YES(?,O(n^1)) * Step 1: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_speedDis1_start(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb0_in(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 1. eval_speedDis1_bb0_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_0(v__0,v__01,v_m,v_n,v_x,v_y) True (?,1) 2. eval_speedDis1_0(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_1(v__0,v__01,v_m,v_n,v_x,v_y) True (?,1) 3. eval_speedDis1_1(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_2(v__0,v__01,v_m,v_n,v_x,v_y) True (?,1) 4. eval_speedDis1_2(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_3(v__0,v__01,v_m,v_n,v_x,v_y) True (?,1) 5. eval_speedDis1_3(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_4(v__0,v__01,v_m,v_n,v_x,v_y) True (?,1) 6. eval_speedDis1_4(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_5(v__0,v__01,v_m,v_n,v_x,v_y) True (?,1) 7. eval_speedDis1_5(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_6(v__0,v__01,v_m,v_n,v_x,v_y) True (?,1) 8. eval_speedDis1_6(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb1_in(v_x,v_y,v_m,v_n,v_x,v_y) True (?,1) 9. eval_speedDis1_bb1_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb2_in(v__0,v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 && v__0 + -1*v_x >= 0 && -1 + v_n >= v__0] (?,1) 10. eval_speedDis1_bb1_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb3_in(v__0,v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 && v__0 + -1*v_x >= 0 && v__0 >= v_n] (?,1) 11. eval_speedDis1_bb2_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb1_in(v__0,1 + v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && -1 + v_n + -1*v_x >= 0 && v__0 + -1*v_x >= 0 && -1 + -1*v__0 + v_n >= 0 && -1 + v_m >= v__01] 12. eval_speedDis1_bb2_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb1_in(1 + v__0,v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && -1 + v_n + -1*v_x >= 0 && v__0 + -1*v_x >= 0 && -1 + -1*v__0 + v_n >= 0 && v__01 >= v_m] 13. eval_speedDis1_bb3_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_stop(v__0,v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 && v__0 + -1*v_x >= 0 && v__0 + -1*v_n >= 0] (?,1) Signature: {(eval_speedDis1_0,6) ;(eval_speedDis1_1,6) ;(eval_speedDis1_2,6) ;(eval_speedDis1_3,6) ;(eval_speedDis1_4,6) ;(eval_speedDis1_5,6) ;(eval_speedDis1_6,6) ;(eval_speedDis1_bb0_in,6) ;(eval_speedDis1_bb1_in,6) ;(eval_speedDis1_bb2_in,6) ;(eval_speedDis1_bb3_in,6) ;(eval_speedDis1_start,6) ;(eval_speedDis1_stop,6)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9,10},9->{11,12},10->{13},11->{9,10},12->{9 ,10},13->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_speedDis1_start(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb0_in(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 1. eval_speedDis1_bb0_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_0(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 2. eval_speedDis1_0(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_1(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 3. eval_speedDis1_1(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_2(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 4. eval_speedDis1_2(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_3(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 5. eval_speedDis1_3(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_4(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 6. eval_speedDis1_4(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_5(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 7. eval_speedDis1_5(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_6(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 8. eval_speedDis1_6(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb1_in(v_x,v_y,v_m,v_n,v_x,v_y) True (1,1) 9. eval_speedDis1_bb1_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb2_in(v__0,v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 && v__0 + -1*v_x >= 0 && -1 + v_n >= v__0] (?,1) 10. eval_speedDis1_bb1_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb3_in(v__0,v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 && v__0 + -1*v_x >= 0 && v__0 >= v_n] (1,1) 11. eval_speedDis1_bb2_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb1_in(v__0,1 + v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && -1 + v_n + -1*v_x >= 0 && v__0 + -1*v_x >= 0 && -1 + -1*v__0 + v_n >= 0 && -1 + v_m >= v__01] 12. eval_speedDis1_bb2_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb1_in(1 + v__0,v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && -1 + v_n + -1*v_x >= 0 && v__0 + -1*v_x >= 0 && -1 + -1*v__0 + v_n >= 0 && v__01 >= v_m] 13. eval_speedDis1_bb3_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_stop(v__0,v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 && v__0 + -1*v_x >= 0 && v__0 + -1*v_n >= 0] (1,1) Signature: {(eval_speedDis1_0,6) ;(eval_speedDis1_1,6) ;(eval_speedDis1_2,6) ;(eval_speedDis1_3,6) ;(eval_speedDis1_4,6) ;(eval_speedDis1_5,6) ;(eval_speedDis1_6,6) ;(eval_speedDis1_bb0_in,6) ;(eval_speedDis1_bb1_in,6) ;(eval_speedDis1_bb2_in,6) ;(eval_speedDis1_bb3_in,6) ;(eval_speedDis1_start,6) ;(eval_speedDis1_stop,6)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9,10},9->{11,12},10->{13},11->{9,10},12->{9 ,10},13->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(11,10)] * Step 3: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_speedDis1_start(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb0_in(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 1. eval_speedDis1_bb0_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_0(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 2. eval_speedDis1_0(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_1(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 3. eval_speedDis1_1(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_2(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 4. eval_speedDis1_2(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_3(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 5. eval_speedDis1_3(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_4(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 6. eval_speedDis1_4(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_5(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 7. eval_speedDis1_5(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_6(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 8. eval_speedDis1_6(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb1_in(v_x,v_y,v_m,v_n,v_x,v_y) True (1,1) 9. eval_speedDis1_bb1_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb2_in(v__0,v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 && v__0 + -1*v_x >= 0 && -1 + v_n >= v__0] (?,1) 10. eval_speedDis1_bb1_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb3_in(v__0,v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 && v__0 + -1*v_x >= 0 && v__0 >= v_n] (1,1) 11. eval_speedDis1_bb2_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb1_in(v__0,1 + v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && -1 + v_n + -1*v_x >= 0 && v__0 + -1*v_x >= 0 && -1 + -1*v__0 + v_n >= 0 && -1 + v_m >= v__01] 12. eval_speedDis1_bb2_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb1_in(1 + v__0,v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && -1 + v_n + -1*v_x >= 0 && v__0 + -1*v_x >= 0 && -1 + -1*v__0 + v_n >= 0 && v__01 >= v_m] 13. eval_speedDis1_bb3_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_stop(v__0,v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 && v__0 + -1*v_x >= 0 && v__0 + -1*v_n >= 0] (1,1) Signature: {(eval_speedDis1_0,6) ;(eval_speedDis1_1,6) ;(eval_speedDis1_2,6) ;(eval_speedDis1_3,6) ;(eval_speedDis1_4,6) ;(eval_speedDis1_5,6) ;(eval_speedDis1_6,6) ;(eval_speedDis1_bb0_in,6) ;(eval_speedDis1_bb1_in,6) ;(eval_speedDis1_bb2_in,6) ;(eval_speedDis1_bb3_in,6) ;(eval_speedDis1_start,6) ;(eval_speedDis1_stop,6)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9,10},9->{11,12},10->{13},11->{9},12->{9,10} ,13->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval_speedDis1_0) = x4 + -1*x5 p(eval_speedDis1_1) = x4 + -1*x5 p(eval_speedDis1_2) = x4 + -1*x5 p(eval_speedDis1_3) = x4 + -1*x5 p(eval_speedDis1_4) = x4 + -1*x5 p(eval_speedDis1_5) = x4 + -1*x5 p(eval_speedDis1_6) = x4 + -1*x5 p(eval_speedDis1_bb0_in) = x4 + -1*x5 p(eval_speedDis1_bb1_in) = -1*x1 + x4 p(eval_speedDis1_bb2_in) = -1*x1 + x4 p(eval_speedDis1_bb3_in) = -1*x1 + x4 p(eval_speedDis1_start) = x4 + -1*x5 p(eval_speedDis1_stop) = -1*x1 + x4 Following rules are strictly oriented: [v__01 + -1*v_y >= 0 ==> && -1 + v_n + -1*v_x >= 0 && v__0 + -1*v_x >= 0 && -1 + -1*v__0 + v_n >= 0 && v__01 >= v_m] eval_speedDis1_bb2_in(v__0,v__01,v_m,v_n,v_x,v_y) = -1*v__0 + v_n > -1 + -1*v__0 + v_n = eval_speedDis1_bb1_in(1 + v__0,v__01,v_m,v_n,v_x,v_y) Following rules are weakly oriented: True ==> eval_speedDis1_start(v__0,v__01,v_m,v_n,v_x,v_y) = v_n + -1*v_x >= v_n + -1*v_x = eval_speedDis1_bb0_in(v__0,v__01,v_m,v_n,v_x,v_y) True ==> eval_speedDis1_bb0_in(v__0,v__01,v_m,v_n,v_x,v_y) = v_n + -1*v_x >= v_n + -1*v_x = eval_speedDis1_0(v__0,v__01,v_m,v_n,v_x,v_y) True ==> eval_speedDis1_0(v__0,v__01,v_m,v_n,v_x,v_y) = v_n + -1*v_x >= v_n + -1*v_x = eval_speedDis1_1(v__0,v__01,v_m,v_n,v_x,v_y) True ==> eval_speedDis1_1(v__0,v__01,v_m,v_n,v_x,v_y) = v_n + -1*v_x >= v_n + -1*v_x = eval_speedDis1_2(v__0,v__01,v_m,v_n,v_x,v_y) True ==> eval_speedDis1_2(v__0,v__01,v_m,v_n,v_x,v_y) = v_n + -1*v_x >= v_n + -1*v_x = eval_speedDis1_3(v__0,v__01,v_m,v_n,v_x,v_y) True ==> eval_speedDis1_3(v__0,v__01,v_m,v_n,v_x,v_y) = v_n + -1*v_x >= v_n + -1*v_x = eval_speedDis1_4(v__0,v__01,v_m,v_n,v_x,v_y) True ==> eval_speedDis1_4(v__0,v__01,v_m,v_n,v_x,v_y) = v_n + -1*v_x >= v_n + -1*v_x = eval_speedDis1_5(v__0,v__01,v_m,v_n,v_x,v_y) True ==> eval_speedDis1_5(v__0,v__01,v_m,v_n,v_x,v_y) = v_n + -1*v_x >= v_n + -1*v_x = eval_speedDis1_6(v__0,v__01,v_m,v_n,v_x,v_y) True ==> eval_speedDis1_6(v__0,v__01,v_m,v_n,v_x,v_y) = v_n + -1*v_x >= v_n + -1*v_x = eval_speedDis1_bb1_in(v_x,v_y,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 && v__0 + -1*v_x >= 0 && -1 + v_n >= v__0] ==> eval_speedDis1_bb1_in(v__0,v__01,v_m,v_n,v_x,v_y) = -1*v__0 + v_n >= -1*v__0 + v_n = eval_speedDis1_bb2_in(v__0,v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 && v__0 + -1*v_x >= 0 && v__0 >= v_n] ==> eval_speedDis1_bb1_in(v__0,v__01,v_m,v_n,v_x,v_y) = -1*v__0 + v_n >= -1*v__0 + v_n = eval_speedDis1_bb3_in(v__0,v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 ==> && -1 + v_n + -1*v_x >= 0 && v__0 + -1*v_x >= 0 && -1 + -1*v__0 + v_n >= 0 && -1 + v_m >= v__01] eval_speedDis1_bb2_in(v__0,v__01,v_m,v_n,v_x,v_y) = -1*v__0 + v_n >= -1*v__0 + v_n = eval_speedDis1_bb1_in(v__0,1 + v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 && v__0 + -1*v_x >= 0 && v__0 + -1*v_n >= 0] ==> eval_speedDis1_bb3_in(v__0,v__01,v_m,v_n,v_x,v_y) = -1*v__0 + v_n >= -1*v__0 + v_n = eval_speedDis1_stop(v__0,v__01,v_m,v_n,v_x,v_y) * Step 4: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_speedDis1_start(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb0_in(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 1. eval_speedDis1_bb0_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_0(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 2. eval_speedDis1_0(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_1(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 3. eval_speedDis1_1(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_2(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 4. eval_speedDis1_2(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_3(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 5. eval_speedDis1_3(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_4(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 6. eval_speedDis1_4(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_5(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 7. eval_speedDis1_5(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_6(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 8. eval_speedDis1_6(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb1_in(v_x,v_y,v_m,v_n,v_x,v_y) True (1,1) 9. eval_speedDis1_bb1_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb2_in(v__0,v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 && v__0 + -1*v_x >= 0 && -1 + v_n >= v__0] (?,1) 10. eval_speedDis1_bb1_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb3_in(v__0,v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 && v__0 + -1*v_x >= 0 && v__0 >= v_n] (1,1) 11. eval_speedDis1_bb2_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb1_in(v__0,1 + v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && -1 + v_n + -1*v_x >= 0 && v__0 + -1*v_x >= 0 && -1 + -1*v__0 + v_n >= 0 && -1 + v_m >= v__01] 12. eval_speedDis1_bb2_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb1_in(1 + v__0,v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 (v_n + v_x,1) && -1 + v_n + -1*v_x >= 0 && v__0 + -1*v_x >= 0 && -1 + -1*v__0 + v_n >= 0 && v__01 >= v_m] 13. eval_speedDis1_bb3_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_stop(v__0,v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 && v__0 + -1*v_x >= 0 && v__0 + -1*v_n >= 0] (1,1) Signature: {(eval_speedDis1_0,6) ;(eval_speedDis1_1,6) ;(eval_speedDis1_2,6) ;(eval_speedDis1_3,6) ;(eval_speedDis1_4,6) ;(eval_speedDis1_5,6) ;(eval_speedDis1_6,6) ;(eval_speedDis1_bb0_in,6) ;(eval_speedDis1_bb1_in,6) ;(eval_speedDis1_bb2_in,6) ;(eval_speedDis1_bb3_in,6) ;(eval_speedDis1_start,6) ;(eval_speedDis1_stop,6)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9,10},9->{11,12},10->{13},11->{9},12->{9,10} ,13->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval_speedDis1_0) = x3 + -1*x6 p(eval_speedDis1_1) = x3 + -1*x6 p(eval_speedDis1_2) = x3 + -1*x6 p(eval_speedDis1_3) = x3 + -1*x6 p(eval_speedDis1_4) = x3 + -1*x6 p(eval_speedDis1_5) = x3 + -1*x6 p(eval_speedDis1_6) = x3 + -1*x6 p(eval_speedDis1_bb0_in) = x3 + -1*x6 p(eval_speedDis1_bb1_in) = -1*x2 + x3 p(eval_speedDis1_bb2_in) = -1*x2 + x3 p(eval_speedDis1_bb3_in) = -1*x2 + x3 p(eval_speedDis1_start) = x3 + -1*x6 p(eval_speedDis1_stop) = -1*x2 + x3 Following rules are strictly oriented: [v__01 + -1*v_y >= 0 ==> && -1 + v_n + -1*v_x >= 0 && v__0 + -1*v_x >= 0 && -1 + -1*v__0 + v_n >= 0 && -1 + v_m >= v__01] eval_speedDis1_bb2_in(v__0,v__01,v_m,v_n,v_x,v_y) = -1*v__01 + v_m > -1 + -1*v__01 + v_m = eval_speedDis1_bb1_in(v__0,1 + v__01,v_m,v_n,v_x,v_y) Following rules are weakly oriented: True ==> eval_speedDis1_start(v__0,v__01,v_m,v_n,v_x,v_y) = v_m + -1*v_y >= v_m + -1*v_y = eval_speedDis1_bb0_in(v__0,v__01,v_m,v_n,v_x,v_y) True ==> eval_speedDis1_bb0_in(v__0,v__01,v_m,v_n,v_x,v_y) = v_m + -1*v_y >= v_m + -1*v_y = eval_speedDis1_0(v__0,v__01,v_m,v_n,v_x,v_y) True ==> eval_speedDis1_0(v__0,v__01,v_m,v_n,v_x,v_y) = v_m + -1*v_y >= v_m + -1*v_y = eval_speedDis1_1(v__0,v__01,v_m,v_n,v_x,v_y) True ==> eval_speedDis1_1(v__0,v__01,v_m,v_n,v_x,v_y) = v_m + -1*v_y >= v_m + -1*v_y = eval_speedDis1_2(v__0,v__01,v_m,v_n,v_x,v_y) True ==> eval_speedDis1_2(v__0,v__01,v_m,v_n,v_x,v_y) = v_m + -1*v_y >= v_m + -1*v_y = eval_speedDis1_3(v__0,v__01,v_m,v_n,v_x,v_y) True ==> eval_speedDis1_3(v__0,v__01,v_m,v_n,v_x,v_y) = v_m + -1*v_y >= v_m + -1*v_y = eval_speedDis1_4(v__0,v__01,v_m,v_n,v_x,v_y) True ==> eval_speedDis1_4(v__0,v__01,v_m,v_n,v_x,v_y) = v_m + -1*v_y >= v_m + -1*v_y = eval_speedDis1_5(v__0,v__01,v_m,v_n,v_x,v_y) True ==> eval_speedDis1_5(v__0,v__01,v_m,v_n,v_x,v_y) = v_m + -1*v_y >= v_m + -1*v_y = eval_speedDis1_6(v__0,v__01,v_m,v_n,v_x,v_y) True ==> eval_speedDis1_6(v__0,v__01,v_m,v_n,v_x,v_y) = v_m + -1*v_y >= v_m + -1*v_y = eval_speedDis1_bb1_in(v_x,v_y,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 && v__0 + -1*v_x >= 0 && -1 + v_n >= v__0] ==> eval_speedDis1_bb1_in(v__0,v__01,v_m,v_n,v_x,v_y) = -1*v__01 + v_m >= -1*v__01 + v_m = eval_speedDis1_bb2_in(v__0,v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 && v__0 + -1*v_x >= 0 && v__0 >= v_n] ==> eval_speedDis1_bb1_in(v__0,v__01,v_m,v_n,v_x,v_y) = -1*v__01 + v_m >= -1*v__01 + v_m = eval_speedDis1_bb3_in(v__0,v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 ==> && -1 + v_n + -1*v_x >= 0 && v__0 + -1*v_x >= 0 && -1 + -1*v__0 + v_n >= 0 && v__01 >= v_m] eval_speedDis1_bb2_in(v__0,v__01,v_m,v_n,v_x,v_y) = -1*v__01 + v_m >= -1*v__01 + v_m = eval_speedDis1_bb1_in(1 + v__0,v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 && v__0 + -1*v_x >= 0 && v__0 + -1*v_n >= 0] ==> eval_speedDis1_bb3_in(v__0,v__01,v_m,v_n,v_x,v_y) = -1*v__01 + v_m >= -1*v__01 + v_m = eval_speedDis1_stop(v__0,v__01,v_m,v_n,v_x,v_y) * Step 5: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_speedDis1_start(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb0_in(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 1. eval_speedDis1_bb0_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_0(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 2. eval_speedDis1_0(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_1(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 3. eval_speedDis1_1(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_2(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 4. eval_speedDis1_2(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_3(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 5. eval_speedDis1_3(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_4(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 6. eval_speedDis1_4(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_5(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 7. eval_speedDis1_5(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_6(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 8. eval_speedDis1_6(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb1_in(v_x,v_y,v_m,v_n,v_x,v_y) True (1,1) 9. eval_speedDis1_bb1_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb2_in(v__0,v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 && v__0 + -1*v_x >= 0 && -1 + v_n >= v__0] (?,1) 10. eval_speedDis1_bb1_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb3_in(v__0,v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 && v__0 + -1*v_x >= 0 && v__0 >= v_n] (1,1) 11. eval_speedDis1_bb2_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb1_in(v__0,1 + v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 (v_m + v_y,1) && -1 + v_n + -1*v_x >= 0 && v__0 + -1*v_x >= 0 && -1 + -1*v__0 + v_n >= 0 && -1 + v_m >= v__01] 12. eval_speedDis1_bb2_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb1_in(1 + v__0,v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 (v_n + v_x,1) && -1 + v_n + -1*v_x >= 0 && v__0 + -1*v_x >= 0 && -1 + -1*v__0 + v_n >= 0 && v__01 >= v_m] 13. eval_speedDis1_bb3_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_stop(v__0,v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 && v__0 + -1*v_x >= 0 && v__0 + -1*v_n >= 0] (1,1) Signature: {(eval_speedDis1_0,6) ;(eval_speedDis1_1,6) ;(eval_speedDis1_2,6) ;(eval_speedDis1_3,6) ;(eval_speedDis1_4,6) ;(eval_speedDis1_5,6) ;(eval_speedDis1_6,6) ;(eval_speedDis1_bb0_in,6) ;(eval_speedDis1_bb1_in,6) ;(eval_speedDis1_bb2_in,6) ;(eval_speedDis1_bb3_in,6) ;(eval_speedDis1_start,6) ;(eval_speedDis1_stop,6)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9,10},9->{11,12},10->{13},11->{9},12->{9,10} ,13->{}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 6: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_speedDis1_start(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb0_in(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 1. eval_speedDis1_bb0_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_0(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 2. eval_speedDis1_0(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_1(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 3. eval_speedDis1_1(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_2(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 4. eval_speedDis1_2(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_3(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 5. eval_speedDis1_3(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_4(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 6. eval_speedDis1_4(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_5(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 7. eval_speedDis1_5(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_6(v__0,v__01,v_m,v_n,v_x,v_y) True (1,1) 8. eval_speedDis1_6(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb1_in(v_x,v_y,v_m,v_n,v_x,v_y) True (1,1) 9. eval_speedDis1_bb1_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb2_in(v__0,v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 && v__0 + -1*v_x >= 0 && -1 + v_n >= v__0] (1 + v_m + v_n + v_x + v_y,1) 10. eval_speedDis1_bb1_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb3_in(v__0,v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 && v__0 + -1*v_x >= 0 && v__0 >= v_n] (1,1) 11. eval_speedDis1_bb2_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb1_in(v__0,1 + v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 (v_m + v_y,1) && -1 + v_n + -1*v_x >= 0 && v__0 + -1*v_x >= 0 && -1 + -1*v__0 + v_n >= 0 && -1 + v_m >= v__01] 12. eval_speedDis1_bb2_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_bb1_in(1 + v__0,v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 (v_n + v_x,1) && -1 + v_n + -1*v_x >= 0 && v__0 + -1*v_x >= 0 && -1 + -1*v__0 + v_n >= 0 && v__01 >= v_m] 13. eval_speedDis1_bb3_in(v__0,v__01,v_m,v_n,v_x,v_y) -> eval_speedDis1_stop(v__0,v__01,v_m,v_n,v_x,v_y) [v__01 + -1*v_y >= 0 && v__0 + -1*v_x >= 0 && v__0 + -1*v_n >= 0] (1,1) Signature: {(eval_speedDis1_0,6) ;(eval_speedDis1_1,6) ;(eval_speedDis1_2,6) ;(eval_speedDis1_3,6) ;(eval_speedDis1_4,6) ;(eval_speedDis1_5,6) ;(eval_speedDis1_6,6) ;(eval_speedDis1_bb0_in,6) ;(eval_speedDis1_bb1_in,6) ;(eval_speedDis1_bb2_in,6) ;(eval_speedDis1_bb3_in,6) ;(eval_speedDis1_start,6) ;(eval_speedDis1_stop,6)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9,10},9->{11,12},10->{13},11->{9},12->{9,10} ,13->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: The problem is already solved. YES(?,O(n^1))