YES(?,O(n^1)) * Step 1: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_random2d_start(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb0_in(v_1,v_2,v_N,v_i_0) True (1,1) 1. eval_random2d_bb0_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_0(v_1,v_2,v_N,v_i_0) True (?,1) 2. eval_random2d_0(v_1,v_2,v_N,v_i_0) -> eval_random2d_1(v_1,v_2,v_N,v_i_0) True (?,1) 3. eval_random2d_1(v_1,v_2,v_N,v_i_0) -> eval_random2d_2(v_1,v_2,v_N,v_i_0) True (?,1) 4. eval_random2d_2(v_1,v_2,v_N,v_i_0) -> eval_random2d_3(v_1,v_2,v_N,v_i_0) True (?,1) 5. eval_random2d_3(v_1,v_2,v_N,v_i_0) -> eval_random2d_4(v_1,v_2,v_N,v_i_0) True (?,1) 6. eval_random2d_4(v_1,v_2,v_N,v_i_0) -> eval_random2d_5(v_1,v_2,v_N,v_i_0) True (?,1) 7. eval_random2d_5(v_1,v_2,v_N,v_i_0) -> eval_random2d_6(v_1,v_2,v_N,v_i_0) True (?,1) 8. eval_random2d_6(v_1,v_2,v_N,v_i_0) -> eval_random2d_7(v_1,v_2,v_N,v_i_0) True (?,1) 9. eval_random2d_7(v_1,v_2,v_N,v_i_0) -> eval_random2d_8(v_1,v_2,v_N,v_i_0) True (?,1) 10. eval_random2d_8(v_1,v_2,v_N,v_i_0) -> eval_random2d_9(v_1,v_2,v_N,v_i_0) True (?,1) 11. eval_random2d_9(v_1,v_2,v_N,v_i_0) -> eval_random2d_10(v_1,v_2,v_N,v_i_0) True (?,1) 12. eval_random2d_10(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,0) True (?,1) 13. eval_random2d_bb1_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb2_in(v_1,v_2,v_N,v_i_0) [-1 + v_N >= v_i_0] (?,1) 14. eval_random2d_bb1_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb8_in(v_1,v_2,v_N,v_i_0) [v_i_0 >= v_N] (?,1) 15. eval_random2d_bb2_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_12(1 + v_i_0,v_2,v_N,v_i_0) True (?,1) 16. eval_random2d_12(v_1,v_2,v_N,v_i_0) -> eval_random2d_13(v_1,nondef_0,v_N,v_i_0) True (?,1) 17. eval_random2d_13(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb3_in(v_1,v_2,v_N,v_i_0) [v_2 >= 0 && 3 >= v_2] (?,1) 18. eval_random2d_13(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) [-1 >= v_2] (?,1) 19. eval_random2d_13(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) [-1 + v_2 >= 3] (?,1) 20. eval_random2d_bb3_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NodeBlock9_in(v_1,v_2,v_N,v_i_0) True (?,1) 21. eval_random2d_NodeBlock9_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NodeBlock_in(v_1,v_2,v_N,v_i_0) [1 >= v_2] (?,1) 22. eval_random2d_NodeBlock9_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NodeBlock7_in(v_1,v_2,v_N,v_i_0) [v_2 >= 2] (?,1) 23. eval_random2d_NodeBlock_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_LeafBlock_in(v_1,v_2,v_N,v_i_0) [0 >= v_2] (?,1) 24. eval_random2d_NodeBlock_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_LeafBlock1_in(v_1,v_2,v_N,v_i_0) [v_2 >= 1] (?,1) 25. eval_random2d_LeafBlock_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb4_in(v_1,v_2,v_N,v_i_0) [v_2 = 0] (?,1) 26. eval_random2d_LeafBlock_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) [-1 >= v_2] (?,1) 27. eval_random2d_LeafBlock_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) [-1 + v_2 >= 0] (?,1) 28. eval_random2d_bb4_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True (?,1) 29. eval_random2d_LeafBlock1_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb5_in(v_1,v_2,v_N,v_i_0) [v_2 = 1] (?,1) 30. eval_random2d_LeafBlock1_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) [0 >= v_2] (?,1) 31. eval_random2d_LeafBlock1_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) [-1 + v_2 >= 1] (?,1) 32. eval_random2d_bb5_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True (?,1) 33. eval_random2d_NodeBlock7_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_LeafBlock3_in(v_1,v_2,v_N,v_i_0) [2 >= v_2] (?,1) 34. eval_random2d_NodeBlock7_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_LeafBlock5_in(v_1,v_2,v_N,v_i_0) [v_2 >= 3] (?,1) 35. eval_random2d_LeafBlock3_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb6_in(v_1,v_2,v_N,v_i_0) [v_2 = 2] (?,1) 36. eval_random2d_LeafBlock3_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) [1 >= v_2] (?,1) 37. eval_random2d_LeafBlock3_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) [-1 + v_2 >= 2] (?,1) 38. eval_random2d_bb6_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True (?,1) 39. eval_random2d_LeafBlock5_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb7_in(v_1,v_2,v_N,v_i_0) [v_2 = 3] (?,1) 40. eval_random2d_LeafBlock5_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) [2 >= v_2] (?,1) 41. eval_random2d_LeafBlock5_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) [-1 + v_2 >= 3] (?,1) 42. eval_random2d_bb7_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True (?,1) 43. eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True (?,1) 44. eval_random2d_bb8_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_stop(v_1,v_2,v_N,v_i_0) True (?,1) Signature: {(eval_random2d_0,4) ;(eval_random2d_1,4) ;(eval_random2d_10,4) ;(eval_random2d_12,4) ;(eval_random2d_13,4) ;(eval_random2d_2,4) ;(eval_random2d_3,4) ;(eval_random2d_4,4) ;(eval_random2d_5,4) ;(eval_random2d_6,4) ;(eval_random2d_7,4) ;(eval_random2d_8,4) ;(eval_random2d_9,4) ;(eval_random2d_LeafBlock1_in,4) ;(eval_random2d_LeafBlock3_in,4) ;(eval_random2d_LeafBlock5_in,4) ;(eval_random2d_LeafBlock_in,4) ;(eval_random2d_NewDefault_in,4) ;(eval_random2d_NodeBlock7_in,4) ;(eval_random2d_NodeBlock9_in,4) ;(eval_random2d_NodeBlock_in,4) ;(eval_random2d_bb0_in,4) ;(eval_random2d_bb1_in,4) ;(eval_random2d_bb2_in,4) ;(eval_random2d_bb3_in,4) ;(eval_random2d_bb4_in,4) ;(eval_random2d_bb5_in,4) ;(eval_random2d_bb6_in,4) ;(eval_random2d_bb7_in,4) ;(eval_random2d_bb8_in,4) ;(eval_random2d_start,4) ;(eval_random2d_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10},10->{11},11->{12},12->{13,14} ,13->{15},14->{44},15->{16},16->{17,18,19},17->{20},18->{13,14},19->{13,14},20->{21,22},21->{23,24},22->{33 ,34},23->{25,26,27},24->{29,30,31},25->{28},26->{43},27->{43},28->{13,14},29->{32},30->{43},31->{43},32->{13 ,14},33->{35,36,37},34->{39,40,41},35->{38},36->{43},37->{43},38->{13,14},39->{42},40->{43},41->{43},42->{13 ,14},43->{13,14},44->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(23,27),(24,30),(33,37),(34,40)] * Step 2: UnreachableRules WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_random2d_start(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb0_in(v_1,v_2,v_N,v_i_0) True (1,1) 1. eval_random2d_bb0_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_0(v_1,v_2,v_N,v_i_0) True (?,1) 2. eval_random2d_0(v_1,v_2,v_N,v_i_0) -> eval_random2d_1(v_1,v_2,v_N,v_i_0) True (?,1) 3. eval_random2d_1(v_1,v_2,v_N,v_i_0) -> eval_random2d_2(v_1,v_2,v_N,v_i_0) True (?,1) 4. eval_random2d_2(v_1,v_2,v_N,v_i_0) -> eval_random2d_3(v_1,v_2,v_N,v_i_0) True (?,1) 5. eval_random2d_3(v_1,v_2,v_N,v_i_0) -> eval_random2d_4(v_1,v_2,v_N,v_i_0) True (?,1) 6. eval_random2d_4(v_1,v_2,v_N,v_i_0) -> eval_random2d_5(v_1,v_2,v_N,v_i_0) True (?,1) 7. eval_random2d_5(v_1,v_2,v_N,v_i_0) -> eval_random2d_6(v_1,v_2,v_N,v_i_0) True (?,1) 8. eval_random2d_6(v_1,v_2,v_N,v_i_0) -> eval_random2d_7(v_1,v_2,v_N,v_i_0) True (?,1) 9. eval_random2d_7(v_1,v_2,v_N,v_i_0) -> eval_random2d_8(v_1,v_2,v_N,v_i_0) True (?,1) 10. eval_random2d_8(v_1,v_2,v_N,v_i_0) -> eval_random2d_9(v_1,v_2,v_N,v_i_0) True (?,1) 11. eval_random2d_9(v_1,v_2,v_N,v_i_0) -> eval_random2d_10(v_1,v_2,v_N,v_i_0) True (?,1) 12. eval_random2d_10(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,0) True (?,1) 13. eval_random2d_bb1_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb2_in(v_1,v_2,v_N,v_i_0) [-1 + v_N >= v_i_0] (?,1) 14. eval_random2d_bb1_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb8_in(v_1,v_2,v_N,v_i_0) [v_i_0 >= v_N] (?,1) 15. eval_random2d_bb2_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_12(1 + v_i_0,v_2,v_N,v_i_0) True (?,1) 16. eval_random2d_12(v_1,v_2,v_N,v_i_0) -> eval_random2d_13(v_1,nondef_0,v_N,v_i_0) True (?,1) 17. eval_random2d_13(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb3_in(v_1,v_2,v_N,v_i_0) [v_2 >= 0 && 3 >= v_2] (?,1) 18. eval_random2d_13(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) [-1 >= v_2] (?,1) 19. eval_random2d_13(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) [-1 + v_2 >= 3] (?,1) 20. eval_random2d_bb3_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NodeBlock9_in(v_1,v_2,v_N,v_i_0) True (?,1) 21. eval_random2d_NodeBlock9_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NodeBlock_in(v_1,v_2,v_N,v_i_0) [1 >= v_2] (?,1) 22. eval_random2d_NodeBlock9_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NodeBlock7_in(v_1,v_2,v_N,v_i_0) [v_2 >= 2] (?,1) 23. eval_random2d_NodeBlock_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_LeafBlock_in(v_1,v_2,v_N,v_i_0) [0 >= v_2] (?,1) 24. eval_random2d_NodeBlock_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_LeafBlock1_in(v_1,v_2,v_N,v_i_0) [v_2 >= 1] (?,1) 25. eval_random2d_LeafBlock_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb4_in(v_1,v_2,v_N,v_i_0) [v_2 = 0] (?,1) 26. eval_random2d_LeafBlock_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) [-1 >= v_2] (?,1) 27. eval_random2d_LeafBlock_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) [-1 + v_2 >= 0] (?,1) 28. eval_random2d_bb4_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True (?,1) 29. eval_random2d_LeafBlock1_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb5_in(v_1,v_2,v_N,v_i_0) [v_2 = 1] (?,1) 30. eval_random2d_LeafBlock1_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) [0 >= v_2] (?,1) 31. eval_random2d_LeafBlock1_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) [-1 + v_2 >= 1] (?,1) 32. eval_random2d_bb5_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True (?,1) 33. eval_random2d_NodeBlock7_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_LeafBlock3_in(v_1,v_2,v_N,v_i_0) [2 >= v_2] (?,1) 34. eval_random2d_NodeBlock7_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_LeafBlock5_in(v_1,v_2,v_N,v_i_0) [v_2 >= 3] (?,1) 35. eval_random2d_LeafBlock3_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb6_in(v_1,v_2,v_N,v_i_0) [v_2 = 2] (?,1) 36. eval_random2d_LeafBlock3_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) [1 >= v_2] (?,1) 37. eval_random2d_LeafBlock3_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) [-1 + v_2 >= 2] (?,1) 38. eval_random2d_bb6_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True (?,1) 39. eval_random2d_LeafBlock5_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb7_in(v_1,v_2,v_N,v_i_0) [v_2 = 3] (?,1) 40. eval_random2d_LeafBlock5_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) [2 >= v_2] (?,1) 41. eval_random2d_LeafBlock5_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) [-1 + v_2 >= 3] (?,1) 42. eval_random2d_bb7_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True (?,1) 43. eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True (?,1) 44. eval_random2d_bb8_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_stop(v_1,v_2,v_N,v_i_0) True (?,1) Signature: {(eval_random2d_0,4) ;(eval_random2d_1,4) ;(eval_random2d_10,4) ;(eval_random2d_12,4) ;(eval_random2d_13,4) ;(eval_random2d_2,4) ;(eval_random2d_3,4) ;(eval_random2d_4,4) ;(eval_random2d_5,4) ;(eval_random2d_6,4) ;(eval_random2d_7,4) ;(eval_random2d_8,4) ;(eval_random2d_9,4) ;(eval_random2d_LeafBlock1_in,4) ;(eval_random2d_LeafBlock3_in,4) ;(eval_random2d_LeafBlock5_in,4) ;(eval_random2d_LeafBlock_in,4) ;(eval_random2d_NewDefault_in,4) ;(eval_random2d_NodeBlock7_in,4) ;(eval_random2d_NodeBlock9_in,4) ;(eval_random2d_NodeBlock_in,4) ;(eval_random2d_bb0_in,4) ;(eval_random2d_bb1_in,4) ;(eval_random2d_bb2_in,4) ;(eval_random2d_bb3_in,4) ;(eval_random2d_bb4_in,4) ;(eval_random2d_bb5_in,4) ;(eval_random2d_bb6_in,4) ;(eval_random2d_bb7_in,4) ;(eval_random2d_bb8_in,4) ;(eval_random2d_start,4) ;(eval_random2d_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10},10->{11},11->{12},12->{13,14} ,13->{15},14->{44},15->{16},16->{17,18,19},17->{20},18->{13,14},19->{13,14},20->{21,22},21->{23,24},22->{33 ,34},23->{25,26},24->{29,31},25->{28},26->{43},27->{43},28->{13,14},29->{32},30->{43},31->{43},32->{13,14} ,33->{35,36},34->{39,41},35->{38},36->{43},37->{43},38->{13,14},39->{42},40->{43},41->{43},42->{13,14} ,43->{13,14},44->{}] + Applied Processor: UnreachableRules + Details: Following transitions are not reachable from the starting states and are revomed: [27,30,37,40] * Step 3: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_random2d_start(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb0_in(v_1,v_2,v_N,v_i_0) True (1,1) 1. eval_random2d_bb0_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_0(v_1,v_2,v_N,v_i_0) True (?,1) 2. eval_random2d_0(v_1,v_2,v_N,v_i_0) -> eval_random2d_1(v_1,v_2,v_N,v_i_0) True (?,1) 3. eval_random2d_1(v_1,v_2,v_N,v_i_0) -> eval_random2d_2(v_1,v_2,v_N,v_i_0) True (?,1) 4. eval_random2d_2(v_1,v_2,v_N,v_i_0) -> eval_random2d_3(v_1,v_2,v_N,v_i_0) True (?,1) 5. eval_random2d_3(v_1,v_2,v_N,v_i_0) -> eval_random2d_4(v_1,v_2,v_N,v_i_0) True (?,1) 6. eval_random2d_4(v_1,v_2,v_N,v_i_0) -> eval_random2d_5(v_1,v_2,v_N,v_i_0) True (?,1) 7. eval_random2d_5(v_1,v_2,v_N,v_i_0) -> eval_random2d_6(v_1,v_2,v_N,v_i_0) True (?,1) 8. eval_random2d_6(v_1,v_2,v_N,v_i_0) -> eval_random2d_7(v_1,v_2,v_N,v_i_0) True (?,1) 9. eval_random2d_7(v_1,v_2,v_N,v_i_0) -> eval_random2d_8(v_1,v_2,v_N,v_i_0) True (?,1) 10. eval_random2d_8(v_1,v_2,v_N,v_i_0) -> eval_random2d_9(v_1,v_2,v_N,v_i_0) True (?,1) 11. eval_random2d_9(v_1,v_2,v_N,v_i_0) -> eval_random2d_10(v_1,v_2,v_N,v_i_0) True (?,1) 12. eval_random2d_10(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,0) True (?,1) 13. eval_random2d_bb1_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb2_in(v_1,v_2,v_N,v_i_0) [-1 + v_N >= v_i_0] (?,1) 14. eval_random2d_bb1_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb8_in(v_1,v_2,v_N,v_i_0) [v_i_0 >= v_N] (?,1) 15. eval_random2d_bb2_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_12(1 + v_i_0,v_2,v_N,v_i_0) True (?,1) 16. eval_random2d_12(v_1,v_2,v_N,v_i_0) -> eval_random2d_13(v_1,nondef_0,v_N,v_i_0) True (?,1) 17. eval_random2d_13(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb3_in(v_1,v_2,v_N,v_i_0) [v_2 >= 0 && 3 >= v_2] (?,1) 18. eval_random2d_13(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) [-1 >= v_2] (?,1) 19. eval_random2d_13(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) [-1 + v_2 >= 3] (?,1) 20. eval_random2d_bb3_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NodeBlock9_in(v_1,v_2,v_N,v_i_0) True (?,1) 21. eval_random2d_NodeBlock9_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NodeBlock_in(v_1,v_2,v_N,v_i_0) [1 >= v_2] (?,1) 22. eval_random2d_NodeBlock9_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NodeBlock7_in(v_1,v_2,v_N,v_i_0) [v_2 >= 2] (?,1) 23. eval_random2d_NodeBlock_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_LeafBlock_in(v_1,v_2,v_N,v_i_0) [0 >= v_2] (?,1) 24. eval_random2d_NodeBlock_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_LeafBlock1_in(v_1,v_2,v_N,v_i_0) [v_2 >= 1] (?,1) 25. eval_random2d_LeafBlock_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb4_in(v_1,v_2,v_N,v_i_0) [v_2 = 0] (?,1) 26. eval_random2d_LeafBlock_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) [-1 >= v_2] (?,1) 28. eval_random2d_bb4_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True (?,1) 29. eval_random2d_LeafBlock1_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb5_in(v_1,v_2,v_N,v_i_0) [v_2 = 1] (?,1) 31. eval_random2d_LeafBlock1_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) [-1 + v_2 >= 1] (?,1) 32. eval_random2d_bb5_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True (?,1) 33. eval_random2d_NodeBlock7_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_LeafBlock3_in(v_1,v_2,v_N,v_i_0) [2 >= v_2] (?,1) 34. eval_random2d_NodeBlock7_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_LeafBlock5_in(v_1,v_2,v_N,v_i_0) [v_2 >= 3] (?,1) 35. eval_random2d_LeafBlock3_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb6_in(v_1,v_2,v_N,v_i_0) [v_2 = 2] (?,1) 36. eval_random2d_LeafBlock3_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) [1 >= v_2] (?,1) 38. eval_random2d_bb6_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True (?,1) 39. eval_random2d_LeafBlock5_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb7_in(v_1,v_2,v_N,v_i_0) [v_2 = 3] (?,1) 41. eval_random2d_LeafBlock5_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) [-1 + v_2 >= 3] (?,1) 42. eval_random2d_bb7_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True (?,1) 43. eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True (?,1) 44. eval_random2d_bb8_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_stop(v_1,v_2,v_N,v_i_0) True (?,1) Signature: {(eval_random2d_0,4) ;(eval_random2d_1,4) ;(eval_random2d_10,4) ;(eval_random2d_12,4) ;(eval_random2d_13,4) ;(eval_random2d_2,4) ;(eval_random2d_3,4) ;(eval_random2d_4,4) ;(eval_random2d_5,4) ;(eval_random2d_6,4) ;(eval_random2d_7,4) ;(eval_random2d_8,4) ;(eval_random2d_9,4) ;(eval_random2d_LeafBlock1_in,4) ;(eval_random2d_LeafBlock3_in,4) ;(eval_random2d_LeafBlock5_in,4) ;(eval_random2d_LeafBlock_in,4) ;(eval_random2d_NewDefault_in,4) ;(eval_random2d_NodeBlock7_in,4) ;(eval_random2d_NodeBlock9_in,4) ;(eval_random2d_NodeBlock_in,4) ;(eval_random2d_bb0_in,4) ;(eval_random2d_bb1_in,4) ;(eval_random2d_bb2_in,4) ;(eval_random2d_bb3_in,4) ;(eval_random2d_bb4_in,4) ;(eval_random2d_bb5_in,4) ;(eval_random2d_bb6_in,4) ;(eval_random2d_bb7_in,4) ;(eval_random2d_bb8_in,4) ;(eval_random2d_start,4) ;(eval_random2d_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10},10->{11},11->{12},12->{13,14} ,13->{15},14->{44},15->{16},16->{17,18,19},17->{20},18->{13,14},19->{13,14},20->{21,22},21->{23,24},22->{33 ,34},23->{25,26},24->{29,31},25->{28},26->{43},28->{13,14},29->{32},31->{43},32->{13,14},33->{35,36},34->{39 ,41},35->{38},36->{43},38->{13,14},39->{42},41->{43},42->{13,14},43->{13,14},44->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 4: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_random2d_start(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb0_in(v_1,v_2,v_N,v_i_0) True (1,1) 1. eval_random2d_bb0_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_0(v_1,v_2,v_N,v_i_0) True (1,1) 2. eval_random2d_0(v_1,v_2,v_N,v_i_0) -> eval_random2d_1(v_1,v_2,v_N,v_i_0) True (1,1) 3. eval_random2d_1(v_1,v_2,v_N,v_i_0) -> eval_random2d_2(v_1,v_2,v_N,v_i_0) True (1,1) 4. eval_random2d_2(v_1,v_2,v_N,v_i_0) -> eval_random2d_3(v_1,v_2,v_N,v_i_0) True (1,1) 5. eval_random2d_3(v_1,v_2,v_N,v_i_0) -> eval_random2d_4(v_1,v_2,v_N,v_i_0) True (1,1) 6. eval_random2d_4(v_1,v_2,v_N,v_i_0) -> eval_random2d_5(v_1,v_2,v_N,v_i_0) True (1,1) 7. eval_random2d_5(v_1,v_2,v_N,v_i_0) -> eval_random2d_6(v_1,v_2,v_N,v_i_0) True (1,1) 8. eval_random2d_6(v_1,v_2,v_N,v_i_0) -> eval_random2d_7(v_1,v_2,v_N,v_i_0) True (1,1) 9. eval_random2d_7(v_1,v_2,v_N,v_i_0) -> eval_random2d_8(v_1,v_2,v_N,v_i_0) True (1,1) 10. eval_random2d_8(v_1,v_2,v_N,v_i_0) -> eval_random2d_9(v_1,v_2,v_N,v_i_0) True (1,1) 11. eval_random2d_9(v_1,v_2,v_N,v_i_0) -> eval_random2d_10(v_1,v_2,v_N,v_i_0) True (1,1) 12. eval_random2d_10(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,0) True (1,1) 13. eval_random2d_bb1_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb2_in(v_1,v_2,v_N,v_i_0) [-1 + v_N >= v_i_0] (?,1) 14. eval_random2d_bb1_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb8_in(v_1,v_2,v_N,v_i_0) [v_i_0 >= v_N] (1,1) 15. eval_random2d_bb2_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_12(1 + v_i_0,v_2,v_N,v_i_0) True (?,1) 16. eval_random2d_12(v_1,v_2,v_N,v_i_0) -> eval_random2d_13(v_1,nondef_0,v_N,v_i_0) True (?,1) 17. eval_random2d_13(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb3_in(v_1,v_2,v_N,v_i_0) [v_2 >= 0 && 3 >= v_2] (?,1) 18. eval_random2d_13(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) [-1 >= v_2] (?,1) 19. eval_random2d_13(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) [-1 + v_2 >= 3] (?,1) 20. eval_random2d_bb3_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NodeBlock9_in(v_1,v_2,v_N,v_i_0) True (?,1) 21. eval_random2d_NodeBlock9_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NodeBlock_in(v_1,v_2,v_N,v_i_0) [1 >= v_2] (?,1) 22. eval_random2d_NodeBlock9_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NodeBlock7_in(v_1,v_2,v_N,v_i_0) [v_2 >= 2] (?,1) 23. eval_random2d_NodeBlock_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_LeafBlock_in(v_1,v_2,v_N,v_i_0) [0 >= v_2] (?,1) 24. eval_random2d_NodeBlock_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_LeafBlock1_in(v_1,v_2,v_N,v_i_0) [v_2 >= 1] (?,1) 25. eval_random2d_LeafBlock_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb4_in(v_1,v_2,v_N,v_i_0) [v_2 = 0] (?,1) 26. eval_random2d_LeafBlock_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) [-1 >= v_2] (?,1) 28. eval_random2d_bb4_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True (?,1) 29. eval_random2d_LeafBlock1_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb5_in(v_1,v_2,v_N,v_i_0) [v_2 = 1] (?,1) 31. eval_random2d_LeafBlock1_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) [-1 + v_2 >= 1] (?,1) 32. eval_random2d_bb5_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True (?,1) 33. eval_random2d_NodeBlock7_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_LeafBlock3_in(v_1,v_2,v_N,v_i_0) [2 >= v_2] (?,1) 34. eval_random2d_NodeBlock7_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_LeafBlock5_in(v_1,v_2,v_N,v_i_0) [v_2 >= 3] (?,1) 35. eval_random2d_LeafBlock3_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb6_in(v_1,v_2,v_N,v_i_0) [v_2 = 2] (?,1) 36. eval_random2d_LeafBlock3_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) [1 >= v_2] (?,1) 38. eval_random2d_bb6_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True (?,1) 39. eval_random2d_LeafBlock5_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb7_in(v_1,v_2,v_N,v_i_0) [v_2 = 3] (?,1) 41. eval_random2d_LeafBlock5_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) [-1 + v_2 >= 3] (?,1) 42. eval_random2d_bb7_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True (?,1) 43. eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True (?,1) 44. eval_random2d_bb8_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_stop(v_1,v_2,v_N,v_i_0) True (1,1) Signature: {(eval_random2d_0,4) ;(eval_random2d_1,4) ;(eval_random2d_10,4) ;(eval_random2d_12,4) ;(eval_random2d_13,4) ;(eval_random2d_2,4) ;(eval_random2d_3,4) ;(eval_random2d_4,4) ;(eval_random2d_5,4) ;(eval_random2d_6,4) ;(eval_random2d_7,4) ;(eval_random2d_8,4) ;(eval_random2d_9,4) ;(eval_random2d_LeafBlock1_in,4) ;(eval_random2d_LeafBlock3_in,4) ;(eval_random2d_LeafBlock5_in,4) ;(eval_random2d_LeafBlock_in,4) ;(eval_random2d_NewDefault_in,4) ;(eval_random2d_NodeBlock7_in,4) ;(eval_random2d_NodeBlock9_in,4) ;(eval_random2d_NodeBlock_in,4) ;(eval_random2d_bb0_in,4) ;(eval_random2d_bb1_in,4) ;(eval_random2d_bb2_in,4) ;(eval_random2d_bb3_in,4) ;(eval_random2d_bb4_in,4) ;(eval_random2d_bb5_in,4) ;(eval_random2d_bb6_in,4) ;(eval_random2d_bb7_in,4) ;(eval_random2d_bb8_in,4) ;(eval_random2d_start,4) ;(eval_random2d_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10},10->{11},11->{12},12->{13,14} ,13->{15},14->{44},15->{16},16->{17,18,19},17->{20},18->{13,14},19->{13,14},20->{21,22},21->{23,24},22->{33 ,34},23->{25,26},24->{29,31},25->{28},26->{43},28->{13,14},29->{32},31->{43},32->{13,14},33->{35,36},34->{39 ,41},35->{38},36->{43},38->{13,14},39->{42},41->{43},42->{13,14},43->{13,14},44->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval_random2d_0) = x3 p(eval_random2d_1) = x3 p(eval_random2d_10) = x3 p(eval_random2d_12) = -1*x1 + x3 p(eval_random2d_13) = -1*x1 + x3 p(eval_random2d_2) = x3 p(eval_random2d_3) = x3 p(eval_random2d_4) = x3 p(eval_random2d_5) = x3 p(eval_random2d_6) = x3 p(eval_random2d_7) = x3 p(eval_random2d_8) = x3 p(eval_random2d_9) = x3 p(eval_random2d_LeafBlock1_in) = -1*x1 + x3 p(eval_random2d_LeafBlock3_in) = -1*x1 + x3 p(eval_random2d_LeafBlock5_in) = -1*x1 + x3 p(eval_random2d_LeafBlock_in) = -1*x1 + x3 p(eval_random2d_NewDefault_in) = -1*x1 + x3 p(eval_random2d_NodeBlock7_in) = -1*x1 + x3 p(eval_random2d_NodeBlock9_in) = -1*x1 + x3 p(eval_random2d_NodeBlock_in) = -1*x1 + x3 p(eval_random2d_bb0_in) = x3 p(eval_random2d_bb1_in) = x3 + -1*x4 p(eval_random2d_bb2_in) = -1 + x3 + -1*x4 p(eval_random2d_bb3_in) = -1*x1 + x3 p(eval_random2d_bb4_in) = -1*x1 + x3 p(eval_random2d_bb5_in) = -1*x1 + x3 p(eval_random2d_bb6_in) = -1*x1 + x3 p(eval_random2d_bb7_in) = -1*x1 + x3 p(eval_random2d_bb8_in) = x3 + -1*x4 p(eval_random2d_start) = x3 p(eval_random2d_stop) = x3 + -1*x4 Following rules are strictly oriented: [-1 + v_N >= v_i_0] ==> eval_random2d_bb1_in(v_1,v_2,v_N,v_i_0) = v_N + -1*v_i_0 > -1 + v_N + -1*v_i_0 = eval_random2d_bb2_in(v_1,v_2,v_N,v_i_0) Following rules are weakly oriented: True ==> eval_random2d_start(v_1,v_2,v_N,v_i_0) = v_N >= v_N = eval_random2d_bb0_in(v_1,v_2,v_N,v_i_0) True ==> eval_random2d_bb0_in(v_1,v_2,v_N,v_i_0) = v_N >= v_N = eval_random2d_0(v_1,v_2,v_N,v_i_0) True ==> eval_random2d_0(v_1,v_2,v_N,v_i_0) = v_N >= v_N = eval_random2d_1(v_1,v_2,v_N,v_i_0) True ==> eval_random2d_1(v_1,v_2,v_N,v_i_0) = v_N >= v_N = eval_random2d_2(v_1,v_2,v_N,v_i_0) True ==> eval_random2d_2(v_1,v_2,v_N,v_i_0) = v_N >= v_N = eval_random2d_3(v_1,v_2,v_N,v_i_0) True ==> eval_random2d_3(v_1,v_2,v_N,v_i_0) = v_N >= v_N = eval_random2d_4(v_1,v_2,v_N,v_i_0) True ==> eval_random2d_4(v_1,v_2,v_N,v_i_0) = v_N >= v_N = eval_random2d_5(v_1,v_2,v_N,v_i_0) True ==> eval_random2d_5(v_1,v_2,v_N,v_i_0) = v_N >= v_N = eval_random2d_6(v_1,v_2,v_N,v_i_0) True ==> eval_random2d_6(v_1,v_2,v_N,v_i_0) = v_N >= v_N = eval_random2d_7(v_1,v_2,v_N,v_i_0) True ==> eval_random2d_7(v_1,v_2,v_N,v_i_0) = v_N >= v_N = eval_random2d_8(v_1,v_2,v_N,v_i_0) True ==> eval_random2d_8(v_1,v_2,v_N,v_i_0) = v_N >= v_N = eval_random2d_9(v_1,v_2,v_N,v_i_0) True ==> eval_random2d_9(v_1,v_2,v_N,v_i_0) = v_N >= v_N = eval_random2d_10(v_1,v_2,v_N,v_i_0) True ==> eval_random2d_10(v_1,v_2,v_N,v_i_0) = v_N >= v_N = eval_random2d_bb1_in(v_1,v_2,v_N,0) [v_i_0 >= v_N] ==> eval_random2d_bb1_in(v_1,v_2,v_N,v_i_0) = v_N + -1*v_i_0 >= v_N + -1*v_i_0 = eval_random2d_bb8_in(v_1,v_2,v_N,v_i_0) True ==> eval_random2d_bb2_in(v_1,v_2,v_N,v_i_0) = -1 + v_N + -1*v_i_0 >= -1 + v_N + -1*v_i_0 = eval_random2d_12(1 + v_i_0,v_2,v_N,v_i_0) True ==> eval_random2d_12(v_1,v_2,v_N,v_i_0) = -1*v_1 + v_N >= -1*v_1 + v_N = eval_random2d_13(v_1,nondef_0,v_N,v_i_0) [v_2 >= 0 && 3 >= v_2] ==> eval_random2d_13(v_1,v_2,v_N,v_i_0) = -1*v_1 + v_N >= -1*v_1 + v_N = eval_random2d_bb3_in(v_1,v_2,v_N,v_i_0) [-1 >= v_2] ==> eval_random2d_13(v_1,v_2,v_N,v_i_0) = -1*v_1 + v_N >= -1*v_1 + v_N = eval_random2d_bb1_in(v_1,v_2,v_N,v_1) [-1 + v_2 >= 3] ==> eval_random2d_13(v_1,v_2,v_N,v_i_0) = -1*v_1 + v_N >= -1*v_1 + v_N = eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True ==> eval_random2d_bb3_in(v_1,v_2,v_N,v_i_0) = -1*v_1 + v_N >= -1*v_1 + v_N = eval_random2d_NodeBlock9_in(v_1,v_2,v_N,v_i_0) [1 >= v_2] ==> eval_random2d_NodeBlock9_in(v_1,v_2,v_N,v_i_0) = -1*v_1 + v_N >= -1*v_1 + v_N = eval_random2d_NodeBlock_in(v_1,v_2,v_N,v_i_0) [v_2 >= 2] ==> eval_random2d_NodeBlock9_in(v_1,v_2,v_N,v_i_0) = -1*v_1 + v_N >= -1*v_1 + v_N = eval_random2d_NodeBlock7_in(v_1,v_2,v_N,v_i_0) [0 >= v_2] ==> eval_random2d_NodeBlock_in(v_1,v_2,v_N,v_i_0) = -1*v_1 + v_N >= -1*v_1 + v_N = eval_random2d_LeafBlock_in(v_1,v_2,v_N,v_i_0) [v_2 >= 1] ==> eval_random2d_NodeBlock_in(v_1,v_2,v_N,v_i_0) = -1*v_1 + v_N >= -1*v_1 + v_N = eval_random2d_LeafBlock1_in(v_1,v_2,v_N,v_i_0) [v_2 = 0] ==> eval_random2d_LeafBlock_in(v_1,v_2,v_N,v_i_0) = -1*v_1 + v_N >= -1*v_1 + v_N = eval_random2d_bb4_in(v_1,v_2,v_N,v_i_0) [-1 >= v_2] ==> eval_random2d_LeafBlock_in(v_1,v_2,v_N,v_i_0) = -1*v_1 + v_N >= -1*v_1 + v_N = eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) True ==> eval_random2d_bb4_in(v_1,v_2,v_N,v_i_0) = -1*v_1 + v_N >= -1*v_1 + v_N = eval_random2d_bb1_in(v_1,v_2,v_N,v_1) [v_2 = 1] ==> eval_random2d_LeafBlock1_in(v_1,v_2,v_N,v_i_0) = -1*v_1 + v_N >= -1*v_1 + v_N = eval_random2d_bb5_in(v_1,v_2,v_N,v_i_0) [-1 + v_2 >= 1] ==> eval_random2d_LeafBlock1_in(v_1,v_2,v_N,v_i_0) = -1*v_1 + v_N >= -1*v_1 + v_N = eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) True ==> eval_random2d_bb5_in(v_1,v_2,v_N,v_i_0) = -1*v_1 + v_N >= -1*v_1 + v_N = eval_random2d_bb1_in(v_1,v_2,v_N,v_1) [2 >= v_2] ==> eval_random2d_NodeBlock7_in(v_1,v_2,v_N,v_i_0) = -1*v_1 + v_N >= -1*v_1 + v_N = eval_random2d_LeafBlock3_in(v_1,v_2,v_N,v_i_0) [v_2 >= 3] ==> eval_random2d_NodeBlock7_in(v_1,v_2,v_N,v_i_0) = -1*v_1 + v_N >= -1*v_1 + v_N = eval_random2d_LeafBlock5_in(v_1,v_2,v_N,v_i_0) [v_2 = 2] ==> eval_random2d_LeafBlock3_in(v_1,v_2,v_N,v_i_0) = -1*v_1 + v_N >= -1*v_1 + v_N = eval_random2d_bb6_in(v_1,v_2,v_N,v_i_0) [1 >= v_2] ==> eval_random2d_LeafBlock3_in(v_1,v_2,v_N,v_i_0) = -1*v_1 + v_N >= -1*v_1 + v_N = eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) True ==> eval_random2d_bb6_in(v_1,v_2,v_N,v_i_0) = -1*v_1 + v_N >= -1*v_1 + v_N = eval_random2d_bb1_in(v_1,v_2,v_N,v_1) [v_2 = 3] ==> eval_random2d_LeafBlock5_in(v_1,v_2,v_N,v_i_0) = -1*v_1 + v_N >= -1*v_1 + v_N = eval_random2d_bb7_in(v_1,v_2,v_N,v_i_0) [-1 + v_2 >= 3] ==> eval_random2d_LeafBlock5_in(v_1,v_2,v_N,v_i_0) = -1*v_1 + v_N >= -1*v_1 + v_N = eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) True ==> eval_random2d_bb7_in(v_1,v_2,v_N,v_i_0) = -1*v_1 + v_N >= -1*v_1 + v_N = eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True ==> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) = -1*v_1 + v_N >= -1*v_1 + v_N = eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True ==> eval_random2d_bb8_in(v_1,v_2,v_N,v_i_0) = v_N + -1*v_i_0 >= v_N + -1*v_i_0 = eval_random2d_stop(v_1,v_2,v_N,v_i_0) * Step 5: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_random2d_start(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb0_in(v_1,v_2,v_N,v_i_0) True (1,1) 1. eval_random2d_bb0_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_0(v_1,v_2,v_N,v_i_0) True (1,1) 2. eval_random2d_0(v_1,v_2,v_N,v_i_0) -> eval_random2d_1(v_1,v_2,v_N,v_i_0) True (1,1) 3. eval_random2d_1(v_1,v_2,v_N,v_i_0) -> eval_random2d_2(v_1,v_2,v_N,v_i_0) True (1,1) 4. eval_random2d_2(v_1,v_2,v_N,v_i_0) -> eval_random2d_3(v_1,v_2,v_N,v_i_0) True (1,1) 5. eval_random2d_3(v_1,v_2,v_N,v_i_0) -> eval_random2d_4(v_1,v_2,v_N,v_i_0) True (1,1) 6. eval_random2d_4(v_1,v_2,v_N,v_i_0) -> eval_random2d_5(v_1,v_2,v_N,v_i_0) True (1,1) 7. eval_random2d_5(v_1,v_2,v_N,v_i_0) -> eval_random2d_6(v_1,v_2,v_N,v_i_0) True (1,1) 8. eval_random2d_6(v_1,v_2,v_N,v_i_0) -> eval_random2d_7(v_1,v_2,v_N,v_i_0) True (1,1) 9. eval_random2d_7(v_1,v_2,v_N,v_i_0) -> eval_random2d_8(v_1,v_2,v_N,v_i_0) True (1,1) 10. eval_random2d_8(v_1,v_2,v_N,v_i_0) -> eval_random2d_9(v_1,v_2,v_N,v_i_0) True (1,1) 11. eval_random2d_9(v_1,v_2,v_N,v_i_0) -> eval_random2d_10(v_1,v_2,v_N,v_i_0) True (1,1) 12. eval_random2d_10(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,0) True (1,1) 13. eval_random2d_bb1_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb2_in(v_1,v_2,v_N,v_i_0) [-1 + v_N >= v_i_0] (v_N,1) 14. eval_random2d_bb1_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb8_in(v_1,v_2,v_N,v_i_0) [v_i_0 >= v_N] (1,1) 15. eval_random2d_bb2_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_12(1 + v_i_0,v_2,v_N,v_i_0) True (?,1) 16. eval_random2d_12(v_1,v_2,v_N,v_i_0) -> eval_random2d_13(v_1,nondef_0,v_N,v_i_0) True (?,1) 17. eval_random2d_13(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb3_in(v_1,v_2,v_N,v_i_0) [v_2 >= 0 && 3 >= v_2] (?,1) 18. eval_random2d_13(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) [-1 >= v_2] (?,1) 19. eval_random2d_13(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) [-1 + v_2 >= 3] (?,1) 20. eval_random2d_bb3_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NodeBlock9_in(v_1,v_2,v_N,v_i_0) True (?,1) 21. eval_random2d_NodeBlock9_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NodeBlock_in(v_1,v_2,v_N,v_i_0) [1 >= v_2] (?,1) 22. eval_random2d_NodeBlock9_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NodeBlock7_in(v_1,v_2,v_N,v_i_0) [v_2 >= 2] (?,1) 23. eval_random2d_NodeBlock_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_LeafBlock_in(v_1,v_2,v_N,v_i_0) [0 >= v_2] (?,1) 24. eval_random2d_NodeBlock_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_LeafBlock1_in(v_1,v_2,v_N,v_i_0) [v_2 >= 1] (?,1) 25. eval_random2d_LeafBlock_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb4_in(v_1,v_2,v_N,v_i_0) [v_2 = 0] (?,1) 26. eval_random2d_LeafBlock_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) [-1 >= v_2] (?,1) 28. eval_random2d_bb4_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True (?,1) 29. eval_random2d_LeafBlock1_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb5_in(v_1,v_2,v_N,v_i_0) [v_2 = 1] (?,1) 31. eval_random2d_LeafBlock1_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) [-1 + v_2 >= 1] (?,1) 32. eval_random2d_bb5_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True (?,1) 33. eval_random2d_NodeBlock7_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_LeafBlock3_in(v_1,v_2,v_N,v_i_0) [2 >= v_2] (?,1) 34. eval_random2d_NodeBlock7_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_LeafBlock5_in(v_1,v_2,v_N,v_i_0) [v_2 >= 3] (?,1) 35. eval_random2d_LeafBlock3_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb6_in(v_1,v_2,v_N,v_i_0) [v_2 = 2] (?,1) 36. eval_random2d_LeafBlock3_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) [1 >= v_2] (?,1) 38. eval_random2d_bb6_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True (?,1) 39. eval_random2d_LeafBlock5_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb7_in(v_1,v_2,v_N,v_i_0) [v_2 = 3] (?,1) 41. eval_random2d_LeafBlock5_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) [-1 + v_2 >= 3] (?,1) 42. eval_random2d_bb7_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True (?,1) 43. eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True (?,1) 44. eval_random2d_bb8_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_stop(v_1,v_2,v_N,v_i_0) True (1,1) Signature: {(eval_random2d_0,4) ;(eval_random2d_1,4) ;(eval_random2d_10,4) ;(eval_random2d_12,4) ;(eval_random2d_13,4) ;(eval_random2d_2,4) ;(eval_random2d_3,4) ;(eval_random2d_4,4) ;(eval_random2d_5,4) ;(eval_random2d_6,4) ;(eval_random2d_7,4) ;(eval_random2d_8,4) ;(eval_random2d_9,4) ;(eval_random2d_LeafBlock1_in,4) ;(eval_random2d_LeafBlock3_in,4) ;(eval_random2d_LeafBlock5_in,4) ;(eval_random2d_LeafBlock_in,4) ;(eval_random2d_NewDefault_in,4) ;(eval_random2d_NodeBlock7_in,4) ;(eval_random2d_NodeBlock9_in,4) ;(eval_random2d_NodeBlock_in,4) ;(eval_random2d_bb0_in,4) ;(eval_random2d_bb1_in,4) ;(eval_random2d_bb2_in,4) ;(eval_random2d_bb3_in,4) ;(eval_random2d_bb4_in,4) ;(eval_random2d_bb5_in,4) ;(eval_random2d_bb6_in,4) ;(eval_random2d_bb7_in,4) ;(eval_random2d_bb8_in,4) ;(eval_random2d_start,4) ;(eval_random2d_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10},10->{11},11->{12},12->{13,14} ,13->{15},14->{44},15->{16},16->{17,18,19},17->{20},18->{13,14},19->{13,14},20->{21,22},21->{23,24},22->{33 ,34},23->{25,26},24->{29,31},25->{28},26->{43},28->{13,14},29->{32},31->{43},32->{13,14},33->{35,36},34->{39 ,41},35->{38},36->{43},38->{13,14},39->{42},41->{43},42->{13,14},43->{13,14},44->{}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 6: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_random2d_start(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb0_in(v_1,v_2,v_N,v_i_0) True (1,1) 1. eval_random2d_bb0_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_0(v_1,v_2,v_N,v_i_0) True (1,1) 2. eval_random2d_0(v_1,v_2,v_N,v_i_0) -> eval_random2d_1(v_1,v_2,v_N,v_i_0) True (1,1) 3. eval_random2d_1(v_1,v_2,v_N,v_i_0) -> eval_random2d_2(v_1,v_2,v_N,v_i_0) True (1,1) 4. eval_random2d_2(v_1,v_2,v_N,v_i_0) -> eval_random2d_3(v_1,v_2,v_N,v_i_0) True (1,1) 5. eval_random2d_3(v_1,v_2,v_N,v_i_0) -> eval_random2d_4(v_1,v_2,v_N,v_i_0) True (1,1) 6. eval_random2d_4(v_1,v_2,v_N,v_i_0) -> eval_random2d_5(v_1,v_2,v_N,v_i_0) True (1,1) 7. eval_random2d_5(v_1,v_2,v_N,v_i_0) -> eval_random2d_6(v_1,v_2,v_N,v_i_0) True (1,1) 8. eval_random2d_6(v_1,v_2,v_N,v_i_0) -> eval_random2d_7(v_1,v_2,v_N,v_i_0) True (1,1) 9. eval_random2d_7(v_1,v_2,v_N,v_i_0) -> eval_random2d_8(v_1,v_2,v_N,v_i_0) True (1,1) 10. eval_random2d_8(v_1,v_2,v_N,v_i_0) -> eval_random2d_9(v_1,v_2,v_N,v_i_0) True (1,1) 11. eval_random2d_9(v_1,v_2,v_N,v_i_0) -> eval_random2d_10(v_1,v_2,v_N,v_i_0) True (1,1) 12. eval_random2d_10(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,0) True (1,1) 13. eval_random2d_bb1_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb2_in(v_1,v_2,v_N,v_i_0) [-1 + v_N >= v_i_0] (v_N,1) 14. eval_random2d_bb1_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb8_in(v_1,v_2,v_N,v_i_0) [v_i_0 >= v_N] (1,1) 15. eval_random2d_bb2_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_12(1 + v_i_0,v_2,v_N,v_i_0) True (v_N,1) 16. eval_random2d_12(v_1,v_2,v_N,v_i_0) -> eval_random2d_13(v_1,nondef_0,v_N,v_i_0) True (v_N,1) 17. eval_random2d_13(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb3_in(v_1,v_2,v_N,v_i_0) [v_2 >= 0 && 3 >= v_2] (v_N,1) 18. eval_random2d_13(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) [-1 >= v_2] (v_N,1) 19. eval_random2d_13(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) [-1 + v_2 >= 3] (v_N,1) 20. eval_random2d_bb3_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NodeBlock9_in(v_1,v_2,v_N,v_i_0) True (v_N,1) 21. eval_random2d_NodeBlock9_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NodeBlock_in(v_1,v_2,v_N,v_i_0) [1 >= v_2] (v_N,1) 22. eval_random2d_NodeBlock9_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NodeBlock7_in(v_1,v_2,v_N,v_i_0) [v_2 >= 2] (v_N,1) 23. eval_random2d_NodeBlock_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_LeafBlock_in(v_1,v_2,v_N,v_i_0) [0 >= v_2] (v_N,1) 24. eval_random2d_NodeBlock_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_LeafBlock1_in(v_1,v_2,v_N,v_i_0) [v_2 >= 1] (v_N,1) 25. eval_random2d_LeafBlock_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb4_in(v_1,v_2,v_N,v_i_0) [v_2 = 0] (v_N,1) 26. eval_random2d_LeafBlock_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) [-1 >= v_2] (v_N,1) 28. eval_random2d_bb4_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True (v_N,1) 29. eval_random2d_LeafBlock1_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb5_in(v_1,v_2,v_N,v_i_0) [v_2 = 1] (v_N,1) 31. eval_random2d_LeafBlock1_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) [-1 + v_2 >= 1] (v_N,1) 32. eval_random2d_bb5_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True (v_N,1) 33. eval_random2d_NodeBlock7_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_LeafBlock3_in(v_1,v_2,v_N,v_i_0) [2 >= v_2] (v_N,1) 34. eval_random2d_NodeBlock7_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_LeafBlock5_in(v_1,v_2,v_N,v_i_0) [v_2 >= 3] (v_N,1) 35. eval_random2d_LeafBlock3_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb6_in(v_1,v_2,v_N,v_i_0) [v_2 = 2] (v_N,1) 36. eval_random2d_LeafBlock3_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) [1 >= v_2] (v_N,1) 38. eval_random2d_bb6_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True (v_N,1) 39. eval_random2d_LeafBlock5_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb7_in(v_1,v_2,v_N,v_i_0) [v_2 = 3] (v_N,1) 41. eval_random2d_LeafBlock5_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) [-1 + v_2 >= 3] (v_N,1) 42. eval_random2d_bb7_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True (v_N,1) 43. eval_random2d_NewDefault_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_bb1_in(v_1,v_2,v_N,v_1) True (4*v_N,1) 44. eval_random2d_bb8_in(v_1,v_2,v_N,v_i_0) -> eval_random2d_stop(v_1,v_2,v_N,v_i_0) True (1,1) Signature: {(eval_random2d_0,4) ;(eval_random2d_1,4) ;(eval_random2d_10,4) ;(eval_random2d_12,4) ;(eval_random2d_13,4) ;(eval_random2d_2,4) ;(eval_random2d_3,4) ;(eval_random2d_4,4) ;(eval_random2d_5,4) ;(eval_random2d_6,4) ;(eval_random2d_7,4) ;(eval_random2d_8,4) ;(eval_random2d_9,4) ;(eval_random2d_LeafBlock1_in,4) ;(eval_random2d_LeafBlock3_in,4) ;(eval_random2d_LeafBlock5_in,4) ;(eval_random2d_LeafBlock_in,4) ;(eval_random2d_NewDefault_in,4) ;(eval_random2d_NodeBlock7_in,4) ;(eval_random2d_NodeBlock9_in,4) ;(eval_random2d_NodeBlock_in,4) ;(eval_random2d_bb0_in,4) ;(eval_random2d_bb1_in,4) ;(eval_random2d_bb2_in,4) ;(eval_random2d_bb3_in,4) ;(eval_random2d_bb4_in,4) ;(eval_random2d_bb5_in,4) ;(eval_random2d_bb6_in,4) ;(eval_random2d_bb7_in,4) ;(eval_random2d_bb8_in,4) ;(eval_random2d_start,4) ;(eval_random2d_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10},10->{11},11->{12},12->{13,14} ,13->{15},14->{44},15->{16},16->{17,18,19},17->{20},18->{13,14},19->{13,14},20->{21,22},21->{23,24},22->{33 ,34},23->{25,26},24->{29,31},25->{28},26->{43},28->{13,14},29->{32},31->{43},32->{13,14},33->{35,36},34->{39 ,41},35->{38},36->{43},38->{13,14},39->{42},41->{43},42->{13,14},43->{13,14},44->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: The problem is already solved. YES(?,O(n^1))