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Compl C Integ Progr 85445 pair #381745893
details
property
value
status
complete
benchmark
realheapsort_step2.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n096.star.cs.uiowa.edu
space
WTC_V2
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
6.00552296638 seconds
cpu usage
7.414042457
max memory
5.65710848E8
stage attributes
key
value
output-size
638539
starexec-result
WORST_CASE(?, O(n^2))
output
/export/starexec/sandbox2/solver/bin/starexec_run_c_complexity /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^2)) proof of /export/starexec/sandbox2/output/output_files/bench.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 4701 ms] (2) BOUNDS(1, n^2) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_realheapsort_step2_start(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb0_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: TRUE eval_realheapsort_step2_bb0_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb1_in(v_14, v_15, v_21, v_22, v_N, v_j.0, 0, v_m.0)) :|: v_N > 2 eval_realheapsort_step2_bb0_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb11_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: v_N <= 2 eval_realheapsort_step2_bb1_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb2_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: v_k.0 <= v_N - 2 eval_realheapsort_step2_bb1_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb11_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: v_k.0 > v_N - 2 eval_realheapsort_step2_bb2_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_2(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: TRUE eval_realheapsort_step2_2(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_2(eval_nondet_start(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0), eval_realheapsort_step2_3(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: TRUE eval_realheapsort_step2_3(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb3_in(v_14, v_15, v_21, v_22, v_N, 0, v_k.0, v_m.0)) :|: TRUE eval_realheapsort_step2_bb3_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb4_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: 2 * v_j.0 + 1 <= v_N - v_k.0 - 2 eval_realheapsort_step2_bb3_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb10_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: 2 * v_j.0 + 1 > v_N - v_k.0 - 2 eval_realheapsort_step2_bb4_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb6_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: 2 * v_j.0 + 1 >= v_N - v_k.0 - 2 && 2 * v_j.0 + 1 <= v_N - v_k.0 - 2 eval_realheapsort_step2_bb4_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb5_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: 2 * v_j.0 + 1 < v_N - v_k.0 - 2 eval_realheapsort_step2_bb4_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb5_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: 2 * v_j.0 + 1 > v_N - v_k.0 - 2 eval_realheapsort_step2_bb5_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_14(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: TRUE eval_realheapsort_step2_14(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_2(eval_nondet_start(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0), eval_realheapsort_step2_15(nondef.1, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: TRUE eval_realheapsort_step2_15(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_2(eval_nondet_start(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0), eval_realheapsort_step2_16(v_14, nondef.2, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: TRUE eval_realheapsort_step2_16(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb6_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: v_14 < v_15 eval_realheapsort_step2_16(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb7_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: v_14 >= v_15 eval_realheapsort_step2_bb6_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb8_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, 2 * v_j.0 + 1)) :|: TRUE eval_realheapsort_step2_bb7_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb8_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, 2 * v_j.0 + 2)) :|: TRUE eval_realheapsort_step2_bb8_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_23(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: TRUE eval_realheapsort_step2_23(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_2(eval_nondet_start(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0), eval_realheapsort_step2_24(v_14, v_15, nondef.3, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: TRUE eval_realheapsort_step2_24(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_2(eval_nondet_start(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0), eval_realheapsort_step2_25(v_14, v_15, v_21, nondef.4, v_N, v_j.0, v_k.0, v_m.0)) :|: TRUE eval_realheapsort_step2_25(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb9_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: v_21 > v_22 eval_realheapsort_step2_25(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb3_in(v_14, v_15, v_21, v_22, v_N, v_N, v_k.0, v_m.0)) :|: v_21 <= v_22 eval_realheapsort_step2_bb9_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_26(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: TRUE eval_realheapsort_step2_26(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_2(eval_nondet_start(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0), eval_realheapsort_step2_27(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: TRUE eval_realheapsort_step2_27(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb3_in(v_14, v_15, v_21, v_22, v_N, v_m.0, v_k.0, v_m.0)) :|: TRUE eval_realheapsort_step2_bb10_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb1_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0 + 1, v_m.0)) :|: TRUE eval_realheapsort_step2_bb11_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_stop(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: TRUE The start-symbols are:[eval_realheapsort_step2_start_8] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 7520*ar_0 + 2496*ar_0^2 + 5031) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalrealheapsortstep2start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrealheapsortstep2bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrealheapsortstep2bb1in(ar_0, 0, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_0 >= 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrealheapsortstep2bb11in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ 2 >= ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrealheapsortstep2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_0 >= ar_1 + 2 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrealheapsortstep2bb11in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_1 + 1 >= ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrealheapsortstep22(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) (Comp: ?, Cost: 1) evalrealheapsortstep22(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_2(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8), evalrealheapsortstep23(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) (Comp: ?, Cost: 1) evalrealheapsortstep23(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrealheapsortstep2bb3in(ar_0, ar_1, 0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrealheapsortstep2bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_0 >= ar_1 + 2*ar_2 + 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrealheapsortstep2bb10in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ 2*ar_2 + ar_1 + 2 >= ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrealheapsortstep2bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_0 = 2*ar_2 + ar_1 + 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrealheapsortstep2bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_0 >= ar_1 + 2*ar_2 + 4 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrealheapsortstep2bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ 2*ar_2 + ar_1 + 2 >= ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrealheapsortstep214(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) (Comp: ?, Cost: 1) evalrealheapsortstep2140(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) (Comp: ?, Cost: 1) evalrealheapsortstep2141(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrealheapsortstep215(ar_0, ar_1, ar_2, ar_4, ar_4, ar_5, ar_6, ar_7, ar_8))
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