YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. eval_sipmabubble_start(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_bb0_in(v_24,v_i_0,v_j_0,v_n) True (1,1) 1. eval_sipmabubble_bb0_in(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_0(v_24,v_i_0,v_j_0,v_n) True (?,1) 2. eval_sipmabubble_0(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_1(v_24,v_i_0,v_j_0,v_n) True (?,1) 3. eval_sipmabubble_1(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_2(v_24,v_i_0,v_j_0,v_n) True (?,1) 4. eval_sipmabubble_2(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_3(v_24,v_i_0,v_j_0,v_n) True (?,1) 5. eval_sipmabubble_3(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_4(v_24,v_i_0,v_j_0,v_n) True (?,1) 6. eval_sipmabubble_4(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_5(v_24,v_i_0,v_j_0,v_n) True (?,1) 7. eval_sipmabubble_5(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_6(v_24,v_i_0,v_j_0,v_n) True (?,1) 8. eval_sipmabubble_6(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_bb1_in(v_24,v_n,v_j_0,v_n) True (?,1) 9. eval_sipmabubble_bb1_in(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_bb2_in(v_24,v_i_0,0,v_n) [-1*v_i_0 + v_n >= 0 && v_i_0 >= 0] (?,1) 10. eval_sipmabubble_bb1_in(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_bb7_in(v_24,v_i_0,v_j_0,v_n) [-1*v_i_0 + v_n >= 0 && -1 >= v_i_0] (?,1) 11. eval_sipmabubble_bb2_in(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_bb3_in(v_24,v_i_0,v_j_0,v_n) [v_n >= 0 (?,1) && v_j_0 + v_n >= 0 && -1*v_j_0 + v_n >= 0 && v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && v_i_0 + -1*v_j_0 >= 0 && v_j_0 >= 0 && v_i_0 + v_j_0 >= 0 && v_i_0 >= 0 && -1 + v_i_0 >= v_j_0] 12. eval_sipmabubble_bb2_in(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_bb6_in(v_24,v_i_0,v_j_0,v_n) [v_n >= 0 (?,1) && v_j_0 + v_n >= 0 && -1*v_j_0 + v_n >= 0 && v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && v_i_0 + -1*v_j_0 >= 0 && v_j_0 >= 0 && v_i_0 + v_j_0 >= 0 && v_i_0 >= 0 && -1 + v_j_0 >= -1 + v_i_0] 13. eval_sipmabubble_bb3_in(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_bb4_in(v_24,v_i_0,v_j_0,v_n) [-1 + v_n >= 0 (?,1) && -1 + v_j_0 + v_n >= 0 && -1 + -1*v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && -1 + v_i_0 + -1*v_j_0 >= 0 && v_j_0 >= 0 && -1 + v_i_0 + v_j_0 >= 0 && -1 + v_i_0 >= 0 && -1 + nondef_0 >= nondef_1] 14. eval_sipmabubble_bb3_in(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_bb5_in(v_24,v_i_0,v_j_0,v_n) [-1 + v_n >= 0 (?,1) && -1 + v_j_0 + v_n >= 0 && -1 + -1*v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && -1 + v_i_0 + -1*v_j_0 >= 0 && v_j_0 >= 0 && -1 + v_i_0 + v_j_0 >= 0 && -1 + v_i_0 >= 0 && nondef_1 >= nondef_0] 15. eval_sipmabubble_bb4_in(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_bb5_in(v_24,v_i_0,v_j_0,v_n) [-1 + v_n >= 0 (?,1) && -1 + v_j_0 + v_n >= 0 && -1 + -1*v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && -1 + v_i_0 + -1*v_j_0 >= 0 && v_j_0 >= 0 && -1 + v_i_0 + v_j_0 >= 0 && -1 + v_i_0 >= 0] 16. eval_sipmabubble_bb5_in(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_bb2_in(v_24,v_i_0,1 + v_j_0,v_n) [-1 + v_n >= 0 (?,1) && -1 + v_j_0 + v_n >= 0 && -1 + -1*v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && -1 + v_i_0 + -1*v_j_0 >= 0 && v_j_0 >= 0 && -1 + v_i_0 + v_j_0 >= 0 && -1 + v_i_0 >= 0] 17. eval_sipmabubble_bb6_in(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_29(-1 + v_i_0,v_i_0,v_j_0,v_n) [v_n >= 0 (?,1) && v_j_0 + v_n >= 0 && -1*v_j_0 + v_n >= 0 && v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && v_i_0 + -1*v_j_0 >= 0 && v_j_0 >= 0 && v_i_0 + v_j_0 >= 0 && -1*v_i_0 + v_j_0 >= 0 && v_i_0 >= 0] 18. eval_sipmabubble_29(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_30(v_24,v_i_0,v_j_0,v_n) [v_n >= 0 (?,1) && v_j_0 + v_n >= 0 && -1*v_j_0 + v_n >= 0 && v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && 1 + v_24 + v_n >= 0 && -1 + -1*v_24 + v_n >= 0 && v_i_0 + -1*v_j_0 >= 0 && 1 + v_24 + -1*v_j_0 >= 0 && v_j_0 >= 0 && v_i_0 + v_j_0 >= 0 && -1*v_i_0 + v_j_0 >= 0 && 1 + v_24 + v_j_0 >= 0 && -1 + -1*v_24 + v_j_0 >= 0 && 1 + v_24 + -1*v_i_0 >= 0 && v_i_0 >= 0 && 1 + v_24 + v_i_0 >= 0 && -1 + -1*v_24 + v_i_0 >= 0 && 1 + v_24 >= 0] 19. eval_sipmabubble_30(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_bb1_in(v_24,v_24,v_j_0,v_n) [v_n >= 0 (?,1) && v_j_0 + v_n >= 0 && -1*v_j_0 + v_n >= 0 && v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && 1 + v_24 + v_n >= 0 && -1 + -1*v_24 + v_n >= 0 && v_i_0 + -1*v_j_0 >= 0 && 1 + v_24 + -1*v_j_0 >= 0 && v_j_0 >= 0 && v_i_0 + v_j_0 >= 0 && -1*v_i_0 + v_j_0 >= 0 && 1 + v_24 + v_j_0 >= 0 && -1 + -1*v_24 + v_j_0 >= 0 && 1 + v_24 + -1*v_i_0 >= 0 && v_i_0 >= 0 && 1 + v_24 + v_i_0 >= 0 && -1 + -1*v_24 + v_i_0 >= 0 && 1 + v_24 >= 0] 20. eval_sipmabubble_bb7_in(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_stop(v_24,v_i_0,v_j_0,v_n) [-1*v_i_0 + v_n >= 0 && -1 + -1*v_i_0 >= 0] (?,1) Signature: {(eval_sipmabubble_0,4) ;(eval_sipmabubble_1,4) ;(eval_sipmabubble_2,4) ;(eval_sipmabubble_29,4) ;(eval_sipmabubble_3,4) ;(eval_sipmabubble_30,4) ;(eval_sipmabubble_4,4) ;(eval_sipmabubble_5,4) ;(eval_sipmabubble_6,4) ;(eval_sipmabubble_bb0_in,4) ;(eval_sipmabubble_bb1_in,4) ;(eval_sipmabubble_bb2_in,4) ;(eval_sipmabubble_bb3_in,4) ;(eval_sipmabubble_bb4_in,4) ;(eval_sipmabubble_bb5_in,4) ;(eval_sipmabubble_bb6_in,4) ;(eval_sipmabubble_bb7_in,4) ;(eval_sipmabubble_start,4) ;(eval_sipmabubble_stop,4)} 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->{17},13->{15},14->{16},15->{16},16->{11,12},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_sipmabubble_start(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_bb0_in(v_24,v_i_0,v_j_0,v_n) True (1,1) 1. eval_sipmabubble_bb0_in(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_0(v_24,v_i_0,v_j_0,v_n) True (1,1) 2. eval_sipmabubble_0(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_1(v_24,v_i_0,v_j_0,v_n) True (1,1) 3. eval_sipmabubble_1(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_2(v_24,v_i_0,v_j_0,v_n) True (1,1) 4. eval_sipmabubble_2(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_3(v_24,v_i_0,v_j_0,v_n) True (1,1) 5. eval_sipmabubble_3(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_4(v_24,v_i_0,v_j_0,v_n) True (1,1) 6. eval_sipmabubble_4(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_5(v_24,v_i_0,v_j_0,v_n) True (1,1) 7. eval_sipmabubble_5(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_6(v_24,v_i_0,v_j_0,v_n) True (1,1) 8. eval_sipmabubble_6(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_bb1_in(v_24,v_n,v_j_0,v_n) True (1,1) 9. eval_sipmabubble_bb1_in(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_bb2_in(v_24,v_i_0,0,v_n) [-1*v_i_0 + v_n >= 0 && v_i_0 >= 0] (?,1) 10. eval_sipmabubble_bb1_in(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_bb7_in(v_24,v_i_0,v_j_0,v_n) [-1*v_i_0 + v_n >= 0 && -1 >= v_i_0] (1,1) 11. eval_sipmabubble_bb2_in(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_bb3_in(v_24,v_i_0,v_j_0,v_n) [v_n >= 0 (?,1) && v_j_0 + v_n >= 0 && -1*v_j_0 + v_n >= 0 && v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && v_i_0 + -1*v_j_0 >= 0 && v_j_0 >= 0 && v_i_0 + v_j_0 >= 0 && v_i_0 >= 0 && -1 + v_i_0 >= v_j_0] 12. eval_sipmabubble_bb2_in(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_bb6_in(v_24,v_i_0,v_j_0,v_n) [v_n >= 0 (?,1) && v_j_0 + v_n >= 0 && -1*v_j_0 + v_n >= 0 && v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && v_i_0 + -1*v_j_0 >= 0 && v_j_0 >= 0 && v_i_0 + v_j_0 >= 0 && v_i_0 >= 0 && -1 + v_j_0 >= -1 + v_i_0] 13. eval_sipmabubble_bb3_in(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_bb4_in(v_24,v_i_0,v_j_0,v_n) [-1 + v_n >= 0 (?,1) && -1 + v_j_0 + v_n >= 0 && -1 + -1*v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && -1 + v_i_0 + -1*v_j_0 >= 0 && v_j_0 >= 0 && -1 + v_i_0 + v_j_0 >= 0 && -1 + v_i_0 >= 0 && -1 + nondef_0 >= nondef_1] 14. eval_sipmabubble_bb3_in(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_bb5_in(v_24,v_i_0,v_j_0,v_n) [-1 + v_n >= 0 (?,1) && -1 + v_j_0 + v_n >= 0 && -1 + -1*v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && -1 + v_i_0 + -1*v_j_0 >= 0 && v_j_0 >= 0 && -1 + v_i_0 + v_j_0 >= 0 && -1 + v_i_0 >= 0 && nondef_1 >= nondef_0] 15. eval_sipmabubble_bb4_in(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_bb5_in(v_24,v_i_0,v_j_0,v_n) [-1 + v_n >= 0 (?,1) && -1 + v_j_0 + v_n >= 0 && -1 + -1*v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && -1 + v_i_0 + -1*v_j_0 >= 0 && v_j_0 >= 0 && -1 + v_i_0 + v_j_0 >= 0 && -1 + v_i_0 >= 0] 16. eval_sipmabubble_bb5_in(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_bb2_in(v_24,v_i_0,1 + v_j_0,v_n) [-1 + v_n >= 0 (?,1) && -1 + v_j_0 + v_n >= 0 && -1 + -1*v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && -1 + v_i_0 + -1*v_j_0 >= 0 && v_j_0 >= 0 && -1 + v_i_0 + v_j_0 >= 0 && -1 + v_i_0 >= 0] 17. eval_sipmabubble_bb6_in(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_29(-1 + v_i_0,v_i_0,v_j_0,v_n) [v_n >= 0 (?,1) && v_j_0 + v_n >= 0 && -1*v_j_0 + v_n >= 0 && v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && v_i_0 + -1*v_j_0 >= 0 && v_j_0 >= 0 && v_i_0 + v_j_0 >= 0 && -1*v_i_0 + v_j_0 >= 0 && v_i_0 >= 0] 18. eval_sipmabubble_29(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_30(v_24,v_i_0,v_j_0,v_n) [v_n >= 0 (?,1) && v_j_0 + v_n >= 0 && -1*v_j_0 + v_n >= 0 && v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && 1 + v_24 + v_n >= 0 && -1 + -1*v_24 + v_n >= 0 && v_i_0 + -1*v_j_0 >= 0 && 1 + v_24 + -1*v_j_0 >= 0 && v_j_0 >= 0 && v_i_0 + v_j_0 >= 0 && -1*v_i_0 + v_j_0 >= 0 && 1 + v_24 + v_j_0 >= 0 && -1 + -1*v_24 + v_j_0 >= 0 && 1 + v_24 + -1*v_i_0 >= 0 && v_i_0 >= 0 && 1 + v_24 + v_i_0 >= 0 && -1 + -1*v_24 + v_i_0 >= 0 && 1 + v_24 >= 0] 19. eval_sipmabubble_30(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_bb1_in(v_24,v_24,v_j_0,v_n) [v_n >= 0 (?,1) && v_j_0 + v_n >= 0 && -1*v_j_0 + v_n >= 0 && v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && 1 + v_24 + v_n >= 0 && -1 + -1*v_24 + v_n >= 0 && v_i_0 + -1*v_j_0 >= 0 && 1 + v_24 + -1*v_j_0 >= 0 && v_j_0 >= 0 && v_i_0 + v_j_0 >= 0 && -1*v_i_0 + v_j_0 >= 0 && 1 + v_24 + v_j_0 >= 0 && -1 + -1*v_24 + v_j_0 >= 0 && 1 + v_24 + -1*v_i_0 >= 0 && v_i_0 >= 0 && 1 + v_24 + v_i_0 >= 0 && -1 + -1*v_24 + v_i_0 >= 0 && 1 + v_24 >= 0] 20. eval_sipmabubble_bb7_in(v_24,v_i_0,v_j_0,v_n) -> eval_sipmabubble_stop(v_24,v_i_0,v_j_0,v_n) [-1*v_i_0 + v_n >= 0 && -1 + -1*v_i_0 >= 0] (1,1) Signature: {(eval_sipmabubble_0,4) ;(eval_sipmabubble_1,4) ;(eval_sipmabubble_2,4) ;(eval_sipmabubble_29,4) ;(eval_sipmabubble_3,4) ;(eval_sipmabubble_30,4) ;(eval_sipmabubble_4,4) ;(eval_sipmabubble_5,4) ;(eval_sipmabubble_6,4) ;(eval_sipmabubble_bb0_in,4) ;(eval_sipmabubble_bb1_in,4) ;(eval_sipmabubble_bb2_in,4) ;(eval_sipmabubble_bb3_in,4) ;(eval_sipmabubble_bb4_in,4) ;(eval_sipmabubble_bb5_in,4) ;(eval_sipmabubble_bb6_in,4) ;(eval_sipmabubble_bb7_in,4) ;(eval_sipmabubble_start,4) ;(eval_sipmabubble_stop,4)} 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->{17},13->{15},14->{16},15->{16},16->{11,12},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:[9,19,18,17,12,16,14,11,15,13] c: [19] | `- p:[11,16,14,15,13] c: [16] YES