YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. eval_p3_start(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_bb0_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) True (1,1) 1. eval_p3_bb0_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_0(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) True (?,1) 2. eval_p3_0(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_1(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) True (?,1) 3. eval_p3_1(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_2(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) True (?,1) 4. eval_p3_2(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_3(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) True (?,1) 5. eval_p3_3(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_4(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) True (?,1) 6. eval_p3_4(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_5(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) True (?,1) 7. eval_p3_5(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_6(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) True (?,1) 8. eval_p3_6(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_7(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) True (?,1) 9. eval_p3_7(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_bb1_in(v_x,v_y,v__1,v__3,v_12,v_x,v_y,v_z) True (?,1) 10. eval_p3_bb1_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_bb2_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) [-1*v__0 + v_x >= 0 && -1 + v__0 >= 0] (?,1) 11. eval_p3_bb1_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_bb7_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) [-1*v__0 + v_x >= 0 && 0 >= v__0] (?,1) 12. eval_p3_bb2_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_bb3_in(v__0,v__01,v__01,v__3,v_12,v_x,v_y,v_z) [-1 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= 0 && -1 >= nondef_0] (?,1) 13. eval_p3_bb2_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_bb3_in(v__0,v__01,v__01,v__3,v_12,v_x,v_y,v_z) [-1 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= 0 && -1 + nondef_0 >= 0] (?,1) 14. eval_p3_bb2_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_bb5_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) [-1 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= 0 && nondef_0 = 0] (?,1) 15. eval_p3_bb3_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_bb4_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) [-1 + v_x >= 0 (?,1) && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && v__01 + -1*v__1 >= 0 && -1 + v__0 >= 0 && -1 >= nondef_1 && -1 + v__1 >= 0] 16. eval_p3_bb3_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_bb4_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) [-1 + v_x >= 0 (?,1) && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && v__01 + -1*v__1 >= 0 && -1 + v__0 >= 0 && -1 + nondef_1 >= 0 && -1 + v__1 >= 0] 17. eval_p3_bb3_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_bb6_in(v__0,v__01,v__1,v__1,v_12,v_x,v_y,v_z) [-1 + v_x >= 0 (?,1) && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && v__01 + -1*v__1 >= 0 && -1 + v__0 >= 0 && nondef_1 = 0] 18. eval_p3_bb3_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_bb6_in(v__0,v__01,v__1,v__1,v_12,v_x,v_y,v_z) [-1 + v_x >= 0 (?,1) && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && v__01 + -1*v__1 >= 0 && -1 + v__0 >= 0 && 0 >= v__1] 19. eval_p3_bb4_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_15(v__0,v__01,v__1,v__3,-1 + v__1,v_x,v_y,v_z) [-1 + v_x >= 0 (?,1) && -2 + v__1 + v_x >= 0 && -2 + v__01 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && v__01 + -1*v__1 >= 0 && -1 + v__1 >= 0 && -2 + v__01 + v__1 >= 0 && -2 + v__0 + v__1 >= 0 && -1 + v__01 >= 0 && -2 + v__0 + v__01 >= 0 && -1 + v__0 >= 0] 20. eval_p3_15(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_16(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) [-1 + v_x >= 0 (?,1) && -1 + v_12 + v_x >= 0 && -2 + v__1 + v_x >= 0 && -2 + v__01 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + -1*v_12 + v__1 >= 0 && -1 + -1*v_12 + v__01 >= 0 && v_12 >= 0 && -1 + v_12 + v__1 >= 0 && 1 + v_12 + -1*v__1 >= 0 && -1 + v_12 + v__01 >= 0 && -1 + v_12 + v__0 >= 0 && v__01 + -1*v__1 >= 0 && -1 + v__1 >= 0 && -2 + v__01 + v__1 >= 0 && -2 + v__0 + v__1 >= 0 && -1 + v__01 >= 0 && -2 + v__0 + v__01 >= 0 && -1 + v__0 >= 0] 21. eval_p3_16(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_bb3_in(v__0,v__01,v_12,v__3,v_12,v_x,v_y,v_z) [-1 + v_x >= 0 (?,1) && -1 + v_12 + v_x >= 0 && -2 + v__1 + v_x >= 0 && -2 + v__01 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + -1*v_12 + v__1 >= 0 && -1 + -1*v_12 + v__01 >= 0 && v_12 >= 0 && -1 + v_12 + v__1 >= 0 && 1 + v_12 + -1*v__1 >= 0 && -1 + v_12 + v__01 >= 0 && -1 + v_12 + v__0 >= 0 && v__01 + -1*v__1 >= 0 && -1 + v__1 >= 0 && -2 + v__01 + v__1 >= 0 && -2 + v__0 + v__1 >= 0 && -1 + v__01 >= 0 && -2 + v__0 + v__01 >= 0 && -1 + v__0 >= 0] 22. eval_p3_bb5_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_bb6_in(v__0,v__01,v__1,1 + v__01,v_12,v_x,v_y,v_z) [-1 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= 0 && -1 >= nondef_2] (?,1) 23. eval_p3_bb5_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_bb6_in(v__0,v__01,v__1,1 + v__01,v_12,v_x,v_y,v_z) [-1 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= 0 && -1 + nondef_2 >= 0] (?,1) 24. eval_p3_bb5_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_bb6_in(v__0,v__01,v__1,v_z,v_12,v_x,v_y,v_z) [-1 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= 0 && nondef_2 = 0] (?,1) 25. eval_p3_bb6_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_bb1_in(-1 + v__0,v__3,v__1,v__3,v_12,v_x,v_y,v_z) [-1 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= 0] (?,1) 26. eval_p3_bb7_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_stop(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) [-1*v__0 + v_x >= 0 && -1*v__0 >= 0] (?,1) Signature: {(eval_p3_0,8) ;(eval_p3_1,8) ;(eval_p3_15,8) ;(eval_p3_16,8) ;(eval_p3_2,8) ;(eval_p3_3,8) ;(eval_p3_4,8) ;(eval_p3_5,8) ;(eval_p3_6,8) ;(eval_p3_7,8) ;(eval_p3_bb0_in,8) ;(eval_p3_bb1_in,8) ;(eval_p3_bb2_in,8) ;(eval_p3_bb3_in,8) ;(eval_p3_bb4_in,8) ;(eval_p3_bb5_in,8) ;(eval_p3_bb6_in,8) ;(eval_p3_bb7_in,8) ;(eval_p3_start,8) ;(eval_p3_stop,8)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10,11},10->{12,13,14},11->{26},12->{15 ,16,17,18},13->{15,16,17,18},14->{22,23,24},15->{19},16->{19},17->{25},18->{25},19->{20},20->{21},21->{15,16 ,17,18},22->{25},23->{25},24->{25},25->{10,11},26->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: Looptree YES + Considered Problem: Rules: 0. eval_p3_start(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_bb0_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) True (1,1) 1. eval_p3_bb0_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_0(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) True (1,1) 2. eval_p3_0(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_1(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) True (1,1) 3. eval_p3_1(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_2(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) True (1,1) 4. eval_p3_2(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_3(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) True (1,1) 5. eval_p3_3(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_4(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) True (1,1) 6. eval_p3_4(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_5(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) True (1,1) 7. eval_p3_5(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_6(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) True (1,1) 8. eval_p3_6(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_7(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) True (1,1) 9. eval_p3_7(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_bb1_in(v_x,v_y,v__1,v__3,v_12,v_x,v_y,v_z) True (1,1) 10. eval_p3_bb1_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_bb2_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) [-1*v__0 + v_x >= 0 && -1 + v__0 >= 0] (?,1) 11. eval_p3_bb1_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_bb7_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) [-1*v__0 + v_x >= 0 && 0 >= v__0] (1,1) 12. eval_p3_bb2_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_bb3_in(v__0,v__01,v__01,v__3,v_12,v_x,v_y,v_z) [-1 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= 0 && -1 >= nondef_0] (?,1) 13. eval_p3_bb2_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_bb3_in(v__0,v__01,v__01,v__3,v_12,v_x,v_y,v_z) [-1 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= 0 && -1 + nondef_0 >= 0] (?,1) 14. eval_p3_bb2_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_bb5_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) [-1 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= 0 && nondef_0 = 0] (?,1) 15. eval_p3_bb3_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_bb4_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) [-1 + v_x >= 0 (?,1) && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && v__01 + -1*v__1 >= 0 && -1 + v__0 >= 0 && -1 >= nondef_1 && -1 + v__1 >= 0] 16. eval_p3_bb3_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_bb4_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) [-1 + v_x >= 0 (?,1) && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && v__01 + -1*v__1 >= 0 && -1 + v__0 >= 0 && -1 + nondef_1 >= 0 && -1 + v__1 >= 0] 17. eval_p3_bb3_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_bb6_in(v__0,v__01,v__1,v__1,v_12,v_x,v_y,v_z) [-1 + v_x >= 0 (?,1) && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && v__01 + -1*v__1 >= 0 && -1 + v__0 >= 0 && nondef_1 = 0] 18. eval_p3_bb3_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_bb6_in(v__0,v__01,v__1,v__1,v_12,v_x,v_y,v_z) [-1 + v_x >= 0 (?,1) && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && v__01 + -1*v__1 >= 0 && -1 + v__0 >= 0 && 0 >= v__1] 19. eval_p3_bb4_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_15(v__0,v__01,v__1,v__3,-1 + v__1,v_x,v_y,v_z) [-1 + v_x >= 0 (?,1) && -2 + v__1 + v_x >= 0 && -2 + v__01 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && v__01 + -1*v__1 >= 0 && -1 + v__1 >= 0 && -2 + v__01 + v__1 >= 0 && -2 + v__0 + v__1 >= 0 && -1 + v__01 >= 0 && -2 + v__0 + v__01 >= 0 && -1 + v__0 >= 0] 20. eval_p3_15(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_16(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) [-1 + v_x >= 0 (?,1) && -1 + v_12 + v_x >= 0 && -2 + v__1 + v_x >= 0 && -2 + v__01 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + -1*v_12 + v__1 >= 0 && -1 + -1*v_12 + v__01 >= 0 && v_12 >= 0 && -1 + v_12 + v__1 >= 0 && 1 + v_12 + -1*v__1 >= 0 && -1 + v_12 + v__01 >= 0 && -1 + v_12 + v__0 >= 0 && v__01 + -1*v__1 >= 0 && -1 + v__1 >= 0 && -2 + v__01 + v__1 >= 0 && -2 + v__0 + v__1 >= 0 && -1 + v__01 >= 0 && -2 + v__0 + v__01 >= 0 && -1 + v__0 >= 0] 21. eval_p3_16(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_bb3_in(v__0,v__01,v_12,v__3,v_12,v_x,v_y,v_z) [-1 + v_x >= 0 (?,1) && -1 + v_12 + v_x >= 0 && -2 + v__1 + v_x >= 0 && -2 + v__01 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + -1*v_12 + v__1 >= 0 && -1 + -1*v_12 + v__01 >= 0 && v_12 >= 0 && -1 + v_12 + v__1 >= 0 && 1 + v_12 + -1*v__1 >= 0 && -1 + v_12 + v__01 >= 0 && -1 + v_12 + v__0 >= 0 && v__01 + -1*v__1 >= 0 && -1 + v__1 >= 0 && -2 + v__01 + v__1 >= 0 && -2 + v__0 + v__1 >= 0 && -1 + v__01 >= 0 && -2 + v__0 + v__01 >= 0 && -1 + v__0 >= 0] 22. eval_p3_bb5_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_bb6_in(v__0,v__01,v__1,1 + v__01,v_12,v_x,v_y,v_z) [-1 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= 0 && -1 >= nondef_2] (?,1) 23. eval_p3_bb5_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_bb6_in(v__0,v__01,v__1,1 + v__01,v_12,v_x,v_y,v_z) [-1 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= 0 && -1 + nondef_2 >= 0] (?,1) 24. eval_p3_bb5_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_bb6_in(v__0,v__01,v__1,v_z,v_12,v_x,v_y,v_z) [-1 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= 0 && nondef_2 = 0] (?,1) 25. eval_p3_bb6_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_bb1_in(-1 + v__0,v__3,v__1,v__3,v_12,v_x,v_y,v_z) [-1 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= 0] (?,1) 26. eval_p3_bb7_in(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) -> eval_p3_stop(v__0,v__01,v__1,v__3,v_12,v_x,v_y,v_z) [-1*v__0 + v_x >= 0 && -1*v__0 >= 0] (1,1) Signature: {(eval_p3_0,8) ;(eval_p3_1,8) ;(eval_p3_15,8) ;(eval_p3_16,8) ;(eval_p3_2,8) ;(eval_p3_3,8) ;(eval_p3_4,8) ;(eval_p3_5,8) ;(eval_p3_6,8) ;(eval_p3_7,8) ;(eval_p3_bb0_in,8) ;(eval_p3_bb1_in,8) ;(eval_p3_bb2_in,8) ;(eval_p3_bb3_in,8) ;(eval_p3_bb4_in,8) ;(eval_p3_bb5_in,8) ;(eval_p3_bb6_in,8) ;(eval_p3_bb7_in,8) ;(eval_p3_start,8) ;(eval_p3_stop,8)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10,11},10->{12,13,14},11->{26},12->{15 ,16,17,18},13->{15,16,17,18},14->{22,23,24},15->{19},16->{19},17->{25},18->{25},19->{20},20->{21},21->{15,16 ,17,18},22->{25},23->{25},24->{25},25->{10,11},26->{}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26] | `- p:[10,25,17,12,13,21,20,19,15,16,18,22,14,23,24] c: [25] | `- p:[15,21,20,19,16] c: [21] YES