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Complexity_ITS 2019-03-21 04.46 pair #429990034
details
property
value
status
complete
benchmark
realheapsort_step1.c.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n062.star.cs.uiowa.edu
space
Flores-Montoya_16
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
17.6501 seconds
cpu usage
25.0217
user time
24.4102
system time
0.611551
max virtual memory
1.8715748E7
max residence set size
277576.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
24.92/17.60 WORST_CASE(?, O(n^2)) 24.92/17.62 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 24.92/17.62 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 24.92/17.62 24.92/17.62 24.92/17.62 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 24.92/17.62 24.92/17.62 (0) CpxIntTrs 24.92/17.62 (1) Koat Proof [FINISHED, 454 ms] 24.92/17.62 (2) BOUNDS(1, n^2) 24.92/17.62 24.92/17.62 24.92/17.62 ---------------------------------------- 24.92/17.62 24.92/17.62 (0) 24.92/17.62 Obligation: 24.92/17.62 Complexity Int TRS consisting of the following rules: 24.92/17.62 eval_realheapsort_step1_start(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb0_in(v_33, v_N, v_j_0, v_k_0)) :|: TRUE 24.92/17.62 eval_realheapsort_step1_bb0_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_0(v_33, v_N, v_j_0, v_k_0)) :|: TRUE 24.92/17.62 eval_realheapsort_step1_0(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_1(v_33, v_N, v_j_0, v_k_0)) :|: TRUE 24.92/17.62 eval_realheapsort_step1_1(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_2(v_33, v_N, v_j_0, v_k_0)) :|: TRUE 24.92/17.62 eval_realheapsort_step1_2(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb1_in(v_33, v_N, v_j_0, 1)) :|: v_N > 2 24.92/17.62 eval_realheapsort_step1_2(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb5_in(v_33, v_N, v_j_0, v_k_0)) :|: v_N <= 2 24.92/17.62 eval_realheapsort_step1_bb1_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, v_k_0, v_k_0)) :|: v_k_0 <= v_N - 1 24.92/17.62 eval_realheapsort_step1_bb1_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb5_in(v_33, v_N, v_j_0, v_k_0)) :|: v_k_0 > v_N - 1 24.92/17.62 eval_realheapsort_step1_bb2_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb3_in(v_33, v_N, v_j_0, v_k_0)) :|: v_j_0 > 0 24.92/17.62 eval_realheapsort_step1_bb2_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1__critedge_in(v_33, v_N, v_j_0, v_k_0)) :|: v_j_0 <= 0 24.92/17.62 eval_realheapsort_step1_bb3_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_0 >= 0 && nondef_0 <= 0 24.92/17.62 eval_realheapsort_step1_bb3_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_0 >= 0 && v_j_0 - 2 * nondef_0 + 1 >= 0 && v_j_0 - 2 * nondef_0 + 1 < 2 24.92/17.62 eval_realheapsort_step1_bb3_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_0 <= 0 && -(v_j_0) + 2 * nondef_0 - 1 >= 0 && -(v_j_0) + 2 * nondef_0 - 1 < 2 24.92/17.62 eval_realheapsort_step1_bb3_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1__critedge_in(v_33, v_N, v_j_0, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_0 >= 0 && nondef_0 <= 0 24.92/17.62 eval_realheapsort_step1_bb3_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1__critedge_in(v_33, v_N, v_j_0, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_0 >= 0 && v_j_0 - 2 * nondef_0 + 1 >= 0 && v_j_0 - 2 * nondef_0 + 1 < 2 24.92/17.62 eval_realheapsort_step1_bb3_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1__critedge_in(v_33, v_N, v_j_0, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_0 <= 0 && -(v_j_0) + 2 * nondef_0 - 1 >= 0 && -(v_j_0) + 2 * nondef_0 - 1 < 2 24.92/17.62 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_1 >= 0 && nondef_1 <= 0 && nondef_2 >= 0 && nondef_2 <= 0 && nondef_3 >= 0 && nondef_3 <= 0 24.92/17.62 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_1 >= 0 && nondef_1 <= 0 && nondef_2 >= 0 && nondef_2 <= 0 && v_j_0 + 1 > 0 && nondef_3 >= 0 && v_j_0 - 2 * nondef_3 + 1 >= 0 && v_j_0 - 2 * nondef_3 + 1 < 2 24.92/17.62 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_1 >= 0 && nondef_1 <= 0 && nondef_2 >= 0 && nondef_2 <= 0 && v_j_0 + 1 < 0 && nondef_3 <= 0 && -(v_j_0) + 2 * nondef_3 - 1 >= 0 && -(v_j_0) + 2 * nondef_3 - 1 < 2 24.92/17.62 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_1 >= 0 && nondef_1 <= 0 && v_j_0 + 1 > 0 && nondef_2 >= 0 && v_j_0 - 2 * nondef_2 + 1 >= 0 && v_j_0 - 2 * nondef_2 + 1 < 2 && nondef_3 >= 0 && nondef_3 <= 0 24.92/17.62 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_1 >= 0 && nondef_1 <= 0 && v_j_0 + 1 > 0 && nondef_2 >= 0 && v_j_0 - 2 * nondef_2 + 1 >= 0 && v_j_0 - 2 * nondef_2 + 1 < 2 && nondef_3 >= 0 && v_j_0 - 2 * nondef_3 + 1 >= 0 && v_j_0 - 2 * nondef_3 + 1 < 2 24.92/17.62 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_1 >= 0 && nondef_1 <= 0 && v_j_0 + 1 > 0 && nondef_2 >= 0 && v_j_0 - 2 * nondef_2 + 1 >= 0 && v_j_0 - 2 * nondef_2 + 1 < 2 && v_j_0 + 1 < 0 && nondef_3 <= 0 && -(v_j_0) + 2 * nondef_3 - 1 >= 0 && -(v_j_0) + 2 * nondef_3 - 1 < 2 24.92/17.62 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_1 >= 0 && nondef_1 <= 0 && v_j_0 + 1 < 0 && nondef_2 <= 0 && -(v_j_0) + 2 * nondef_2 - 1 >= 0 && -(v_j_0) + 2 * nondef_2 - 1 < 2 && nondef_3 >= 0 && nondef_3 <= 0 24.92/17.62 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_1 >= 0 && nondef_1 <= 0 && v_j_0 + 1 < 0 && nondef_2 <= 0 && -(v_j_0) + 2 * nondef_2 - 1 >= 0 && -(v_j_0) + 2 * nondef_2 - 1 < 2 && v_j_0 + 1 > 0 && nondef_3 >= 0 && v_j_0 - 2 * nondef_3 + 1 >= 0 && v_j_0 - 2 * nondef_3 + 1 < 2 24.92/17.62 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_1 >= 0 && nondef_1 <= 0 && v_j_0 + 1 < 0 && nondef_2 <= 0 && -(v_j_0) + 2 * nondef_2 - 1 >= 0 && -(v_j_0) + 2 * nondef_2 - 1 < 2 && nondef_3 <= 0 && -(v_j_0) + 2 * nondef_3 - 1 >= 0 && -(v_j_0) + 2 * nondef_3 - 1 < 2 24.92/17.62 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_1 >= 0 && v_j_0 - 2 * nondef_1 + 1 >= 0 && v_j_0 - 2 * nondef_1 + 1 < 2 && v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_2 >= 0 && nondef_2 <= 0 && nondef_3 >= 0 && nondef_3 <= 0 24.92/17.62 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_1 >= 0 && v_j_0 - 2 * nondef_1 + 1 >= 0 && v_j_0 - 2 * nondef_1 + 1 < 2 && v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_2 >= 0 && nondef_2 <= 0 && nondef_3 >= 0 && v_j_0 - 2 * nondef_3 + 1 >= 0 && v_j_0 - 2 * nondef_3 + 1 < 2 24.92/17.62 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_1 >= 0 && v_j_0 - 2 * nondef_1 + 1 >= 0 && v_j_0 - 2 * nondef_1 + 1 < 2 && v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_2 >= 0 && nondef_2 <= 0 && v_j_0 + 1 < 0 && nondef_3 <= 0 && -(v_j_0) + 2 * nondef_3 - 1 >= 0 && -(v_j_0) + 2 * nondef_3 - 1 < 2 24.92/17.62 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_1 >= 0 && v_j_0 - 2 * nondef_1 + 1 >= 0 && v_j_0 - 2 * nondef_1 + 1 < 2 && nondef_2 >= 0 && v_j_0 - 2 * nondef_2 + 1 >= 0 && v_j_0 - 2 * nondef_2 + 1 < 2 && v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_3 >= 0 && nondef_3 <= 0 24.92/17.62 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_1 >= 0 && v_j_0 - 2 * nondef_1 + 1 >= 0 && v_j_0 - 2 * nondef_1 + 1 < 2 && nondef_2 >= 0 && v_j_0 - 2 * nondef_2 + 1 >= 0 && v_j_0 - 2 * nondef_2 + 1 < 2 && nondef_3 >= 0 && v_j_0 - 2 * nondef_3 + 1 >= 0 && v_j_0 - 2 * nondef_3 + 1 < 2 24.92/17.62 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_1 >= 0 && v_j_0 - 2 * nondef_1 + 1 >= 0 && v_j_0 - 2 * nondef_1 + 1 < 2 && nondef_2 >= 0 && v_j_0 - 2 * nondef_2 + 1 >= 0 && v_j_0 - 2 * nondef_2 + 1 < 2 && v_j_0 + 1 < 0 && nondef_3 <= 0 && -(v_j_0) + 2 * nondef_3 - 1 >= 0 && -(v_j_0) + 2 * nondef_3 - 1 < 2 24.92/17.62 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_1 >= 0 && v_j_0 - 2 * nondef_1 + 1 >= 0 && v_j_0 - 2 * nondef_1 + 1 < 2 && v_j_0 + 1 < 0 && nondef_2 <= 0 && -(v_j_0) + 2 * nondef_2 - 1 >= 0 && -(v_j_0) + 2 * nondef_2 - 1 < 2 && v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_3 >= 0 && nondef_3 <= 0 24.92/17.62 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_1 >= 0 && v_j_0 - 2 * nondef_1 + 1 >= 0 && v_j_0 - 2 * nondef_1 + 1 < 2 && v_j_0 + 1 < 0 && nondef_2 <= 0 && -(v_j_0) + 2 * nondef_2 - 1 >= 0 && -(v_j_0) + 2 * nondef_2 - 1 < 2 && nondef_3 >= 0 && v_j_0 - 2 * nondef_3 + 1 >= 0 && v_j_0 - 2 * nondef_3 + 1 < 2 24.92/17.62 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_1 >= 0 && v_j_0 - 2 * nondef_1 + 1 >= 0 && v_j_0 - 2 * nondef_1 + 1 < 2 && v_j_0 + 1 < 0 && nondef_2 <= 0 && -(v_j_0) + 2 * nondef_2 - 1 >= 0 && -(v_j_0) + 2 * nondef_2 - 1 < 2 && nondef_3 <= 0 && -(v_j_0) + 2 * nondef_3 - 1 >= 0 && -(v_j_0) + 2 * nondef_3 - 1 < 2 24.92/17.62 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_1 <= 0 && -(v_j_0) + 2 * nondef_1 - 1 >= 0 && -(v_j_0) + 2 * nondef_1 - 1 < 2 && v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_2 >= 0 && nondef_2 <= 0 && nondef_3 >= 0 && nondef_3 <= 0 24.92/17.62 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_1 <= 0 && -(v_j_0) + 2 * nondef_1 - 1 >= 0 && -(v_j_0) + 2 * nondef_1 - 1 < 2 && v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_2 >= 0 && nondef_2 <= 0 && v_j_0 + 1 > 0 && nondef_3 >= 0 && v_j_0 - 2 * nondef_3 + 1 >= 0 && v_j_0 - 2 * nondef_3 + 1 < 2 24.92/17.62 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_1 <= 0 && -(v_j_0) + 2 * nondef_1 - 1 >= 0 && -(v_j_0) + 2 * nondef_1 - 1 < 2 && v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_2 >= 0 && nondef_2 <= 0 && nondef_3 <= 0 && -(v_j_0) + 2 * nondef_3 - 1 >= 0 && -(v_j_0) + 2 * nondef_3 - 1 < 2 24.92/17.62 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_1 <= 0 && -(v_j_0) + 2 * nondef_1 - 1 >= 0 && -(v_j_0) + 2 * nondef_1 - 1 < 2 && v_j_0 + 1 > 0 && nondef_2 >= 0 && v_j_0 - 2 * nondef_2 + 1 >= 0 && v_j_0 - 2 * nondef_2 + 1 < 2 && v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_3 >= 0 && nondef_3 <= 0 24.92/17.62 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_1 <= 0 && -(v_j_0) + 2 * nondef_1 - 1 >= 0 && -(v_j_0) + 2 * nondef_1 - 1 < 2 && v_j_0 + 1 > 0 && nondef_2 >= 0 && v_j_0 - 2 * nondef_2 + 1 >= 0 && v_j_0 - 2 * nondef_2 + 1 < 2 && nondef_3 >= 0 && v_j_0 - 2 * nondef_3 + 1 >= 0 && v_j_0 - 2 * nondef_3 + 1 < 2 24.92/17.62 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_1 <= 0 && -(v_j_0) + 2 * nondef_1 - 1 >= 0 && -(v_j_0) + 2 * nondef_1 - 1 < 2 && v_j_0 + 1 > 0 && nondef_2 >= 0 && v_j_0 - 2 * nondef_2 + 1 >= 0 && v_j_0 - 2 * nondef_2 + 1 < 2 && nondef_3 <= 0 && -(v_j_0) + 2 * nondef_3 - 1 >= 0 && -(v_j_0) + 2 * nondef_3 - 1 < 2 24.92/17.62 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_1 <= 0 && -(v_j_0) + 2 * nondef_1 - 1 >= 0 && -(v_j_0) + 2 * nondef_1 - 1 < 2 && nondef_2 <= 0 && -(v_j_0) + 2 * nondef_2 - 1 >= 0 && -(v_j_0) + 2 * nondef_2 - 1 < 2 && v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_3 >= 0 && nondef_3 <= 0 24.92/17.62 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_1 <= 0 && -(v_j_0) + 2 * nondef_1 - 1 >= 0 && -(v_j_0) + 2 * nondef_1 - 1 < 2 && nondef_2 <= 0 && -(v_j_0) + 2 * nondef_2 - 1 >= 0 && -(v_j_0) + 2 * nondef_2 - 1 < 2 && v_j_0 + 1 > 0 && nondef_3 >= 0 && v_j_0 - 2 * nondef_3 + 1 >= 0 && v_j_0 - 2 * nondef_3 + 1 < 2 24.92/17.62 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_1 <= 0 && -(v_j_0) + 2 * nondef_1 - 1 >= 0 && -(v_j_0) + 2 * nondef_1 - 1 < 2 && nondef_2 <= 0 && -(v_j_0) + 2 * nondef_2 - 1 >= 0 && -(v_j_0) + 2 * nondef_2 - 1 < 2 && nondef_3 <= 0 && -(v_j_0) + 2 * nondef_3 - 1 >= 0 && -(v_j_0) + 2 * nondef_3 - 1 < 2 24.92/17.62 eval_realheapsort_step1__critedge_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_28(v_k_0 + 1, v_N, v_j_0, v_k_0)) :|: TRUE 24.92/17.62 eval_realheapsort_step1_28(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_29(v_33, v_N, v_j_0, v_k_0)) :|: TRUE 24.92/17.62 eval_realheapsort_step1_29(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb1_in(v_33, v_N, v_j_0, v_33)) :|: TRUE 24.92/17.62 eval_realheapsort_step1_bb5_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_stop(v_33, v_N, v_j_0, v_k_0)) :|: TRUE 24.92/17.62 24.92/17.62 The start-symbols are:[eval_realheapsort_step1_start_4] 24.92/17.62 24.92/17.62 24.92/17.62 ---------------------------------------- 24.92/17.62 24.92/17.62 (1) Koat Proof (FINISHED) 24.92/17.62 YES(?, 5931*ar_0 + 72*ar_0^2 + 5869) 24.92/17.62 24.92/17.62 24.92/17.62 24.92/17.62 Initial complexity problem: 24.92/17.62 24.92/17.62 1: T: 24.92/17.62 24.92/17.62 (Comp: ?, Cost: 1) evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3)) 24.92/17.62 24.92/17.62 (Comp: ?, Cost: 1) evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3)) 24.92/17.62 24.92/17.62 (Comp: ?, Cost: 1) evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3)) 24.92/17.62 24.92/17.62 (Comp: ?, Cost: 1) evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3)) 24.92/17.62 24.92/17.62 (Comp: ?, Cost: 1) evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ] 24.92/17.62 24.92/17.62 (Comp: ?, Cost: 1) evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ] 24.92/17.62 24.92/17.62 (Comp: ?, Cost: 1) evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ] 24.92/17.62 24.92/17.62 (Comp: ?, Cost: 1) evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ] 24.92/17.62 24.92/17.62 (Comp: ?, Cost: 1) evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ] 24.92/17.62 24.92/17.62 (Comp: ?, Cost: 1) evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ] 24.92/17.62 24.92/17.62 (Comp: ?, Cost: 1) evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 + 1 = 0 ]
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return to Complexity_ITS 2019-03-21 04.46