YES(?,POLY) * Step 1: TrivialSCCs WORST_CASE(?,POLY) + 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: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths WORST_CASE(?,POLY) + 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 (1,1) 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 (1,1) 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 (1,1) 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] (1,1) 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] (1,1) 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 (1,1) 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] (1,1) 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 3: AddSinks WORST_CASE(?,POLY) + 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 (1,1) 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 (1,1) 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 (1,1) 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] (1,1) 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] (1,1) 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 (1,1) 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] (1,1) 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: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,POLY) + 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) 17. eval_realheapsort_step1_bb5_in(v_33,v_N,v_j_0,v_k_0) -> exitus616(v_33,v_N,v_j_0,v_k_0) True (?,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) ;(exitus616,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5},4->{6,17},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->{6,17},17->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(5,16),(7,8)] * Step 5: LooptreeTransformer WORST_CASE(?,POLY) + 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) 17. eval_realheapsort_step1_bb5_in(v_33,v_N,v_j_0,v_k_0) -> exitus616(v_33,v_N,v_j_0,v_k_0) True (?,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) ;(exitus616,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5},4->{6,17},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->{6,17},17->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] | `- p:[7,15,13,10,8,14,12,9,11] c: [15] | `- p:[9,14,12] c: [14] * Step 6: SizeAbstraction WORST_CASE(?,POLY) + 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) 17. eval_realheapsort_step1_bb5_in(v_33,v_N,v_j_0,v_k_0) -> exitus616(v_33,v_N,v_j_0,v_k_0) True (?,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) ;(exitus616,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5},4->{6,17},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->{6,17},17->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] | `- p:[7,15,13,10,8,14,12,9,11] c: [15] | `- p:[9,14,12] c: [14]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [v_33,v_N,v_j_0,v_k_0,0.0,0.0.0] eval_realheapsort_step1_start ~> eval_realheapsort_step1_bb0_in [v_33 <= v_33, v_N <= v_N, v_j_0 <= v_j_0, v_k_0 <= v_k_0] eval_realheapsort_step1_bb0_in ~> eval_realheapsort_step1_0 [v_33 <= v_33, v_N <= v_N, v_j_0 <= v_j_0, v_k_0 <= v_k_0] eval_realheapsort_step1_0 ~> eval_realheapsort_step1_1 [v_33 <= v_33, v_N <= v_N, v_j_0 <= v_j_0, v_k_0 <= v_k_0] eval_realheapsort_step1_1 ~> eval_realheapsort_step1_2 [v_33 <= v_33, v_N <= v_N, v_j_0 <= v_j_0, v_k_0 <= v_k_0] eval_realheapsort_step1_2 ~> eval_realheapsort_step1_bb5_in [v_33 <= v_33, v_N <= v_N, v_j_0 <= v_j_0, v_k_0 <= v_k_0] eval_realheapsort_step1_2 ~> eval_realheapsort_step1_bb1_in [v_33 <= v_33, v_N <= v_N, v_j_0 <= v_j_0, v_k_0 <= K] eval_realheapsort_step1_bb5_in ~> eval_realheapsort_step1_stop [v_33 <= v_33, v_N <= v_N, v_j_0 <= v_j_0, v_k_0 <= v_k_0] eval_realheapsort_step1_bb1_in ~> eval_realheapsort_step1_bb2_in [v_33 <= v_33, v_N <= v_N, v_j_0 <= v_k_0, v_k_0 <= v_k_0] eval_realheapsort_step1_bb2_in ~> eval_realheapsort_step1__critedge_in [v_33 <= v_33, v_N <= v_N, v_j_0 <= v_j_0, v_k_0 <= v_k_0] eval_realheapsort_step1_bb2_in ~> eval_realheapsort_step1_bb3_in [v_33 <= v_33, v_N <= v_N, v_j_0 <= v_j_0, v_k_0 <= v_k_0] eval_realheapsort_step1__critedge_in ~> eval_realheapsort_step1_28 [v_33 <= v_N, v_N <= v_N, v_j_0 <= v_j_0, v_k_0 <= v_k_0] eval_realheapsort_step1_bb3_in ~> eval_realheapsort_step1__critedge_in [v_33 <= v_33, v_N <= v_N, v_j_0 <= v_j_0, v_k_0 <= v_k_0] eval_realheapsort_step1_bb3_in ~> eval_realheapsort_step1_bb4_in [v_33 <= v_33, v_N <= v_N, v_j_0 <= v_j_0, v_k_0 <= v_k_0] eval_realheapsort_step1_28 ~> eval_realheapsort_step1_29 [v_33 <= v_33, v_N <= v_N, v_j_0 <= v_j_0, v_k_0 <= v_k_0] eval_realheapsort_step1_bb4_in ~> eval_realheapsort_step1_bb2_in [v_33 <= v_33, v_N <= v_N, v_j_0 <= v_N, v_k_0 <= v_k_0] eval_realheapsort_step1_29 ~> eval_realheapsort_step1_bb1_in [v_33 <= v_33, v_N <= v_N, v_j_0 <= v_j_0, v_k_0 <= v_33] eval_realheapsort_step1_bb1_in ~> eval_realheapsort_step1_bb5_in [v_33 <= v_33, v_N <= v_N, v_j_0 <= v_j_0, v_k_0 <= v_k_0] eval_realheapsort_step1_bb5_in ~> exitus616 [v_33 <= v_33, v_N <= v_N, v_j_0 <= v_j_0, v_k_0 <= v_k_0] + Loop: [0.0 <= v_N + v_k_0] eval_realheapsort_step1_bb1_in ~> eval_realheapsort_step1_bb2_in [v_33 <= v_33, v_N <= v_N, v_j_0 <= v_k_0, v_k_0 <= v_k_0] eval_realheapsort_step1_29 ~> eval_realheapsort_step1_bb1_in [v_33 <= v_33, v_N <= v_N, v_j_0 <= v_j_0, v_k_0 <= v_33] eval_realheapsort_step1_28 ~> eval_realheapsort_step1_29 [v_33 <= v_33, v_N <= v_N, v_j_0 <= v_j_0, v_k_0 <= v_k_0] eval_realheapsort_step1__critedge_in ~> eval_realheapsort_step1_28 [v_33 <= v_N, v_N <= v_N, v_j_0 <= v_j_0, v_k_0 <= v_k_0] eval_realheapsort_step1_bb2_in ~> eval_realheapsort_step1__critedge_in [v_33 <= v_33, v_N <= v_N, v_j_0 <= v_j_0, v_k_0 <= v_k_0] eval_realheapsort_step1_bb4_in ~> eval_realheapsort_step1_bb2_in [v_33 <= v_33, v_N <= v_N, v_j_0 <= v_N, v_k_0 <= v_k_0] eval_realheapsort_step1_bb3_in ~> eval_realheapsort_step1_bb4_in [v_33 <= v_33, v_N <= v_N, v_j_0 <= v_j_0, v_k_0 <= v_k_0] eval_realheapsort_step1_bb2_in ~> eval_realheapsort_step1_bb3_in [v_33 <= v_33, v_N <= v_N, v_j_0 <= v_j_0, v_k_0 <= v_k_0] eval_realheapsort_step1_bb3_in ~> eval_realheapsort_step1__critedge_in [v_33 <= v_33, v_N <= v_N, v_j_0 <= v_j_0, v_k_0 <= v_k_0] + Loop: [0.0.0 <= K + 2*v_j_0] eval_realheapsort_step1_bb2_in ~> eval_realheapsort_step1_bb3_in [v_33 <= v_33, v_N <= v_N, v_j_0 <= v_j_0, v_k_0 <= v_k_0] eval_realheapsort_step1_bb4_in ~> eval_realheapsort_step1_bb2_in [v_33 <= v_33, v_N <= v_N, v_j_0 <= v_N, v_k_0 <= v_k_0] eval_realheapsort_step1_bb3_in ~> eval_realheapsort_step1_bb4_in [v_33 <= v_33, v_N <= v_N, v_j_0 <= v_j_0, v_k_0 <= v_k_0] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,v_33,v_N,v_j_0,v_k_0,0.0,0.0.0] eval_realheapsort_step1_start ~> eval_realheapsort_step1_bb0_in [] eval_realheapsort_step1_bb0_in ~> eval_realheapsort_step1_0 [] eval_realheapsort_step1_0 ~> eval_realheapsort_step1_1 [] eval_realheapsort_step1_1 ~> eval_realheapsort_step1_2 [] eval_realheapsort_step1_2 ~> eval_realheapsort_step1_bb5_in [] eval_realheapsort_step1_2 ~> eval_realheapsort_step1_bb1_in [K ~=> v_k_0] eval_realheapsort_step1_bb5_in ~> eval_realheapsort_step1_stop [] eval_realheapsort_step1_bb1_in ~> eval_realheapsort_step1_bb2_in [v_k_0 ~=> v_j_0] eval_realheapsort_step1_bb2_in ~> eval_realheapsort_step1__critedge_in [] eval_realheapsort_step1_bb2_in ~> eval_realheapsort_step1_bb3_in [] eval_realheapsort_step1__critedge_in ~> eval_realheapsort_step1_28 [v_N ~=> v_33] eval_realheapsort_step1_bb3_in ~> eval_realheapsort_step1__critedge_in [] eval_realheapsort_step1_bb3_in ~> eval_realheapsort_step1_bb4_in [] eval_realheapsort_step1_28 ~> eval_realheapsort_step1_29 [] eval_realheapsort_step1_bb4_in ~> eval_realheapsort_step1_bb2_in [v_N ~=> v_j_0] eval_realheapsort_step1_29 ~> eval_realheapsort_step1_bb1_in [v_33 ~=> v_k_0] eval_realheapsort_step1_bb1_in ~> eval_realheapsort_step1_bb5_in [] eval_realheapsort_step1_bb5_in ~> exitus616 [] + Loop: [v_N ~+> 0.0,v_k_0 ~+> 0.0] eval_realheapsort_step1_bb1_in ~> eval_realheapsort_step1_bb2_in [v_k_0 ~=> v_j_0] eval_realheapsort_step1_29 ~> eval_realheapsort_step1_bb1_in [v_33 ~=> v_k_0] eval_realheapsort_step1_28 ~> eval_realheapsort_step1_29 [] eval_realheapsort_step1__critedge_in ~> eval_realheapsort_step1_28 [v_N ~=> v_33] eval_realheapsort_step1_bb2_in ~> eval_realheapsort_step1__critedge_in [] eval_realheapsort_step1_bb4_in ~> eval_realheapsort_step1_bb2_in [v_N ~=> v_j_0] eval_realheapsort_step1_bb3_in ~> eval_realheapsort_step1_bb4_in [] eval_realheapsort_step1_bb2_in ~> eval_realheapsort_step1_bb3_in [] eval_realheapsort_step1_bb3_in ~> eval_realheapsort_step1__critedge_in [] + Loop: [K ~+> 0.0.0,v_j_0 ~*> 0.0.0] eval_realheapsort_step1_bb2_in ~> eval_realheapsort_step1_bb3_in [] eval_realheapsort_step1_bb4_in ~> eval_realheapsort_step1_bb2_in [v_N ~=> v_j_0] eval_realheapsort_step1_bb3_in ~> eval_realheapsort_step1_bb4_in [] + Applied Processor: LareProcessor + Details: eval_realheapsort_step1_start ~> eval_realheapsort_step1_stop [v_N ~=> v_33 ,v_N ~=> v_j_0 ,v_N ~=> v_k_0 ,K ~=> v_j_0 ,K ~=> v_k_0 ,v_N ~+> 0.0 ,v_N ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,v_N ~*> 0.0.0 ,v_N ~*> tick ,K ~*> 0.0.0 ,K ~*> tick] eval_realheapsort_step1_start ~> exitus616 [v_N ~=> v_33 ,v_N ~=> v_j_0 ,v_N ~=> v_k_0 ,K ~=> v_j_0 ,K ~=> v_k_0 ,v_N ~+> 0.0 ,v_N ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,v_N ~*> 0.0.0 ,v_N ~*> tick ,K ~*> 0.0.0 ,K ~*> tick] + eval_realheapsort_step1_bb1_in> [v_N ~=> v_33 ,v_N ~=> v_j_0 ,v_N ~=> v_k_0 ,v_k_0 ~=> v_j_0 ,v_N ~+> 0.0 ,v_N ~+> tick ,v_k_0 ~+> 0.0 ,v_k_0 ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,v_N ~*> 0.0.0 ,v_N ~*> tick ,v_k_0 ~*> 0.0.0 ,v_k_0 ~*> tick ,K ~*> tick] + eval_realheapsort_step1_bb3_in> [v_N ~=> v_j_0 ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,v_j_0 ~*> 0.0.0 ,v_j_0 ~*> tick] eval_realheapsort_step1_bb2_in> [v_N ~=> v_j_0 ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,v_j_0 ~*> 0.0.0 ,v_j_0 ~*> tick] YES(?,POLY)