YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. eval_complex_start(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_bb0_in(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) True (1,1) 1. eval_complex_bb0_in(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_0(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) True (?,1) 2. eval_complex_0(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_1(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) True (?,1) 3. eval_complex_1(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_2(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) True (?,1) 4. eval_complex_2(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_3(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) True (?,1) 5. eval_complex_3(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_4(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) True (?,1) 6. eval_complex_4(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_5(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) True (?,1) 7. eval_complex_5(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_6(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) True (?,1) 8. eval_complex_6(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_bb1_in(v_a,v_b,v__1,v__12,v_10,v_9,v_a,v_b) True (?,1) 9. eval_complex_bb1_in(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_bb2_in(v__0,v__01,v__0,v__01,v_10,v_9,v_a,v_b) [v__0 + -1*v_a >= 0 && 29 >= v__0] (?,1) 10. eval_complex_bb1_in(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_bb5_in(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) [v__0 + -1*v_a >= 0 && v__0 >= 30] (?,1) 11. eval_complex_bb2_in(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_bb3_in(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) [29 + -1*v_a >= 0 (?,1) && v__1 + -1*v_a >= 0 && v__0 + -1*v_a >= 0 && 58 + -1*v__0 + -1*v_a >= 0 && -1*v__01 + v__12 >= 0 && -1*v__0 + v__1 >= 0 && 29 + -1*v__0 >= 0 && -1 + v__1 >= v__12] 12. eval_complex_bb2_in(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_bb4_in(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) [29 + -1*v_a >= 0 (?,1) && v__1 + -1*v_a >= 0 && v__0 + -1*v_a >= 0 && 58 + -1*v__0 + -1*v_a >= 0 && -1*v__01 + v__12 >= 0 && -1*v__0 + v__1 >= 0 && 29 + -1*v__0 >= 0 && v__12 >= v__1] 13. eval_complex_bb3_in(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_bb2_in(v__0,v__01,1 + v__1,7 + v__12,v_10,v_9,v_a,v_b) [29 + -1*v_a >= 0 (?,1) && v__1 + -1*v_a >= 0 && v__0 + -1*v_a >= 0 && 58 + -1*v__0 + -1*v_a >= 0 && -1 + v__1 + -1*v__12 >= 0 && -1*v__01 + v__12 >= 0 && -1 + -1*v__01 + v__1 >= 0 && -1*v__0 + v__1 >= 0 && 29 + -1*v__0 >= 0 && -1 + v__12 >= 5 && 6 + v__12 >= 12] 14. eval_complex_bb3_in(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_bb2_in(v__0,v__01,1 + v__1,2 + v__12,v_10,v_9,v_a,v_b) [29 + -1*v_a >= 0 (?,1) && v__1 + -1*v_a >= 0 && v__0 + -1*v_a >= 0 && 58 + -1*v__0 + -1*v_a >= 0 && -1 + v__1 + -1*v__12 >= 0 && -1*v__01 + v__12 >= 0 && -1 + -1*v__01 + v__1 >= 0 && -1*v__0 + v__1 >= 0 && 29 + -1*v__0 >= 0 && 5 >= v__12 && 9 >= 2 + v__12] 15. eval_complex_bb4_in(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_15(v__0,v__01,v__1,v__12,v_10,2 + v__1,v_a,v_b) [29 + -1*v_a >= 0 (?,1) && v__12 + -1*v_a >= 0 && v__1 + -1*v_a >= 0 && v__0 + -1*v_a >= 0 && 58 + -1*v__0 + -1*v_a >= 0 && -1*v__1 + v__12 >= 0 && -1*v__01 + v__12 >= 0 && -1*v__0 + v__12 >= 0 && -1*v__0 + v__1 >= 0 && 29 + -1*v__0 >= 0] 16. eval_complex_15(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_16(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) [29 + -1*v_a >= 0 (?,1) && -2 + v_9 + -1*v_a >= 0 && v__12 + -1*v_a >= 0 && v__1 + -1*v_a >= 0 && v__0 + -1*v_a >= 0 && 58 + -1*v__0 + -1*v_a >= 0 && 2 + -1*v_9 + v__12 >= 0 && 2 + -1*v_9 + v__1 >= 0 && -2 + v_9 + -1*v__1 >= 0 && -2 + v_9 + -1*v__0 >= 0 && -1*v__1 + v__12 >= 0 && -1*v__01 + v__12 >= 0 && -1*v__0 + v__12 >= 0 && -1*v__0 + v__1 >= 0 && 29 + -1*v__0 >= 0] 17. eval_complex_16(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_17(v__0,v__01,v__1,v__12,-10 + v__12,v_9,v_a,v_b) [29 + -1*v_a >= 0 (?,1) && -2 + v_9 + -1*v_a >= 0 && v__12 + -1*v_a >= 0 && v__1 + -1*v_a >= 0 && v__0 + -1*v_a >= 0 && 58 + -1*v__0 + -1*v_a >= 0 && 2 + -1*v_9 + v__12 >= 0 && 2 + -1*v_9 + v__1 >= 0 && -2 + v_9 + -1*v__1 >= 0 && -2 + v_9 + -1*v__0 >= 0 && -1*v__1 + v__12 >= 0 && -1*v__01 + v__12 >= 0 && -1*v__0 + v__12 >= 0 && -1*v__0 + v__1 >= 0 && 29 + -1*v__0 >= 0] 18. eval_complex_17(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_18(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) [29 + -1*v_a >= 0 (?,1) && -2 + v_9 + -1*v_a >= 0 && 10 + v_10 + -1*v_a >= 0 && v__12 + -1*v_a >= 0 && v__1 + -1*v_a >= 0 && v__0 + -1*v_a >= 0 && 58 + -1*v__0 + -1*v_a >= 0 && 12 + v_10 + -1*v_9 >= 0 && 2 + -1*v_9 + v__12 >= 0 && 2 + -1*v_9 + v__1 >= 0 && -2 + v_9 + -1*v__1 >= 0 && -2 + v_9 + -1*v__0 >= 0 && -10 + -1*v_10 + v__12 >= 0 && 10 + v_10 + -1*v__12 >= 0 && 10 + v_10 + -1*v__1 >= 0 && 10 + v_10 + -1*v__01 >= 0 && 10 + v_10 + -1*v__0 >= 0 && -1*v__1 + v__12 >= 0 && -1*v__01 + v__12 >= 0 && -1*v__0 + v__12 >= 0 && -1*v__0 + v__1 >= 0 && 29 + -1*v__0 >= 0] 19. eval_complex_18(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_bb1_in(v_9,v_10,v__1,v__12,v_10,v_9,v_a,v_b) [29 + -1*v_a >= 0 (?,1) && -2 + v_9 + -1*v_a >= 0 && 10 + v_10 + -1*v_a >= 0 && v__12 + -1*v_a >= 0 && v__1 + -1*v_a >= 0 && v__0 + -1*v_a >= 0 && 58 + -1*v__0 + -1*v_a >= 0 && 12 + v_10 + -1*v_9 >= 0 && 2 + -1*v_9 + v__12 >= 0 && 2 + -1*v_9 + v__1 >= 0 && -2 + v_9 + -1*v__1 >= 0 && -2 + v_9 + -1*v__0 >= 0 && -10 + -1*v_10 + v__12 >= 0 && 10 + v_10 + -1*v__12 >= 0 && 10 + v_10 + -1*v__1 >= 0 && 10 + v_10 + -1*v__01 >= 0 && 10 + v_10 + -1*v__0 >= 0 && -1*v__1 + v__12 >= 0 && -1*v__01 + v__12 >= 0 && -1*v__0 + v__12 >= 0 && -1*v__0 + v__1 >= 0 && 29 + -1*v__0 >= 0] 20. eval_complex_bb5_in(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_stop(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) [v__0 + -1*v_a >= 0 && -30 + v__0 >= 0] (?,1) Signature: {(eval_complex_0,8) ;(eval_complex_1,8) ;(eval_complex_15,8) ;(eval_complex_16,8) ;(eval_complex_17,8) ;(eval_complex_18,8) ;(eval_complex_2,8) ;(eval_complex_3,8) ;(eval_complex_4,8) ;(eval_complex_5,8) ;(eval_complex_6,8) ;(eval_complex_bb0_in,8) ;(eval_complex_bb1_in,8) ;(eval_complex_bb2_in,8) ;(eval_complex_bb3_in,8) ;(eval_complex_bb4_in,8) ;(eval_complex_bb5_in,8) ;(eval_complex_start,8) ;(eval_complex_stop,8)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9,10},9->{11,12},10->{20},11->{13,14} ,12->{15},13->{11,12},14->{11,12},15->{16},16->{17},17->{18},18->{19},19->{9,10},20->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: Looptree YES + Considered Problem: Rules: 0. eval_complex_start(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_bb0_in(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) True (1,1) 1. eval_complex_bb0_in(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_0(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) True (1,1) 2. eval_complex_0(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_1(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) True (1,1) 3. eval_complex_1(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_2(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) True (1,1) 4. eval_complex_2(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_3(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) True (1,1) 5. eval_complex_3(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_4(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) True (1,1) 6. eval_complex_4(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_5(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) True (1,1) 7. eval_complex_5(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_6(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) True (1,1) 8. eval_complex_6(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_bb1_in(v_a,v_b,v__1,v__12,v_10,v_9,v_a,v_b) True (1,1) 9. eval_complex_bb1_in(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_bb2_in(v__0,v__01,v__0,v__01,v_10,v_9,v_a,v_b) [v__0 + -1*v_a >= 0 && 29 >= v__0] (?,1) 10. eval_complex_bb1_in(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_bb5_in(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) [v__0 + -1*v_a >= 0 && v__0 >= 30] (1,1) 11. eval_complex_bb2_in(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_bb3_in(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) [29 + -1*v_a >= 0 (?,1) && v__1 + -1*v_a >= 0 && v__0 + -1*v_a >= 0 && 58 + -1*v__0 + -1*v_a >= 0 && -1*v__01 + v__12 >= 0 && -1*v__0 + v__1 >= 0 && 29 + -1*v__0 >= 0 && -1 + v__1 >= v__12] 12. eval_complex_bb2_in(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_bb4_in(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) [29 + -1*v_a >= 0 (?,1) && v__1 + -1*v_a >= 0 && v__0 + -1*v_a >= 0 && 58 + -1*v__0 + -1*v_a >= 0 && -1*v__01 + v__12 >= 0 && -1*v__0 + v__1 >= 0 && 29 + -1*v__0 >= 0 && v__12 >= v__1] 13. eval_complex_bb3_in(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_bb2_in(v__0,v__01,1 + v__1,7 + v__12,v_10,v_9,v_a,v_b) [29 + -1*v_a >= 0 (?,1) && v__1 + -1*v_a >= 0 && v__0 + -1*v_a >= 0 && 58 + -1*v__0 + -1*v_a >= 0 && -1 + v__1 + -1*v__12 >= 0 && -1*v__01 + v__12 >= 0 && -1 + -1*v__01 + v__1 >= 0 && -1*v__0 + v__1 >= 0 && 29 + -1*v__0 >= 0 && -1 + v__12 >= 5 && 6 + v__12 >= 12] 14. eval_complex_bb3_in(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_bb2_in(v__0,v__01,1 + v__1,2 + v__12,v_10,v_9,v_a,v_b) [29 + -1*v_a >= 0 (?,1) && v__1 + -1*v_a >= 0 && v__0 + -1*v_a >= 0 && 58 + -1*v__0 + -1*v_a >= 0 && -1 + v__1 + -1*v__12 >= 0 && -1*v__01 + v__12 >= 0 && -1 + -1*v__01 + v__1 >= 0 && -1*v__0 + v__1 >= 0 && 29 + -1*v__0 >= 0 && 5 >= v__12 && 9 >= 2 + v__12] 15. eval_complex_bb4_in(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_15(v__0,v__01,v__1,v__12,v_10,2 + v__1,v_a,v_b) [29 + -1*v_a >= 0 (?,1) && v__12 + -1*v_a >= 0 && v__1 + -1*v_a >= 0 && v__0 + -1*v_a >= 0 && 58 + -1*v__0 + -1*v_a >= 0 && -1*v__1 + v__12 >= 0 && -1*v__01 + v__12 >= 0 && -1*v__0 + v__12 >= 0 && -1*v__0 + v__1 >= 0 && 29 + -1*v__0 >= 0] 16. eval_complex_15(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_16(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) [29 + -1*v_a >= 0 (?,1) && -2 + v_9 + -1*v_a >= 0 && v__12 + -1*v_a >= 0 && v__1 + -1*v_a >= 0 && v__0 + -1*v_a >= 0 && 58 + -1*v__0 + -1*v_a >= 0 && 2 + -1*v_9 + v__12 >= 0 && 2 + -1*v_9 + v__1 >= 0 && -2 + v_9 + -1*v__1 >= 0 && -2 + v_9 + -1*v__0 >= 0 && -1*v__1 + v__12 >= 0 && -1*v__01 + v__12 >= 0 && -1*v__0 + v__12 >= 0 && -1*v__0 + v__1 >= 0 && 29 + -1*v__0 >= 0] 17. eval_complex_16(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_17(v__0,v__01,v__1,v__12,-10 + v__12,v_9,v_a,v_b) [29 + -1*v_a >= 0 (?,1) && -2 + v_9 + -1*v_a >= 0 && v__12 + -1*v_a >= 0 && v__1 + -1*v_a >= 0 && v__0 + -1*v_a >= 0 && 58 + -1*v__0 + -1*v_a >= 0 && 2 + -1*v_9 + v__12 >= 0 && 2 + -1*v_9 + v__1 >= 0 && -2 + v_9 + -1*v__1 >= 0 && -2 + v_9 + -1*v__0 >= 0 && -1*v__1 + v__12 >= 0 && -1*v__01 + v__12 >= 0 && -1*v__0 + v__12 >= 0 && -1*v__0 + v__1 >= 0 && 29 + -1*v__0 >= 0] 18. eval_complex_17(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_18(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) [29 + -1*v_a >= 0 (?,1) && -2 + v_9 + -1*v_a >= 0 && 10 + v_10 + -1*v_a >= 0 && v__12 + -1*v_a >= 0 && v__1 + -1*v_a >= 0 && v__0 + -1*v_a >= 0 && 58 + -1*v__0 + -1*v_a >= 0 && 12 + v_10 + -1*v_9 >= 0 && 2 + -1*v_9 + v__12 >= 0 && 2 + -1*v_9 + v__1 >= 0 && -2 + v_9 + -1*v__1 >= 0 && -2 + v_9 + -1*v__0 >= 0 && -10 + -1*v_10 + v__12 >= 0 && 10 + v_10 + -1*v__12 >= 0 && 10 + v_10 + -1*v__1 >= 0 && 10 + v_10 + -1*v__01 >= 0 && 10 + v_10 + -1*v__0 >= 0 && -1*v__1 + v__12 >= 0 && -1*v__01 + v__12 >= 0 && -1*v__0 + v__12 >= 0 && -1*v__0 + v__1 >= 0 && 29 + -1*v__0 >= 0] 19. eval_complex_18(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_bb1_in(v_9,v_10,v__1,v__12,v_10,v_9,v_a,v_b) [29 + -1*v_a >= 0 (?,1) && -2 + v_9 + -1*v_a >= 0 && 10 + v_10 + -1*v_a >= 0 && v__12 + -1*v_a >= 0 && v__1 + -1*v_a >= 0 && v__0 + -1*v_a >= 0 && 58 + -1*v__0 + -1*v_a >= 0 && 12 + v_10 + -1*v_9 >= 0 && 2 + -1*v_9 + v__12 >= 0 && 2 + -1*v_9 + v__1 >= 0 && -2 + v_9 + -1*v__1 >= 0 && -2 + v_9 + -1*v__0 >= 0 && -10 + -1*v_10 + v__12 >= 0 && 10 + v_10 + -1*v__12 >= 0 && 10 + v_10 + -1*v__1 >= 0 && 10 + v_10 + -1*v__01 >= 0 && 10 + v_10 + -1*v__0 >= 0 && -1*v__1 + v__12 >= 0 && -1*v__01 + v__12 >= 0 && -1*v__0 + v__12 >= 0 && -1*v__0 + v__1 >= 0 && 29 + -1*v__0 >= 0] 20. eval_complex_bb5_in(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) -> eval_complex_stop(v__0,v__01,v__1,v__12,v_10,v_9,v_a,v_b) [v__0 + -1*v_a >= 0 && -30 + v__0 >= 0] (1,1) Signature: {(eval_complex_0,8) ;(eval_complex_1,8) ;(eval_complex_15,8) ;(eval_complex_16,8) ;(eval_complex_17,8) ;(eval_complex_18,8) ;(eval_complex_2,8) ;(eval_complex_3,8) ;(eval_complex_4,8) ;(eval_complex_5,8) ;(eval_complex_6,8) ;(eval_complex_bb0_in,8) ;(eval_complex_bb1_in,8) ;(eval_complex_bb2_in,8) ;(eval_complex_bb3_in,8) ;(eval_complex_bb4_in,8) ;(eval_complex_bb5_in,8) ;(eval_complex_start,8) ;(eval_complex_stop,8)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9,10},9->{11,12},10->{20},11->{13,14} ,12->{15},13->{11,12},14->{11,12},15->{16},16->{17},17->{18},18->{19},19->{9,10},20->{}] + 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] | `- p:[9,19,18,17,16,15,12,13,11,14] c: [19] | `- p:[11,13,14] c: [14] | `- p:[11,13] c: [13] YES