YES(?,O(n^1)) * Step 1: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_speedNestedMultiple_start(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb0_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 1. eval_speedNestedMultiple_bb0_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_0(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (?,1) 2. eval_speedNestedMultiple_0(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_1(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (?,1) 3. eval_speedNestedMultiple_1(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_2(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (?,1) 4. eval_speedNestedMultiple_2(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_3(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (?,1) 5. eval_speedNestedMultiple_3(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_4(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (?,1) 6. eval_speedNestedMultiple_4(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_5(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (?,1) 7. eval_speedNestedMultiple_5(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb1_in(v_x,v_y,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (?,1) 8. eval_speedNestedMultiple_bb1_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb2_in(v__0,v__01,v__01,v_2,v_5,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) 9. eval_speedNestedMultiple_bb1_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb5_in(v__0,v__01,v__1,v_2,v_5,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) 10. eval_speedNestedMultiple_bb2_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb3_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 (?,1) && 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__01 + v__1 >= 0 && -1 + v_m >= v__1] 11. eval_speedNestedMultiple_bb2_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple__critedge_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 (?,1) && 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__01 + v__1 >= 0 && v__1 >= v_m] 12. eval_speedNestedMultiple_bb3_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_6(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 (?,1) && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1*v__01 + v__1 >= 0] 13. eval_speedNestedMultiple_6(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_7(v__0,v__01,v__1,nondef_0,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 (?,1) && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1*v__01 + v__1 >= 0] 14. eval_speedNestedMultiple_7(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb4_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 (?,1) && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1*v__01 + v__1 >= 0 && -1 + v_2 >= 0] 15. eval_speedNestedMultiple_7(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple__critedge_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 (?,1) && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1*v__01 + v__1 >= 0 && 0 >= v_2] 16. eval_speedNestedMultiple_bb4_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb2_in(v__0,v__01,1 + v__1,v_2,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 (?,1) && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1 + v_2 >= 0 && -1*v__01 + v__1 >= 0] 17. eval_speedNestedMultiple__critedge_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_11(v__0,v__01,v__1,v_2,1 + v__0,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 (?,1) && 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__01 + v__1 >= 0] 18. eval_speedNestedMultiple_11(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_12(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 (?,1) && v__01 + -1*v_y >= 0 && -1 + v_n + -1*v_x >= 0 && -1 + v_5 + -1*v_x >= 0 && v__0 + -1*v_x >= 0 && -1*v_5 + v_n >= 0 && -1 + -1*v__0 + v_n >= 0 && 1 + -1*v_5 + v__0 >= 0 && -1 + v_5 + -1*v__0 >= 0 && -1*v__01 + v__1 >= 0] 19. eval_speedNestedMultiple_12(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb1_in(v_5,v__1,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 (?,1) && v__01 + -1*v_y >= 0 && -1 + v_n + -1*v_x >= 0 && -1 + v_5 + -1*v_x >= 0 && v__0 + -1*v_x >= 0 && -1*v_5 + v_n >= 0 && -1 + -1*v__0 + v_n >= 0 && 1 + -1*v_5 + v__0 >= 0 && -1 + v_5 + -1*v__0 >= 0 && -1*v__01 + v__1 >= 0] 20. eval_speedNestedMultiple_bb5_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_stop(v__0,v__01,v__1,v_2,v_5,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_speedNestedMultiple_0,9) ;(eval_speedNestedMultiple_1,9) ;(eval_speedNestedMultiple_11,9) ;(eval_speedNestedMultiple_12,9) ;(eval_speedNestedMultiple_2,9) ;(eval_speedNestedMultiple_3,9) ;(eval_speedNestedMultiple_4,9) ;(eval_speedNestedMultiple_5,9) ;(eval_speedNestedMultiple_6,9) ;(eval_speedNestedMultiple_7,9) ;(eval_speedNestedMultiple__critedge_in,9) ;(eval_speedNestedMultiple_bb0_in,9) ;(eval_speedNestedMultiple_bb1_in,9) ;(eval_speedNestedMultiple_bb2_in,9) ;(eval_speedNestedMultiple_bb3_in,9) ;(eval_speedNestedMultiple_bb4_in,9) ;(eval_speedNestedMultiple_bb5_in,9) ;(eval_speedNestedMultiple_start,9) ;(eval_speedNestedMultiple_stop,9)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8,9},8->{10,11},9->{20},10->{12},11->{17},12->{13} ,13->{14,15},14->{16},15->{17},16->{10,11},17->{18},18->{19},19->{8,9},20->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_speedNestedMultiple_start(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb0_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 1. eval_speedNestedMultiple_bb0_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_0(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 2. eval_speedNestedMultiple_0(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_1(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 3. eval_speedNestedMultiple_1(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_2(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 4. eval_speedNestedMultiple_2(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_3(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 5. eval_speedNestedMultiple_3(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_4(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 6. eval_speedNestedMultiple_4(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_5(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 7. eval_speedNestedMultiple_5(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb1_in(v_x,v_y,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 8. eval_speedNestedMultiple_bb1_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb2_in(v__0,v__01,v__01,v_2,v_5,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) 9. eval_speedNestedMultiple_bb1_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb5_in(v__0,v__01,v__1,v_2,v_5,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) 10. eval_speedNestedMultiple_bb2_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb3_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 (?,1) && 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__01 + v__1 >= 0 && -1 + v_m >= v__1] 11. eval_speedNestedMultiple_bb2_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple__critedge_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 (?,1) && 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__01 + v__1 >= 0 && v__1 >= v_m] 12. eval_speedNestedMultiple_bb3_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_6(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 (?,1) && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1*v__01 + v__1 >= 0] 13. eval_speedNestedMultiple_6(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_7(v__0,v__01,v__1,nondef_0,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 (?,1) && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1*v__01 + v__1 >= 0] 14. eval_speedNestedMultiple_7(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb4_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 (?,1) && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1*v__01 + v__1 >= 0 && -1 + v_2 >= 0] 15. eval_speedNestedMultiple_7(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple__critedge_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 (?,1) && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1*v__01 + v__1 >= 0 && 0 >= v_2] 16. eval_speedNestedMultiple_bb4_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb2_in(v__0,v__01,1 + v__1,v_2,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 (?,1) && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1 + v_2 >= 0 && -1*v__01 + v__1 >= 0] 17. eval_speedNestedMultiple__critedge_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_11(v__0,v__01,v__1,v_2,1 + v__0,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 (?,1) && 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__01 + v__1 >= 0] 18. eval_speedNestedMultiple_11(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_12(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 (?,1) && v__01 + -1*v_y >= 0 && -1 + v_n + -1*v_x >= 0 && -1 + v_5 + -1*v_x >= 0 && v__0 + -1*v_x >= 0 && -1*v_5 + v_n >= 0 && -1 + -1*v__0 + v_n >= 0 && 1 + -1*v_5 + v__0 >= 0 && -1 + v_5 + -1*v__0 >= 0 && -1*v__01 + v__1 >= 0] 19. eval_speedNestedMultiple_12(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb1_in(v_5,v__1,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 (?,1) && v__01 + -1*v_y >= 0 && -1 + v_n + -1*v_x >= 0 && -1 + v_5 + -1*v_x >= 0 && v__0 + -1*v_x >= 0 && -1*v_5 + v_n >= 0 && -1 + -1*v__0 + v_n >= 0 && 1 + -1*v_5 + v__0 >= 0 && -1 + v_5 + -1*v__0 >= 0 && -1*v__01 + v__1 >= 0] 20. eval_speedNestedMultiple_bb5_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_stop(v__0,v__01,v__1,v_2,v_5,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_speedNestedMultiple_0,9) ;(eval_speedNestedMultiple_1,9) ;(eval_speedNestedMultiple_11,9) ;(eval_speedNestedMultiple_12,9) ;(eval_speedNestedMultiple_2,9) ;(eval_speedNestedMultiple_3,9) ;(eval_speedNestedMultiple_4,9) ;(eval_speedNestedMultiple_5,9) ;(eval_speedNestedMultiple_6,9) ;(eval_speedNestedMultiple_7,9) ;(eval_speedNestedMultiple__critedge_in,9) ;(eval_speedNestedMultiple_bb0_in,9) ;(eval_speedNestedMultiple_bb1_in,9) ;(eval_speedNestedMultiple_bb2_in,9) ;(eval_speedNestedMultiple_bb3_in,9) ;(eval_speedNestedMultiple_bb4_in,9) ;(eval_speedNestedMultiple_bb5_in,9) ;(eval_speedNestedMultiple_start,9) ;(eval_speedNestedMultiple_stop,9)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8,9},8->{10,11},9->{20},10->{12},11->{17},12->{13} ,13->{14,15},14->{16},15->{17},16->{10,11},17->{18},18->{19},19->{8,9},20->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval_speedNestedMultiple_0) = x7 + -1*x8 p(eval_speedNestedMultiple_1) = x7 + -1*x8 p(eval_speedNestedMultiple_11) = -1*x1 + x7 p(eval_speedNestedMultiple_12) = -1*x1 + x7 p(eval_speedNestedMultiple_2) = x7 + -1*x8 p(eval_speedNestedMultiple_3) = x7 + -1*x8 p(eval_speedNestedMultiple_4) = x7 + -1*x8 p(eval_speedNestedMultiple_5) = x7 + -1*x8 p(eval_speedNestedMultiple_6) = -1*x1 + x7 p(eval_speedNestedMultiple_7) = -1*x1 + x7 p(eval_speedNestedMultiple__critedge_in) = -1*x1 + x7 p(eval_speedNestedMultiple_bb0_in) = x7 + -1*x8 p(eval_speedNestedMultiple_bb1_in) = -1*x1 + x7 p(eval_speedNestedMultiple_bb2_in) = -1*x1 + x7 p(eval_speedNestedMultiple_bb3_in) = -1*x1 + x7 p(eval_speedNestedMultiple_bb4_in) = -1*x1 + x7 p(eval_speedNestedMultiple_bb5_in) = -1*x1 + x7 p(eval_speedNestedMultiple_start) = x7 + -1*x8 p(eval_speedNestedMultiple_stop) = -1*x1 + x7 Following rules are strictly oriented: [v__1 + -1*v_y >= 0 ==> && v__01 + -1*v_y >= 0 && -1 + v_n + -1*v_x >= 0 && -1 + v_5 + -1*v_x >= 0 && v__0 + -1*v_x >= 0 && -1*v_5 + v_n >= 0 && -1 + -1*v__0 + v_n >= 0 && 1 + -1*v_5 + v__0 >= 0 && -1 + v_5 + -1*v__0 >= 0 && -1*v__01 + v__1 >= 0] eval_speedNestedMultiple_12(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = -1*v__0 + v_n > -1*v_5 + v_n = eval_speedNestedMultiple_bb1_in(v_5,v__1,v__1,v_2,v_5,v_m,v_n,v_x,v_y) Following rules are weakly oriented: True ==> eval_speedNestedMultiple_start(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = v_n + -1*v_x >= v_n + -1*v_x = eval_speedNestedMultiple_bb0_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True ==> eval_speedNestedMultiple_bb0_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = v_n + -1*v_x >= v_n + -1*v_x = eval_speedNestedMultiple_0(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True ==> eval_speedNestedMultiple_0(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = v_n + -1*v_x >= v_n + -1*v_x = eval_speedNestedMultiple_1(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True ==> eval_speedNestedMultiple_1(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = v_n + -1*v_x >= v_n + -1*v_x = eval_speedNestedMultiple_2(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True ==> eval_speedNestedMultiple_2(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = v_n + -1*v_x >= v_n + -1*v_x = eval_speedNestedMultiple_3(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True ==> eval_speedNestedMultiple_3(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = v_n + -1*v_x >= v_n + -1*v_x = eval_speedNestedMultiple_4(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True ==> eval_speedNestedMultiple_4(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = v_n + -1*v_x >= v_n + -1*v_x = eval_speedNestedMultiple_5(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True ==> eval_speedNestedMultiple_5(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = v_n + -1*v_x >= v_n + -1*v_x = eval_speedNestedMultiple_bb1_in(v_x,v_y,v__1,v_2,v_5,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_speedNestedMultiple_bb1_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = -1*v__0 + v_n >= -1*v__0 + v_n = eval_speedNestedMultiple_bb2_in(v__0,v__01,v__01,v_2,v_5,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_speedNestedMultiple_bb1_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = -1*v__0 + v_n >= -1*v__0 + v_n = eval_speedNestedMultiple_bb5_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 ==> && 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__01 + v__1 >= 0 && -1 + v_m >= v__1] eval_speedNestedMultiple_bb2_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = -1*v__0 + v_n >= -1*v__0 + v_n = eval_speedNestedMultiple_bb3_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 ==> && 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__01 + v__1 >= 0 && v__1 >= v_m] eval_speedNestedMultiple_bb2_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = -1*v__0 + v_n >= -1*v__0 + v_n = eval_speedNestedMultiple__critedge_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 ==> && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1*v__01 + v__1 >= 0] eval_speedNestedMultiple_bb3_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = -1*v__0 + v_n >= -1*v__0 + v_n = eval_speedNestedMultiple_6(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 ==> && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1*v__01 + v__1 >= 0] eval_speedNestedMultiple_6(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = -1*v__0 + v_n >= -1*v__0 + v_n = eval_speedNestedMultiple_7(v__0,v__01,v__1,nondef_0,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 ==> && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1*v__01 + v__1 >= 0 && -1 + v_2 >= 0] eval_speedNestedMultiple_7(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = -1*v__0 + v_n >= -1*v__0 + v_n = eval_speedNestedMultiple_bb4_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 ==> && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1*v__01 + v__1 >= 0 && 0 >= v_2] eval_speedNestedMultiple_7(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = -1*v__0 + v_n >= -1*v__0 + v_n = eval_speedNestedMultiple__critedge_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 ==> && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1 + v_2 >= 0 && -1*v__01 + v__1 >= 0] eval_speedNestedMultiple_bb4_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = -1*v__0 + v_n >= -1*v__0 + v_n = eval_speedNestedMultiple_bb2_in(v__0,v__01,1 + v__1,v_2,v_5,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 ==> && 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__01 + v__1 >= 0] eval_speedNestedMultiple__critedge_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = -1*v__0 + v_n >= -1*v__0 + v_n = eval_speedNestedMultiple_11(v__0,v__01,v__1,v_2,1 + v__0,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 ==> && v__01 + -1*v_y >= 0 && -1 + v_n + -1*v_x >= 0 && -1 + v_5 + -1*v_x >= 0 && v__0 + -1*v_x >= 0 && -1*v_5 + v_n >= 0 && -1 + -1*v__0 + v_n >= 0 && 1 + -1*v_5 + v__0 >= 0 && -1 + v_5 + -1*v__0 >= 0 && -1*v__01 + v__1 >= 0] eval_speedNestedMultiple_11(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = -1*v__0 + v_n >= -1*v__0 + v_n = eval_speedNestedMultiple_12(v__0,v__01,v__1,v_2,v_5,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_speedNestedMultiple_bb5_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = -1*v__0 + v_n >= -1*v__0 + v_n = eval_speedNestedMultiple_stop(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) * Step 3: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_speedNestedMultiple_start(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb0_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 1. eval_speedNestedMultiple_bb0_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_0(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 2. eval_speedNestedMultiple_0(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_1(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 3. eval_speedNestedMultiple_1(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_2(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 4. eval_speedNestedMultiple_2(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_3(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 5. eval_speedNestedMultiple_3(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_4(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 6. eval_speedNestedMultiple_4(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_5(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 7. eval_speedNestedMultiple_5(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb1_in(v_x,v_y,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 8. eval_speedNestedMultiple_bb1_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb2_in(v__0,v__01,v__01,v_2,v_5,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) 9. eval_speedNestedMultiple_bb1_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb5_in(v__0,v__01,v__1,v_2,v_5,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) 10. eval_speedNestedMultiple_bb2_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb3_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 (?,1) && 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__01 + v__1 >= 0 && -1 + v_m >= v__1] 11. eval_speedNestedMultiple_bb2_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple__critedge_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 (?,1) && 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__01 + v__1 >= 0 && v__1 >= v_m] 12. eval_speedNestedMultiple_bb3_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_6(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 (?,1) && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1*v__01 + v__1 >= 0] 13. eval_speedNestedMultiple_6(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_7(v__0,v__01,v__1,nondef_0,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 (?,1) && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1*v__01 + v__1 >= 0] 14. eval_speedNestedMultiple_7(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb4_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 (?,1) && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1*v__01 + v__1 >= 0 && -1 + v_2 >= 0] 15. eval_speedNestedMultiple_7(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple__critedge_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 (?,1) && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1*v__01 + v__1 >= 0 && 0 >= v_2] 16. eval_speedNestedMultiple_bb4_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb2_in(v__0,v__01,1 + v__1,v_2,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 (?,1) && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1 + v_2 >= 0 && -1*v__01 + v__1 >= 0] 17. eval_speedNestedMultiple__critedge_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_11(v__0,v__01,v__1,v_2,1 + v__0,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 (?,1) && 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__01 + v__1 >= 0] 18. eval_speedNestedMultiple_11(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_12(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 (?,1) && v__01 + -1*v_y >= 0 && -1 + v_n + -1*v_x >= 0 && -1 + v_5 + -1*v_x >= 0 && v__0 + -1*v_x >= 0 && -1*v_5 + v_n >= 0 && -1 + -1*v__0 + v_n >= 0 && 1 + -1*v_5 + v__0 >= 0 && -1 + v_5 + -1*v__0 >= 0 && -1*v__01 + v__1 >= 0] 19. eval_speedNestedMultiple_12(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb1_in(v_5,v__1,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 (v_n + v_x,1) && v__01 + -1*v_y >= 0 && -1 + v_n + -1*v_x >= 0 && -1 + v_5 + -1*v_x >= 0 && v__0 + -1*v_x >= 0 && -1*v_5 + v_n >= 0 && -1 + -1*v__0 + v_n >= 0 && 1 + -1*v_5 + v__0 >= 0 && -1 + v_5 + -1*v__0 >= 0 && -1*v__01 + v__1 >= 0] 20. eval_speedNestedMultiple_bb5_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_stop(v__0,v__01,v__1,v_2,v_5,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_speedNestedMultiple_0,9) ;(eval_speedNestedMultiple_1,9) ;(eval_speedNestedMultiple_11,9) ;(eval_speedNestedMultiple_12,9) ;(eval_speedNestedMultiple_2,9) ;(eval_speedNestedMultiple_3,9) ;(eval_speedNestedMultiple_4,9) ;(eval_speedNestedMultiple_5,9) ;(eval_speedNestedMultiple_6,9) ;(eval_speedNestedMultiple_7,9) ;(eval_speedNestedMultiple__critedge_in,9) ;(eval_speedNestedMultiple_bb0_in,9) ;(eval_speedNestedMultiple_bb1_in,9) ;(eval_speedNestedMultiple_bb2_in,9) ;(eval_speedNestedMultiple_bb3_in,9) ;(eval_speedNestedMultiple_bb4_in,9) ;(eval_speedNestedMultiple_bb5_in,9) ;(eval_speedNestedMultiple_start,9) ;(eval_speedNestedMultiple_stop,9)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8,9},8->{10,11},9->{20},10->{12},11->{17},12->{13} ,13->{14,15},14->{16},15->{17},16->{10,11},17->{18},18->{19},19->{8,9},20->{}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 4: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_speedNestedMultiple_start(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb0_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 1. eval_speedNestedMultiple_bb0_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_0(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 2. eval_speedNestedMultiple_0(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_1(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 3. eval_speedNestedMultiple_1(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_2(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 4. eval_speedNestedMultiple_2(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_3(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 5. eval_speedNestedMultiple_3(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_4(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 6. eval_speedNestedMultiple_4(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_5(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 7. eval_speedNestedMultiple_5(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb1_in(v_x,v_y,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 8. eval_speedNestedMultiple_bb1_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb2_in(v__0,v__01,v__01,v_2,v_5,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_n + v_x,1) 9. eval_speedNestedMultiple_bb1_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb5_in(v__0,v__01,v__1,v_2,v_5,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) 10. eval_speedNestedMultiple_bb2_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb3_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 (?,1) && 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__01 + v__1 >= 0 && -1 + v_m >= v__1] 11. eval_speedNestedMultiple_bb2_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple__critedge_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 (?,1) && 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__01 + v__1 >= 0 && v__1 >= v_m] 12. eval_speedNestedMultiple_bb3_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_6(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 (?,1) && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1*v__01 + v__1 >= 0] 13. eval_speedNestedMultiple_6(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_7(v__0,v__01,v__1,nondef_0,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 (?,1) && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1*v__01 + v__1 >= 0] 14. eval_speedNestedMultiple_7(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb4_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 (?,1) && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1*v__01 + v__1 >= 0 && -1 + v_2 >= 0] 15. eval_speedNestedMultiple_7(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple__critedge_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 (?,1) && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1*v__01 + v__1 >= 0 && 0 >= v_2] 16. eval_speedNestedMultiple_bb4_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb2_in(v__0,v__01,1 + v__1,v_2,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 (?,1) && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1 + v_2 >= 0 && -1*v__01 + v__1 >= 0] 17. eval_speedNestedMultiple__critedge_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_11(v__0,v__01,v__1,v_2,1 + v__0,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 (?,1) && 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__01 + v__1 >= 0] 18. eval_speedNestedMultiple_11(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_12(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 (?,1) && v__01 + -1*v_y >= 0 && -1 + v_n + -1*v_x >= 0 && -1 + v_5 + -1*v_x >= 0 && v__0 + -1*v_x >= 0 && -1*v_5 + v_n >= 0 && -1 + -1*v__0 + v_n >= 0 && 1 + -1*v_5 + v__0 >= 0 && -1 + v_5 + -1*v__0 >= 0 && -1*v__01 + v__1 >= 0] 19. eval_speedNestedMultiple_12(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb1_in(v_5,v__1,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 (v_n + v_x,1) && v__01 + -1*v_y >= 0 && -1 + v_n + -1*v_x >= 0 && -1 + v_5 + -1*v_x >= 0 && v__0 + -1*v_x >= 0 && -1*v_5 + v_n >= 0 && -1 + -1*v__0 + v_n >= 0 && 1 + -1*v_5 + v__0 >= 0 && -1 + v_5 + -1*v__0 >= 0 && -1*v__01 + v__1 >= 0] 20. eval_speedNestedMultiple_bb5_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_stop(v__0,v__01,v__1,v_2,v_5,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_speedNestedMultiple_0,9) ;(eval_speedNestedMultiple_1,9) ;(eval_speedNestedMultiple_11,9) ;(eval_speedNestedMultiple_12,9) ;(eval_speedNestedMultiple_2,9) ;(eval_speedNestedMultiple_3,9) ;(eval_speedNestedMultiple_4,9) ;(eval_speedNestedMultiple_5,9) ;(eval_speedNestedMultiple_6,9) ;(eval_speedNestedMultiple_7,9) ;(eval_speedNestedMultiple__critedge_in,9) ;(eval_speedNestedMultiple_bb0_in,9) ;(eval_speedNestedMultiple_bb1_in,9) ;(eval_speedNestedMultiple_bb2_in,9) ;(eval_speedNestedMultiple_bb3_in,9) ;(eval_speedNestedMultiple_bb4_in,9) ;(eval_speedNestedMultiple_bb5_in,9) ;(eval_speedNestedMultiple_start,9) ;(eval_speedNestedMultiple_stop,9)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8,9},8->{10,11},9->{20},10->{12},11->{17},12->{13} ,13->{14,15},14->{16},15->{17},16->{10,11},17->{18},18->{19},19->{8,9},20->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval_speedNestedMultiple_0) = x6 + -1*x9 p(eval_speedNestedMultiple_1) = x6 + -1*x9 p(eval_speedNestedMultiple_11) = -1*x3 + x6 p(eval_speedNestedMultiple_12) = -1*x3 + x6 p(eval_speedNestedMultiple_2) = x6 + -1*x9 p(eval_speedNestedMultiple_3) = x6 + -1*x9 p(eval_speedNestedMultiple_4) = x6 + -1*x9 p(eval_speedNestedMultiple_5) = x6 + -1*x9 p(eval_speedNestedMultiple_6) = -1*x3 + x6 p(eval_speedNestedMultiple_7) = -1*x3 + x6 p(eval_speedNestedMultiple__critedge_in) = -1*x3 + x6 p(eval_speedNestedMultiple_bb0_in) = x6 + -1*x9 p(eval_speedNestedMultiple_bb1_in) = -1*x2 + x6 p(eval_speedNestedMultiple_bb2_in) = -1*x3 + x6 p(eval_speedNestedMultiple_bb3_in) = -1*x3 + x6 p(eval_speedNestedMultiple_bb4_in) = -1*x3 + x6 p(eval_speedNestedMultiple_bb5_in) = -1*x2 + x6 p(eval_speedNestedMultiple_start) = x6 + -1*x9 p(eval_speedNestedMultiple_stop) = -1*x2 + x6 Following rules are strictly oriented: [-1 + v_m + -1*v_y >= 0 ==> && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1 + v_2 >= 0 && -1*v__01 + v__1 >= 0] eval_speedNestedMultiple_bb4_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = -1*v__1 + v_m > -1 + -1*v__1 + v_m = eval_speedNestedMultiple_bb2_in(v__0,v__01,1 + v__1,v_2,v_5,v_m,v_n,v_x,v_y) Following rules are weakly oriented: True ==> eval_speedNestedMultiple_start(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = v_m + -1*v_y >= v_m + -1*v_y = eval_speedNestedMultiple_bb0_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True ==> eval_speedNestedMultiple_bb0_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = v_m + -1*v_y >= v_m + -1*v_y = eval_speedNestedMultiple_0(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True ==> eval_speedNestedMultiple_0(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = v_m + -1*v_y >= v_m + -1*v_y = eval_speedNestedMultiple_1(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True ==> eval_speedNestedMultiple_1(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = v_m + -1*v_y >= v_m + -1*v_y = eval_speedNestedMultiple_2(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True ==> eval_speedNestedMultiple_2(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = v_m + -1*v_y >= v_m + -1*v_y = eval_speedNestedMultiple_3(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True ==> eval_speedNestedMultiple_3(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = v_m + -1*v_y >= v_m + -1*v_y = eval_speedNestedMultiple_4(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True ==> eval_speedNestedMultiple_4(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = v_m + -1*v_y >= v_m + -1*v_y = eval_speedNestedMultiple_5(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True ==> eval_speedNestedMultiple_5(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = v_m + -1*v_y >= v_m + -1*v_y = eval_speedNestedMultiple_bb1_in(v_x,v_y,v__1,v_2,v_5,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_speedNestedMultiple_bb1_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = -1*v__01 + v_m >= -1*v__01 + v_m = eval_speedNestedMultiple_bb2_in(v__0,v__01,v__01,v_2,v_5,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_speedNestedMultiple_bb1_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = -1*v__01 + v_m >= -1*v__01 + v_m = eval_speedNestedMultiple_bb5_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 ==> && 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__01 + v__1 >= 0 && -1 + v_m >= v__1] eval_speedNestedMultiple_bb2_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = -1*v__1 + v_m >= -1*v__1 + v_m = eval_speedNestedMultiple_bb3_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 ==> && 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__01 + v__1 >= 0 && v__1 >= v_m] eval_speedNestedMultiple_bb2_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = -1*v__1 + v_m >= -1*v__1 + v_m = eval_speedNestedMultiple__critedge_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 ==> && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1*v__01 + v__1 >= 0] eval_speedNestedMultiple_bb3_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = -1*v__1 + v_m >= -1*v__1 + v_m = eval_speedNestedMultiple_6(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 ==> && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1*v__01 + v__1 >= 0] eval_speedNestedMultiple_6(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = -1*v__1 + v_m >= -1*v__1 + v_m = eval_speedNestedMultiple_7(v__0,v__01,v__1,nondef_0,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 ==> && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1*v__01 + v__1 >= 0 && -1 + v_2 >= 0] eval_speedNestedMultiple_7(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = -1*v__1 + v_m >= -1*v__1 + v_m = eval_speedNestedMultiple_bb4_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 ==> && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1*v__01 + v__1 >= 0 && 0 >= v_2] eval_speedNestedMultiple_7(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = -1*v__1 + v_m >= -1*v__1 + v_m = eval_speedNestedMultiple__critedge_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 ==> && 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__01 + v__1 >= 0] eval_speedNestedMultiple__critedge_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = -1*v__1 + v_m >= -1*v__1 + v_m = eval_speedNestedMultiple_11(v__0,v__01,v__1,v_2,1 + v__0,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 ==> && v__01 + -1*v_y >= 0 && -1 + v_n + -1*v_x >= 0 && -1 + v_5 + -1*v_x >= 0 && v__0 + -1*v_x >= 0 && -1*v_5 + v_n >= 0 && -1 + -1*v__0 + v_n >= 0 && 1 + -1*v_5 + v__0 >= 0 && -1 + v_5 + -1*v__0 >= 0 && -1*v__01 + v__1 >= 0] eval_speedNestedMultiple_11(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = -1*v__1 + v_m >= -1*v__1 + v_m = eval_speedNestedMultiple_12(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 ==> && v__01 + -1*v_y >= 0 && -1 + v_n + -1*v_x >= 0 && -1 + v_5 + -1*v_x >= 0 && v__0 + -1*v_x >= 0 && -1*v_5 + v_n >= 0 && -1 + -1*v__0 + v_n >= 0 && 1 + -1*v_5 + v__0 >= 0 && -1 + v_5 + -1*v__0 >= 0 && -1*v__01 + v__1 >= 0] eval_speedNestedMultiple_12(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = -1*v__1 + v_m >= -1*v__1 + v_m = eval_speedNestedMultiple_bb1_in(v_5,v__1,v__1,v_2,v_5,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_speedNestedMultiple_bb5_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) = -1*v__01 + v_m >= -1*v__01 + v_m = eval_speedNestedMultiple_stop(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) * Step 5: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_speedNestedMultiple_start(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb0_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 1. eval_speedNestedMultiple_bb0_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_0(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 2. eval_speedNestedMultiple_0(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_1(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 3. eval_speedNestedMultiple_1(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_2(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 4. eval_speedNestedMultiple_2(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_3(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 5. eval_speedNestedMultiple_3(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_4(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 6. eval_speedNestedMultiple_4(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_5(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 7. eval_speedNestedMultiple_5(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb1_in(v_x,v_y,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 8. eval_speedNestedMultiple_bb1_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb2_in(v__0,v__01,v__01,v_2,v_5,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_n + v_x,1) 9. eval_speedNestedMultiple_bb1_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb5_in(v__0,v__01,v__1,v_2,v_5,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) 10. eval_speedNestedMultiple_bb2_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb3_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 (?,1) && 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__01 + v__1 >= 0 && -1 + v_m >= v__1] 11. eval_speedNestedMultiple_bb2_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple__critedge_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 (?,1) && 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__01 + v__1 >= 0 && v__1 >= v_m] 12. eval_speedNestedMultiple_bb3_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_6(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 (?,1) && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1*v__01 + v__1 >= 0] 13. eval_speedNestedMultiple_6(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_7(v__0,v__01,v__1,nondef_0,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 (?,1) && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1*v__01 + v__1 >= 0] 14. eval_speedNestedMultiple_7(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb4_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 (?,1) && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1*v__01 + v__1 >= 0 && -1 + v_2 >= 0] 15. eval_speedNestedMultiple_7(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple__critedge_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 (?,1) && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1*v__01 + v__1 >= 0 && 0 >= v_2] 16. eval_speedNestedMultiple_bb4_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb2_in(v__0,v__01,1 + v__1,v_2,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 (v_m + v_y,1) && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1 + v_2 >= 0 && -1*v__01 + v__1 >= 0] 17. eval_speedNestedMultiple__critedge_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_11(v__0,v__01,v__1,v_2,1 + v__0,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 (?,1) && 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__01 + v__1 >= 0] 18. eval_speedNestedMultiple_11(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_12(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 (?,1) && v__01 + -1*v_y >= 0 && -1 + v_n + -1*v_x >= 0 && -1 + v_5 + -1*v_x >= 0 && v__0 + -1*v_x >= 0 && -1*v_5 + v_n >= 0 && -1 + -1*v__0 + v_n >= 0 && 1 + -1*v_5 + v__0 >= 0 && -1 + v_5 + -1*v__0 >= 0 && -1*v__01 + v__1 >= 0] 19. eval_speedNestedMultiple_12(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb1_in(v_5,v__1,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 (v_n + v_x,1) && v__01 + -1*v_y >= 0 && -1 + v_n + -1*v_x >= 0 && -1 + v_5 + -1*v_x >= 0 && v__0 + -1*v_x >= 0 && -1*v_5 + v_n >= 0 && -1 + -1*v__0 + v_n >= 0 && 1 + -1*v_5 + v__0 >= 0 && -1 + v_5 + -1*v__0 >= 0 && -1*v__01 + v__1 >= 0] 20. eval_speedNestedMultiple_bb5_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_stop(v__0,v__01,v__1,v_2,v_5,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_speedNestedMultiple_0,9) ;(eval_speedNestedMultiple_1,9) ;(eval_speedNestedMultiple_11,9) ;(eval_speedNestedMultiple_12,9) ;(eval_speedNestedMultiple_2,9) ;(eval_speedNestedMultiple_3,9) ;(eval_speedNestedMultiple_4,9) ;(eval_speedNestedMultiple_5,9) ;(eval_speedNestedMultiple_6,9) ;(eval_speedNestedMultiple_7,9) ;(eval_speedNestedMultiple__critedge_in,9) ;(eval_speedNestedMultiple_bb0_in,9) ;(eval_speedNestedMultiple_bb1_in,9) ;(eval_speedNestedMultiple_bb2_in,9) ;(eval_speedNestedMultiple_bb3_in,9) ;(eval_speedNestedMultiple_bb4_in,9) ;(eval_speedNestedMultiple_bb5_in,9) ;(eval_speedNestedMultiple_start,9) ;(eval_speedNestedMultiple_stop,9)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8,9},8->{10,11},9->{20},10->{12},11->{17},12->{13} ,13->{14,15},14->{16},15->{17},16->{10,11},17->{18},18->{19},19->{8,9},20->{}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 6: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_speedNestedMultiple_start(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb0_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 1. eval_speedNestedMultiple_bb0_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_0(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 2. eval_speedNestedMultiple_0(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_1(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 3. eval_speedNestedMultiple_1(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_2(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 4. eval_speedNestedMultiple_2(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_3(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 5. eval_speedNestedMultiple_3(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_4(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 6. eval_speedNestedMultiple_4(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_5(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 7. eval_speedNestedMultiple_5(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb1_in(v_x,v_y,v__1,v_2,v_5,v_m,v_n,v_x,v_y) True (1,1) 8. eval_speedNestedMultiple_bb1_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb2_in(v__0,v__01,v__01,v_2,v_5,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_n + v_x,1) 9. eval_speedNestedMultiple_bb1_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb5_in(v__0,v__01,v__1,v_2,v_5,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) 10. eval_speedNestedMultiple_bb2_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb3_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 (1 + v_m + v_n + v_x + v_y,1) && 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__01 + v__1 >= 0 && -1 + v_m >= v__1] 11. eval_speedNestedMultiple_bb2_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple__critedge_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 (1 + v_m + v_n + v_x + v_y,1) && 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__01 + v__1 >= 0 && v__1 >= v_m] 12. eval_speedNestedMultiple_bb3_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_6(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 (1 + v_m + v_n + v_x + v_y,1) && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1*v__01 + v__1 >= 0] 13. eval_speedNestedMultiple_6(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_7(v__0,v__01,v__1,nondef_0,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 (1 + v_m + v_n + v_x + v_y,1) && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1*v__01 + v__1 >= 0] 14. eval_speedNestedMultiple_7(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb4_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 (1 + v_m + v_n + v_x + v_y,1) && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1*v__01 + v__1 >= 0 && -1 + v_2 >= 0] 15. eval_speedNestedMultiple_7(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple__critedge_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 (1 + v_m + v_n + v_x + v_y,1) && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1*v__01 + v__1 >= 0 && 0 >= v_2] 16. eval_speedNestedMultiple_bb4_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb2_in(v__0,v__01,1 + v__1,v_2,v_5,v_m,v_n,v_x,v_y) [-1 + v_m + -1*v_y >= 0 (v_m + v_y,1) && v__1 + -1*v_y >= 0 && 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 + -1*v__1 + v_m >= 0 && -1 + -1*v__01 + v_m >= 0 && -1 + v_2 >= 0 && -1*v__01 + v__1 >= 0] 17. eval_speedNestedMultiple__critedge_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_11(v__0,v__01,v__1,v_2,1 + v__0,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 (2 + 2*v_m + 2*v_n + 2*v_x + 2*v_y,1) && 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__01 + v__1 >= 0] 18. eval_speedNestedMultiple_11(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_12(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 (2 + 2*v_m + 2*v_n + 2*v_x + 2*v_y,1) && v__01 + -1*v_y >= 0 && -1 + v_n + -1*v_x >= 0 && -1 + v_5 + -1*v_x >= 0 && v__0 + -1*v_x >= 0 && -1*v_5 + v_n >= 0 && -1 + -1*v__0 + v_n >= 0 && 1 + -1*v_5 + v__0 >= 0 && -1 + v_5 + -1*v__0 >= 0 && -1*v__01 + v__1 >= 0] 19. eval_speedNestedMultiple_12(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_bb1_in(v_5,v__1,v__1,v_2,v_5,v_m,v_n,v_x,v_y) [v__1 + -1*v_y >= 0 (v_n + v_x,1) && v__01 + -1*v_y >= 0 && -1 + v_n + -1*v_x >= 0 && -1 + v_5 + -1*v_x >= 0 && v__0 + -1*v_x >= 0 && -1*v_5 + v_n >= 0 && -1 + -1*v__0 + v_n >= 0 && 1 + -1*v_5 + v__0 >= 0 && -1 + v_5 + -1*v__0 >= 0 && -1*v__01 + v__1 >= 0] 20. eval_speedNestedMultiple_bb5_in(v__0,v__01,v__1,v_2,v_5,v_m,v_n,v_x,v_y) -> eval_speedNestedMultiple_stop(v__0,v__01,v__1,v_2,v_5,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_speedNestedMultiple_0,9) ;(eval_speedNestedMultiple_1,9) ;(eval_speedNestedMultiple_11,9) ;(eval_speedNestedMultiple_12,9) ;(eval_speedNestedMultiple_2,9) ;(eval_speedNestedMultiple_3,9) ;(eval_speedNestedMultiple_4,9) ;(eval_speedNestedMultiple_5,9) ;(eval_speedNestedMultiple_6,9) ;(eval_speedNestedMultiple_7,9) ;(eval_speedNestedMultiple__critedge_in,9) ;(eval_speedNestedMultiple_bb0_in,9) ;(eval_speedNestedMultiple_bb1_in,9) ;(eval_speedNestedMultiple_bb2_in,9) ;(eval_speedNestedMultiple_bb3_in,9) ;(eval_speedNestedMultiple_bb4_in,9) ;(eval_speedNestedMultiple_bb5_in,9) ;(eval_speedNestedMultiple_start,9) ;(eval_speedNestedMultiple_stop,9)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8,9},8->{10,11},9->{20},10->{12},11->{17},12->{13} ,13->{14,15},14->{16},15->{17},16->{10,11},17->{18},18->{19},19->{8,9},20->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: The problem is already solved. YES(?,O(n^1))