YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. eval_ax_start(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_bb0_in(v__0,v__01,v_3,v_i,v_j,v_n) True (1,1) 1. eval_ax_bb0_in(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_0(v__0,v__01,v_3,v_i,v_j,v_n) True (?,1) 2. eval_ax_0(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_1(v__0,v__01,v_3,v_i,v_j,v_n) True (?,1) 3. eval_ax_1(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_2(v__0,v__01,v_3,v_i,v_j,v_n) True (?,1) 4. eval_ax_2(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_3(v__0,v__01,v_3,v_i,v_j,v_n) True (?,1) 5. eval_ax_3(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_4(v__0,v__01,v_3,v_i,v_j,v_n) True (?,1) 6. eval_ax_4(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_5(v__0,v__01,v_3,v_i,v_j,v_n) True (?,1) 7. eval_ax_5(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_6(v__0,v__01,v_3,v_i,v_j,v_n) True (?,1) 8. eval_ax_6(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_bb1_in(0,v__01,v_3,v_i,v_j,v_n) True (?,1) 9. eval_ax_bb1_in(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_bb2_in(v__0,0,v_3,v_i,v_j,v_n) [v__0 >= 0] (?,1) 10. eval_ax_bb2_in(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_bb3_in(v__0,v__01,v_3,v_i,v_j,v_n) [v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0 && -2 + v_n >= v__01] (?,1) 11. eval_ax_bb2_in(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_bb4_in(v__0,v__01,v_3,v_i,v_j,v_n) [v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0 && v__01 >= -1 + v_n] (?,1) 12. eval_ax_bb3_in(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_bb2_in(v__0,1 + v__01,v_3,v_i,v_j,v_n) [-2 + v_n >= 0 (?,1) && -2 + v__01 + v_n >= 0 && -2 + -1*v__01 + v_n >= 0 && -2 + v__0 + v_n >= 0 && v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0] 13. eval_ax_bb4_in(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_12(v__0,v__01,1 + v__0,v_i,v_j,v_n) [1 + v__01 + -1*v_n >= 0 && v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0] (?,1) 14. eval_ax_12(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_13(v__0,v__01,v_3,v_i,v_j,v_n) [1 + v__01 + -1*v_n >= 0 (?,1) && 1 + -1*v_3 + v__0 >= 0 && -1 + v_3 >= 0 && -1 + v_3 + v__01 >= 0 && -1 + v_3 + v__0 >= 0 && -1 + v_3 + -1*v__0 >= 0 && v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0] 15. eval_ax_13(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_bb1_in(v_3,v__01,v_3,v_i,v_j,v_n) [1 + v__01 + -1*v_n >= 0 (?,1) && 1 + -1*v_3 + v__0 >= 0 && -1 + v_3 >= 0 && -1 + v_3 + v__01 >= 0 && -1 + v_3 + v__0 >= 0 && -1 + v_3 + -1*v__0 >= 0 && v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0 && v__01 >= -1 + v_n && -2 + v_n >= v_3] 16. eval_ax_13(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_bb5_in(v__0,v__01,v_3,v_i,v_j,v_n) [1 + v__01 + -1*v_n >= 0 (?,1) && 1 + -1*v_3 + v__0 >= 0 && -1 + v_3 >= 0 && -1 + v_3 + v__01 >= 0 && -1 + v_3 + v__0 >= 0 && -1 + v_3 + -1*v__0 >= 0 && v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0 && v_3 >= -1 + v_n] 17. eval_ax_bb5_in(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_stop(v__0,v__01,v_3,v_i,v_j,v_n) [1 + v_3 + -1*v_n >= 0 (?,1) && 1 + v__01 + -1*v_n >= 0 && 2 + v__0 + -1*v_n >= 0 && 1 + -1*v_3 + v__0 >= 0 && -1 + v_3 >= 0 && -1 + v_3 + v__01 >= 0 && -1 + v_3 + v__0 >= 0 && -1 + v_3 + -1*v__0 >= 0 && v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0] Signature: {(eval_ax_0,6) ;(eval_ax_1,6) ;(eval_ax_12,6) ;(eval_ax_13,6) ;(eval_ax_2,6) ;(eval_ax_3,6) ;(eval_ax_4,6) ;(eval_ax_5,6) ;(eval_ax_6,6) ;(eval_ax_bb0_in,6) ;(eval_ax_bb1_in,6) ;(eval_ax_bb2_in,6) ;(eval_ax_bb3_in,6) ;(eval_ax_bb4_in,6) ;(eval_ax_bb5_in,6) ;(eval_ax_start,6) ;(eval_ax_stop,6)} 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},11->{13},12->{10,11} ,13->{14},14->{15,16},15->{9},16->{17},17->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: Looptree YES + Considered Problem: Rules: 0. eval_ax_start(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_bb0_in(v__0,v__01,v_3,v_i,v_j,v_n) True (1,1) 1. eval_ax_bb0_in(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_0(v__0,v__01,v_3,v_i,v_j,v_n) True (1,1) 2. eval_ax_0(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_1(v__0,v__01,v_3,v_i,v_j,v_n) True (1,1) 3. eval_ax_1(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_2(v__0,v__01,v_3,v_i,v_j,v_n) True (1,1) 4. eval_ax_2(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_3(v__0,v__01,v_3,v_i,v_j,v_n) True (1,1) 5. eval_ax_3(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_4(v__0,v__01,v_3,v_i,v_j,v_n) True (1,1) 6. eval_ax_4(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_5(v__0,v__01,v_3,v_i,v_j,v_n) True (1,1) 7. eval_ax_5(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_6(v__0,v__01,v_3,v_i,v_j,v_n) True (1,1) 8. eval_ax_6(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_bb1_in(0,v__01,v_3,v_i,v_j,v_n) True (1,1) 9. eval_ax_bb1_in(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_bb2_in(v__0,0,v_3,v_i,v_j,v_n) [v__0 >= 0] (?,1) 10. eval_ax_bb2_in(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_bb3_in(v__0,v__01,v_3,v_i,v_j,v_n) [v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0 && -2 + v_n >= v__01] (?,1) 11. eval_ax_bb2_in(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_bb4_in(v__0,v__01,v_3,v_i,v_j,v_n) [v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0 && v__01 >= -1 + v_n] (?,1) 12. eval_ax_bb3_in(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_bb2_in(v__0,1 + v__01,v_3,v_i,v_j,v_n) [-2 + v_n >= 0 (?,1) && -2 + v__01 + v_n >= 0 && -2 + -1*v__01 + v_n >= 0 && -2 + v__0 + v_n >= 0 && v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0] 13. eval_ax_bb4_in(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_12(v__0,v__01,1 + v__0,v_i,v_j,v_n) [1 + v__01 + -1*v_n >= 0 && v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0] (?,1) 14. eval_ax_12(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_13(v__0,v__01,v_3,v_i,v_j,v_n) [1 + v__01 + -1*v_n >= 0 (?,1) && 1 + -1*v_3 + v__0 >= 0 && -1 + v_3 >= 0 && -1 + v_3 + v__01 >= 0 && -1 + v_3 + v__0 >= 0 && -1 + v_3 + -1*v__0 >= 0 && v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0] 15. eval_ax_13(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_bb1_in(v_3,v__01,v_3,v_i,v_j,v_n) [1 + v__01 + -1*v_n >= 0 (?,1) && 1 + -1*v_3 + v__0 >= 0 && -1 + v_3 >= 0 && -1 + v_3 + v__01 >= 0 && -1 + v_3 + v__0 >= 0 && -1 + v_3 + -1*v__0 >= 0 && v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0 && v__01 >= -1 + v_n && -2 + v_n >= v_3] 16. eval_ax_13(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_bb5_in(v__0,v__01,v_3,v_i,v_j,v_n) [1 + v__01 + -1*v_n >= 0 (1,1) && 1 + -1*v_3 + v__0 >= 0 && -1 + v_3 >= 0 && -1 + v_3 + v__01 >= 0 && -1 + v_3 + v__0 >= 0 && -1 + v_3 + -1*v__0 >= 0 && v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0 && v_3 >= -1 + v_n] 17. eval_ax_bb5_in(v__0,v__01,v_3,v_i,v_j,v_n) -> eval_ax_stop(v__0,v__01,v_3,v_i,v_j,v_n) [1 + v_3 + -1*v_n >= 0 (1,1) && 1 + v__01 + -1*v_n >= 0 && 2 + v__0 + -1*v_n >= 0 && 1 + -1*v_3 + v__0 >= 0 && -1 + v_3 >= 0 && -1 + v_3 + v__01 >= 0 && -1 + v_3 + v__0 >= 0 && -1 + v_3 + -1*v__0 >= 0 && v__01 >= 0 && v__0 + v__01 >= 0 && v__0 >= 0] Signature: {(eval_ax_0,6) ;(eval_ax_1,6) ;(eval_ax_12,6) ;(eval_ax_13,6) ;(eval_ax_2,6) ;(eval_ax_3,6) ;(eval_ax_4,6) ;(eval_ax_5,6) ;(eval_ax_6,6) ;(eval_ax_bb0_in,6) ;(eval_ax_bb1_in,6) ;(eval_ax_bb2_in,6) ;(eval_ax_bb3_in,6) ;(eval_ax_bb4_in,6) ;(eval_ax_bb5_in,6) ;(eval_ax_start,6) ;(eval_ax_stop,6)} 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},11->{13},12->{10,11} ,13->{14},14->{15,16},15->{9},16->{17},17->{}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] | `- p:[9,15,14,13,11,12,10] c: [15] | `- p:[10,12] c: [12] YES