YES(?,O(n^1)) * Step 1: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_speedSimpleMultiple_start(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb0_in(v_m,v_n,v_x_0,v_y_0) True (1,1) 1. eval_speedSimpleMultiple_bb0_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_0(v_m,v_n,v_x_0,v_y_0) True (?,1) 2. eval_speedSimpleMultiple_0(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_1(v_m,v_n,v_x_0,v_y_0) True (?,1) 3. eval_speedSimpleMultiple_1(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_2(v_m,v_n,v_x_0,v_y_0) True (?,1) 4. eval_speedSimpleMultiple_2(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_3(v_m,v_n,v_x_0,v_y_0) True (?,1) 5. eval_speedSimpleMultiple_3(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_4(v_m,v_n,v_x_0,v_y_0) True (?,1) 6. eval_speedSimpleMultiple_4(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_5(v_m,v_n,v_x_0,v_y_0) True (?,1) 7. eval_speedSimpleMultiple_5(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_6(v_m,v_n,v_x_0,v_y_0) True (?,1) 8. eval_speedSimpleMultiple_6(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb1_in(v_m,v_n,0,0) True (?,1) 9. eval_speedSimpleMultiple_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb2_in(v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_0] (?,1) 10. eval_speedSimpleMultiple_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb3_in(v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && v_x_0 >= v_n] (?,1) 11. eval_speedSimpleMultiple_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb1_in(v_m,v_n,v_x_0,1 + v_y_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 && -1 + v_m >= v_y_0] 12. eval_speedSimpleMultiple_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb1_in(v_m,v_n,1 + v_x_0,v_y_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 && v_y_0 >= v_m] 13. eval_speedSimpleMultiple_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_stop(v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] (?,1) Signature: {(eval_speedSimpleMultiple_0,4) ;(eval_speedSimpleMultiple_1,4) ;(eval_speedSimpleMultiple_2,4) ;(eval_speedSimpleMultiple_3,4) ;(eval_speedSimpleMultiple_4,4) ;(eval_speedSimpleMultiple_5,4) ;(eval_speedSimpleMultiple_6,4) ;(eval_speedSimpleMultiple_bb0_in,4) ;(eval_speedSimpleMultiple_bb1_in,4) ;(eval_speedSimpleMultiple_bb2_in,4) ;(eval_speedSimpleMultiple_bb3_in,4) ;(eval_speedSimpleMultiple_start,4) ;(eval_speedSimpleMultiple_stop,4)} 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_speedSimpleMultiple_start(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb0_in(v_m,v_n,v_x_0,v_y_0) True (1,1) 1. eval_speedSimpleMultiple_bb0_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_0(v_m,v_n,v_x_0,v_y_0) True (1,1) 2. eval_speedSimpleMultiple_0(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_1(v_m,v_n,v_x_0,v_y_0) True (1,1) 3. eval_speedSimpleMultiple_1(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_2(v_m,v_n,v_x_0,v_y_0) True (1,1) 4. eval_speedSimpleMultiple_2(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_3(v_m,v_n,v_x_0,v_y_0) True (1,1) 5. eval_speedSimpleMultiple_3(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_4(v_m,v_n,v_x_0,v_y_0) True (1,1) 6. eval_speedSimpleMultiple_4(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_5(v_m,v_n,v_x_0,v_y_0) True (1,1) 7. eval_speedSimpleMultiple_5(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_6(v_m,v_n,v_x_0,v_y_0) True (1,1) 8. eval_speedSimpleMultiple_6(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb1_in(v_m,v_n,0,0) True (1,1) 9. eval_speedSimpleMultiple_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb2_in(v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_0] (?,1) 10. eval_speedSimpleMultiple_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb3_in(v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && v_x_0 >= v_n] (1,1) 11. eval_speedSimpleMultiple_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb1_in(v_m,v_n,v_x_0,1 + v_y_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 && -1 + v_m >= v_y_0] 12. eval_speedSimpleMultiple_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb1_in(v_m,v_n,1 + v_x_0,v_y_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 && v_y_0 >= v_m] 13. eval_speedSimpleMultiple_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_stop(v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] (1,1) Signature: {(eval_speedSimpleMultiple_0,4) ;(eval_speedSimpleMultiple_1,4) ;(eval_speedSimpleMultiple_2,4) ;(eval_speedSimpleMultiple_3,4) ;(eval_speedSimpleMultiple_4,4) ;(eval_speedSimpleMultiple_5,4) ;(eval_speedSimpleMultiple_6,4) ;(eval_speedSimpleMultiple_bb0_in,4) ;(eval_speedSimpleMultiple_bb1_in,4) ;(eval_speedSimpleMultiple_bb2_in,4) ;(eval_speedSimpleMultiple_bb3_in,4) ;(eval_speedSimpleMultiple_start,4) ;(eval_speedSimpleMultiple_stop,4)} 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_speedSimpleMultiple_start(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb0_in(v_m,v_n,v_x_0,v_y_0) True (1,1) 1. eval_speedSimpleMultiple_bb0_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_0(v_m,v_n,v_x_0,v_y_0) True (1,1) 2. eval_speedSimpleMultiple_0(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_1(v_m,v_n,v_x_0,v_y_0) True (1,1) 3. eval_speedSimpleMultiple_1(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_2(v_m,v_n,v_x_0,v_y_0) True (1,1) 4. eval_speedSimpleMultiple_2(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_3(v_m,v_n,v_x_0,v_y_0) True (1,1) 5. eval_speedSimpleMultiple_3(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_4(v_m,v_n,v_x_0,v_y_0) True (1,1) 6. eval_speedSimpleMultiple_4(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_5(v_m,v_n,v_x_0,v_y_0) True (1,1) 7. eval_speedSimpleMultiple_5(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_6(v_m,v_n,v_x_0,v_y_0) True (1,1) 8. eval_speedSimpleMultiple_6(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb1_in(v_m,v_n,0,0) True (1,1) 9. eval_speedSimpleMultiple_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb2_in(v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_0] (?,1) 10. eval_speedSimpleMultiple_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb3_in(v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && v_x_0 >= v_n] (1,1) 11. eval_speedSimpleMultiple_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb1_in(v_m,v_n,v_x_0,1 + v_y_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 && -1 + v_m >= v_y_0] 12. eval_speedSimpleMultiple_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb1_in(v_m,v_n,1 + v_x_0,v_y_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 && v_y_0 >= v_m] 13. eval_speedSimpleMultiple_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_stop(v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] (1,1) Signature: {(eval_speedSimpleMultiple_0,4) ;(eval_speedSimpleMultiple_1,4) ;(eval_speedSimpleMultiple_2,4) ;(eval_speedSimpleMultiple_3,4) ;(eval_speedSimpleMultiple_4,4) ;(eval_speedSimpleMultiple_5,4) ;(eval_speedSimpleMultiple_6,4) ;(eval_speedSimpleMultiple_bb0_in,4) ;(eval_speedSimpleMultiple_bb1_in,4) ;(eval_speedSimpleMultiple_bb2_in,4) ;(eval_speedSimpleMultiple_bb3_in,4) ;(eval_speedSimpleMultiple_start,4) ;(eval_speedSimpleMultiple_stop,4)} 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_speedSimpleMultiple_0) = x2 p(eval_speedSimpleMultiple_1) = x2 p(eval_speedSimpleMultiple_2) = x2 p(eval_speedSimpleMultiple_3) = x2 p(eval_speedSimpleMultiple_4) = x2 p(eval_speedSimpleMultiple_5) = x2 p(eval_speedSimpleMultiple_6) = x2 p(eval_speedSimpleMultiple_bb0_in) = x2 p(eval_speedSimpleMultiple_bb1_in) = x2 + -1*x3 p(eval_speedSimpleMultiple_bb2_in) = x2 + -1*x3 p(eval_speedSimpleMultiple_bb3_in) = x2 + -1*x3 p(eval_speedSimpleMultiple_start) = x2 p(eval_speedSimpleMultiple_stop) = x2 + -1*x3 Following rules are strictly oriented: [v_y_0 >= 0 ==> && 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 && v_y_0 >= v_m] eval_speedSimpleMultiple_bb2_in(v_m,v_n,v_x_0,v_y_0) = v_n + -1*v_x_0 > -1 + v_n + -1*v_x_0 = eval_speedSimpleMultiple_bb1_in(v_m,v_n,1 + v_x_0,v_y_0) Following rules are weakly oriented: True ==> eval_speedSimpleMultiple_start(v_m,v_n,v_x_0,v_y_0) = v_n >= v_n = eval_speedSimpleMultiple_bb0_in(v_m,v_n,v_x_0,v_y_0) True ==> eval_speedSimpleMultiple_bb0_in(v_m,v_n,v_x_0,v_y_0) = v_n >= v_n = eval_speedSimpleMultiple_0(v_m,v_n,v_x_0,v_y_0) True ==> eval_speedSimpleMultiple_0(v_m,v_n,v_x_0,v_y_0) = v_n >= v_n = eval_speedSimpleMultiple_1(v_m,v_n,v_x_0,v_y_0) True ==> eval_speedSimpleMultiple_1(v_m,v_n,v_x_0,v_y_0) = v_n >= v_n = eval_speedSimpleMultiple_2(v_m,v_n,v_x_0,v_y_0) True ==> eval_speedSimpleMultiple_2(v_m,v_n,v_x_0,v_y_0) = v_n >= v_n = eval_speedSimpleMultiple_3(v_m,v_n,v_x_0,v_y_0) True ==> eval_speedSimpleMultiple_3(v_m,v_n,v_x_0,v_y_0) = v_n >= v_n = eval_speedSimpleMultiple_4(v_m,v_n,v_x_0,v_y_0) True ==> eval_speedSimpleMultiple_4(v_m,v_n,v_x_0,v_y_0) = v_n >= v_n = eval_speedSimpleMultiple_5(v_m,v_n,v_x_0,v_y_0) True ==> eval_speedSimpleMultiple_5(v_m,v_n,v_x_0,v_y_0) = v_n >= v_n = eval_speedSimpleMultiple_6(v_m,v_n,v_x_0,v_y_0) True ==> eval_speedSimpleMultiple_6(v_m,v_n,v_x_0,v_y_0) = v_n >= v_n = eval_speedSimpleMultiple_bb1_in(v_m,v_n,0,0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_0] ==> eval_speedSimpleMultiple_bb1_in(v_m,v_n,v_x_0,v_y_0) = v_n + -1*v_x_0 >= v_n + -1*v_x_0 = eval_speedSimpleMultiple_bb2_in(v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && v_x_0 >= v_n] ==> eval_speedSimpleMultiple_bb1_in(v_m,v_n,v_x_0,v_y_0) = v_n + -1*v_x_0 >= v_n + -1*v_x_0 = eval_speedSimpleMultiple_bb3_in(v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 ==> && 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 && -1 + v_m >= v_y_0] eval_speedSimpleMultiple_bb2_in(v_m,v_n,v_x_0,v_y_0) = v_n + -1*v_x_0 >= v_n + -1*v_x_0 = eval_speedSimpleMultiple_bb1_in(v_m,v_n,v_x_0,1 + v_y_0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] ==> eval_speedSimpleMultiple_bb3_in(v_m,v_n,v_x_0,v_y_0) = v_n + -1*v_x_0 >= v_n + -1*v_x_0 = eval_speedSimpleMultiple_stop(v_m,v_n,v_x_0,v_y_0) * Step 4: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_speedSimpleMultiple_start(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb0_in(v_m,v_n,v_x_0,v_y_0) True (1,1) 1. eval_speedSimpleMultiple_bb0_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_0(v_m,v_n,v_x_0,v_y_0) True (1,1) 2. eval_speedSimpleMultiple_0(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_1(v_m,v_n,v_x_0,v_y_0) True (1,1) 3. eval_speedSimpleMultiple_1(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_2(v_m,v_n,v_x_0,v_y_0) True (1,1) 4. eval_speedSimpleMultiple_2(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_3(v_m,v_n,v_x_0,v_y_0) True (1,1) 5. eval_speedSimpleMultiple_3(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_4(v_m,v_n,v_x_0,v_y_0) True (1,1) 6. eval_speedSimpleMultiple_4(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_5(v_m,v_n,v_x_0,v_y_0) True (1,1) 7. eval_speedSimpleMultiple_5(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_6(v_m,v_n,v_x_0,v_y_0) True (1,1) 8. eval_speedSimpleMultiple_6(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb1_in(v_m,v_n,0,0) True (1,1) 9. eval_speedSimpleMultiple_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb2_in(v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_0] (?,1) 10. eval_speedSimpleMultiple_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb3_in(v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && v_x_0 >= v_n] (1,1) 11. eval_speedSimpleMultiple_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb1_in(v_m,v_n,v_x_0,1 + v_y_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 && -1 + v_m >= v_y_0] 12. eval_speedSimpleMultiple_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb1_in(v_m,v_n,1 + v_x_0,v_y_0) [v_y_0 >= 0 (v_n,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 && v_y_0 >= v_m] 13. eval_speedSimpleMultiple_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_stop(v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] (1,1) Signature: {(eval_speedSimpleMultiple_0,4) ;(eval_speedSimpleMultiple_1,4) ;(eval_speedSimpleMultiple_2,4) ;(eval_speedSimpleMultiple_3,4) ;(eval_speedSimpleMultiple_4,4) ;(eval_speedSimpleMultiple_5,4) ;(eval_speedSimpleMultiple_6,4) ;(eval_speedSimpleMultiple_bb0_in,4) ;(eval_speedSimpleMultiple_bb1_in,4) ;(eval_speedSimpleMultiple_bb2_in,4) ;(eval_speedSimpleMultiple_bb3_in,4) ;(eval_speedSimpleMultiple_start,4) ;(eval_speedSimpleMultiple_stop,4)} 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_speedSimpleMultiple_0) = x1 p(eval_speedSimpleMultiple_1) = x1 p(eval_speedSimpleMultiple_2) = x1 p(eval_speedSimpleMultiple_3) = x1 p(eval_speedSimpleMultiple_4) = x1 p(eval_speedSimpleMultiple_5) = x1 p(eval_speedSimpleMultiple_6) = x1 p(eval_speedSimpleMultiple_bb0_in) = x1 p(eval_speedSimpleMultiple_bb1_in) = x1 + -1*x4 p(eval_speedSimpleMultiple_bb2_in) = x1 + -1*x4 p(eval_speedSimpleMultiple_bb3_in) = x1 + -1*x4 p(eval_speedSimpleMultiple_start) = x1 p(eval_speedSimpleMultiple_stop) = x1 + -1*x4 Following rules are strictly oriented: [v_y_0 >= 0 ==> && 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 && -1 + v_m >= v_y_0] eval_speedSimpleMultiple_bb2_in(v_m,v_n,v_x_0,v_y_0) = v_m + -1*v_y_0 > -1 + v_m + -1*v_y_0 = eval_speedSimpleMultiple_bb1_in(v_m,v_n,v_x_0,1 + v_y_0) Following rules are weakly oriented: True ==> eval_speedSimpleMultiple_start(v_m,v_n,v_x_0,v_y_0) = v_m >= v_m = eval_speedSimpleMultiple_bb0_in(v_m,v_n,v_x_0,v_y_0) True ==> eval_speedSimpleMultiple_bb0_in(v_m,v_n,v_x_0,v_y_0) = v_m >= v_m = eval_speedSimpleMultiple_0(v_m,v_n,v_x_0,v_y_0) True ==> eval_speedSimpleMultiple_0(v_m,v_n,v_x_0,v_y_0) = v_m >= v_m = eval_speedSimpleMultiple_1(v_m,v_n,v_x_0,v_y_0) True ==> eval_speedSimpleMultiple_1(v_m,v_n,v_x_0,v_y_0) = v_m >= v_m = eval_speedSimpleMultiple_2(v_m,v_n,v_x_0,v_y_0) True ==> eval_speedSimpleMultiple_2(v_m,v_n,v_x_0,v_y_0) = v_m >= v_m = eval_speedSimpleMultiple_3(v_m,v_n,v_x_0,v_y_0) True ==> eval_speedSimpleMultiple_3(v_m,v_n,v_x_0,v_y_0) = v_m >= v_m = eval_speedSimpleMultiple_4(v_m,v_n,v_x_0,v_y_0) True ==> eval_speedSimpleMultiple_4(v_m,v_n,v_x_0,v_y_0) = v_m >= v_m = eval_speedSimpleMultiple_5(v_m,v_n,v_x_0,v_y_0) True ==> eval_speedSimpleMultiple_5(v_m,v_n,v_x_0,v_y_0) = v_m >= v_m = eval_speedSimpleMultiple_6(v_m,v_n,v_x_0,v_y_0) True ==> eval_speedSimpleMultiple_6(v_m,v_n,v_x_0,v_y_0) = v_m >= v_m = eval_speedSimpleMultiple_bb1_in(v_m,v_n,0,0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_0] ==> eval_speedSimpleMultiple_bb1_in(v_m,v_n,v_x_0,v_y_0) = v_m + -1*v_y_0 >= v_m + -1*v_y_0 = eval_speedSimpleMultiple_bb2_in(v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && v_x_0 >= v_n] ==> eval_speedSimpleMultiple_bb1_in(v_m,v_n,v_x_0,v_y_0) = v_m + -1*v_y_0 >= v_m + -1*v_y_0 = eval_speedSimpleMultiple_bb3_in(v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 ==> && 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 && v_y_0 >= v_m] eval_speedSimpleMultiple_bb2_in(v_m,v_n,v_x_0,v_y_0) = v_m + -1*v_y_0 >= v_m + -1*v_y_0 = eval_speedSimpleMultiple_bb1_in(v_m,v_n,1 + v_x_0,v_y_0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] ==> eval_speedSimpleMultiple_bb3_in(v_m,v_n,v_x_0,v_y_0) = v_m + -1*v_y_0 >= v_m + -1*v_y_0 = eval_speedSimpleMultiple_stop(v_m,v_n,v_x_0,v_y_0) * Step 5: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_speedSimpleMultiple_start(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb0_in(v_m,v_n,v_x_0,v_y_0) True (1,1) 1. eval_speedSimpleMultiple_bb0_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_0(v_m,v_n,v_x_0,v_y_0) True (1,1) 2. eval_speedSimpleMultiple_0(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_1(v_m,v_n,v_x_0,v_y_0) True (1,1) 3. eval_speedSimpleMultiple_1(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_2(v_m,v_n,v_x_0,v_y_0) True (1,1) 4. eval_speedSimpleMultiple_2(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_3(v_m,v_n,v_x_0,v_y_0) True (1,1) 5. eval_speedSimpleMultiple_3(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_4(v_m,v_n,v_x_0,v_y_0) True (1,1) 6. eval_speedSimpleMultiple_4(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_5(v_m,v_n,v_x_0,v_y_0) True (1,1) 7. eval_speedSimpleMultiple_5(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_6(v_m,v_n,v_x_0,v_y_0) True (1,1) 8. eval_speedSimpleMultiple_6(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb1_in(v_m,v_n,0,0) True (1,1) 9. eval_speedSimpleMultiple_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb2_in(v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_0] (?,1) 10. eval_speedSimpleMultiple_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb3_in(v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && v_x_0 >= v_n] (1,1) 11. eval_speedSimpleMultiple_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb1_in(v_m,v_n,v_x_0,1 + v_y_0) [v_y_0 >= 0 (v_m,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 && -1 + v_m >= v_y_0] 12. eval_speedSimpleMultiple_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb1_in(v_m,v_n,1 + v_x_0,v_y_0) [v_y_0 >= 0 (v_n,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 && v_y_0 >= v_m] 13. eval_speedSimpleMultiple_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_stop(v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] (1,1) Signature: {(eval_speedSimpleMultiple_0,4) ;(eval_speedSimpleMultiple_1,4) ;(eval_speedSimpleMultiple_2,4) ;(eval_speedSimpleMultiple_3,4) ;(eval_speedSimpleMultiple_4,4) ;(eval_speedSimpleMultiple_5,4) ;(eval_speedSimpleMultiple_6,4) ;(eval_speedSimpleMultiple_bb0_in,4) ;(eval_speedSimpleMultiple_bb1_in,4) ;(eval_speedSimpleMultiple_bb2_in,4) ;(eval_speedSimpleMultiple_bb3_in,4) ;(eval_speedSimpleMultiple_start,4) ;(eval_speedSimpleMultiple_stop,4)} 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_speedSimpleMultiple_start(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb0_in(v_m,v_n,v_x_0,v_y_0) True (1,1) 1. eval_speedSimpleMultiple_bb0_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_0(v_m,v_n,v_x_0,v_y_0) True (1,1) 2. eval_speedSimpleMultiple_0(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_1(v_m,v_n,v_x_0,v_y_0) True (1,1) 3. eval_speedSimpleMultiple_1(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_2(v_m,v_n,v_x_0,v_y_0) True (1,1) 4. eval_speedSimpleMultiple_2(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_3(v_m,v_n,v_x_0,v_y_0) True (1,1) 5. eval_speedSimpleMultiple_3(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_4(v_m,v_n,v_x_0,v_y_0) True (1,1) 6. eval_speedSimpleMultiple_4(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_5(v_m,v_n,v_x_0,v_y_0) True (1,1) 7. eval_speedSimpleMultiple_5(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_6(v_m,v_n,v_x_0,v_y_0) True (1,1) 8. eval_speedSimpleMultiple_6(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb1_in(v_m,v_n,0,0) True (1,1) 9. eval_speedSimpleMultiple_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb2_in(v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_0] (1 + v_m + v_n,1) 10. eval_speedSimpleMultiple_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb3_in(v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && v_x_0 >= v_n] (1,1) 11. eval_speedSimpleMultiple_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb1_in(v_m,v_n,v_x_0,1 + v_y_0) [v_y_0 >= 0 (v_m,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 && -1 + v_m >= v_y_0] 12. eval_speedSimpleMultiple_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb1_in(v_m,v_n,1 + v_x_0,v_y_0) [v_y_0 >= 0 (v_n,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 && v_y_0 >= v_m] 13. eval_speedSimpleMultiple_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_stop(v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] (1,1) Signature: {(eval_speedSimpleMultiple_0,4) ;(eval_speedSimpleMultiple_1,4) ;(eval_speedSimpleMultiple_2,4) ;(eval_speedSimpleMultiple_3,4) ;(eval_speedSimpleMultiple_4,4) ;(eval_speedSimpleMultiple_5,4) ;(eval_speedSimpleMultiple_6,4) ;(eval_speedSimpleMultiple_bb0_in,4) ;(eval_speedSimpleMultiple_bb1_in,4) ;(eval_speedSimpleMultiple_bb2_in,4) ;(eval_speedSimpleMultiple_bb3_in,4) ;(eval_speedSimpleMultiple_start,4) ;(eval_speedSimpleMultiple_stop,4)} 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))