YES * Step 1: FromIts YES + Considered Problem: Rules: 0. eval_insertsort_start(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb0_in(v_20,v_3,v_i_0,v_j_0,v_length) True (1,1) 1. eval_insertsort_bb0_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_0(v_20,v_3,v_i_0,v_j_0,v_length) True (?,1) 2. eval_insertsort_0(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_1(v_20,v_3,v_i_0,v_j_0,v_length) True (?,1) 3. eval_insertsort_1(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_2(v_20,v_3,v_i_0,v_j_0,v_length) True (?,1) 4. eval_insertsort_2(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_3(v_20,v_3,v_i_0,v_j_0,v_length) True (?,1) 5. eval_insertsort_3(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_4(v_20,v_3,v_i_0,v_j_0,v_length) True (?,1) 6. eval_insertsort_4(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_5(v_20,v_3,v_i_0,v_j_0,v_length) True (?,1) 7. eval_insertsort_5(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_6(v_20,v_3,v_i_0,v_j_0,v_length) True (?,1) 8. eval_insertsort_6(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb1_in(v_20,v_3,1,v_j_0,v_length) True (?,1) 9. eval_insertsort_bb1_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb2_in(v_20,v_3,v_i_0,v_j_0,v_length) [-1 + v_length >= v_i_0] (?,1) 10. eval_insertsort_bb1_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb7_in(v_20,v_3,v_i_0,v_j_0,v_length) [v_i_0 >= v_length] (?,1) 11. eval_insertsort_bb2_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb3_in(v_20,nondef_0,v_i_0,-1 + v_i_0,v_length) True (?,1) 12. eval_insertsort_bb3_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb4_in(v_20,v_3,v_i_0,v_j_0,v_length) [v_j_0 >= 0] (?,1) 13. eval_insertsort_bb3_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb6_in(v_20,v_3,v_i_0,v_j_0,v_length) [-1 >= v_j_0] (?,1) 14. eval_insertsort_bb4_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb5_in(v_20,v_3,v_i_0,v_j_0,v_length) [-1 + nondef_1 >= v_3] (?,1) 15. eval_insertsort_bb4_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb6_in(v_20,v_3,v_i_0,v_j_0,v_length) [v_3 >= nondef_1] (?,1) 16. eval_insertsort_bb5_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb3_in(v_20,v_3,v_i_0,-1 + v_j_0,v_length) True (?,1) 17. eval_insertsort_bb6_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_25(1 + v_i_0,v_3,v_i_0,v_j_0,v_length) True (?,1) 18. eval_insertsort_25(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_26(v_20,v_3,v_i_0,v_j_0,v_length) True (?,1) 19. eval_insertsort_26(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb1_in(v_20,v_3,v_20,v_j_0,v_length) True (?,1) 20. eval_insertsort_bb7_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_stop(v_20,v_3,v_i_0,v_j_0,v_length) True (?,1) Signature: {(eval_insertsort_0,5) ;(eval_insertsort_1,5) ;(eval_insertsort_2,5) ;(eval_insertsort_25,5) ;(eval_insertsort_26,5) ;(eval_insertsort_3,5) ;(eval_insertsort_4,5) ;(eval_insertsort_5,5) ;(eval_insertsort_6,5) ;(eval_insertsort_bb0_in,5) ;(eval_insertsort_bb1_in,5) ;(eval_insertsort_bb2_in,5) ;(eval_insertsort_bb3_in,5) ;(eval_insertsort_bb4_in,5) ;(eval_insertsort_bb5_in,5) ;(eval_insertsort_bb6_in,5) ;(eval_insertsort_bb7_in,5) ;(eval_insertsort_start,5) ;(eval_insertsort_stop,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9,10},9->{11},10->{20},11->{12,13},12->{14 ,15},13->{17},14->{16},15->{17},16->{12,13},17->{18},18->{19},19->{9,10},20->{}] + Applied Processor: FromIts + Details: () * Step 2: Decompose YES + Considered Problem: Rules: eval_insertsort_start(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb0_in(v_20,v_3,v_i_0,v_j_0 ,v_length) True eval_insertsort_bb0_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_0(v_20,v_3,v_i_0,v_j_0 ,v_length) True eval_insertsort_0(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_1(v_20,v_3,v_i_0,v_j_0 ,v_length) True eval_insertsort_1(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_2(v_20,v_3,v_i_0,v_j_0 ,v_length) True eval_insertsort_2(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_3(v_20,v_3,v_i_0,v_j_0 ,v_length) True eval_insertsort_3(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_4(v_20,v_3,v_i_0,v_j_0 ,v_length) True eval_insertsort_4(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_5(v_20,v_3,v_i_0,v_j_0 ,v_length) True eval_insertsort_5(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_6(v_20,v_3,v_i_0,v_j_0 ,v_length) True eval_insertsort_6(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb1_in(v_20,v_3,1,v_j_0 ,v_length) True eval_insertsort_bb1_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb2_in(v_20,v_3,v_i_0,v_j_0 ,v_length) [-1 + v_length >= v_i_0] eval_insertsort_bb1_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb7_in(v_20,v_3,v_i_0,v_j_0 ,v_length) [v_i_0 >= v_length] eval_insertsort_bb2_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb3_in(v_20,nondef_0,v_i_0 ,-1 + v_i_0 ,v_length) True eval_insertsort_bb3_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb4_in(v_20,v_3,v_i_0,v_j_0 ,v_length) [v_j_0 >= 0] eval_insertsort_bb3_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb6_in(v_20,v_3,v_i_0,v_j_0 ,v_length) [-1 >= v_j_0] eval_insertsort_bb4_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb5_in(v_20,v_3,v_i_0,v_j_0 ,v_length) [-1 + nondef_1 >= v_3] eval_insertsort_bb4_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb6_in(v_20,v_3,v_i_0,v_j_0 ,v_length) [v_3 >= nondef_1] eval_insertsort_bb5_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb3_in(v_20,v_3,v_i_0,-1 + v_j_0 ,v_length) True eval_insertsort_bb6_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_25(1 + v_i_0,v_3,v_i_0,v_j_0 ,v_length) True eval_insertsort_25(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_26(v_20,v_3,v_i_0,v_j_0 ,v_length) True eval_insertsort_26(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb1_in(v_20,v_3,v_20,v_j_0 ,v_length) True eval_insertsort_bb7_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_stop(v_20,v_3,v_i_0,v_j_0 ,v_length) True Signature: {(eval_insertsort_0,5) ;(eval_insertsort_1,5) ;(eval_insertsort_2,5) ;(eval_insertsort_25,5) ;(eval_insertsort_26,5) ;(eval_insertsort_3,5) ;(eval_insertsort_4,5) ;(eval_insertsort_5,5) ;(eval_insertsort_6,5) ;(eval_insertsort_bb0_in,5) ;(eval_insertsort_bb1_in,5) ;(eval_insertsort_bb2_in,5) ;(eval_insertsort_bb3_in,5) ;(eval_insertsort_bb4_in,5) ;(eval_insertsort_bb5_in,5) ;(eval_insertsort_bb6_in,5) ;(eval_insertsort_bb7_in,5) ;(eval_insertsort_start,5) ;(eval_insertsort_stop,5)} Rule Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9,10},9->{11},10->{20},11->{12,13},12->{14 ,15},13->{17},14->{16},15->{17},16->{12,13},17->{18},18->{19},19->{9,10},20->{}] + Applied Processor: Decompose NoGreedy + 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:[9,19,18,17,13,11,16,14,12,15] c: [9,11,13,15,17,18,19] | `- p:[12,16,14] c: [12,14,16] * Step 3: CloseWith YES + Considered Problem: (Rules: eval_insertsort_start(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb0_in(v_20,v_3,v_i_0,v_j_0 ,v_length) True eval_insertsort_bb0_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_0(v_20,v_3,v_i_0,v_j_0 ,v_length) True eval_insertsort_0(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_1(v_20,v_3,v_i_0,v_j_0 ,v_length) True eval_insertsort_1(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_2(v_20,v_3,v_i_0,v_j_0 ,v_length) True eval_insertsort_2(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_3(v_20,v_3,v_i_0,v_j_0 ,v_length) True eval_insertsort_3(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_4(v_20,v_3,v_i_0,v_j_0 ,v_length) True eval_insertsort_4(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_5(v_20,v_3,v_i_0,v_j_0 ,v_length) True eval_insertsort_5(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_6(v_20,v_3,v_i_0,v_j_0 ,v_length) True eval_insertsort_6(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb1_in(v_20,v_3,1,v_j_0 ,v_length) True eval_insertsort_bb1_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb2_in(v_20,v_3,v_i_0,v_j_0 ,v_length) [-1 + v_length >= v_i_0] eval_insertsort_bb1_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb7_in(v_20,v_3,v_i_0,v_j_0 ,v_length) [v_i_0 >= v_length] eval_insertsort_bb2_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb3_in(v_20,nondef_0,v_i_0 ,-1 + v_i_0 ,v_length) True eval_insertsort_bb3_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb4_in(v_20,v_3,v_i_0,v_j_0 ,v_length) [v_j_0 >= 0] eval_insertsort_bb3_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb6_in(v_20,v_3,v_i_0,v_j_0 ,v_length) [-1 >= v_j_0] eval_insertsort_bb4_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb5_in(v_20,v_3,v_i_0,v_j_0 ,v_length) [-1 + nondef_1 >= v_3] eval_insertsort_bb4_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb6_in(v_20,v_3,v_i_0,v_j_0 ,v_length) [v_3 >= nondef_1] eval_insertsort_bb5_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb3_in(v_20,v_3,v_i_0,-1 + v_j_0 ,v_length) True eval_insertsort_bb6_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_25(1 + v_i_0,v_3,v_i_0,v_j_0 ,v_length) True eval_insertsort_25(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_26(v_20,v_3,v_i_0,v_j_0 ,v_length) True eval_insertsort_26(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_bb1_in(v_20,v_3,v_20,v_j_0 ,v_length) True eval_insertsort_bb7_in(v_20,v_3,v_i_0,v_j_0,v_length) -> eval_insertsort_stop(v_20,v_3,v_i_0,v_j_0 ,v_length) True Signature: {(eval_insertsort_0,5) ;(eval_insertsort_1,5) ;(eval_insertsort_2,5) ;(eval_insertsort_25,5) ;(eval_insertsort_26,5) ;(eval_insertsort_3,5) ;(eval_insertsort_4,5) ;(eval_insertsort_5,5) ;(eval_insertsort_6,5) ;(eval_insertsort_bb0_in,5) ;(eval_insertsort_bb1_in,5) ;(eval_insertsort_bb2_in,5) ;(eval_insertsort_bb3_in,5) ;(eval_insertsort_bb4_in,5) ;(eval_insertsort_bb5_in,5) ;(eval_insertsort_bb6_in,5) ;(eval_insertsort_bb7_in,5) ;(eval_insertsort_start,5) ;(eval_insertsort_stop,5)} Rule Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9,10},9->{11},10->{20},11->{12,13},12->{14 ,15},13->{17},14->{16},15->{17},16->{12,13},17->{18},18->{19},19->{9,10},20->{}] ,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:[9,19,18,17,13,11,16,14,12,15] c: [9,11,13,15,17,18,19] | `- p:[12,16,14] c: [12,14,16]) + Applied Processor: CloseWith True + Details: () YES