YES(?,O(n^1)) * Step 1: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb0_in(v_m,v_n,v_x_0,v_y_0) True (1,1) 1. eval_start_bb0_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_0(v_m,v_n,v_x_0,v_y_0) True (?,1) 2. eval_start_0(v_m,v_n,v_x_0,v_y_0) -> eval_start_1(v_m,v_n,v_x_0,v_y_0) True (?,1) 3. eval_start_1(v_m,v_n,v_x_0,v_y_0) -> eval_start_2(v_m,v_n,v_x_0,v_y_0) True (?,1) 4. eval_start_2(v_m,v_n,v_x_0,v_y_0) -> eval_start_3(v_m,v_n,v_x_0,v_y_0) True (?,1) 5. eval_start_3(v_m,v_n,v_x_0,v_y_0) -> eval_start_4(v_m,v_n,v_x_0,v_y_0) True (?,1) 6. eval_start_4(v_m,v_n,v_x_0,v_y_0) -> eval_start_5(v_m,v_n,v_x_0,v_y_0) True (?,1) 7. eval_start_5(v_m,v_n,v_x_0,v_y_0) -> eval_start_6(v_m,v_n,v_x_0,v_y_0) True (?,1) 8. eval_start_6(v_m,v_n,v_x_0,v_y_0) -> eval_start_7(v_m,v_n,v_x_0,v_y_0) True (?,1) 9. eval_start_7(v_m,v_n,v_x_0,v_y_0) -> eval_start_8(v_m,v_n,v_x_0,v_y_0) True (?,1) 10. eval_start_8(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_m,v_n,0,0) True (?,1) 11. eval_start_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb2_in(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_0] 12. eval_start_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && v_x_0 >= v_n] 13. eval_start_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_m,v_n,1 + v_x_0,1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && -1 + v_n + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1 + v_n + v_y_0 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] 14. eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb4_in(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1 + v_m >= v_y_0] 15. eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb5_in(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && v_y_0 >= v_m] 16. eval_start_bb4_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_m,v_n,1 + v_x_0,1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && -1 + v_m + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && -1 + v_m + v_y_0 >= 0 && -1 + v_m + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1 + v_m + v_x_0 >= 0 && -1 + v_m + -1*v_n >= 0 && -1 + v_m >= 0] 17. eval_start_bb5_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_stop(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && -1*v_m + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1*v_m + v_x_0 >= 0] 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_6,4) ;(eval_start_7,4) ;(eval_start_8,4) ;(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_start,4) ;(eval_start_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10},10->{11,12},11->{13},12->{14,15} ,13->{11,12},14->{16},15->{17},16->{11,12},17->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(16,11)] * Step 2: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb0_in(v_m,v_n,v_x_0,v_y_0) True (1,1) 1. eval_start_bb0_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_0(v_m,v_n,v_x_0,v_y_0) True (?,1) 2. eval_start_0(v_m,v_n,v_x_0,v_y_0) -> eval_start_1(v_m,v_n,v_x_0,v_y_0) True (?,1) 3. eval_start_1(v_m,v_n,v_x_0,v_y_0) -> eval_start_2(v_m,v_n,v_x_0,v_y_0) True (?,1) 4. eval_start_2(v_m,v_n,v_x_0,v_y_0) -> eval_start_3(v_m,v_n,v_x_0,v_y_0) True (?,1) 5. eval_start_3(v_m,v_n,v_x_0,v_y_0) -> eval_start_4(v_m,v_n,v_x_0,v_y_0) True (?,1) 6. eval_start_4(v_m,v_n,v_x_0,v_y_0) -> eval_start_5(v_m,v_n,v_x_0,v_y_0) True (?,1) 7. eval_start_5(v_m,v_n,v_x_0,v_y_0) -> eval_start_6(v_m,v_n,v_x_0,v_y_0) True (?,1) 8. eval_start_6(v_m,v_n,v_x_0,v_y_0) -> eval_start_7(v_m,v_n,v_x_0,v_y_0) True (?,1) 9. eval_start_7(v_m,v_n,v_x_0,v_y_0) -> eval_start_8(v_m,v_n,v_x_0,v_y_0) True (?,1) 10. eval_start_8(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_m,v_n,0,0) True (?,1) 11. eval_start_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb2_in(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_0] 12. eval_start_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && v_x_0 >= v_n] 13. eval_start_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_m,v_n,1 + v_x_0,1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && -1 + v_n + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1 + v_n + v_y_0 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] 14. eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb4_in(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1 + v_m >= v_y_0] 15. eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb5_in(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && v_y_0 >= v_m] 16. eval_start_bb4_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_m,v_n,1 + v_x_0,1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && -1 + v_m + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && -1 + v_m + v_y_0 >= 0 && -1 + v_m + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1 + v_m + v_x_0 >= 0 && -1 + v_m + -1*v_n >= 0 && -1 + v_m >= 0] 17. eval_start_bb5_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_stop(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && -1*v_m + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1*v_m + v_x_0 >= 0] 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_6,4) ;(eval_start_7,4) ;(eval_start_8,4) ;(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_start,4) ;(eval_start_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10},10->{11,12},11->{13},12->{14,15} ,13->{11,12},14->{16},15->{17},16->{12},17->{}] + 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_m,v_n,v_x_0,v_y_0) -> eval_start_bb0_in(v_m,v_n,v_x_0,v_y_0) True (1,1) 1. eval_start_bb0_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_0(v_m,v_n,v_x_0,v_y_0) True (1,1) 2. eval_start_0(v_m,v_n,v_x_0,v_y_0) -> eval_start_1(v_m,v_n,v_x_0,v_y_0) True (1,1) 3. eval_start_1(v_m,v_n,v_x_0,v_y_0) -> eval_start_2(v_m,v_n,v_x_0,v_y_0) True (1,1) 4. eval_start_2(v_m,v_n,v_x_0,v_y_0) -> eval_start_3(v_m,v_n,v_x_0,v_y_0) True (1,1) 5. eval_start_3(v_m,v_n,v_x_0,v_y_0) -> eval_start_4(v_m,v_n,v_x_0,v_y_0) True (1,1) 6. eval_start_4(v_m,v_n,v_x_0,v_y_0) -> eval_start_5(v_m,v_n,v_x_0,v_y_0) True (1,1) 7. eval_start_5(v_m,v_n,v_x_0,v_y_0) -> eval_start_6(v_m,v_n,v_x_0,v_y_0) True (1,1) 8. eval_start_6(v_m,v_n,v_x_0,v_y_0) -> eval_start_7(v_m,v_n,v_x_0,v_y_0) True (1,1) 9. eval_start_7(v_m,v_n,v_x_0,v_y_0) -> eval_start_8(v_m,v_n,v_x_0,v_y_0) True (1,1) 10. eval_start_8(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_m,v_n,0,0) True (1,1) 11. eval_start_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb2_in(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_0] 12. eval_start_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && v_x_0 >= v_n] 13. eval_start_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_m,v_n,1 + v_x_0,1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && -1 + v_n + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1 + v_n + v_y_0 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] 14. eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb4_in(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1 + v_m >= v_y_0] 15. eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb5_in(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (1,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && v_y_0 >= v_m] 16. eval_start_bb4_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_m,v_n,1 + v_x_0,1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && -1 + v_m + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && -1 + v_m + v_y_0 >= 0 && -1 + v_m + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1 + v_m + v_x_0 >= 0 && -1 + v_m + -1*v_n >= 0 && -1 + v_m >= 0] 17. eval_start_bb5_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_stop(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (1,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && -1*v_m + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1*v_m + v_x_0 >= 0] 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_6,4) ;(eval_start_7,4) ;(eval_start_8,4) ;(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_start,4) ;(eval_start_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10},10->{11,12},11->{13},12->{14,15} ,13->{11,12},14->{16},15->{17},16->{12},17->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval_start_0) = x1 p(eval_start_1) = x1 p(eval_start_2) = x1 p(eval_start_3) = x1 p(eval_start_4) = x1 p(eval_start_5) = x1 p(eval_start_6) = x1 p(eval_start_7) = x1 p(eval_start_8) = x1 p(eval_start_bb0_in) = x1 p(eval_start_bb1_in) = x1 + -1*x3 p(eval_start_bb2_in) = -1 + x1 + -1*x3 p(eval_start_bb3_in) = x1 + -1*x3 p(eval_start_bb4_in) = x1 + -1*x3 p(eval_start_bb5_in) = x1 + -1*x3 p(eval_start_start) = x1 p(eval_start_stop) = x1 + -1*x3 Following rules are strictly oriented: [v_x_0 + -1*v_y_0 >= 0 ==> && -1 + v_m + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && -1 + v_m + v_y_0 >= 0 && -1 + v_m + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1 + v_m + v_x_0 >= 0 && -1 + v_m + -1*v_n >= 0 && -1 + v_m >= 0] eval_start_bb4_in(v_m,v_n,v_x_0,v_y_0) = v_m + -1*v_x_0 > -1 + v_m + -1*v_x_0 = eval_start_bb1_in(v_m,v_n,1 + v_x_0,1 + v_y_0) Following rules are weakly oriented: True ==> eval_start_start(v_m,v_n,v_x_0,v_y_0) = v_m >= v_m = eval_start_bb0_in(v_m,v_n,v_x_0,v_y_0) True ==> eval_start_bb0_in(v_m,v_n,v_x_0,v_y_0) = v_m >= v_m = eval_start_0(v_m,v_n,v_x_0,v_y_0) True ==> eval_start_0(v_m,v_n,v_x_0,v_y_0) = v_m >= v_m = eval_start_1(v_m,v_n,v_x_0,v_y_0) True ==> eval_start_1(v_m,v_n,v_x_0,v_y_0) = v_m >= v_m = eval_start_2(v_m,v_n,v_x_0,v_y_0) True ==> eval_start_2(v_m,v_n,v_x_0,v_y_0) = v_m >= v_m = eval_start_3(v_m,v_n,v_x_0,v_y_0) True ==> eval_start_3(v_m,v_n,v_x_0,v_y_0) = v_m >= v_m = eval_start_4(v_m,v_n,v_x_0,v_y_0) True ==> eval_start_4(v_m,v_n,v_x_0,v_y_0) = v_m >= v_m = eval_start_5(v_m,v_n,v_x_0,v_y_0) True ==> eval_start_5(v_m,v_n,v_x_0,v_y_0) = v_m >= v_m = eval_start_6(v_m,v_n,v_x_0,v_y_0) True ==> eval_start_6(v_m,v_n,v_x_0,v_y_0) = v_m >= v_m = eval_start_7(v_m,v_n,v_x_0,v_y_0) True ==> eval_start_7(v_m,v_n,v_x_0,v_y_0) = v_m >= v_m = eval_start_8(v_m,v_n,v_x_0,v_y_0) True ==> eval_start_8(v_m,v_n,v_x_0,v_y_0) = v_m >= v_m = eval_start_bb1_in(v_m,v_n,0,0) [v_x_0 + -1*v_y_0 >= 0 ==> && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_0] eval_start_bb1_in(v_m,v_n,v_x_0,v_y_0) = v_m + -1*v_x_0 >= -1 + v_m + -1*v_x_0 = eval_start_bb2_in(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 ==> && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && v_x_0 >= v_n] eval_start_bb1_in(v_m,v_n,v_x_0,v_y_0) = v_m + -1*v_x_0 >= v_m + -1*v_x_0 = eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 ==> && -1 + v_n + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1 + v_n + v_y_0 >= 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_m,v_n,v_x_0,v_y_0) = -1 + v_m + -1*v_x_0 >= -1 + v_m + -1*v_x_0 = eval_start_bb1_in(v_m,v_n,1 + v_x_0,1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 ==> && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1 + v_m >= v_y_0] eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) = v_m + -1*v_x_0 >= v_m + -1*v_x_0 = eval_start_bb4_in(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 ==> && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && v_y_0 >= v_m] eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) = v_m + -1*v_x_0 >= v_m + -1*v_x_0 = eval_start_bb5_in(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 ==> && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && -1*v_m + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1*v_m + v_x_0 >= 0] eval_start_bb5_in(v_m,v_n,v_x_0,v_y_0) = v_m + -1*v_x_0 >= v_m + -1*v_x_0 = eval_start_stop(v_m,v_n,v_x_0,v_y_0) * Step 4: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb0_in(v_m,v_n,v_x_0,v_y_0) True (1,1) 1. eval_start_bb0_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_0(v_m,v_n,v_x_0,v_y_0) True (1,1) 2. eval_start_0(v_m,v_n,v_x_0,v_y_0) -> eval_start_1(v_m,v_n,v_x_0,v_y_0) True (1,1) 3. eval_start_1(v_m,v_n,v_x_0,v_y_0) -> eval_start_2(v_m,v_n,v_x_0,v_y_0) True (1,1) 4. eval_start_2(v_m,v_n,v_x_0,v_y_0) -> eval_start_3(v_m,v_n,v_x_0,v_y_0) True (1,1) 5. eval_start_3(v_m,v_n,v_x_0,v_y_0) -> eval_start_4(v_m,v_n,v_x_0,v_y_0) True (1,1) 6. eval_start_4(v_m,v_n,v_x_0,v_y_0) -> eval_start_5(v_m,v_n,v_x_0,v_y_0) True (1,1) 7. eval_start_5(v_m,v_n,v_x_0,v_y_0) -> eval_start_6(v_m,v_n,v_x_0,v_y_0) True (1,1) 8. eval_start_6(v_m,v_n,v_x_0,v_y_0) -> eval_start_7(v_m,v_n,v_x_0,v_y_0) True (1,1) 9. eval_start_7(v_m,v_n,v_x_0,v_y_0) -> eval_start_8(v_m,v_n,v_x_0,v_y_0) True (1,1) 10. eval_start_8(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_m,v_n,0,0) True (1,1) 11. eval_start_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb2_in(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_0] 12. eval_start_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && v_x_0 >= v_n] 13. eval_start_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_m,v_n,1 + v_x_0,1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && -1 + v_n + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1 + v_n + v_y_0 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] 14. eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb4_in(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1 + v_m >= v_y_0] 15. eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb5_in(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (1,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && v_y_0 >= v_m] 16. eval_start_bb4_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_m,v_n,1 + v_x_0,1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 (v_m,1) && -1 + v_m + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && -1 + v_m + v_y_0 >= 0 && -1 + v_m + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1 + v_m + v_x_0 >= 0 && -1 + v_m + -1*v_n >= 0 && -1 + v_m >= 0] 17. eval_start_bb5_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_stop(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (1,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && -1*v_m + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1*v_m + v_x_0 >= 0] 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_6,4) ;(eval_start_7,4) ;(eval_start_8,4) ;(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_start,4) ;(eval_start_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10},10->{11,12},11->{13},12->{14,15} ,13->{11,12},14->{16},15->{17},16->{12},17->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval_start_0) = 1 + x2 p(eval_start_1) = 1 + x2 p(eval_start_2) = 1 + x2 p(eval_start_3) = 1 + x2 p(eval_start_4) = 1 + x2 p(eval_start_5) = 1 + x2 p(eval_start_6) = 1 + x2 p(eval_start_7) = 1 + x2 p(eval_start_8) = 1 + x2 p(eval_start_bb0_in) = 1 + x2 p(eval_start_bb1_in) = 1 + x2 + -1*x3 p(eval_start_bb2_in) = 1 + x2 + -1*x3 p(eval_start_bb3_in) = 1 + x2 + -1*x3 p(eval_start_bb4_in) = x2 + -1*x3 p(eval_start_bb5_in) = 1 + x2 + -1*x3 p(eval_start_start) = 1 + x2 p(eval_start_stop) = 1 + x2 + -1*x3 Following rules are strictly oriented: [v_x_0 + -1*v_y_0 >= 0 ==> && -1 + v_n + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1 + v_n + v_y_0 >= 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_m,v_n,v_x_0,v_y_0) = 1 + v_n + -1*v_x_0 > v_n + -1*v_x_0 = eval_start_bb1_in(v_m,v_n,1 + v_x_0,1 + v_y_0) Following rules are weakly oriented: True ==> eval_start_start(v_m,v_n,v_x_0,v_y_0) = 1 + v_n >= 1 + v_n = eval_start_bb0_in(v_m,v_n,v_x_0,v_y_0) True ==> eval_start_bb0_in(v_m,v_n,v_x_0,v_y_0) = 1 + v_n >= 1 + v_n = eval_start_0(v_m,v_n,v_x_0,v_y_0) True ==> eval_start_0(v_m,v_n,v_x_0,v_y_0) = 1 + v_n >= 1 + v_n = eval_start_1(v_m,v_n,v_x_0,v_y_0) True ==> eval_start_1(v_m,v_n,v_x_0,v_y_0) = 1 + v_n >= 1 + v_n = eval_start_2(v_m,v_n,v_x_0,v_y_0) True ==> eval_start_2(v_m,v_n,v_x_0,v_y_0) = 1 + v_n >= 1 + v_n = eval_start_3(v_m,v_n,v_x_0,v_y_0) True ==> eval_start_3(v_m,v_n,v_x_0,v_y_0) = 1 + v_n >= 1 + v_n = eval_start_4(v_m,v_n,v_x_0,v_y_0) True ==> eval_start_4(v_m,v_n,v_x_0,v_y_0) = 1 + v_n >= 1 + v_n = eval_start_5(v_m,v_n,v_x_0,v_y_0) True ==> eval_start_5(v_m,v_n,v_x_0,v_y_0) = 1 + v_n >= 1 + v_n = eval_start_6(v_m,v_n,v_x_0,v_y_0) True ==> eval_start_6(v_m,v_n,v_x_0,v_y_0) = 1 + v_n >= 1 + v_n = eval_start_7(v_m,v_n,v_x_0,v_y_0) True ==> eval_start_7(v_m,v_n,v_x_0,v_y_0) = 1 + v_n >= 1 + v_n = eval_start_8(v_m,v_n,v_x_0,v_y_0) True ==> eval_start_8(v_m,v_n,v_x_0,v_y_0) = 1 + v_n >= 1 + v_n = eval_start_bb1_in(v_m,v_n,0,0) [v_x_0 + -1*v_y_0 >= 0 ==> && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_0] eval_start_bb1_in(v_m,v_n,v_x_0,v_y_0) = 1 + v_n + -1*v_x_0 >= 1 + v_n + -1*v_x_0 = eval_start_bb2_in(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 ==> && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && v_x_0 >= v_n] eval_start_bb1_in(v_m,v_n,v_x_0,v_y_0) = 1 + v_n + -1*v_x_0 >= 1 + v_n + -1*v_x_0 = eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 ==> && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1 + v_m >= v_y_0] eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) = 1 + v_n + -1*v_x_0 >= v_n + -1*v_x_0 = eval_start_bb4_in(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 ==> && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && v_y_0 >= v_m] eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) = 1 + v_n + -1*v_x_0 >= 1 + v_n + -1*v_x_0 = eval_start_bb5_in(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 ==> && -1 + v_m + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && -1 + v_m + v_y_0 >= 0 && -1 + v_m + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1 + v_m + v_x_0 >= 0 && -1 + v_m + -1*v_n >= 0 && -1 + v_m >= 0] eval_start_bb4_in(v_m,v_n,v_x_0,v_y_0) = v_n + -1*v_x_0 >= v_n + -1*v_x_0 = eval_start_bb1_in(v_m,v_n,1 + v_x_0,1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 ==> && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && -1*v_m + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1*v_m + v_x_0 >= 0] eval_start_bb5_in(v_m,v_n,v_x_0,v_y_0) = 1 + v_n + -1*v_x_0 >= 1 + v_n + -1*v_x_0 = eval_start_stop(v_m,v_n,v_x_0,v_y_0) * Step 5: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb0_in(v_m,v_n,v_x_0,v_y_0) True (1,1) 1. eval_start_bb0_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_0(v_m,v_n,v_x_0,v_y_0) True (1,1) 2. eval_start_0(v_m,v_n,v_x_0,v_y_0) -> eval_start_1(v_m,v_n,v_x_0,v_y_0) True (1,1) 3. eval_start_1(v_m,v_n,v_x_0,v_y_0) -> eval_start_2(v_m,v_n,v_x_0,v_y_0) True (1,1) 4. eval_start_2(v_m,v_n,v_x_0,v_y_0) -> eval_start_3(v_m,v_n,v_x_0,v_y_0) True (1,1) 5. eval_start_3(v_m,v_n,v_x_0,v_y_0) -> eval_start_4(v_m,v_n,v_x_0,v_y_0) True (1,1) 6. eval_start_4(v_m,v_n,v_x_0,v_y_0) -> eval_start_5(v_m,v_n,v_x_0,v_y_0) True (1,1) 7. eval_start_5(v_m,v_n,v_x_0,v_y_0) -> eval_start_6(v_m,v_n,v_x_0,v_y_0) True (1,1) 8. eval_start_6(v_m,v_n,v_x_0,v_y_0) -> eval_start_7(v_m,v_n,v_x_0,v_y_0) True (1,1) 9. eval_start_7(v_m,v_n,v_x_0,v_y_0) -> eval_start_8(v_m,v_n,v_x_0,v_y_0) True (1,1) 10. eval_start_8(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_m,v_n,0,0) True (1,1) 11. eval_start_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb2_in(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_0] 12. eval_start_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && v_x_0 >= v_n] 13. eval_start_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_m,v_n,1 + v_x_0,1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 (1 + v_n,1) && -1 + v_n + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1 + v_n + v_y_0 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] 14. eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb4_in(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1 + v_m >= v_y_0] 15. eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb5_in(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (1,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && v_y_0 >= v_m] 16. eval_start_bb4_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_m,v_n,1 + v_x_0,1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 (v_m,1) && -1 + v_m + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && -1 + v_m + v_y_0 >= 0 && -1 + v_m + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1 + v_m + v_x_0 >= 0 && -1 + v_m + -1*v_n >= 0 && -1 + v_m >= 0] 17. eval_start_bb5_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_stop(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (1,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && -1*v_m + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1*v_m + v_x_0 >= 0] 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_6,4) ;(eval_start_7,4) ;(eval_start_8,4) ;(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_start,4) ;(eval_start_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10},10->{11,12},11->{13},12->{14,15} ,13->{11,12},14->{16},15->{17},16->{12},17->{}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 6: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb0_in(v_m,v_n,v_x_0,v_y_0) True (1,1) 1. eval_start_bb0_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_0(v_m,v_n,v_x_0,v_y_0) True (1,1) 2. eval_start_0(v_m,v_n,v_x_0,v_y_0) -> eval_start_1(v_m,v_n,v_x_0,v_y_0) True (1,1) 3. eval_start_1(v_m,v_n,v_x_0,v_y_0) -> eval_start_2(v_m,v_n,v_x_0,v_y_0) True (1,1) 4. eval_start_2(v_m,v_n,v_x_0,v_y_0) -> eval_start_3(v_m,v_n,v_x_0,v_y_0) True (1,1) 5. eval_start_3(v_m,v_n,v_x_0,v_y_0) -> eval_start_4(v_m,v_n,v_x_0,v_y_0) True (1,1) 6. eval_start_4(v_m,v_n,v_x_0,v_y_0) -> eval_start_5(v_m,v_n,v_x_0,v_y_0) True (1,1) 7. eval_start_5(v_m,v_n,v_x_0,v_y_0) -> eval_start_6(v_m,v_n,v_x_0,v_y_0) True (1,1) 8. eval_start_6(v_m,v_n,v_x_0,v_y_0) -> eval_start_7(v_m,v_n,v_x_0,v_y_0) True (1,1) 9. eval_start_7(v_m,v_n,v_x_0,v_y_0) -> eval_start_8(v_m,v_n,v_x_0,v_y_0) True (1,1) 10. eval_start_8(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_m,v_n,0,0) True (1,1) 11. eval_start_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb2_in(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (2 + v_n,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_0] 12. eval_start_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (2 + v_m + v_n,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && v_x_0 >= v_n] 13. eval_start_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_m,v_n,1 + v_x_0,1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 (1 + v_n,1) && -1 + v_n + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1 + v_n + v_y_0 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] 14. eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb4_in(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (2 + v_m + v_n,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1 + v_m >= v_y_0] 15. eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb5_in(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (1,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && v_y_0 >= v_m] 16. eval_start_bb4_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_m,v_n,1 + v_x_0,1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 (v_m,1) && -1 + v_m + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && -1 + v_m + v_y_0 >= 0 && -1 + v_m + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1 + v_m + v_x_0 >= 0 && -1 + v_m + -1*v_n >= 0 && -1 + v_m >= 0] 17. eval_start_bb5_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_stop(v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (1,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && -1*v_m + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1*v_m + v_x_0 >= 0] 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_6,4) ;(eval_start_7,4) ;(eval_start_8,4) ;(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_start,4) ;(eval_start_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10},10->{11,12},11->{13},12->{14,15} ,13->{11,12},14->{16},15->{17},16->{12},17->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: The problem is already solved. YES(?,O(n^1))