YES(?,O(n^1)) * Step 1: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_wise_start(v__0,v__01,v_x,v_y) -> eval_wise_bb0_in(v__0,v__01,v_x,v_y) True (1,1) 1. eval_wise_bb0_in(v__0,v__01,v_x,v_y) -> eval_wise_0(v__0,v__01,v_x,v_y) True (?,1) 2. eval_wise_0(v__0,v__01,v_x,v_y) -> eval_wise_1(v__0,v__01,v_x,v_y) True (?,1) 3. eval_wise_1(v__0,v__01,v_x,v_y) -> eval_wise_2(v__0,v__01,v_x,v_y) True (?,1) 4. eval_wise_2(v__0,v__01,v_x,v_y) -> eval_wise_bb2_in(v__0,v__01,v_x,v_y) [-1 >= v_x] (?,1) 5. eval_wise_2(v__0,v__01,v_x,v_y) -> eval_wise_bb2_in(v__0,v__01,v_x,v_y) [-1 >= v_y] (?,1) 6. eval_wise_2(v__0,v__01,v_x,v_y) -> eval_wise_bb1_in(v_x,v_y,v_x,v_y) [v_x >= 0 && v_y >= 0] (?,1) 7. eval_wise_bb1_in(v__0,v__01,v_x,v_y) -> eval_wise__critedge_in(v__0,v__01,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && v_y >= 0 && v_x + v_y >= 0 && v__01 + v_y >= 0 && v__0 + v_y >= 0 && v__0 + -1*v_x >= 0 && v_x >= 0 && v__01 + v_x >= 0 && v__0 + v_x >= 0 && v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0 && -1 + v__0 + -1*v__01 >= 2] 8. eval_wise_bb1_in(v__0,v__01,v_x,v_y) -> eval_wise__critedge_in(v__0,v__01,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && v_y >= 0 && v_x + v_y >= 0 && v__01 + v_y >= 0 && v__0 + v_y >= 0 && v__0 + -1*v_x >= 0 && v_x >= 0 && v__01 + v_x >= 0 && v__0 + v_x >= 0 && v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0 && -1 + -1*v__0 + v__01 >= 2] 9. eval_wise_bb1_in(v__0,v__01,v_x,v_y) -> eval_wise_bb2_in(v__0,v__01,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && v_y >= 0 && v_x + v_y >= 0 && v__01 + v_y >= 0 && v__0 + v_y >= 0 && v__0 + -1*v_x >= 0 && v_x >= 0 && v__01 + v_x >= 0 && v__0 + v_x >= 0 && v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0 && 2 >= v__0 + -1*v__01 && 2 >= -1*v__0 + v__01] 10. eval_wise__critedge_in(v__0,v__01,v_x,v_y) -> eval_wise_bb1_in(1 + v__0,v__01,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && v_y >= 0 && v_x + v_y >= 0 && v__01 + v_y >= 0 && v__0 + v_y >= 0 && v__0 + -1*v_x >= 0 && v_x >= 0 && v__01 + v_x >= 0 && v__0 + v_x >= 0 && v__01 >= 0 && -3 + v__0 + v__01 >= 0 && v__0 >= 0 && -1 + v__01 >= v__0] 11. eval_wise__critedge_in(v__0,v__01,v_x,v_y) -> eval_wise_bb1_in(v__0,1 + v__01,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && v_y >= 0 && v_x + v_y >= 0 && v__01 + v_y >= 0 && v__0 + v_y >= 0 && v__0 + -1*v_x >= 0 && v_x >= 0 && v__01 + v_x >= 0 && v__0 + v_x >= 0 && v__01 >= 0 && -3 + v__0 + v__01 >= 0 && v__0 >= 0 && v__0 >= v__01] 12. eval_wise_bb2_in(v__0,v__01,v_x,v_y) -> eval_wise_stop(v__0,v__01,v_x,v_y) True (?,1) Signature: {(eval_wise_0,4) ;(eval_wise_1,4) ;(eval_wise_2,4) ;(eval_wise__critedge_in,4) ;(eval_wise_bb0_in,4) ;(eval_wise_bb1_in,4) ;(eval_wise_bb2_in,4) ;(eval_wise_start,4) ;(eval_wise_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5,6},4->{12},5->{12},6->{7,8,9},7->{10,11},8->{10,11},9->{12},10->{7,8,9} ,11->{7,8,9},12->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_wise_start(v__0,v__01,v_x,v_y) -> eval_wise_bb0_in(v__0,v__01,v_x,v_y) True (1,1) 1. eval_wise_bb0_in(v__0,v__01,v_x,v_y) -> eval_wise_0(v__0,v__01,v_x,v_y) True (1,1) 2. eval_wise_0(v__0,v__01,v_x,v_y) -> eval_wise_1(v__0,v__01,v_x,v_y) True (1,1) 3. eval_wise_1(v__0,v__01,v_x,v_y) -> eval_wise_2(v__0,v__01,v_x,v_y) True (1,1) 4. eval_wise_2(v__0,v__01,v_x,v_y) -> eval_wise_bb2_in(v__0,v__01,v_x,v_y) [-1 >= v_x] (1,1) 5. eval_wise_2(v__0,v__01,v_x,v_y) -> eval_wise_bb2_in(v__0,v__01,v_x,v_y) [-1 >= v_y] (1,1) 6. eval_wise_2(v__0,v__01,v_x,v_y) -> eval_wise_bb1_in(v_x,v_y,v_x,v_y) [v_x >= 0 && v_y >= 0] (1,1) 7. eval_wise_bb1_in(v__0,v__01,v_x,v_y) -> eval_wise__critedge_in(v__0,v__01,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && v_y >= 0 && v_x + v_y >= 0 && v__01 + v_y >= 0 && v__0 + v_y >= 0 && v__0 + -1*v_x >= 0 && v_x >= 0 && v__01 + v_x >= 0 && v__0 + v_x >= 0 && v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0 && -1 + v__0 + -1*v__01 >= 2] 8. eval_wise_bb1_in(v__0,v__01,v_x,v_y) -> eval_wise__critedge_in(v__0,v__01,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && v_y >= 0 && v_x + v_y >= 0 && v__01 + v_y >= 0 && v__0 + v_y >= 0 && v__0 + -1*v_x >= 0 && v_x >= 0 && v__01 + v_x >= 0 && v__0 + v_x >= 0 && v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0 && -1 + -1*v__0 + v__01 >= 2] 9. eval_wise_bb1_in(v__0,v__01,v_x,v_y) -> eval_wise_bb2_in(v__0,v__01,v_x,v_y) [v__01 + -1*v_y >= 0 (1,1) && v_y >= 0 && v_x + v_y >= 0 && v__01 + v_y >= 0 && v__0 + v_y >= 0 && v__0 + -1*v_x >= 0 && v_x >= 0 && v__01 + v_x >= 0 && v__0 + v_x >= 0 && v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0 && 2 >= v__0 + -1*v__01 && 2 >= -1*v__0 + v__01] 10. eval_wise__critedge_in(v__0,v__01,v_x,v_y) -> eval_wise_bb1_in(1 + v__0,v__01,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && v_y >= 0 && v_x + v_y >= 0 && v__01 + v_y >= 0 && v__0 + v_y >= 0 && v__0 + -1*v_x >= 0 && v_x >= 0 && v__01 + v_x >= 0 && v__0 + v_x >= 0 && v__01 >= 0 && -3 + v__0 + v__01 >= 0 && v__0 >= 0 && -1 + v__01 >= v__0] 11. eval_wise__critedge_in(v__0,v__01,v_x,v_y) -> eval_wise_bb1_in(v__0,1 + v__01,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && v_y >= 0 && v_x + v_y >= 0 && v__01 + v_y >= 0 && v__0 + v_y >= 0 && v__0 + -1*v_x >= 0 && v_x >= 0 && v__01 + v_x >= 0 && v__0 + v_x >= 0 && v__01 >= 0 && -3 + v__0 + v__01 >= 0 && v__0 >= 0 && v__0 >= v__01] 12. eval_wise_bb2_in(v__0,v__01,v_x,v_y) -> eval_wise_stop(v__0,v__01,v_x,v_y) True (1,1) Signature: {(eval_wise_0,4) ;(eval_wise_1,4) ;(eval_wise_2,4) ;(eval_wise__critedge_in,4) ;(eval_wise_bb0_in,4) ;(eval_wise_bb1_in,4) ;(eval_wise_bb2_in,4) ;(eval_wise_start,4) ;(eval_wise_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5,6},4->{12},5->{12},6->{7,8,9},7->{10,11},8->{10,11},9->{12},10->{7,8,9} ,11->{7,8,9},12->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(7,10),(8,11),(10,7),(11,8)] * Step 3: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_wise_start(v__0,v__01,v_x,v_y) -> eval_wise_bb0_in(v__0,v__01,v_x,v_y) True (1,1) 1. eval_wise_bb0_in(v__0,v__01,v_x,v_y) -> eval_wise_0(v__0,v__01,v_x,v_y) True (1,1) 2. eval_wise_0(v__0,v__01,v_x,v_y) -> eval_wise_1(v__0,v__01,v_x,v_y) True (1,1) 3. eval_wise_1(v__0,v__01,v_x,v_y) -> eval_wise_2(v__0,v__01,v_x,v_y) True (1,1) 4. eval_wise_2(v__0,v__01,v_x,v_y) -> eval_wise_bb2_in(v__0,v__01,v_x,v_y) [-1 >= v_x] (1,1) 5. eval_wise_2(v__0,v__01,v_x,v_y) -> eval_wise_bb2_in(v__0,v__01,v_x,v_y) [-1 >= v_y] (1,1) 6. eval_wise_2(v__0,v__01,v_x,v_y) -> eval_wise_bb1_in(v_x,v_y,v_x,v_y) [v_x >= 0 && v_y >= 0] (1,1) 7. eval_wise_bb1_in(v__0,v__01,v_x,v_y) -> eval_wise__critedge_in(v__0,v__01,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && v_y >= 0 && v_x + v_y >= 0 && v__01 + v_y >= 0 && v__0 + v_y >= 0 && v__0 + -1*v_x >= 0 && v_x >= 0 && v__01 + v_x >= 0 && v__0 + v_x >= 0 && v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0 && -1 + v__0 + -1*v__01 >= 2] 8. eval_wise_bb1_in(v__0,v__01,v_x,v_y) -> eval_wise__critedge_in(v__0,v__01,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && v_y >= 0 && v_x + v_y >= 0 && v__01 + v_y >= 0 && v__0 + v_y >= 0 && v__0 + -1*v_x >= 0 && v_x >= 0 && v__01 + v_x >= 0 && v__0 + v_x >= 0 && v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0 && -1 + -1*v__0 + v__01 >= 2] 9. eval_wise_bb1_in(v__0,v__01,v_x,v_y) -> eval_wise_bb2_in(v__0,v__01,v_x,v_y) [v__01 + -1*v_y >= 0 (1,1) && v_y >= 0 && v_x + v_y >= 0 && v__01 + v_y >= 0 && v__0 + v_y >= 0 && v__0 + -1*v_x >= 0 && v_x >= 0 && v__01 + v_x >= 0 && v__0 + v_x >= 0 && v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0 && 2 >= v__0 + -1*v__01 && 2 >= -1*v__0 + v__01] 10. eval_wise__critedge_in(v__0,v__01,v_x,v_y) -> eval_wise_bb1_in(1 + v__0,v__01,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && v_y >= 0 && v_x + v_y >= 0 && v__01 + v_y >= 0 && v__0 + v_y >= 0 && v__0 + -1*v_x >= 0 && v_x >= 0 && v__01 + v_x >= 0 && v__0 + v_x >= 0 && v__01 >= 0 && -3 + v__0 + v__01 >= 0 && v__0 >= 0 && -1 + v__01 >= v__0] 11. eval_wise__critedge_in(v__0,v__01,v_x,v_y) -> eval_wise_bb1_in(v__0,1 + v__01,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && v_y >= 0 && v_x + v_y >= 0 && v__01 + v_y >= 0 && v__0 + v_y >= 0 && v__0 + -1*v_x >= 0 && v_x >= 0 && v__01 + v_x >= 0 && v__0 + v_x >= 0 && v__01 >= 0 && -3 + v__0 + v__01 >= 0 && v__0 >= 0 && v__0 >= v__01] 12. eval_wise_bb2_in(v__0,v__01,v_x,v_y) -> eval_wise_stop(v__0,v__01,v_x,v_y) True (1,1) Signature: {(eval_wise_0,4) ;(eval_wise_1,4) ;(eval_wise_2,4) ;(eval_wise__critedge_in,4) ;(eval_wise_bb0_in,4) ;(eval_wise_bb1_in,4) ;(eval_wise_bb2_in,4) ;(eval_wise_start,4) ;(eval_wise_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5,6},4->{12},5->{12},6->{7,8,9},7->{11},8->{10},9->{12},10->{8,9},11->{7,9} ,12->{}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_wise_start(v__0,v__01,v_x,v_y) -> eval_wise_bb0_in(v__0,v__01,v_x,v_y) True (1,1) 1. eval_wise_bb0_in(v__0,v__01,v_x,v_y) -> eval_wise_0(v__0,v__01,v_x,v_y) True (?,1) 2. eval_wise_0(v__0,v__01,v_x,v_y) -> eval_wise_1(v__0,v__01,v_x,v_y) True (?,1) 3. eval_wise_1(v__0,v__01,v_x,v_y) -> eval_wise_2(v__0,v__01,v_x,v_y) True (?,1) 4. eval_wise_2(v__0,v__01,v_x,v_y) -> eval_wise_bb2_in(v__0,v__01,v_x,v_y) [-1 >= v_x] (?,1) 5. eval_wise_2(v__0,v__01,v_x,v_y) -> eval_wise_bb2_in(v__0,v__01,v_x,v_y) [-1 >= v_y] (?,1) 6. eval_wise_2(v__0,v__01,v_x,v_y) -> eval_wise_bb1_in(v_x,v_y,v_x,v_y) [v_x >= 0 && v_y >= 0] (?,1) 7. eval_wise_bb1_in(v__0,v__01,v_x,v_y) -> eval_wise__critedge_in(v__0,v__01,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && v_y >= 0 && v_x + v_y >= 0 && v__01 + v_y >= 0 && v__0 + v_y >= 0 && v__0 + -1*v_x >= 0 && v_x >= 0 && v__01 + v_x >= 0 && v__0 + v_x >= 0 && v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0 && -1 + v__0 + -1*v__01 >= 2] 8. eval_wise_bb1_in(v__0,v__01,v_x,v_y) -> eval_wise__critedge_in(v__0,v__01,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && v_y >= 0 && v_x + v_y >= 0 && v__01 + v_y >= 0 && v__0 + v_y >= 0 && v__0 + -1*v_x >= 0 && v_x >= 0 && v__01 + v_x >= 0 && v__0 + v_x >= 0 && v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0 && -1 + -1*v__0 + v__01 >= 2] 9. eval_wise_bb1_in(v__0,v__01,v_x,v_y) -> eval_wise_bb2_in(v__0,v__01,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && v_y >= 0 && v_x + v_y >= 0 && v__01 + v_y >= 0 && v__0 + v_y >= 0 && v__0 + -1*v_x >= 0 && v_x >= 0 && v__01 + v_x >= 0 && v__0 + v_x >= 0 && v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0 && 2 >= v__0 + -1*v__01 && 2 >= -1*v__0 + v__01] 10. eval_wise__critedge_in(v__0,v__01,v_x,v_y) -> eval_wise_bb1_in(1 + v__0,v__01,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && v_y >= 0 && v_x + v_y >= 0 && v__01 + v_y >= 0 && v__0 + v_y >= 0 && v__0 + -1*v_x >= 0 && v_x >= 0 && v__01 + v_x >= 0 && v__0 + v_x >= 0 && v__01 >= 0 && -3 + v__0 + v__01 >= 0 && v__0 >= 0 && -1 + v__01 >= v__0] 11. eval_wise__critedge_in(v__0,v__01,v_x,v_y) -> eval_wise_bb1_in(v__0,1 + v__01,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && v_y >= 0 && v_x + v_y >= 0 && v__01 + v_y >= 0 && v__0 + v_y >= 0 && v__0 + -1*v_x >= 0 && v_x >= 0 && v__01 + v_x >= 0 && v__0 + v_x >= 0 && v__01 >= 0 && -3 + v__0 + v__01 >= 0 && v__0 >= 0 && v__0 >= v__01] 12. eval_wise_bb2_in(v__0,v__01,v_x,v_y) -> eval_wise_stop(v__0,v__01,v_x,v_y) True (?,1) 13. eval_wise_bb2_in(v__0,v__01,v_x,v_y) -> exitus616(v__0,v__01,v_x,v_y) True (?,1) Signature: {(eval_wise_0,4) ;(eval_wise_1,4) ;(eval_wise_2,4) ;(eval_wise__critedge_in,4) ;(eval_wise_bb0_in,4) ;(eval_wise_bb1_in,4) ;(eval_wise_bb2_in,4) ;(eval_wise_start,4) ;(eval_wise_stop,4) ;(exitus616,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5,6},4->{12,13},5->{12,13},6->{7,8,9},7->{10,11},8->{10,11},9->{12,13},10->{7 ,8,9},11->{7,8,9},12->{},13->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(7,10),(8,11),(10,7),(11,8)] * Step 5: LooptreeTransformer WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_wise_start(v__0,v__01,v_x,v_y) -> eval_wise_bb0_in(v__0,v__01,v_x,v_y) True (1,1) 1. eval_wise_bb0_in(v__0,v__01,v_x,v_y) -> eval_wise_0(v__0,v__01,v_x,v_y) True (?,1) 2. eval_wise_0(v__0,v__01,v_x,v_y) -> eval_wise_1(v__0,v__01,v_x,v_y) True (?,1) 3. eval_wise_1(v__0,v__01,v_x,v_y) -> eval_wise_2(v__0,v__01,v_x,v_y) True (?,1) 4. eval_wise_2(v__0,v__01,v_x,v_y) -> eval_wise_bb2_in(v__0,v__01,v_x,v_y) [-1 >= v_x] (?,1) 5. eval_wise_2(v__0,v__01,v_x,v_y) -> eval_wise_bb2_in(v__0,v__01,v_x,v_y) [-1 >= v_y] (?,1) 6. eval_wise_2(v__0,v__01,v_x,v_y) -> eval_wise_bb1_in(v_x,v_y,v_x,v_y) [v_x >= 0 && v_y >= 0] (?,1) 7. eval_wise_bb1_in(v__0,v__01,v_x,v_y) -> eval_wise__critedge_in(v__0,v__01,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && v_y >= 0 && v_x + v_y >= 0 && v__01 + v_y >= 0 && v__0 + v_y >= 0 && v__0 + -1*v_x >= 0 && v_x >= 0 && v__01 + v_x >= 0 && v__0 + v_x >= 0 && v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0 && -1 + v__0 + -1*v__01 >= 2] 8. eval_wise_bb1_in(v__0,v__01,v_x,v_y) -> eval_wise__critedge_in(v__0,v__01,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && v_y >= 0 && v_x + v_y >= 0 && v__01 + v_y >= 0 && v__0 + v_y >= 0 && v__0 + -1*v_x >= 0 && v_x >= 0 && v__01 + v_x >= 0 && v__0 + v_x >= 0 && v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0 && -1 + -1*v__0 + v__01 >= 2] 9. eval_wise_bb1_in(v__0,v__01,v_x,v_y) -> eval_wise_bb2_in(v__0,v__01,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && v_y >= 0 && v_x + v_y >= 0 && v__01 + v_y >= 0 && v__0 + v_y >= 0 && v__0 + -1*v_x >= 0 && v_x >= 0 && v__01 + v_x >= 0 && v__0 + v_x >= 0 && v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0 && 2 >= v__0 + -1*v__01 && 2 >= -1*v__0 + v__01] 10. eval_wise__critedge_in(v__0,v__01,v_x,v_y) -> eval_wise_bb1_in(1 + v__0,v__01,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && v_y >= 0 && v_x + v_y >= 0 && v__01 + v_y >= 0 && v__0 + v_y >= 0 && v__0 + -1*v_x >= 0 && v_x >= 0 && v__01 + v_x >= 0 && v__0 + v_x >= 0 && v__01 >= 0 && -3 + v__0 + v__01 >= 0 && v__0 >= 0 && -1 + v__01 >= v__0] 11. eval_wise__critedge_in(v__0,v__01,v_x,v_y) -> eval_wise_bb1_in(v__0,1 + v__01,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && v_y >= 0 && v_x + v_y >= 0 && v__01 + v_y >= 0 && v__0 + v_y >= 0 && v__0 + -1*v_x >= 0 && v_x >= 0 && v__01 + v_x >= 0 && v__0 + v_x >= 0 && v__01 >= 0 && -3 + v__0 + v__01 >= 0 && v__0 >= 0 && v__0 >= v__01] 12. eval_wise_bb2_in(v__0,v__01,v_x,v_y) -> eval_wise_stop(v__0,v__01,v_x,v_y) True (?,1) 13. eval_wise_bb2_in(v__0,v__01,v_x,v_y) -> exitus616(v__0,v__01,v_x,v_y) True (?,1) Signature: {(eval_wise_0,4) ;(eval_wise_1,4) ;(eval_wise_2,4) ;(eval_wise__critedge_in,4) ;(eval_wise_bb0_in,4) ;(eval_wise_bb1_in,4) ;(eval_wise_bb2_in,4) ;(eval_wise_start,4) ;(eval_wise_stop,4) ;(exitus616,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5,6},4->{12,13},5->{12,13},6->{7,8,9},7->{11},8->{10},9->{12,13},10->{8,9} ,11->{7,9},12->{},13->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13] | +- p:[8,10] c: [10] | `- p:[7,11] c: [11] * Step 6: SizeAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: 0. eval_wise_start(v__0,v__01,v_x,v_y) -> eval_wise_bb0_in(v__0,v__01,v_x,v_y) True (1,1) 1. eval_wise_bb0_in(v__0,v__01,v_x,v_y) -> eval_wise_0(v__0,v__01,v_x,v_y) True (?,1) 2. eval_wise_0(v__0,v__01,v_x,v_y) -> eval_wise_1(v__0,v__01,v_x,v_y) True (?,1) 3. eval_wise_1(v__0,v__01,v_x,v_y) -> eval_wise_2(v__0,v__01,v_x,v_y) True (?,1) 4. eval_wise_2(v__0,v__01,v_x,v_y) -> eval_wise_bb2_in(v__0,v__01,v_x,v_y) [-1 >= v_x] (?,1) 5. eval_wise_2(v__0,v__01,v_x,v_y) -> eval_wise_bb2_in(v__0,v__01,v_x,v_y) [-1 >= v_y] (?,1) 6. eval_wise_2(v__0,v__01,v_x,v_y) -> eval_wise_bb1_in(v_x,v_y,v_x,v_y) [v_x >= 0 && v_y >= 0] (?,1) 7. eval_wise_bb1_in(v__0,v__01,v_x,v_y) -> eval_wise__critedge_in(v__0,v__01,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && v_y >= 0 && v_x + v_y >= 0 && v__01 + v_y >= 0 && v__0 + v_y >= 0 && v__0 + -1*v_x >= 0 && v_x >= 0 && v__01 + v_x >= 0 && v__0 + v_x >= 0 && v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0 && -1 + v__0 + -1*v__01 >= 2] 8. eval_wise_bb1_in(v__0,v__01,v_x,v_y) -> eval_wise__critedge_in(v__0,v__01,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && v_y >= 0 && v_x + v_y >= 0 && v__01 + v_y >= 0 && v__0 + v_y >= 0 && v__0 + -1*v_x >= 0 && v_x >= 0 && v__01 + v_x >= 0 && v__0 + v_x >= 0 && v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0 && -1 + -1*v__0 + v__01 >= 2] 9. eval_wise_bb1_in(v__0,v__01,v_x,v_y) -> eval_wise_bb2_in(v__0,v__01,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && v_y >= 0 && v_x + v_y >= 0 && v__01 + v_y >= 0 && v__0 + v_y >= 0 && v__0 + -1*v_x >= 0 && v_x >= 0 && v__01 + v_x >= 0 && v__0 + v_x >= 0 && v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0 && 2 >= v__0 + -1*v__01 && 2 >= -1*v__0 + v__01] 10. eval_wise__critedge_in(v__0,v__01,v_x,v_y) -> eval_wise_bb1_in(1 + v__0,v__01,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && v_y >= 0 && v_x + v_y >= 0 && v__01 + v_y >= 0 && v__0 + v_y >= 0 && v__0 + -1*v_x >= 0 && v_x >= 0 && v__01 + v_x >= 0 && v__0 + v_x >= 0 && v__01 >= 0 && -3 + v__0 + v__01 >= 0 && v__0 >= 0 && -1 + v__01 >= v__0] 11. eval_wise__critedge_in(v__0,v__01,v_x,v_y) -> eval_wise_bb1_in(v__0,1 + v__01,v_x,v_y) [v__01 + -1*v_y >= 0 (?,1) && v_y >= 0 && v_x + v_y >= 0 && v__01 + v_y >= 0 && v__0 + v_y >= 0 && v__0 + -1*v_x >= 0 && v_x >= 0 && v__01 + v_x >= 0 && v__0 + v_x >= 0 && v__01 >= 0 && -3 + v__0 + v__01 >= 0 && v__0 >= 0 && v__0 >= v__01] 12. eval_wise_bb2_in(v__0,v__01,v_x,v_y) -> eval_wise_stop(v__0,v__01,v_x,v_y) True (?,1) 13. eval_wise_bb2_in(v__0,v__01,v_x,v_y) -> exitus616(v__0,v__01,v_x,v_y) True (?,1) Signature: {(eval_wise_0,4) ;(eval_wise_1,4) ;(eval_wise_2,4) ;(eval_wise__critedge_in,4) ;(eval_wise_bb0_in,4) ;(eval_wise_bb1_in,4) ;(eval_wise_bb2_in,4) ;(eval_wise_start,4) ;(eval_wise_stop,4) ;(exitus616,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5,6},4->{12,13},5->{12,13},6->{7,8,9},7->{11},8->{10},9->{12,13},10->{8,9} ,11->{7,9},12->{},13->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13] | +- p:[8,10] c: [10] | `- p:[7,11] c: [11]) + Applied Processor: SizeAbstraction UseTG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [v__0,v__01,v_x,v_y,0.0,0.1] eval_wise_start.0 ~> eval_wise_bb0_in.1 [v__0 <= v__0, v__01 <= v__01, v_x <= v_x, v_y <= v_y] eval_wise_bb0_in.1 ~> eval_wise_0.2 [v__0 <= v__0, v__01 <= v__01, v_x <= v_x, v_y <= v_y] eval_wise_0.2 ~> eval_wise_1.3 [v__0 <= v__0, v__01 <= v__01, v_x <= v_x, v_y <= v_y] eval_wise_1.3 ~> eval_wise_2.4 [v__0 <= v__0, v__01 <= v__01, v_x <= v_x, v_y <= v_y] eval_wise_1.3 ~> eval_wise_2.5 [v__0 <= v__0, v__01 <= v__01, v_x <= v_x, v_y <= v_y] eval_wise_1.3 ~> eval_wise_2.6 [v__0 <= v__0, v__01 <= v__01, v_x <= v_x, v_y <= v_y] eval_wise_2.4 ~> eval_wise_bb2_in.12 [v__0 <= v__0, v__01 <= v__01, v_x <= v_x, v_y <= v_y] eval_wise_2.4 ~> eval_wise_bb2_in.13 [v__0 <= v__0, v__01 <= v__01, v_x <= v_x, v_y <= v_y] eval_wise_2.5 ~> eval_wise_bb2_in.12 [v__0 <= v__0, v__01 <= v__01, v_x <= v_x, v_y <= v_y] eval_wise_2.5 ~> eval_wise_bb2_in.13 [v__0 <= v__0, v__01 <= v__01, v_x <= v_x, v_y <= v_y] eval_wise_2.6 ~> eval_wise_bb1_in.7 [v__0 <= v_x, v__01 <= v_y, v_x <= v_x, v_y <= v_y] eval_wise_2.6 ~> eval_wise_bb1_in.8 [v__0 <= v_x, v__01 <= v_y, v_x <= v_x, v_y <= v_y] eval_wise_2.6 ~> eval_wise_bb1_in.9 [v__0 <= v_x, v__01 <= v_y, v_x <= v_x, v_y <= v_y] eval_wise_bb1_in.7 ~> eval_wise__critedge_in.11 [v__0 <= v__0, v__01 <= v__01, v_x <= v_x, v_y <= v_y] eval_wise_bb1_in.8 ~> eval_wise__critedge_in.10 [v__0 <= v__0, v__01 <= v__01, v_x <= v_x, v_y <= v_y] eval_wise_bb1_in.9 ~> eval_wise_bb2_in.12 [v__0 <= v__0, v__01 <= v__01, v_x <= v_x, v_y <= v_y] eval_wise_bb1_in.9 ~> eval_wise_bb2_in.13 [v__0 <= v__0, v__01 <= v__01, v_x <= v_x, v_y <= v_y] eval_wise__critedge_in.10 ~> eval_wise_bb1_in.8 [v__0 <= v__01, v__01 <= v__01, v_x <= v_x, v_y <= v_y] eval_wise__critedge_in.10 ~> eval_wise_bb1_in.9 [v__0 <= v__01, v__01 <= v__01, v_x <= v_x, v_y <= v_y] eval_wise__critedge_in.11 ~> eval_wise_bb1_in.7 [v__0 <= v__0, v__01 <= K + v__0, v_x <= v_x, v_y <= v_y] eval_wise__critedge_in.11 ~> eval_wise_bb1_in.9 [v__0 <= v__0, v__01 <= K + v__0, v_x <= v_x, v_y <= v_y] eval_wise_bb2_in.12 ~> eval_wise_stop.12 [v__0 <= v__0, v__01 <= v__01, v_x <= v_x, v_y <= v_y] eval_wise_bb2_in.13 ~> exitus616.13 [v__0 <= v__0, v__01 <= v__01, v_x <= v_x, v_y <= v_y] + Loop: [0.0 <= v__0 + v__01] eval_wise_bb1_in.8 ~> eval_wise__critedge_in.10 [v__0 <= v__0, v__01 <= v__01, v_x <= v_x, v_y <= v_y] eval_wise__critedge_in.10 ~> eval_wise_bb1_in.8 [v__0 <= v__01, v__01 <= v__01, v_x <= v_x, v_y <= v_y] eval_wise__critedge_in.10 ~> eval_wise_bb1_in.9 [v__0 <= v__01, v__01 <= v__01, v_x <= v_x, v_y <= v_y] + Loop: [0.1 <= K + v__0 + v__01] eval_wise_bb1_in.7 ~> eval_wise__critedge_in.11 [v__0 <= v__0, v__01 <= v__01, v_x <= v_x, v_y <= v_y] eval_wise__critedge_in.11 ~> eval_wise_bb1_in.7 [v__0 <= v__0, v__01 <= K + v__0, v_x <= v_x, v_y <= v_y] eval_wise__critedge_in.11 ~> eval_wise_bb1_in.9 [v__0 <= v__0, v__01 <= K + v__0, v_x <= v_x, v_y <= v_y] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,v__0,v__01,v_x,v_y,0.0,0.1] eval_wise_start.0 ~> eval_wise_bb0_in.1 [] eval_wise_bb0_in.1 ~> eval_wise_0.2 [] eval_wise_0.2 ~> eval_wise_1.3 [] eval_wise_1.3 ~> eval_wise_2.4 [] eval_wise_1.3 ~> eval_wise_2.5 [] eval_wise_1.3 ~> eval_wise_2.6 [] eval_wise_2.4 ~> eval_wise_bb2_in.12 [] eval_wise_2.4 ~> eval_wise_bb2_in.13 [] eval_wise_2.5 ~> eval_wise_bb2_in.12 [] eval_wise_2.5 ~> eval_wise_bb2_in.13 [] eval_wise_2.6 ~> eval_wise_bb1_in.7 [v_x ~=> v__0,v_y ~=> v__01] eval_wise_2.6 ~> eval_wise_bb1_in.8 [v_x ~=> v__0,v_y ~=> v__01] eval_wise_2.6 ~> eval_wise_bb1_in.9 [v_x ~=> v__0,v_y ~=> v__01] eval_wise_bb1_in.7 ~> eval_wise__critedge_in.11 [] eval_wise_bb1_in.8 ~> eval_wise__critedge_in.10 [] eval_wise_bb1_in.9 ~> eval_wise_bb2_in.12 [] eval_wise_bb1_in.9 ~> eval_wise_bb2_in.13 [] eval_wise__critedge_in.10 ~> eval_wise_bb1_in.8 [v__01 ~=> v__0] eval_wise__critedge_in.10 ~> eval_wise_bb1_in.9 [v__01 ~=> v__0] eval_wise__critedge_in.11 ~> eval_wise_bb1_in.7 [v__0 ~+> v__01,K ~+> v__01] eval_wise__critedge_in.11 ~> eval_wise_bb1_in.9 [v__0 ~+> v__01,K ~+> v__01] eval_wise_bb2_in.12 ~> eval_wise_stop.12 [] eval_wise_bb2_in.13 ~> exitus616.13 [] + Loop: [v__0 ~+> 0.0,v__01 ~+> 0.0] eval_wise_bb1_in.8 ~> eval_wise__critedge_in.10 [] eval_wise__critedge_in.10 ~> eval_wise_bb1_in.8 [v__01 ~=> v__0] eval_wise__critedge_in.10 ~> eval_wise_bb1_in.9 [v__01 ~=> v__0] + Loop: [v__0 ~+> 0.1,v__01 ~+> 0.1,K ~+> 0.1] eval_wise_bb1_in.7 ~> eval_wise__critedge_in.11 [] eval_wise__critedge_in.11 ~> eval_wise_bb1_in.7 [v__0 ~+> v__01,K ~+> v__01] eval_wise__critedge_in.11 ~> eval_wise_bb1_in.9 [v__0 ~+> v__01,K ~+> v__01] + Applied Processor: LareProcessor + Details: eval_wise_start.0 ~> exitus616.13 [v_x ~=> v__0 ,v_y ~=> v__0 ,v_y ~=> v__01 ,v_x ~+> v__01 ,v_x ~+> 0.0 ,v_x ~+> 0.1 ,v_x ~+> tick ,v_y ~+> 0.0 ,v_y ~+> 0.1 ,v_y ~+> tick ,tick ~+> tick ,K ~+> v__01 ,K ~+> 0.1 ,K ~+> tick] eval_wise_start.0 ~> eval_wise_stop.12 [v_x ~=> v__0 ,v_y ~=> v__0 ,v_y ~=> v__01 ,v_x ~+> v__01 ,v_x ~+> 0.0 ,v_x ~+> 0.1 ,v_x ~+> tick ,v_y ~+> 0.0 ,v_y ~+> 0.1 ,v_y ~+> tick ,tick ~+> tick ,K ~+> v__01 ,K ~+> 0.1 ,K ~+> tick] + eval_wise_bb1_in.9> [v__01 ~=> v__0 ,v__0 ~+> 0.0 ,v__0 ~+> tick ,v__01 ~+> 0.0 ,v__01 ~+> tick ,tick ~+> tick] + eval_wise_bb1_in.9> [v__0 ~+> v__01 ,v__0 ~+> 0.1 ,v__0 ~+> tick ,v__01 ~+> 0.1 ,v__01 ~+> tick ,tick ~+> tick ,K ~+> v__01 ,K ~+> 0.1 ,K ~+> tick] YES(?,O(n^1))