NO * Step 1: TrivialSCCs NO + Considered Problem: Rules: 0. eval_aaron12_start(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_bb0_in(v__0,v__01,v__03,v_1,v_x,v_y,v_z) True (1,1) 1. eval_aaron12_bb0_in(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_0(v__0,v__01,v__03,v_1,v_x,v_y,v_z) True (?,1) 2. eval_aaron12_0(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_1(v__0,v__01,v__03,v_1,v_x,v_y,v_z) True (?,1) 3. eval_aaron12_1(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_2(v__0,v__01,v__03,v_1,v_x,v_y,v_z) True (?,1) 4. eval_aaron12_2(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_3(v__0,v__01,v__03,v_1,v_x,v_y,v_z) True (?,1) 5. eval_aaron12_3(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_4(v__0,v__01,v__03,v_1,v_x,v_y,v_z) True (?,1) 6. eval_aaron12_4(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_5(v__0,v__01,v__03,v_1,v_x,v_y,v_z) True (?,1) 7. eval_aaron12_5(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_6(v__0,v__01,v__03,v_1,v_x,v_y,v_z) True (?,1) 8. eval_aaron12_6(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_7(v__0,v__01,v__03,v_1,v_x,v_y,v_z) True (?,1) 9. eval_aaron12_7(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_8(v__0,v__01,v__03,v_1,v_x,v_y,v_z) True (?,1) 10. eval_aaron12_8(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_bb1_in(v_x,v_y,v_z,v_1,v_x,v_y,v_z) True (?,1) 11. eval_aaron12_bb1_in(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_bb2_in(v__0,v__01,v__03,v_1,v_x,v_y,v_z) [-1*v__03 + v_z >= 0 && v__0 >= v__01] (?,1) 12. eval_aaron12_bb1_in(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_bb5_in(v__0,v__01,v__03,v_1,v_x,v_y,v_z) [-1*v__03 + v_z >= 0 && -1 + v__01 >= v__0] (?,1) 13. eval_aaron12_bb2_in(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_9(v__0,v__01,v__03,v_1,v_x,v_y,v_z) [-1*v__03 + v_z >= 0 && v__0 + -1*v__01 >= 0] (?,1) 14. eval_aaron12_9(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_10(v__0,v__01,v__03,nondef_0,v_x,v_y,v_z) [-1*v__03 + v_z >= 0 && v__0 + -1*v__01 >= 0] (?,1) 15. eval_aaron12_10(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_bb3_in(v__0,v__01,v__03,v_1,v_x,v_y,v_z) [-1*v__03 + v_z >= 0 && v__0 + -1*v__01 >= 0 && -1 + v_1 >= 0] (?,1) 16. eval_aaron12_10(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_bb4_in(v__0,v__01,v__03,v_1,v_x,v_y,v_z) [-1*v__03 + v_z >= 0 && v__0 + -1*v__01 >= 0 && 0 >= v_1] (?,1) 17. eval_aaron12_bb3_in(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_bb1_in(1 + v__0,1 + v__0 + v__01,v__03,v_1,v_x,v_y,v_z) [-1*v__03 + v_z >= 0 && -1 + v_1 >= 0 && v__0 + -1*v__01 >= 0] (?,1) 18. eval_aaron12_bb4_in(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_bb1_in(v__0 + -1*v__03,v__01 + v__03^2,-1 + v__03,v_1,v_x,v_y,v_z) [-1*v__03 + v_z >= 0 && -1*v_1 >= 0 && v__0 + -1*v__01 >= 0] (?,1) 19. eval_aaron12_bb5_in(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_stop(v__0,v__01,v__03,v_1,v_x,v_y,v_z) [-1*v__03 + v_z >= 0 && -1 + -1*v__0 + v__01 >= 0] (?,1) Signature: {(eval_aaron12_0,7) ;(eval_aaron12_1,7) ;(eval_aaron12_10,7) ;(eval_aaron12_2,7) ;(eval_aaron12_3,7) ;(eval_aaron12_4,7) ;(eval_aaron12_5,7) ;(eval_aaron12_6,7) ;(eval_aaron12_7,7) ;(eval_aaron12_8,7) ;(eval_aaron12_9,7) ;(eval_aaron12_bb0_in,7) ;(eval_aaron12_bb1_in,7) ;(eval_aaron12_bb2_in,7) ;(eval_aaron12_bb3_in,7) ;(eval_aaron12_bb4_in,7) ;(eval_aaron12_bb5_in,7) ;(eval_aaron12_start,7) ;(eval_aaron12_stop,7)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10},10->{11,12},11->{13},12->{19} ,13->{14},14->{15,16},15->{17},16->{18},17->{11,12},18->{11,12},19->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: Looptree NO + Considered Problem: Rules: 0. eval_aaron12_start(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_bb0_in(v__0,v__01,v__03,v_1,v_x,v_y,v_z) True (1,1) 1. eval_aaron12_bb0_in(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_0(v__0,v__01,v__03,v_1,v_x,v_y,v_z) True (1,1) 2. eval_aaron12_0(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_1(v__0,v__01,v__03,v_1,v_x,v_y,v_z) True (1,1) 3. eval_aaron12_1(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_2(v__0,v__01,v__03,v_1,v_x,v_y,v_z) True (1,1) 4. eval_aaron12_2(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_3(v__0,v__01,v__03,v_1,v_x,v_y,v_z) True (1,1) 5. eval_aaron12_3(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_4(v__0,v__01,v__03,v_1,v_x,v_y,v_z) True (1,1) 6. eval_aaron12_4(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_5(v__0,v__01,v__03,v_1,v_x,v_y,v_z) True (1,1) 7. eval_aaron12_5(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_6(v__0,v__01,v__03,v_1,v_x,v_y,v_z) True (1,1) 8. eval_aaron12_6(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_7(v__0,v__01,v__03,v_1,v_x,v_y,v_z) True (1,1) 9. eval_aaron12_7(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_8(v__0,v__01,v__03,v_1,v_x,v_y,v_z) True (1,1) 10. eval_aaron12_8(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_bb1_in(v_x,v_y,v_z,v_1,v_x,v_y,v_z) True (1,1) 11. eval_aaron12_bb1_in(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_bb2_in(v__0,v__01,v__03,v_1,v_x,v_y,v_z) [-1*v__03 + v_z >= 0 && v__0 >= v__01] (?,1) 12. eval_aaron12_bb1_in(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_bb5_in(v__0,v__01,v__03,v_1,v_x,v_y,v_z) [-1*v__03 + v_z >= 0 && -1 + v__01 >= v__0] (1,1) 13. eval_aaron12_bb2_in(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_9(v__0,v__01,v__03,v_1,v_x,v_y,v_z) [-1*v__03 + v_z >= 0 && v__0 + -1*v__01 >= 0] (?,1) 14. eval_aaron12_9(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_10(v__0,v__01,v__03,nondef_0,v_x,v_y,v_z) [-1*v__03 + v_z >= 0 && v__0 + -1*v__01 >= 0] (?,1) 15. eval_aaron12_10(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_bb3_in(v__0,v__01,v__03,v_1,v_x,v_y,v_z) [-1*v__03 + v_z >= 0 && v__0 + -1*v__01 >= 0 && -1 + v_1 >= 0] (?,1) 16. eval_aaron12_10(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_bb4_in(v__0,v__01,v__03,v_1,v_x,v_y,v_z) [-1*v__03 + v_z >= 0 && v__0 + -1*v__01 >= 0 && 0 >= v_1] (?,1) 17. eval_aaron12_bb3_in(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_bb1_in(1 + v__0,1 + v__0 + v__01,v__03,v_1,v_x,v_y,v_z) [-1*v__03 + v_z >= 0 && -1 + v_1 >= 0 && v__0 + -1*v__01 >= 0] (?,1) 18. eval_aaron12_bb4_in(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_bb1_in(v__0 + -1*v__03,v__01 + v__03^2,-1 + v__03,v_1,v_x,v_y,v_z) [-1*v__03 + v_z >= 0 && -1*v_1 >= 0 && v__0 + -1*v__01 >= 0] (?,1) 19. eval_aaron12_bb5_in(v__0,v__01,v__03,v_1,v_x,v_y,v_z) -> eval_aaron12_stop(v__0,v__01,v__03,v_1,v_x,v_y,v_z) [-1*v__03 + v_z >= 0 && -1 + -1*v__0 + v__01 >= 0] (1,1) Signature: {(eval_aaron12_0,7) ;(eval_aaron12_1,7) ;(eval_aaron12_10,7) ;(eval_aaron12_2,7) ;(eval_aaron12_3,7) ;(eval_aaron12_4,7) ;(eval_aaron12_5,7) ;(eval_aaron12_6,7) ;(eval_aaron12_7,7) ;(eval_aaron12_8,7) ;(eval_aaron12_9,7) ;(eval_aaron12_bb0_in,7) ;(eval_aaron12_bb1_in,7) ;(eval_aaron12_bb2_in,7) ;(eval_aaron12_bb3_in,7) ;(eval_aaron12_bb4_in,7) ;(eval_aaron12_bb5_in,7) ;(eval_aaron12_start,7) ;(eval_aaron12_stop,7)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10},10->{11,12},11->{13},12->{19} ,13->{14},14->{15,16},15->{17},16->{18},17->{11,12},18->{11,12},19->{}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19] | `- p:[11,17,15,14,13,18,16] c: [] NO