YES(?,POLY) * Step 1: TrivialSCCs WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval_abc_start(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_bb0_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (1,1) 1. eval_abc_bb0_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_0(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (?,1) 2. eval_abc_0(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_1(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (?,1) 3. eval_abc_1(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_2(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (?,1) 4. eval_abc_2(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_3(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (?,1) 5. eval_abc_3(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_4(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (?,1) 6. eval_abc_4(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_5(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (?,1) 7. eval_abc_5(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_6(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (?,1) 8. eval_abc_6(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_7(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (?,1) 9. eval_abc_7(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_bb1_in(v_3,v_a,v_b,v_c,v_d,v_a,v_j_0) True (?,1) 10. eval_abc_bb1_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_bb2_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_c) [-1*v_a + v_i_0 >= 0 && v_b >= v_i_0] (?,1) 11. eval_abc_bb1_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_bb5_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) [-1*v_a + v_i_0 >= 0 && -1 + v_i_0 >= v_b] (?,1) 12. eval_abc_bb2_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_bb3_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) [-1*v_c + v_j_0 >= 0 && v_b + -1*v_i_0 >= 0 && -1*v_a + v_i_0 >= 0 && -1*v_a + v_b >= 0 && v_d >= v_j_0] (?,1) 13. eval_abc_bb2_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_bb4_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) [-1*v_c + v_j_0 >= 0 (?,1) && v_b + -1*v_i_0 >= 0 && -1*v_a + v_i_0 >= 0 && -1*v_a + v_b >= 0 && -1 + v_j_0 >= v_d] 14. eval_abc_bb3_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_bb2_in(v_3,v_a,v_b,v_c,v_d,v_i_0,1 + v_j_0) [v_d + -1*v_j_0 >= 0 (?,1) && -1*v_c + v_j_0 >= 0 && v_b + -1*v_i_0 >= 0 && -1*v_a + v_i_0 >= 0 && -1*v_c + v_d >= 0 && -1*v_a + v_b >= 0] 15. eval_abc_bb4_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_11(1 + v_i_0,v_a,v_b,v_c,v_d,v_i_0,v_j_0) [-1 + -1*v_d + v_j_0 >= 0 (?,1) && -1*v_c + v_j_0 >= 0 && v_b + -1*v_i_0 >= 0 && -1*v_a + v_i_0 >= 0 && -1*v_a + v_b >= 0] 16. eval_abc_11(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_12(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) [-1 + -1*v_d + v_j_0 >= 0 (?,1) && -1*v_c + v_j_0 >= 0 && v_b + -1*v_i_0 >= 0 && -1 + v_3 + -1*v_i_0 >= 0 && -1*v_a + v_i_0 >= 0 && 1 + -1*v_3 + v_i_0 >= 0 && -1*v_a + v_b >= 0 && 1 + -1*v_3 + v_b >= 0 && -1 + v_3 + -1*v_a >= 0] 17. eval_abc_12(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_bb1_in(v_3,v_a,v_b,v_c,v_d,v_3,v_j_0) [-1 + -1*v_d + v_j_0 >= 0 (?,1) && -1*v_c + v_j_0 >= 0 && v_b + -1*v_i_0 >= 0 && -1 + v_3 + -1*v_i_0 >= 0 && -1*v_a + v_i_0 >= 0 && 1 + -1*v_3 + v_i_0 >= 0 && -1*v_a + v_b >= 0 && 1 + -1*v_3 + v_b >= 0 && -1 + v_3 + -1*v_a >= 0] 18. eval_abc_bb5_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_stop(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) [-1 + -1*v_b + v_i_0 >= 0 && -1*v_a + v_i_0 >= 0] (?,1) Signature: {(eval_abc_0,7) ;(eval_abc_1,7) ;(eval_abc_11,7) ;(eval_abc_12,7) ;(eval_abc_2,7) ;(eval_abc_3,7) ;(eval_abc_4,7) ;(eval_abc_5,7) ;(eval_abc_6,7) ;(eval_abc_7,7) ;(eval_abc_bb0_in,7) ;(eval_abc_bb1_in,7) ;(eval_abc_bb2_in,7) ;(eval_abc_bb3_in,7) ;(eval_abc_bb4_in,7) ;(eval_abc_bb5_in,7) ;(eval_abc_start,7) ;(eval_abc_stop,7)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10,11},10->{12,13},11->{18},12->{14} ,13->{15},14->{12,13},15->{16},16->{17},17->{10,11},18->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval_abc_start(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_bb0_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (1,1) 1. eval_abc_bb0_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_0(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (1,1) 2. eval_abc_0(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_1(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (1,1) 3. eval_abc_1(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_2(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (1,1) 4. eval_abc_2(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_3(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (1,1) 5. eval_abc_3(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_4(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (1,1) 6. eval_abc_4(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_5(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (1,1) 7. eval_abc_5(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_6(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (1,1) 8. eval_abc_6(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_7(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (1,1) 9. eval_abc_7(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_bb1_in(v_3,v_a,v_b,v_c,v_d,v_a,v_j_0) True (1,1) 10. eval_abc_bb1_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_bb2_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_c) [-1*v_a + v_i_0 >= 0 && v_b >= v_i_0] (?,1) 11. eval_abc_bb1_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_bb5_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) [-1*v_a + v_i_0 >= 0 && -1 + v_i_0 >= v_b] (1,1) 12. eval_abc_bb2_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_bb3_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) [-1*v_c + v_j_0 >= 0 && v_b + -1*v_i_0 >= 0 && -1*v_a + v_i_0 >= 0 && -1*v_a + v_b >= 0 && v_d >= v_j_0] (?,1) 13. eval_abc_bb2_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_bb4_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) [-1*v_c + v_j_0 >= 0 (?,1) && v_b + -1*v_i_0 >= 0 && -1*v_a + v_i_0 >= 0 && -1*v_a + v_b >= 0 && -1 + v_j_0 >= v_d] 14. eval_abc_bb3_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_bb2_in(v_3,v_a,v_b,v_c,v_d,v_i_0,1 + v_j_0) [v_d + -1*v_j_0 >= 0 (?,1) && -1*v_c + v_j_0 >= 0 && v_b + -1*v_i_0 >= 0 && -1*v_a + v_i_0 >= 0 && -1*v_c + v_d >= 0 && -1*v_a + v_b >= 0] 15. eval_abc_bb4_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_11(1 + v_i_0,v_a,v_b,v_c,v_d,v_i_0,v_j_0) [-1 + -1*v_d + v_j_0 >= 0 (?,1) && -1*v_c + v_j_0 >= 0 && v_b + -1*v_i_0 >= 0 && -1*v_a + v_i_0 >= 0 && -1*v_a + v_b >= 0] 16. eval_abc_11(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_12(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) [-1 + -1*v_d + v_j_0 >= 0 (?,1) && -1*v_c + v_j_0 >= 0 && v_b + -1*v_i_0 >= 0 && -1 + v_3 + -1*v_i_0 >= 0 && -1*v_a + v_i_0 >= 0 && 1 + -1*v_3 + v_i_0 >= 0 && -1*v_a + v_b >= 0 && 1 + -1*v_3 + v_b >= 0 && -1 + v_3 + -1*v_a >= 0] 17. eval_abc_12(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_bb1_in(v_3,v_a,v_b,v_c,v_d,v_3,v_j_0) [-1 + -1*v_d + v_j_0 >= 0 (?,1) && -1*v_c + v_j_0 >= 0 && v_b + -1*v_i_0 >= 0 && -1 + v_3 + -1*v_i_0 >= 0 && -1*v_a + v_i_0 >= 0 && 1 + -1*v_3 + v_i_0 >= 0 && -1*v_a + v_b >= 0 && 1 + -1*v_3 + v_b >= 0 && -1 + v_3 + -1*v_a >= 0] 18. eval_abc_bb5_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_stop(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) [-1 + -1*v_b + v_i_0 >= 0 && -1*v_a + v_i_0 >= 0] (1,1) Signature: {(eval_abc_0,7) ;(eval_abc_1,7) ;(eval_abc_11,7) ;(eval_abc_12,7) ;(eval_abc_2,7) ;(eval_abc_3,7) ;(eval_abc_4,7) ;(eval_abc_5,7) ;(eval_abc_6,7) ;(eval_abc_7,7) ;(eval_abc_bb0_in,7) ;(eval_abc_bb1_in,7) ;(eval_abc_bb2_in,7) ;(eval_abc_bb3_in,7) ;(eval_abc_bb4_in,7) ;(eval_abc_bb5_in,7) ;(eval_abc_start,7) ;(eval_abc_stop,7)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10,11},10->{12,13},11->{18},12->{14} ,13->{15},14->{12,13},15->{16},16->{17},17->{10,11},18->{}] + Applied Processor: AddSinks + Details: () * Step 3: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval_abc_start(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_bb0_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (1,1) 1. eval_abc_bb0_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_0(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (?,1) 2. eval_abc_0(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_1(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (?,1) 3. eval_abc_1(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_2(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (?,1) 4. eval_abc_2(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_3(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (?,1) 5. eval_abc_3(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_4(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (?,1) 6. eval_abc_4(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_5(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (?,1) 7. eval_abc_5(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_6(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (?,1) 8. eval_abc_6(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_7(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (?,1) 9. eval_abc_7(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_bb1_in(v_3,v_a,v_b,v_c,v_d,v_a,v_j_0) True (?,1) 10. eval_abc_bb1_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_bb2_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_c) [-1*v_a + v_i_0 >= 0 && v_b >= v_i_0] (?,1) 11. eval_abc_bb1_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_bb5_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) [-1*v_a + v_i_0 >= 0 && -1 + v_i_0 >= v_b] (?,1) 12. eval_abc_bb2_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_bb3_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) [-1*v_c + v_j_0 >= 0 && v_b + -1*v_i_0 >= 0 && -1*v_a + v_i_0 >= 0 && -1*v_a + v_b >= 0 && v_d >= v_j_0] (?,1) 13. eval_abc_bb2_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_bb4_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) [-1*v_c + v_j_0 >= 0 (?,1) && v_b + -1*v_i_0 >= 0 && -1*v_a + v_i_0 >= 0 && -1*v_a + v_b >= 0 && -1 + v_j_0 >= v_d] 14. eval_abc_bb3_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_bb2_in(v_3,v_a,v_b,v_c,v_d,v_i_0,1 + v_j_0) [v_d + -1*v_j_0 >= 0 (?,1) && -1*v_c + v_j_0 >= 0 && v_b + -1*v_i_0 >= 0 && -1*v_a + v_i_0 >= 0 && -1*v_c + v_d >= 0 && -1*v_a + v_b >= 0] 15. eval_abc_bb4_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_11(1 + v_i_0,v_a,v_b,v_c,v_d,v_i_0,v_j_0) [-1 + -1*v_d + v_j_0 >= 0 (?,1) && -1*v_c + v_j_0 >= 0 && v_b + -1*v_i_0 >= 0 && -1*v_a + v_i_0 >= 0 && -1*v_a + v_b >= 0] 16. eval_abc_11(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_12(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) [-1 + -1*v_d + v_j_0 >= 0 (?,1) && -1*v_c + v_j_0 >= 0 && v_b + -1*v_i_0 >= 0 && -1 + v_3 + -1*v_i_0 >= 0 && -1*v_a + v_i_0 >= 0 && 1 + -1*v_3 + v_i_0 >= 0 && -1*v_a + v_b >= 0 && 1 + -1*v_3 + v_b >= 0 && -1 + v_3 + -1*v_a >= 0] 17. eval_abc_12(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_bb1_in(v_3,v_a,v_b,v_c,v_d,v_3,v_j_0) [-1 + -1*v_d + v_j_0 >= 0 (?,1) && -1*v_c + v_j_0 >= 0 && v_b + -1*v_i_0 >= 0 && -1 + v_3 + -1*v_i_0 >= 0 && -1*v_a + v_i_0 >= 0 && 1 + -1*v_3 + v_i_0 >= 0 && -1*v_a + v_b >= 0 && 1 + -1*v_3 + v_b >= 0 && -1 + v_3 + -1*v_a >= 0] 18. eval_abc_bb5_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_stop(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) [-1 + -1*v_b + v_i_0 >= 0 && -1*v_a + v_i_0 >= 0] (?,1) 19. eval_abc_bb5_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> exitus616(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (?,1) Signature: {(eval_abc_0,7) ;(eval_abc_1,7) ;(eval_abc_11,7) ;(eval_abc_12,7) ;(eval_abc_2,7) ;(eval_abc_3,7) ;(eval_abc_4,7) ;(eval_abc_5,7) ;(eval_abc_6,7) ;(eval_abc_7,7) ;(eval_abc_bb0_in,7) ;(eval_abc_bb1_in,7) ;(eval_abc_bb2_in,7) ;(eval_abc_bb3_in,7) ;(eval_abc_bb4_in,7) ;(eval_abc_bb5_in,7) ;(eval_abc_start,7) ;(eval_abc_stop,7) ;(exitus616,7)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10,11},10->{12,13},11->{18,19} ,12->{14},13->{15},14->{12,13},15->{16},16->{17},17->{10,11},18->{},19->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19] | `- p:[10,17,16,15,13,14,12] c: [17] | `- p:[12,14] c: [14] * Step 4: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. eval_abc_start(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_bb0_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (1,1) 1. eval_abc_bb0_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_0(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (?,1) 2. eval_abc_0(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_1(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (?,1) 3. eval_abc_1(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_2(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (?,1) 4. eval_abc_2(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_3(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (?,1) 5. eval_abc_3(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_4(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (?,1) 6. eval_abc_4(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_5(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (?,1) 7. eval_abc_5(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_6(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (?,1) 8. eval_abc_6(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_7(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (?,1) 9. eval_abc_7(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_bb1_in(v_3,v_a,v_b,v_c,v_d,v_a,v_j_0) True (?,1) 10. eval_abc_bb1_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_bb2_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_c) [-1*v_a + v_i_0 >= 0 && v_b >= v_i_0] (?,1) 11. eval_abc_bb1_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_bb5_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) [-1*v_a + v_i_0 >= 0 && -1 + v_i_0 >= v_b] (?,1) 12. eval_abc_bb2_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_bb3_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) [-1*v_c + v_j_0 >= 0 && v_b + -1*v_i_0 >= 0 && -1*v_a + v_i_0 >= 0 && -1*v_a + v_b >= 0 && v_d >= v_j_0] (?,1) 13. eval_abc_bb2_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_bb4_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) [-1*v_c + v_j_0 >= 0 (?,1) && v_b + -1*v_i_0 >= 0 && -1*v_a + v_i_0 >= 0 && -1*v_a + v_b >= 0 && -1 + v_j_0 >= v_d] 14. eval_abc_bb3_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_bb2_in(v_3,v_a,v_b,v_c,v_d,v_i_0,1 + v_j_0) [v_d + -1*v_j_0 >= 0 (?,1) && -1*v_c + v_j_0 >= 0 && v_b + -1*v_i_0 >= 0 && -1*v_a + v_i_0 >= 0 && -1*v_c + v_d >= 0 && -1*v_a + v_b >= 0] 15. eval_abc_bb4_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_11(1 + v_i_0,v_a,v_b,v_c,v_d,v_i_0,v_j_0) [-1 + -1*v_d + v_j_0 >= 0 (?,1) && -1*v_c + v_j_0 >= 0 && v_b + -1*v_i_0 >= 0 && -1*v_a + v_i_0 >= 0 && -1*v_a + v_b >= 0] 16. eval_abc_11(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_12(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) [-1 + -1*v_d + v_j_0 >= 0 (?,1) && -1*v_c + v_j_0 >= 0 && v_b + -1*v_i_0 >= 0 && -1 + v_3 + -1*v_i_0 >= 0 && -1*v_a + v_i_0 >= 0 && 1 + -1*v_3 + v_i_0 >= 0 && -1*v_a + v_b >= 0 && 1 + -1*v_3 + v_b >= 0 && -1 + v_3 + -1*v_a >= 0] 17. eval_abc_12(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_bb1_in(v_3,v_a,v_b,v_c,v_d,v_3,v_j_0) [-1 + -1*v_d + v_j_0 >= 0 (?,1) && -1*v_c + v_j_0 >= 0 && v_b + -1*v_i_0 >= 0 && -1 + v_3 + -1*v_i_0 >= 0 && -1*v_a + v_i_0 >= 0 && 1 + -1*v_3 + v_i_0 >= 0 && -1*v_a + v_b >= 0 && 1 + -1*v_3 + v_b >= 0 && -1 + v_3 + -1*v_a >= 0] 18. eval_abc_bb5_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> eval_abc_stop(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) [-1 + -1*v_b + v_i_0 >= 0 && -1*v_a + v_i_0 >= 0] (?,1) 19. eval_abc_bb5_in(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) -> exitus616(v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0) True (?,1) Signature: {(eval_abc_0,7) ;(eval_abc_1,7) ;(eval_abc_11,7) ;(eval_abc_12,7) ;(eval_abc_2,7) ;(eval_abc_3,7) ;(eval_abc_4,7) ;(eval_abc_5,7) ;(eval_abc_6,7) ;(eval_abc_7,7) ;(eval_abc_bb0_in,7) ;(eval_abc_bb1_in,7) ;(eval_abc_bb2_in,7) ;(eval_abc_bb3_in,7) ;(eval_abc_bb4_in,7) ;(eval_abc_bb5_in,7) ;(eval_abc_start,7) ;(eval_abc_stop,7) ;(exitus616,7)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10,11},10->{12,13},11->{18,19} ,12->{14},13->{15},14->{12,13},15->{16},16->{17},17->{10,11},18->{},19->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19] | `- p:[10,17,16,15,13,14,12] c: [17] | `- p:[12,14] c: [14]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 5: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0,0.0,0.0.0] eval_abc_start ~> eval_abc_bb0_in [v_3 <= v_3, v_a <= v_a, v_b <= v_b, v_c <= v_c, v_d <= v_d, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_abc_bb0_in ~> eval_abc_0 [v_3 <= v_3, v_a <= v_a, v_b <= v_b, v_c <= v_c, v_d <= v_d, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_abc_0 ~> eval_abc_1 [v_3 <= v_3, v_a <= v_a, v_b <= v_b, v_c <= v_c, v_d <= v_d, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_abc_1 ~> eval_abc_2 [v_3 <= v_3, v_a <= v_a, v_b <= v_b, v_c <= v_c, v_d <= v_d, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_abc_2 ~> eval_abc_3 [v_3 <= v_3, v_a <= v_a, v_b <= v_b, v_c <= v_c, v_d <= v_d, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_abc_3 ~> eval_abc_4 [v_3 <= v_3, v_a <= v_a, v_b <= v_b, v_c <= v_c, v_d <= v_d, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_abc_4 ~> eval_abc_5 [v_3 <= v_3, v_a <= v_a, v_b <= v_b, v_c <= v_c, v_d <= v_d, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_abc_5 ~> eval_abc_6 [v_3 <= v_3, v_a <= v_a, v_b <= v_b, v_c <= v_c, v_d <= v_d, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_abc_6 ~> eval_abc_7 [v_3 <= v_3, v_a <= v_a, v_b <= v_b, v_c <= v_c, v_d <= v_d, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_abc_7 ~> eval_abc_bb1_in [v_3 <= v_3, v_a <= v_a, v_b <= v_b, v_c <= v_c, v_d <= v_d, v_i_0 <= v_a, v_j_0 <= v_j_0] eval_abc_bb1_in ~> eval_abc_bb2_in [v_3 <= v_3, v_a <= v_a, v_b <= v_b, v_c <= v_c, v_d <= v_d, v_i_0 <= v_i_0, v_j_0 <= v_c] eval_abc_bb1_in ~> eval_abc_bb5_in [v_3 <= v_3, v_a <= v_a, v_b <= v_b, v_c <= v_c, v_d <= v_d, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_abc_bb2_in ~> eval_abc_bb3_in [v_3 <= v_3, v_a <= v_a, v_b <= v_b, v_c <= v_c, v_d <= v_d, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_abc_bb2_in ~> eval_abc_bb4_in [v_3 <= v_3, v_a <= v_a, v_b <= v_b, v_c <= v_c, v_d <= v_d, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_abc_bb3_in ~> eval_abc_bb2_in [v_3 <= v_3, v_a <= v_a, v_b <= v_b, v_c <= v_c, v_d <= v_d, v_i_0 <= v_i_0, v_j_0 <= K + v_j_0] eval_abc_bb4_in ~> eval_abc_11 [v_3 <= K + v_i_0, v_a <= v_a, v_b <= v_b, v_c <= v_c, v_d <= v_d, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_abc_11 ~> eval_abc_12 [v_3 <= v_3, v_a <= v_a, v_b <= v_b, v_c <= v_c, v_d <= v_d, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_abc_12 ~> eval_abc_bb1_in [v_3 <= v_3, v_a <= v_a, v_b <= v_b, v_c <= v_c, v_d <= v_d, v_i_0 <= v_3, v_j_0 <= v_j_0] eval_abc_bb5_in ~> eval_abc_stop [v_3 <= v_3, v_a <= v_a, v_b <= v_b, v_c <= v_c, v_d <= v_d, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_abc_bb5_in ~> exitus616 [v_3 <= v_3, v_a <= v_a, v_b <= v_b, v_c <= v_c, v_d <= v_d, v_i_0 <= v_i_0, v_j_0 <= v_j_0] + Loop: [0.0 <= 2*K + v_3 + v_b + v_i_0] eval_abc_bb1_in ~> eval_abc_bb2_in [v_3 <= v_3, v_a <= v_a, v_b <= v_b, v_c <= v_c, v_d <= v_d, v_i_0 <= v_i_0, v_j_0 <= v_c] eval_abc_12 ~> eval_abc_bb1_in [v_3 <= v_3, v_a <= v_a, v_b <= v_b, v_c <= v_c, v_d <= v_d, v_i_0 <= v_3, v_j_0 <= v_j_0] eval_abc_11 ~> eval_abc_12 [v_3 <= v_3, v_a <= v_a, v_b <= v_b, v_c <= v_c, v_d <= v_d, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_abc_bb4_in ~> eval_abc_11 [v_3 <= K + v_i_0, v_a <= v_a, v_b <= v_b, v_c <= v_c, v_d <= v_d, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_abc_bb2_in ~> eval_abc_bb4_in [v_3 <= v_3, v_a <= v_a, v_b <= v_b, v_c <= v_c, v_d <= v_d, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_abc_bb3_in ~> eval_abc_bb2_in [v_3 <= v_3, v_a <= v_a, v_b <= v_b, v_c <= v_c, v_d <= v_d, v_i_0 <= v_i_0, v_j_0 <= K + v_j_0] eval_abc_bb2_in ~> eval_abc_bb3_in [v_3 <= v_3, v_a <= v_a, v_b <= v_b, v_c <= v_c, v_d <= v_d, v_i_0 <= v_i_0, v_j_0 <= v_j_0] + Loop: [0.0.0 <= K + v_d + v_j_0] eval_abc_bb2_in ~> eval_abc_bb3_in [v_3 <= v_3, v_a <= v_a, v_b <= v_b, v_c <= v_c, v_d <= v_d, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_abc_bb3_in ~> eval_abc_bb2_in [v_3 <= v_3, v_a <= v_a, v_b <= v_b, v_c <= v_c, v_d <= v_d, v_i_0 <= v_i_0, v_j_0 <= K + v_j_0] + Applied Processor: FlowAbstraction + Details: () * Step 6: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,v_3,v_a,v_b,v_c,v_d,v_i_0,v_j_0,0.0,0.0.0] eval_abc_start ~> eval_abc_bb0_in [] eval_abc_bb0_in ~> eval_abc_0 [] eval_abc_0 ~> eval_abc_1 [] eval_abc_1 ~> eval_abc_2 [] eval_abc_2 ~> eval_abc_3 [] eval_abc_3 ~> eval_abc_4 [] eval_abc_4 ~> eval_abc_5 [] eval_abc_5 ~> eval_abc_6 [] eval_abc_6 ~> eval_abc_7 [] eval_abc_7 ~> eval_abc_bb1_in [v_a ~=> v_i_0] eval_abc_bb1_in ~> eval_abc_bb2_in [v_c ~=> v_j_0] eval_abc_bb1_in ~> eval_abc_bb5_in [] eval_abc_bb2_in ~> eval_abc_bb3_in [] eval_abc_bb2_in ~> eval_abc_bb4_in [] eval_abc_bb3_in ~> eval_abc_bb2_in [v_j_0 ~+> v_j_0,K ~+> v_j_0] eval_abc_bb4_in ~> eval_abc_11 [v_i_0 ~+> v_3,K ~+> v_3] eval_abc_11 ~> eval_abc_12 [] eval_abc_12 ~> eval_abc_bb1_in [v_3 ~=> v_i_0] eval_abc_bb5_in ~> eval_abc_stop [] eval_abc_bb5_in ~> exitus616 [] + Loop: [v_3 ~+> 0.0,v_b ~+> 0.0,v_i_0 ~+> 0.0,K ~*> 0.0] eval_abc_bb1_in ~> eval_abc_bb2_in [v_c ~=> v_j_0] eval_abc_12 ~> eval_abc_bb1_in [v_3 ~=> v_i_0] eval_abc_11 ~> eval_abc_12 [] eval_abc_bb4_in ~> eval_abc_11 [v_i_0 ~+> v_3,K ~+> v_3] eval_abc_bb2_in ~> eval_abc_bb4_in [] eval_abc_bb3_in ~> eval_abc_bb2_in [v_j_0 ~+> v_j_0,K ~+> v_j_0] eval_abc_bb2_in ~> eval_abc_bb3_in [] + Loop: [v_d ~+> 0.0.0,v_j_0 ~+> 0.0.0,K ~+> 0.0.0] eval_abc_bb2_in ~> eval_abc_bb3_in [] eval_abc_bb3_in ~> eval_abc_bb2_in [v_j_0 ~+> v_j_0,K ~+> v_j_0] + Applied Processor: LareProcessor + Details: eval_abc_start ~> exitus616 [v_a ~=> v_i_0 ,v_c ~=> v_j_0 ,v_3 ~+> 0.0 ,v_3 ~+> tick ,v_a ~+> v_3 ,v_a ~+> v_i_0 ,v_a ~+> 0.0 ,v_a ~+> tick ,v_b ~+> 0.0 ,v_b ~+> tick ,v_c ~+> v_j_0 ,v_c ~+> 0.0.0 ,v_c ~+> tick ,v_d ~+> 0.0.0 ,v_d ~+> tick ,tick ~+> tick ,K ~+> v_3 ,K ~+> v_i_0 ,K ~+> v_j_0 ,K ~+> 0.0.0 ,K ~+> tick ,v_3 ~*> v_i_0 ,v_3 ~*> v_j_0 ,v_3 ~*> tick ,v_a ~*> v_i_0 ,v_a ~*> v_j_0 ,v_a ~*> tick ,v_b ~*> v_i_0 ,v_b ~*> v_j_0 ,v_b ~*> tick ,v_c ~*> v_j_0 ,v_c ~*> 0.0.0 ,v_c ~*> tick ,v_d ~*> v_j_0 ,v_d ~*> 0.0.0 ,v_d ~*> tick ,K ~*> v_3 ,K ~*> v_i_0 ,K ~*> v_j_0 ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick ,v_3 ~^> v_j_0 ,v_a ~^> v_j_0 ,v_b ~^> v_j_0 ,K ~^> v_j_0] eval_abc_start ~> eval_abc_stop [v_a ~=> v_i_0 ,v_c ~=> v_j_0 ,v_3 ~+> 0.0 ,v_3 ~+> tick ,v_a ~+> v_3 ,v_a ~+> v_i_0 ,v_a ~+> 0.0 ,v_a ~+> tick ,v_b ~+> 0.0 ,v_b ~+> tick ,v_c ~+> v_j_0 ,v_c ~+> 0.0.0 ,v_c ~+> tick ,v_d ~+> 0.0.0 ,v_d ~+> tick ,tick ~+> tick ,K ~+> v_3 ,K ~+> v_i_0 ,K ~+> v_j_0 ,K ~+> 0.0.0 ,K ~+> tick ,v_3 ~*> v_i_0 ,v_3 ~*> v_j_0 ,v_3 ~*> tick ,v_a ~*> v_i_0 ,v_a ~*> v_j_0 ,v_a ~*> tick ,v_b ~*> v_i_0 ,v_b ~*> v_j_0 ,v_b ~*> tick ,v_c ~*> v_j_0 ,v_c ~*> 0.0.0 ,v_c ~*> tick ,v_d ~*> v_j_0 ,v_d ~*> 0.0.0 ,v_d ~*> tick ,K ~*> v_3 ,K ~*> v_i_0 ,K ~*> v_j_0 ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick ,v_3 ~^> v_j_0 ,v_a ~^> v_j_0 ,v_b ~^> v_j_0 ,K ~^> v_j_0] + eval_abc_bb1_in> [v_c ~=> v_j_0 ,v_3 ~+> 0.0 ,v_3 ~+> tick ,v_b ~+> 0.0 ,v_b ~+> tick ,v_c ~+> v_j_0 ,v_c ~+> 0.0.0 ,v_c ~+> tick ,v_d ~+> 0.0.0 ,v_d ~+> tick ,v_i_0 ~+> v_3 ,v_i_0 ~+> v_i_0 ,v_i_0 ~+> 0.0 ,v_i_0 ~+> tick ,tick ~+> tick ,K ~+> v_3 ,K ~+> v_i_0 ,K ~+> v_j_0 ,K ~+> 0.0.0 ,K ~+> tick ,v_3 ~*> v_i_0 ,v_3 ~*> v_j_0 ,v_3 ~*> tick ,v_b ~*> v_i_0 ,v_b ~*> v_j_0 ,v_b ~*> tick ,v_c ~*> v_j_0 ,v_c ~*> 0.0.0 ,v_c ~*> tick ,v_d ~*> v_j_0 ,v_d ~*> 0.0.0 ,v_d ~*> tick ,v_i_0 ~*> v_i_0 ,v_i_0 ~*> v_j_0 ,v_i_0 ~*> tick ,K ~*> v_3 ,K ~*> v_i_0 ,K ~*> v_j_0 ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick ,v_3 ~^> v_j_0 ,v_b ~^> v_j_0 ,v_i_0 ~^> v_j_0 ,K ~^> v_j_0] + eval_abc_bb2_in> [v_d ~+> 0.0.0 ,v_d ~+> tick ,v_j_0 ~+> v_j_0 ,v_j_0 ~+> 0.0.0 ,v_j_0 ~+> tick ,tick ~+> tick ,K ~+> v_j_0 ,K ~+> 0.0.0 ,K ~+> tick ,v_d ~*> v_j_0 ,v_j_0 ~*> v_j_0 ,K ~*> v_j_0] YES(?,POLY)