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Complexity_ITS 2019-03-21 04.46 pair #429989854
details
property
value
status
complete
benchmark
realheapsort.c.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n133.star.cs.uiowa.edu
space
Flores-Montoya_16
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
45.3847 seconds
cpu usage
74.9004
user time
72.2824
system time
2.61798
max virtual memory
1.9162536E7
max residence set size
445768.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
74.64/45.32 WORST_CASE(?, O(n^2)) 74.75/45.34 proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat 74.75/45.34 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 74.75/45.34 74.75/45.34 74.75/45.34 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 74.75/45.34 74.75/45.34 (0) CpxIntTrs 74.75/45.34 (1) Koat Proof [FINISHED, 4264 ms] 74.75/45.34 (2) BOUNDS(1, n^2) 74.75/45.34 74.75/45.34 74.75/45.34 ---------------------------------------- 74.75/45.34 74.75/45.34 (0) 74.75/45.34 Obligation: 74.75/45.34 Complexity Int TRS consisting of the following rules: 74.75/45.34 eval_realheapsort_start(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb0_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: TRUE 74.75/45.34 eval_realheapsort_bb0_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_0(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: TRUE 74.75/45.34 eval_realheapsort_0(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_1(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: TRUE 74.75/45.34 eval_realheapsort_1(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_2(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: TRUE 74.75/45.34 eval_realheapsort_2(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb1_in(v_33, v_90, v_N, v_j_0, v_j_1, 1, v_k_1, v_m_0)) :|: v_N > 2 74.75/45.34 eval_realheapsort_2(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb16_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: v_N <= 2 74.75/45.34 eval_realheapsort_bb1_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb2_in(v_33, v_90, v_N, v_k_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: v_k_0 <= v_N - 1 74.75/45.34 eval_realheapsort_bb1_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb5_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: v_k_0 > v_N - 1 74.75/45.34 eval_realheapsort_bb2_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb3_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: v_j_0 > 0 74.75/45.34 eval_realheapsort_bb2_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort__critedge_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: v_j_0 <= 0 74.75/45.34 eval_realheapsort_bb3_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb4_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_0 >= 0 && nondef_0 <= 0 74.75/45.34 eval_realheapsort_bb3_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb4_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_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 74.75/45.34 eval_realheapsort_bb3_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb4_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_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 74.75/45.34 eval_realheapsort_bb3_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort__critedge_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_0 >= 0 && nondef_0 <= 0 74.75/45.34 eval_realheapsort_bb3_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort__critedge_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_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 74.75/45.34 eval_realheapsort_bb3_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort__critedge_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_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 74.75/45.34 eval_realheapsort_bb4_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb2_in(v_33, v_90, v_N, nondef_3 - 1, v_j_1, v_k_0, v_k_1, v_m_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 74.75/45.34 eval_realheapsort_bb4_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb2_in(v_33, v_90, v_N, nondef_3 - 1, v_j_1, v_k_0, v_k_1, v_m_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 74.75/45.34 eval_realheapsort_bb4_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb2_in(v_33, v_90, v_N, nondef_3 - 1, v_j_1, v_k_0, v_k_1, v_m_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 74.75/45.34 eval_realheapsort_bb4_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb2_in(v_33, v_90, v_N, nondef_3 - 1, v_j_1, v_k_0, v_k_1, v_m_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 74.75/45.34 eval_realheapsort_bb4_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb2_in(v_33, v_90, v_N, nondef_3 - 1, v_j_1, v_k_0, v_k_1, v_m_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 74.75/45.34 eval_realheapsort_bb4_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb2_in(v_33, v_90, v_N, nondef_3 - 1, v_j_1, v_k_0, v_k_1, v_m_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 74.75/45.34 eval_realheapsort_bb4_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb2_in(v_33, v_90, v_N, nondef_3 - 1, v_j_1, v_k_0, v_k_1, v_m_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 74.75/45.34 eval_realheapsort_bb4_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb2_in(v_33, v_90, v_N, nondef_3 - 1, v_j_1, v_k_0, v_k_1, v_m_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 74.75/45.34 eval_realheapsort_bb4_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb2_in(v_33, v_90, v_N, nondef_3 - 1, v_j_1, v_k_0, v_k_1, v_m_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 74.75/45.34 eval_realheapsort_bb4_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb2_in(v_33, v_90, v_N, nondef_3 - 1, v_j_1, v_k_0, v_k_1, v_m_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 74.75/45.34 eval_realheapsort_bb4_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb2_in(v_33, v_90, v_N, nondef_3 - 1, v_j_1, v_k_0, v_k_1, v_m_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 74.75/45.34 eval_realheapsort_bb4_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb2_in(v_33, v_90, v_N, nondef_3 - 1, v_j_1, v_k_0, v_k_1, v_m_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 74.75/45.34 eval_realheapsort_bb4_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb2_in(v_33, v_90, v_N, nondef_3 - 1, v_j_1, v_k_0, v_k_1, v_m_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 74.75/45.34 eval_realheapsort_bb4_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb2_in(v_33, v_90, v_N, nondef_3 - 1, v_j_1, v_k_0, v_k_1, v_m_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 74.75/45.34 eval_realheapsort_bb4_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb2_in(v_33, v_90, v_N, nondef_3 - 1, v_j_1, v_k_0, v_k_1, v_m_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 74.75/45.34 eval_realheapsort_bb4_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb2_in(v_33, v_90, v_N, nondef_3 - 1, v_j_1, v_k_0, v_k_1, v_m_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 74.75/45.34 eval_realheapsort_bb4_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb2_in(v_33, v_90, v_N, nondef_3 - 1, v_j_1, v_k_0, v_k_1, v_m_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 74.75/45.34 eval_realheapsort_bb4_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb2_in(v_33, v_90, v_N, nondef_3 - 1, v_j_1, v_k_0, v_k_1, v_m_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 74.75/45.34 eval_realheapsort_bb4_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb2_in(v_33, v_90, v_N, nondef_3 - 1, v_j_1, v_k_0, v_k_1, v_m_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 74.75/45.34 eval_realheapsort_bb4_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb2_in(v_33, v_90, v_N, nondef_3 - 1, v_j_1, v_k_0, v_k_1, v_m_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 74.75/45.34 eval_realheapsort_bb4_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb2_in(v_33, v_90, v_N, nondef_3 - 1, v_j_1, v_k_0, v_k_1, v_m_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 74.75/45.34 eval_realheapsort_bb4_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb2_in(v_33, v_90, v_N, nondef_3 - 1, v_j_1, v_k_0, v_k_1, v_m_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 74.75/45.34 eval_realheapsort_bb4_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb2_in(v_33, v_90, v_N, nondef_3 - 1, v_j_1, v_k_0, v_k_1, v_m_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 74.75/45.34 eval_realheapsort_bb4_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb2_in(v_33, v_90, v_N, nondef_3 - 1, v_j_1, v_k_0, v_k_1, v_m_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 74.75/45.34 eval_realheapsort_bb4_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb2_in(v_33, v_90, v_N, nondef_3 - 1, v_j_1, v_k_0, v_k_1, v_m_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 74.75/45.34 eval_realheapsort_bb4_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb2_in(v_33, v_90, v_N, nondef_3 - 1, v_j_1, v_k_0, v_k_1, v_m_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 74.75/45.34 eval_realheapsort_bb4_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb2_in(v_33, v_90, v_N, nondef_3 - 1, v_j_1, v_k_0, v_k_1, v_m_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 74.75/45.34 eval_realheapsort__critedge_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_28(v_k_0 + 1, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: TRUE 74.75/45.34 eval_realheapsort_28(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_29(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: TRUE 74.75/45.34 eval_realheapsort_29(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb1_in(v_33, v_90, v_N, v_j_0, v_j_1, v_33, v_k_1, v_m_0)) :|: TRUE 74.75/45.34 eval_realheapsort_bb5_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_30(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: TRUE 74.75/45.34 eval_realheapsort_30(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_31(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: TRUE 74.75/45.34 eval_realheapsort_31(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_32(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: TRUE 74.75/45.34 eval_realheapsort_32(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_33(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: TRUE 74.75/45.34 eval_realheapsort_33(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_34(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: TRUE 74.75/45.34 eval_realheapsort_34(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_35(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: TRUE 74.75/45.34 eval_realheapsort_35(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_36(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: TRUE 74.75/45.34 eval_realheapsort_36(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_37(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: TRUE 74.75/45.34 eval_realheapsort_37(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_38(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: TRUE 74.75/45.34 eval_realheapsort_38(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_39(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: TRUE 74.75/45.34 eval_realheapsort_39(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb6_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, 0, v_m_0)) :|: TRUE 74.75/45.34 eval_realheapsort_bb6_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb7_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: v_k_1 <= v_N - 2 74.75/45.34 eval_realheapsort_bb6_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb16_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: v_k_1 > v_N - 2 74.75/45.34 eval_realheapsort_bb7_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb8_in(v_33, v_90, v_N, v_j_0, 0, v_k_0, v_k_1, v_m_0)) :|: TRUE 74.75/45.34 eval_realheapsort_bb8_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb9_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: 2 * v_j_1 + 1 <= v_N - v_k_1 - 2 74.75/45.34 eval_realheapsort_bb8_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb15_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: 2 * v_j_1 + 1 > v_N - v_k_1 - 2 74.75/45.34 eval_realheapsort_bb9_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb11_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: 2 * v_j_1 + 1 >= v_N - v_k_1 - 2 && 2 * v_j_1 + 1 <= v_N - v_k_1 - 2 74.75/45.34 eval_realheapsort_bb9_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb10_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: 2 * v_j_1 + 1 < v_N - v_k_1 - 2 74.75/45.34 eval_realheapsort_bb9_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb10_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: 2 * v_j_1 + 1 > v_N - v_k_1 - 2 74.75/45.34 eval_realheapsort_bb10_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb11_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: TRUE 74.75/45.34 eval_realheapsort_bb10_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb12_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: TRUE 74.75/45.34 eval_realheapsort_bb11_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb13_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, 2 * v_j_1 + 1)) :|: TRUE 74.75/45.34 eval_realheapsort_bb12_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb13_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, 2 * v_j_1 + 2)) :|: TRUE 74.75/45.34 eval_realheapsort_bb13_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb14_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: TRUE 74.75/45.34 eval_realheapsort_bb13_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb8_in(v_33, v_90, v_N, v_j_0, v_N, v_k_0, v_k_1, v_m_0)) :|: TRUE 74.75/45.34 eval_realheapsort_bb14_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb8_in(v_33, v_90, v_N, v_j_0, v_m_0, v_k_0, v_k_1, v_m_0)) :|: TRUE 74.75/45.34 eval_realheapsort_bb15_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_85(v_33, v_k_1 + 1, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: TRUE 74.75/45.34 eval_realheapsort_85(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_86(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: TRUE 74.75/45.34 eval_realheapsort_86(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_bb6_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_90, v_m_0)) :|: TRUE 74.75/45.34 eval_realheapsort_bb16_in(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0) -> Com_1(eval_realheapsort_stop(v_33, v_90, v_N, v_j_0, v_j_1, v_k_0, v_k_1, v_m_0)) :|: TRUE 74.75/45.34 74.75/45.34 The start-symbols are:[eval_realheapsort_start_8] 74.75/45.34 74.75/45.34 74.75/45.34 ---------------------------------------- 74.75/45.34 74.75/45.34 (1) Koat Proof (FINISHED)
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return to Complexity_ITS 2019-03-21 04.46