YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. eval_realheapsort_step1_start(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb0_in(v_33,v_N,v_j_0,v_k_0) True (1,1) 1. eval_realheapsort_step1_bb0_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_0(v_33,v_N,v_j_0,v_k_0) True (?,1) 2. eval_realheapsort_step1_0(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_1(v_33,v_N,v_j_0,v_k_0) True (?,1) 3. eval_realheapsort_step1_1(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_2(v_33,v_N,v_j_0,v_k_0) True (?,1) 4. eval_realheapsort_step1_2(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb5_in(v_33,v_N,v_j_0,v_k_0) [2 >= v_N] (?,1) 5. eval_realheapsort_step1_2(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb1_in(v_33,v_N,v_j_0,1) [-1 + v_N >= 2] (?,1) 6. eval_realheapsort_step1_bb5_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_stop(v_33,v_N,v_j_0,v_k_0) True (?,1) 7. eval_realheapsort_step1_bb1_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb2_in(v_33,v_N,v_k_0,v_k_0) [-1 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -3 + v_N >= 0 && -1 + v_N >= v_k_0] (?,1) 8. eval_realheapsort_step1_bb2_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1__critedge_in(v_33,v_N,v_j_0,v_k_0) [-1 + v_N + -1*v_k_0 >= 0 (?,1) && -1 + v_k_0 >= 0 && -1*v_j_0 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -1 + v_N + -1*v_j_0 >= 0 && -3 + v_N >= 0 && 0 >= v_j_0] 9. eval_realheapsort_step1_bb2_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb3_in(v_33,v_N,v_j_0,v_k_0) [-1 + v_N + -1*v_k_0 >= 0 (?,1) && -1 + v_k_0 >= 0 && -1*v_j_0 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -1 + v_N + -1*v_j_0 >= 0 && -3 + v_N >= 0 && -1 + v_j_0 >= 0] 10. eval_realheapsort_step1__critedge_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_28(1 + v_k_0,v_N,v_j_0,v_k_0) [-1 + v_N + -1*v_k_0 >= 0 (?,1) && -1 + v_k_0 >= 0 && -1*v_j_0 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -1 + v_N + -1*v_j_0 >= 0 && -3 + v_N >= 0] 11. eval_realheapsort_step1_bb3_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1__critedge_in(v_33,v_N,v_j_0,v_k_0) [-1 + v_N + -1*v_k_0 >= 0 (?,1) && -1 + v_k_0 >= 0 && -2 + v_j_0 + v_k_0 >= 0 && -1*v_j_0 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -1 + v_N + -1*v_j_0 >= 0 && -1 + v_j_0 >= 0 && -4 + v_N + v_j_0 >= 0 && -3 + v_N >= 0 && v_j_0 >= 0 && nondef_0 >= 0 && 1 + -2*nondef_0 + v_j_0 >= 0 && 1 >= 1 + -2*nondef_0 + v_j_0] 12. eval_realheapsort_step1_bb3_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb4_in(v_33,v_N,v_j_0,v_k_0) [-1 + v_N + -1*v_k_0 >= 0 (?,1) && -1 + v_k_0 >= 0 && -2 + v_j_0 + v_k_0 >= 0 && -1*v_j_0 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -1 + v_N + -1*v_j_0 >= 0 && -1 + v_j_0 >= 0 && -4 + v_N + v_j_0 >= 0 && -3 + v_N >= 0 && v_j_0 >= 0 && nondef_0 >= 0 && 1 + -2*nondef_0 + v_j_0 >= 0 && 1 >= 1 + -2*nondef_0 + v_j_0] 13. eval_realheapsort_step1_28(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_29(v_33,v_N,v_j_0,v_k_0) [-1 + v_N + -1*v_k_0 >= 0 (?,1) && -1 + v_33 + -1*v_k_0 >= 0 && -1 + v_k_0 >= 0 && -1*v_j_0 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -3 + v_33 + v_k_0 >= 0 && 1 + -1*v_33 + v_k_0 >= 0 && -1 + v_N + -1*v_j_0 >= 0 && -1 + v_33 + -1*v_j_0 >= 0 && -3 + v_N >= 0 && -5 + v_33 + v_N >= 0 && -1*v_33 + v_N >= 0 && -2 + v_33 >= 0] 14. eval_realheapsort_step1_bb4_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb2_in(v_33,v_N,-1 + nondef_3,v_k_0) [-1 + v_N + -1*v_k_0 >= 0 (?,1) && -1 + v_k_0 >= 0 && -2 + v_j_0 + v_k_0 >= 0 && -1*v_j_0 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -1 + v_N + -1*v_j_0 >= 0 && -1 + v_j_0 >= 0 && -4 + v_N + v_j_0 >= 0 && -3 + v_N >= 0 && v_j_0 >= 0 && nondef_1 >= 0 && 1 + -2*nondef_1 + v_j_0 >= 0 && 1 >= 1 + -2*nondef_1 + v_j_0 && nondef_2 >= 0 && 1 + -2*nondef_2 + v_j_0 >= 0 && 1 >= 1 + -2*nondef_2 + v_j_0 && nondef_3 >= 0 && 1 + -2*nondef_3 + v_j_0 >= 0 && 1 >= 1 + -2*nondef_3 + v_j_0] 15. eval_realheapsort_step1_29(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb1_in(v_33,v_N,v_j_0,v_33) [-1 + v_N + -1*v_k_0 >= 0 (?,1) && -1 + v_33 + -1*v_k_0 >= 0 && -1 + v_k_0 >= 0 && -1*v_j_0 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -3 + v_33 + v_k_0 >= 0 && 1 + -1*v_33 + v_k_0 >= 0 && -1 + v_N + -1*v_j_0 >= 0 && -1 + v_33 + -1*v_j_0 >= 0 && -3 + v_N >= 0 && -5 + v_33 + v_N >= 0 && -1*v_33 + v_N >= 0 && -2 + v_33 >= 0] 16. eval_realheapsort_step1_bb1_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb5_in(v_33,v_N,v_j_0,v_k_0) [-1 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -3 + v_N >= 0 && -1 + v_k_0 >= -1 + v_N] (?,1) Signature: {(eval_realheapsort_step1_0,4) ;(eval_realheapsort_step1_1,4) ;(eval_realheapsort_step1_2,4) ;(eval_realheapsort_step1_28,4) ;(eval_realheapsort_step1_29,4) ;(eval_realheapsort_step1__critedge_in,4) ;(eval_realheapsort_step1_bb0_in,4) ;(eval_realheapsort_step1_bb1_in,4) ;(eval_realheapsort_step1_bb2_in,4) ;(eval_realheapsort_step1_bb3_in,4) ;(eval_realheapsort_step1_bb4_in,4) ;(eval_realheapsort_step1_bb5_in,4) ;(eval_realheapsort_step1_start,4) ;(eval_realheapsort_step1_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5},4->{6},5->{7,16},6->{},7->{8,9},8->{10},9->{11,12},10->{13},11->{10} ,12->{14},13->{15},14->{8,9},15->{7,16},16->{6}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(5,16),(7,8)] * Step 2: FromIts YES + Considered Problem: Rules: 0. eval_realheapsort_step1_start(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb0_in(v_33,v_N,v_j_0,v_k_0) True (1,1) 1. eval_realheapsort_step1_bb0_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_0(v_33,v_N,v_j_0,v_k_0) True (?,1) 2. eval_realheapsort_step1_0(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_1(v_33,v_N,v_j_0,v_k_0) True (?,1) 3. eval_realheapsort_step1_1(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_2(v_33,v_N,v_j_0,v_k_0) True (?,1) 4. eval_realheapsort_step1_2(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb5_in(v_33,v_N,v_j_0,v_k_0) [2 >= v_N] (?,1) 5. eval_realheapsort_step1_2(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb1_in(v_33,v_N,v_j_0,1) [-1 + v_N >= 2] (?,1) 6. eval_realheapsort_step1_bb5_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_stop(v_33,v_N,v_j_0,v_k_0) True (?,1) 7. eval_realheapsort_step1_bb1_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb2_in(v_33,v_N,v_k_0,v_k_0) [-1 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -3 + v_N >= 0 && -1 + v_N >= v_k_0] (?,1) 8. eval_realheapsort_step1_bb2_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1__critedge_in(v_33,v_N,v_j_0,v_k_0) [-1 + v_N + -1*v_k_0 >= 0 (?,1) && -1 + v_k_0 >= 0 && -1*v_j_0 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -1 + v_N + -1*v_j_0 >= 0 && -3 + v_N >= 0 && 0 >= v_j_0] 9. eval_realheapsort_step1_bb2_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb3_in(v_33,v_N,v_j_0,v_k_0) [-1 + v_N + -1*v_k_0 >= 0 (?,1) && -1 + v_k_0 >= 0 && -1*v_j_0 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -1 + v_N + -1*v_j_0 >= 0 && -3 + v_N >= 0 && -1 + v_j_0 >= 0] 10. eval_realheapsort_step1__critedge_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_28(1 + v_k_0,v_N,v_j_0,v_k_0) [-1 + v_N + -1*v_k_0 >= 0 (?,1) && -1 + v_k_0 >= 0 && -1*v_j_0 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -1 + v_N + -1*v_j_0 >= 0 && -3 + v_N >= 0] 11. eval_realheapsort_step1_bb3_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1__critedge_in(v_33,v_N,v_j_0,v_k_0) [-1 + v_N + -1*v_k_0 >= 0 (?,1) && -1 + v_k_0 >= 0 && -2 + v_j_0 + v_k_0 >= 0 && -1*v_j_0 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -1 + v_N + -1*v_j_0 >= 0 && -1 + v_j_0 >= 0 && -4 + v_N + v_j_0 >= 0 && -3 + v_N >= 0 && v_j_0 >= 0 && nondef_0 >= 0 && 1 + -2*nondef_0 + v_j_0 >= 0 && 1 >= 1 + -2*nondef_0 + v_j_0] 12. eval_realheapsort_step1_bb3_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb4_in(v_33,v_N,v_j_0,v_k_0) [-1 + v_N + -1*v_k_0 >= 0 (?,1) && -1 + v_k_0 >= 0 && -2 + v_j_0 + v_k_0 >= 0 && -1*v_j_0 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -1 + v_N + -1*v_j_0 >= 0 && -1 + v_j_0 >= 0 && -4 + v_N + v_j_0 >= 0 && -3 + v_N >= 0 && v_j_0 >= 0 && nondef_0 >= 0 && 1 + -2*nondef_0 + v_j_0 >= 0 && 1 >= 1 + -2*nondef_0 + v_j_0] 13. eval_realheapsort_step1_28(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_29(v_33,v_N,v_j_0,v_k_0) [-1 + v_N + -1*v_k_0 >= 0 (?,1) && -1 + v_33 + -1*v_k_0 >= 0 && -1 + v_k_0 >= 0 && -1*v_j_0 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -3 + v_33 + v_k_0 >= 0 && 1 + -1*v_33 + v_k_0 >= 0 && -1 + v_N + -1*v_j_0 >= 0 && -1 + v_33 + -1*v_j_0 >= 0 && -3 + v_N >= 0 && -5 + v_33 + v_N >= 0 && -1*v_33 + v_N >= 0 && -2 + v_33 >= 0] 14. eval_realheapsort_step1_bb4_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb2_in(v_33,v_N,-1 + nondef_3,v_k_0) [-1 + v_N + -1*v_k_0 >= 0 (?,1) && -1 + v_k_0 >= 0 && -2 + v_j_0 + v_k_0 >= 0 && -1*v_j_0 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -1 + v_N + -1*v_j_0 >= 0 && -1 + v_j_0 >= 0 && -4 + v_N + v_j_0 >= 0 && -3 + v_N >= 0 && v_j_0 >= 0 && nondef_1 >= 0 && 1 + -2*nondef_1 + v_j_0 >= 0 && 1 >= 1 + -2*nondef_1 + v_j_0 && nondef_2 >= 0 && 1 + -2*nondef_2 + v_j_0 >= 0 && 1 >= 1 + -2*nondef_2 + v_j_0 && nondef_3 >= 0 && 1 + -2*nondef_3 + v_j_0 >= 0 && 1 >= 1 + -2*nondef_3 + v_j_0] 15. eval_realheapsort_step1_29(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb1_in(v_33,v_N,v_j_0,v_33) [-1 + v_N + -1*v_k_0 >= 0 (?,1) && -1 + v_33 + -1*v_k_0 >= 0 && -1 + v_k_0 >= 0 && -1*v_j_0 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -3 + v_33 + v_k_0 >= 0 && 1 + -1*v_33 + v_k_0 >= 0 && -1 + v_N + -1*v_j_0 >= 0 && -1 + v_33 + -1*v_j_0 >= 0 && -3 + v_N >= 0 && -5 + v_33 + v_N >= 0 && -1*v_33 + v_N >= 0 && -2 + v_33 >= 0] 16. eval_realheapsort_step1_bb1_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb5_in(v_33,v_N,v_j_0,v_k_0) [-1 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -3 + v_N >= 0 && -1 + v_k_0 >= -1 + v_N] (?,1) Signature: {(eval_realheapsort_step1_0,4) ;(eval_realheapsort_step1_1,4) ;(eval_realheapsort_step1_2,4) ;(eval_realheapsort_step1_28,4) ;(eval_realheapsort_step1_29,4) ;(eval_realheapsort_step1__critedge_in,4) ;(eval_realheapsort_step1_bb0_in,4) ;(eval_realheapsort_step1_bb1_in,4) ;(eval_realheapsort_step1_bb2_in,4) ;(eval_realheapsort_step1_bb3_in,4) ;(eval_realheapsort_step1_bb4_in,4) ;(eval_realheapsort_step1_bb5_in,4) ;(eval_realheapsort_step1_start,4) ;(eval_realheapsort_step1_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5},4->{6},5->{7},6->{},7->{9},8->{10},9->{11,12},10->{13},11->{10},12->{14} ,13->{15},14->{8,9},15->{7,16},16->{6}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: eval_realheapsort_step1_start(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb0_in(v_33,v_N ,v_j_0 ,v_k_0) True eval_realheapsort_step1_bb0_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_0(v_33,v_N,v_j_0 ,v_k_0) True eval_realheapsort_step1_0(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_1(v_33,v_N,v_j_0 ,v_k_0) True eval_realheapsort_step1_1(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_2(v_33,v_N,v_j_0 ,v_k_0) True eval_realheapsort_step1_2(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb5_in(v_33,v_N,v_j_0 ,v_k_0) [2 >= v_N] eval_realheapsort_step1_2(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb1_in(v_33,v_N,v_j_0 ,1) [-1 + v_N >= 2] eval_realheapsort_step1_bb5_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_stop(v_33,v_N,v_j_0 ,v_k_0) True eval_realheapsort_step1_bb1_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb2_in(v_33,v_N,v_k_0 ,v_k_0) [-1 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -3 + v_N >= 0 && -1 + v_N >= v_k_0] eval_realheapsort_step1_bb2_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1__critedge_in(v_33,v_N ,v_j_0 ,v_k_0) [-1 + v_N + -1*v_k_0 >= 0 && -1 + v_k_0 >= 0 && -1*v_j_0 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -1 + v_N + -1*v_j_0 >= 0 && -3 + v_N >= 0 && 0 >= v_j_0] eval_realheapsort_step1_bb2_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb3_in(v_33,v_N,v_j_0 ,v_k_0) [-1 + v_N + -1*v_k_0 >= 0 && -1 + v_k_0 >= 0 && -1*v_j_0 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -1 + v_N + -1*v_j_0 >= 0 && -3 + v_N >= 0 && -1 + v_j_0 >= 0] eval_realheapsort_step1__critedge_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_28(1 + v_k_0,v_N ,v_j_0 ,v_k_0) [-1 + v_N + -1*v_k_0 >= 0 && -1 + v_k_0 >= 0 && -1*v_j_0 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -1 + v_N + -1*v_j_0 >= 0 && -3 + v_N >= 0] eval_realheapsort_step1_bb3_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1__critedge_in(v_33,v_N ,v_j_0 ,v_k_0) [-1 + v_N + -1*v_k_0 >= 0 && -1 + v_k_0 >= 0 && -2 + v_j_0 + v_k_0 >= 0 && -1*v_j_0 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -1 + v_N + -1*v_j_0 >= 0 && -1 + v_j_0 >= 0 && -4 + v_N + v_j_0 >= 0 && -3 + v_N >= 0 && v_j_0 >= 0 && nondef_0 >= 0 && 1 + -2*nondef_0 + v_j_0 >= 0 && 1 >= 1 + -2*nondef_0 + v_j_0] eval_realheapsort_step1_bb3_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb4_in(v_33,v_N,v_j_0 ,v_k_0) [-1 + v_N + -1*v_k_0 >= 0 && -1 + v_k_0 >= 0 && -2 + v_j_0 + v_k_0 >= 0 && -1*v_j_0 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -1 + v_N + -1*v_j_0 >= 0 && -1 + v_j_0 >= 0 && -4 + v_N + v_j_0 >= 0 && -3 + v_N >= 0 && v_j_0 >= 0 && nondef_0 >= 0 && 1 + -2*nondef_0 + v_j_0 >= 0 && 1 >= 1 + -2*nondef_0 + v_j_0] eval_realheapsort_step1_28(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_29(v_33,v_N,v_j_0 ,v_k_0) [-1 + v_N + -1*v_k_0 >= 0 && -1 + v_33 + -1*v_k_0 >= 0 && -1 + v_k_0 >= 0 && -1*v_j_0 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -3 + v_33 + v_k_0 >= 0 && 1 + -1*v_33 + v_k_0 >= 0 && -1 + v_N + -1*v_j_0 >= 0 && -1 + v_33 + -1*v_j_0 >= 0 && -3 + v_N >= 0 && -5 + v_33 + v_N >= 0 && -1*v_33 + v_N >= 0 && -2 + v_33 >= 0] eval_realheapsort_step1_bb4_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb2_in(v_33,v_N ,-1 + nondef_3 ,v_k_0) [-1 + v_N + -1*v_k_0 >= 0 && -1 + v_k_0 >= 0 && -2 + v_j_0 + v_k_0 >= 0 && -1*v_j_0 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -1 + v_N + -1*v_j_0 >= 0 && -1 + v_j_0 >= 0 && -4 + v_N + v_j_0 >= 0 && -3 + v_N >= 0 && v_j_0 >= 0 && nondef_1 >= 0 && 1 + -2*nondef_1 + v_j_0 >= 0 && 1 >= 1 + -2*nondef_1 + v_j_0 && nondef_2 >= 0 && 1 + -2*nondef_2 + v_j_0 >= 0 && 1 >= 1 + -2*nondef_2 + v_j_0 && nondef_3 >= 0 && 1 + -2*nondef_3 + v_j_0 >= 0 && 1 >= 1 + -2*nondef_3 + v_j_0] eval_realheapsort_step1_29(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb1_in(v_33,v_N,v_j_0 ,v_33) [-1 + v_N + -1*v_k_0 >= 0 && -1 + v_33 + -1*v_k_0 >= 0 && -1 + v_k_0 >= 0 && -1*v_j_0 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -3 + v_33 + v_k_0 >= 0 && 1 + -1*v_33 + v_k_0 >= 0 && -1 + v_N + -1*v_j_0 >= 0 && -1 + v_33 + -1*v_j_0 >= 0 && -3 + v_N >= 0 && -5 + v_33 + v_N >= 0 && -1*v_33 + v_N >= 0 && -2 + v_33 >= 0] eval_realheapsort_step1_bb1_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb5_in(v_33,v_N,v_j_0 ,v_k_0) [-1 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -3 + v_N >= 0 && -1 + v_k_0 >= -1 + v_N] Signature: {(eval_realheapsort_step1_0,4) ;(eval_realheapsort_step1_1,4) ;(eval_realheapsort_step1_2,4) ;(eval_realheapsort_step1_28,4) ;(eval_realheapsort_step1_29,4) ;(eval_realheapsort_step1__critedge_in,4) ;(eval_realheapsort_step1_bb0_in,4) ;(eval_realheapsort_step1_bb1_in,4) ;(eval_realheapsort_step1_bb2_in,4) ;(eval_realheapsort_step1_bb3_in,4) ;(eval_realheapsort_step1_bb4_in,4) ;(eval_realheapsort_step1_bb5_in,4) ;(eval_realheapsort_step1_start,4) ;(eval_realheapsort_step1_stop,4)} Rule Graph: [0->{1},1->{2},2->{3},3->{4,5},4->{6},5->{7},6->{},7->{9},8->{10},9->{11,12},10->{13},11->{10},12->{14} ,13->{15},14->{8,9},15->{7,16},16->{6}] + 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] | `- p:[7,15,13,10,8,14,12,9,11] c: [7,8,10,11,13,15] | `- p:[9,14,12] c: [9,12,14] * Step 4: CloseWith YES + Considered Problem: (Rules: eval_realheapsort_step1_start(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb0_in(v_33,v_N ,v_j_0 ,v_k_0) True eval_realheapsort_step1_bb0_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_0(v_33,v_N,v_j_0 ,v_k_0) True eval_realheapsort_step1_0(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_1(v_33,v_N,v_j_0 ,v_k_0) True eval_realheapsort_step1_1(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_2(v_33,v_N,v_j_0 ,v_k_0) True eval_realheapsort_step1_2(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb5_in(v_33,v_N,v_j_0 ,v_k_0) [2 >= v_N] eval_realheapsort_step1_2(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb1_in(v_33,v_N,v_j_0 ,1) [-1 + v_N >= 2] eval_realheapsort_step1_bb5_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_stop(v_33,v_N,v_j_0 ,v_k_0) True eval_realheapsort_step1_bb1_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb2_in(v_33,v_N,v_k_0 ,v_k_0) [-1 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -3 + v_N >= 0 && -1 + v_N >= v_k_0] eval_realheapsort_step1_bb2_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1__critedge_in(v_33,v_N ,v_j_0 ,v_k_0) [-1 + v_N + -1*v_k_0 >= 0 && -1 + v_k_0 >= 0 && -1*v_j_0 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -1 + v_N + -1*v_j_0 >= 0 && -3 + v_N >= 0 && 0 >= v_j_0] eval_realheapsort_step1_bb2_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb3_in(v_33,v_N,v_j_0 ,v_k_0) [-1 + v_N + -1*v_k_0 >= 0 && -1 + v_k_0 >= 0 && -1*v_j_0 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -1 + v_N + -1*v_j_0 >= 0 && -3 + v_N >= 0 && -1 + v_j_0 >= 0] eval_realheapsort_step1__critedge_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_28(1 + v_k_0,v_N ,v_j_0 ,v_k_0) [-1 + v_N + -1*v_k_0 >= 0 && -1 + v_k_0 >= 0 && -1*v_j_0 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -1 + v_N + -1*v_j_0 >= 0 && -3 + v_N >= 0] eval_realheapsort_step1_bb3_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1__critedge_in(v_33,v_N ,v_j_0 ,v_k_0) [-1 + v_N + -1*v_k_0 >= 0 && -1 + v_k_0 >= 0 && -2 + v_j_0 + v_k_0 >= 0 && -1*v_j_0 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -1 + v_N + -1*v_j_0 >= 0 && -1 + v_j_0 >= 0 && -4 + v_N + v_j_0 >= 0 && -3 + v_N >= 0 && v_j_0 >= 0 && nondef_0 >= 0 && 1 + -2*nondef_0 + v_j_0 >= 0 && 1 >= 1 + -2*nondef_0 + v_j_0] eval_realheapsort_step1_bb3_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb4_in(v_33,v_N,v_j_0 ,v_k_0) [-1 + v_N + -1*v_k_0 >= 0 && -1 + v_k_0 >= 0 && -2 + v_j_0 + v_k_0 >= 0 && -1*v_j_0 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -1 + v_N + -1*v_j_0 >= 0 && -1 + v_j_0 >= 0 && -4 + v_N + v_j_0 >= 0 && -3 + v_N >= 0 && v_j_0 >= 0 && nondef_0 >= 0 && 1 + -2*nondef_0 + v_j_0 >= 0 && 1 >= 1 + -2*nondef_0 + v_j_0] eval_realheapsort_step1_28(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_29(v_33,v_N,v_j_0 ,v_k_0) [-1 + v_N + -1*v_k_0 >= 0 && -1 + v_33 + -1*v_k_0 >= 0 && -1 + v_k_0 >= 0 && -1*v_j_0 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -3 + v_33 + v_k_0 >= 0 && 1 + -1*v_33 + v_k_0 >= 0 && -1 + v_N + -1*v_j_0 >= 0 && -1 + v_33 + -1*v_j_0 >= 0 && -3 + v_N >= 0 && -5 + v_33 + v_N >= 0 && -1*v_33 + v_N >= 0 && -2 + v_33 >= 0] eval_realheapsort_step1_bb4_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb2_in(v_33,v_N ,-1 + nondef_3 ,v_k_0) [-1 + v_N + -1*v_k_0 >= 0 && -1 + v_k_0 >= 0 && -2 + v_j_0 + v_k_0 >= 0 && -1*v_j_0 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -1 + v_N + -1*v_j_0 >= 0 && -1 + v_j_0 >= 0 && -4 + v_N + v_j_0 >= 0 && -3 + v_N >= 0 && v_j_0 >= 0 && nondef_1 >= 0 && 1 + -2*nondef_1 + v_j_0 >= 0 && 1 >= 1 + -2*nondef_1 + v_j_0 && nondef_2 >= 0 && 1 + -2*nondef_2 + v_j_0 >= 0 && 1 >= 1 + -2*nondef_2 + v_j_0 && nondef_3 >= 0 && 1 + -2*nondef_3 + v_j_0 >= 0 && 1 >= 1 + -2*nondef_3 + v_j_0] eval_realheapsort_step1_29(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb1_in(v_33,v_N,v_j_0 ,v_33) [-1 + v_N + -1*v_k_0 >= 0 && -1 + v_33 + -1*v_k_0 >= 0 && -1 + v_k_0 >= 0 && -1*v_j_0 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -3 + v_33 + v_k_0 >= 0 && 1 + -1*v_33 + v_k_0 >= 0 && -1 + v_N + -1*v_j_0 >= 0 && -1 + v_33 + -1*v_j_0 >= 0 && -3 + v_N >= 0 && -5 + v_33 + v_N >= 0 && -1*v_33 + v_N >= 0 && -2 + v_33 >= 0] eval_realheapsort_step1_bb1_in(v_33,v_N,v_j_0,v_k_0) -> eval_realheapsort_step1_bb5_in(v_33,v_N,v_j_0 ,v_k_0) [-1 + v_k_0 >= 0 && -4 + v_N + v_k_0 >= 0 && -3 + v_N >= 0 && -1 + v_k_0 >= -1 + v_N] Signature: {(eval_realheapsort_step1_0,4) ;(eval_realheapsort_step1_1,4) ;(eval_realheapsort_step1_2,4) ;(eval_realheapsort_step1_28,4) ;(eval_realheapsort_step1_29,4) ;(eval_realheapsort_step1__critedge_in,4) ;(eval_realheapsort_step1_bb0_in,4) ;(eval_realheapsort_step1_bb1_in,4) ;(eval_realheapsort_step1_bb2_in,4) ;(eval_realheapsort_step1_bb3_in,4) ;(eval_realheapsort_step1_bb4_in,4) ;(eval_realheapsort_step1_bb5_in,4) ;(eval_realheapsort_step1_start,4) ;(eval_realheapsort_step1_stop,4)} Rule Graph: [0->{1},1->{2},2->{3},3->{4,5},4->{6},5->{7},6->{},7->{9},8->{10},9->{11,12},10->{13},11->{10},12->{14} ,13->{15},14->{8,9},15->{7,16},16->{6}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] | `- p:[7,15,13,10,8,14,12,9,11] c: [7,8,10,11,13,15] | `- p:[9,14,12] c: [9,12,14]) + Applied Processor: CloseWith True + Details: () YES