16. eval_start_bb6_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_stop(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && -1*v_n + v_x_1 >= 0 && v_x_0 >= 0] (1,1) Signature: {(eval_start_0,4) ;(eval_start_1,4) ;(eval_start_2,4) ;(eval_start_3,4) ;(eval_start_4,4) ;(eval_start_5,4) ;(eval_start_bb0_in,4) ;(eval_start_bb1_in,4) ;(eval_start_bb2_in,4) ;(eval_start_bb3_in,4) ;(eval_start_bb4_in,4) ;(eval_start_bb5_in,4) ;(eval_start_bb6_in,4) ;(eval_start_start,4) ;(eval_start_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8},7->{14},8->{9},9->{10,11},10->{13},11->{12},12->{6,7} ,13->{15},14->{16},15->{13,14},16->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval_start_0) = x2 p(eval_start_1) = x2 p(eval_start_2) = x2 p(eval_start_3) = x2 p(eval_start_4) = x2 + -1*x3 p(eval_start_5) = x2 + -1*x3 p(eval_start_bb0_in) = x2 p(eval_start_bb1_in) = x2 + -1*x3 p(eval_start_bb2_in) = x2 + -1*x3 p(eval_start_bb3_in) = x2 + -1*x3 p(eval_start_bb4_in) = x2 + -1*x4 p(eval_start_bb5_in) = x2 + -1*x4 p(eval_start_bb6_in) = x2 + -1*x4 p(eval_start_start) = x2 p(eval_start_stop) = x2 + -1*x4 Following rules are strictly oriented: [-1 + v_n + -1*v_x_0 >= 0 ==> && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1*v_1 + v_x_0 >= 0 && -1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1*v_1 >= 0] eval_start_bb3_in(v_1,v_n,v_x_0,v_x_1) = v_n + -1*v_x_0 > -1 + v_n + -1*v_x_0 = eval_start_bb1_in(v_1,v_n,1 + v_x_0,v_x_1) [-1 + v_n + -1*v_x_1 >= 0 ==> && v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && -1 + v_n + v_x_1 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] eval_start_bb5_in(v_1,v_n,v_x_0,v_x_1) = v_n + -1*v_x_1 > -1 + v_n + -1*v_x_1 = eval_start_bb4_in(v_1,v_n,v_x_0,1 + v_x_1) Following rules are weakly oriented: True ==> eval_start_start(v_1,v_n,v_x_0,v_x_1) = v_n >= v_n = eval_start_bb0_in(v_1,v_n,v_x_0,v_x_1) True ==> eval_start_bb0_in(v_1,v_n,v_x_0,v_x_1) = v_n >= v_n = eval_start_0(v_1,v_n,v_x_0,v_x_1) True ==> eval_start_0(v_1,v_n,v_x_0,v_x_1) = v_n >= v_n = eval_start_1(v_1,v_n,v_x_0,v_x_1) True ==> eval_start_1(v_1,v_n,v_x_0,v_x_1) = v_n >= v_n = eval_start_2(v_1,v_n,v_x_0,v_x_1) True ==> eval_start_2(v_1,v_n,v_x_0,v_x_1) = v_n >= v_n = eval_start_3(v_1,v_n,v_x_0,v_x_1) True ==> eval_start_3(v_1,v_n,v_x_0,v_x_1) = v_n >= v_n = eval_start_bb1_in(v_1,v_n,0,v_x_1) [v_x_0 >= 0 && -1 + v_n >= v_x_0] ==> eval_start_bb1_in(v_1,v_n,v_x_0,v_x_1) = v_n + -1*v_x_0 >= v_n + -1*v_x_0 = eval_start_bb2_in(v_1,v_n,v_x_0,v_x_1) [v_x_0 >= 0 && v_x_0 >= v_n] ==> eval_start_bb1_in(v_1,v_n,v_x_0,v_x_1) = v_n + -1*v_x_0 >= v_n + -1*v_x_0 = eval_start_bb4_in(v_1,v_n,v_x_0,v_x_0) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] ==> eval_start_bb2_in(v_1,v_n,v_x_0,v_x_1) = v_n + -1*v_x_0 >= v_n + -1*v_x_0 = eval_start_4(v_1,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] ==> eval_start_4(v_1,v_n,v_x_0,v_x_1) = v_n + -1*v_x_0 >= v_n + -1*v_x_0 = eval_start_5(nondef_0,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0 && -1 + v_1 >= 0] ==> eval_start_5(v_1,v_n,v_x_0,v_x_1) = v_n + -1*v_x_0 >= v_n + -1*v_x_0 = eval_start_bb4_in(v_1,v_n,v_x_0,v_x_0) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0 && 0 >= v_1] ==> eval_start_5(v_1,v_n,v_x_0,v_x_1) = v_n + -1*v_x_0 >= v_n + -1*v_x_0 = eval_start_bb3_in(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_1] ==> eval_start_bb4_in(v_1,v_n,v_x_0,v_x_1) = v_n + -1*v_x_1 >= v_n + -1*v_x_1 = eval_start_bb5_in(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && v_x_0 >= 0 && v_x_1 >= v_n] ==> eval_start_bb4_in(v_1,v_n,v_x_0,v_x_1) = v_n + -1*v_x_1 >= v_n + -1*v_x_1 = eval_start_bb6_in(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && -1*v_n + v_x_1 >= 0 && v_x_0 >= 0] ==> eval_start_bb6_in(v_1,v_n,v_x_0,v_x_1) = v_n + -1*v_x_1 >= v_n + -1*v_x_1 = eval_start_stop(v_1,v_n,v_x_0,v_x_1) * Step 6: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb0_in(v_1,v_n,v_x_0,v_x_1) True (1,1) 1. eval_start_bb0_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_0(v_1,v_n,v_x_0,v_x_1) True (1,1) 2. eval_start_0(v_1,v_n,v_x_0,v_x_1) -> eval_start_1(v_1,v_n,v_x_0,v_x_1) True (1,1) 3. eval_start_1(v_1,v_n,v_x_0,v_x_1) -> eval_start_2(v_1,v_n,v_x_0,v_x_1) True (1,1) 4. eval_start_2(v_1,v_n,v_x_0,v_x_1) -> eval_start_3(v_1,v_n,v_x_0,v_x_1) True (1,1) 5. eval_start_3(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb1_in(v_1,v_n,0,v_x_1) True (1,1) 6. eval_start_bb1_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb2_in(v_1,v_n,v_x_0,v_x_1) [v_x_0 >= 0 && -1 + v_n >= v_x_0] (?,1) 7. eval_start_bb1_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,v_x_0) [v_x_0 >= 0 && v_x_0 >= v_n] (1,1) 8. eval_start_bb2_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_4(v_1,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] (?,1) 9. eval_start_4(v_1,v_n,v_x_0,v_x_1) -> eval_start_5(nondef_0,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] (?,1) 10. eval_start_5(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,v_x_0) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0 && -1 + v_1 >= 0] (1,1) 11. eval_start_5(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb3_in(v_1,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0 && 0 >= v_1] (?,1) 12. eval_start_bb3_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb1_in(v_1,v_n,1 + v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 (v_n,1) && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1*v_1 + v_x_0 >= 0 && -1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1*v_1 >= 0] 13. eval_start_bb4_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb5_in(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_1] (1 + v_n,1) 14. eval_start_bb4_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb6_in(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && v_x_0 >= 0 && v_x_1 >= v_n] (1,1) 15. eval_start_bb5_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,1 + v_x_1) [-1 + v_n + -1*v_x_1 >= 0 (v_n,1) && v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && -1 + v_n + v_x_1 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] 16. eval_start_bb6_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_stop(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && -1*v_n + v_x_1 >= 0 && v_x_0 >= 0] (1,1) Signature: {(eval_start_0,4) ;(eval_start_1,4) ;(eval_start_2,4) ;(eval_start_3,4) ;(eval_start_4,4) ;(eval_start_5,4) ;(eval_start_bb0_in,4) ;(eval_start_bb1_in,4) ;(eval_start_bb2_in,4) ;(eval_start_bb3_in,4) ;(eval_start_bb4_in,4) ;(eval_start_bb5_in,4) ;(eval_start_bb6_in,4) ;(eval_start_start,4) ;(eval_start_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8},7->{14},8->{9},9->{10,11},10->{13},11->{12},12->{6,7} ,13->{15},14->{16},15->{13,14},16->{}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 7: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb0_in(v_1,v_n,v_x_0,v_x_1) True (1,1) 1. eval_start_bb0_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_0(v_1,v_n,v_x_0,v_x_1) True (1,1) 2. eval_start_0(v_1,v_n,v_x_0,v_x_1) -> eval_start_1(v_1,v_n,v_x_0,v_x_1) True (1,1) 3. eval_start_1(v_1,v_n,v_x_0,v_x_1) -> eval_start_2(v_1,v_n,v_x_0,v_x_1) True (1,1) 4. eval_start_2(v_1,v_n,v_x_0,v_x_1) -> eval_start_3(v_1,v_n,v_x_0,v_x_1) True (1,1) 5. eval_start_3(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb1_in(v_1,v_n,0,v_x_1) True (1,1) 6. eval_start_bb1_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb2_in(v_1,v_n,v_x_0,v_x_1) [v_x_0 >= 0 && -1 + v_n >= v_x_0] (1 + v_n,1) 7. eval_start_bb1_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,v_x_0) [v_x_0 >= 0 && v_x_0 >= v_n] (1,1) 8. eval_start_bb2_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_4(v_1,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] (1 + v_n,1) 9. eval_start_4(v_1,v_n,v_x_0,v_x_1) -> eval_start_5(nondef_0,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] (1 + v_n,1) 10. eval_start_5(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,v_x_0) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0 && -1 + v_1 >= 0] (1,1) 11. eval_start_5(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb3_in(v_1,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0 && 0 >= v_1] (1 + v_n,1) 12. eval_start_bb3_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb1_in(v_1,v_n,1 + v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 (v_n,1) && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1*v_1 + v_x_0 >= 0 && -1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1*v_1 >= 0] 13. eval_start_bb4_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb5_in(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_1] (1 + v_n,1) 14. eval_start_bb4_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb6_in(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && v_x_0 >= 0 && v_x_1 >= v_n] (1,1) 15. eval_start_bb5_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,1 + v_x_1) [-1 + v_n + -1*v_x_1 >= 0 (v_n,1) && v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && -1 + v_n + v_x_1 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] 16. eval_start_bb6_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_stop(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && -1*v_n + v_x_1 >= 0 && v_x_0 >= 0] (1,1) Signature: {(eval_start_0,4) ;(eval_start_1,4) ;(eval_start_2,4) ;(eval_start_3,4) ;(eval_start_4,4) ;(eval_start_5,4) ;(eval_start_bb0_in,4) ;(eval_start_bb1_in,4) ;(eval_start_bb2_in,4) ;(eval_start_bb3_in,4) ;(eval_start_bb4_in,4) ;(eval_start_bb5_in,4) ;(eval_start_bb6_in,4) ;(eval_start_start,4) ;(eval_start_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8},7->{14},8->{9},9->{10,11},10->{13},11->{12},12->{6,7} ,13->{15},14->{16},15->{13,14},16->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: The problem is already solved. YES(?,O(n^1))