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Compl C Integ Progr 85445 pair #381745826
details
property
value
status
complete
benchmark
realheapsort_step1.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n192.star.cs.uiowa.edu
space
WTC_V2
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
2.50938606262 seconds
cpu usage
3.64870014
max memory
3.45493504E8
stage attributes
key
value
output-size
169007
starexec-result
WORST_CASE(?, O(n^2))
output
/export/starexec/sandbox/solver/bin/starexec_run_c_complexity /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^2)) proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2).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, 1284 ms] (2) BOUNDS(1, n^2) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_realheapsort_step1_start(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_1(eval_realheapsort_step1_bb0_in(v_4, v_5, v_N, v_j.0, v_k.0)) :|: TRUE eval_realheapsort_step1_bb0_in(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_1(eval_realheapsort_step1_bb1_in(v_4, v_5, v_N, v_j.0, 1)) :|: v_N > 2 eval_realheapsort_step1_bb0_in(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_1(eval_realheapsort_step1_bb5_in(v_4, v_5, v_N, v_j.0, v_k.0)) :|: v_N <= 2 eval_realheapsort_step1_bb1_in(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_1(eval_realheapsort_step1_bb2_in(v_4, v_5, v_N, v_k.0, v_k.0)) :|: v_k.0 <= v_N - 1 eval_realheapsort_step1_bb1_in(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_1(eval_realheapsort_step1_bb5_in(v_4, v_5, v_N, v_j.0, v_k.0)) :|: v_k.0 > v_N - 1 eval_realheapsort_step1_bb2_in(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_1(eval_realheapsort_step1_bb3_in(v_4, v_5, v_N, v_j.0, v_k.0)) :|: v_j.0 > 0 eval_realheapsort_step1_bb2_in(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_1(eval_realheapsort_step1_.critedge_in(v_4, v_5, v_N, v_j.0, v_k.0)) :|: v_j.0 <= 0 eval_realheapsort_step1_bb3_in(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_1(eval_realheapsort_step1_2(v_4, v_5, v_N, v_j.0, v_k.0)) :|: TRUE eval_realheapsort_step1_2(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_2(eval_nondet_start(v_4, v_5, v_N, v_j.0, v_k.0), eval_realheapsort_step1_3(nondef.0, v_5, v_N, v_j.0, v_k.0)) :|: TRUE eval_realheapsort_step1_3(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_2(eval_nondet_start(v_4, v_5, v_N, v_j.0, v_k.0), eval_realheapsort_step1_4(v_4, nondef.1, v_N, v_j.0, v_k.0)) :|: TRUE eval_realheapsort_step1_4(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_1(eval_realheapsort_step1_bb4_in(v_4, v_5, v_N, v_j.0, v_k.0)) :|: v_4 > v_5 eval_realheapsort_step1_4(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_1(eval_realheapsort_step1_.critedge_in(v_4, v_5, v_N, v_j.0, v_k.0)) :|: v_4 <= v_5 eval_realheapsort_step1_bb4_in(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_1(eval_realheapsort_step1_5(v_4, v_5, v_N, v_j.0, v_k.0)) :|: TRUE eval_realheapsort_step1_5(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_2(eval_nondet_start(v_4, v_5, v_N, v_j.0, v_k.0), eval_realheapsort_step1_6(v_4, v_5, v_N, v_j.0, v_k.0)) :|: TRUE eval_realheapsort_step1_6(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_1(eval_realheapsort_step1_bb2_in(v_4, v_5, v_N, nondef.3 - 1, v_k.0)) :|: v_j.0 + 1 >= 0 && v_j.0 + 1 <= 0 && nondef.3 >= 0 && nondef.3 <= 0 eval_realheapsort_step1_6(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_1(eval_realheapsort_step1_bb2_in(v_4, v_5, v_N, nondef.3 - 1, v_k.0)) :|: v_j.0 + 1 > 0 && nondef.3 >= 0 && nondef.3 < v_j.0 + 1 eval_realheapsort_step1_6(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_1(eval_realheapsort_step1_bb2_in(v_4, v_5, v_N, nondef.3 - 1, v_k.0)) :|: v_j.0 + 1 < 0 && nondef.3 <= 0 && nondef.3 > v_j.0 + 1 eval_realheapsort_step1_.critedge_in(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_1(eval_realheapsort_step1_bb1_in(v_4, v_5, v_N, v_j.0, v_k.0 + 1)) :|: TRUE eval_realheapsort_step1_bb5_in(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_1(eval_realheapsort_step1_stop(v_4, v_5, v_N, v_j.0, v_k.0)) :|: TRUE The start-symbols are:[eval_realheapsort_step1_start_5] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 876*ar_0 + 432*ar_0^2 + 451) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: ?, Cost: 1) evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 2 >= ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3, ar_4, ar_5)) [ ar_0 >= ar_1 + 1 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= 1 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: ?, Cost: 1) evalrealheapsortstep120(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: ?, Cost: 1) evalrealheapsortstep121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep13(ar_0, ar_1, ar_2, ar_4, ar_4, ar_5)) (Comp: ?, Cost: 1) evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_2(evalrealheapsortstep120(ar_0, ar_1, ar_2, ar_3, g, ar_5), evalrealheapsortstep121(ar_0, ar_1, ar_2, ar_3, g, ar_5)) (Comp: ?, Cost: 1) evalrealheapsortstep130(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: ?, Cost: 1) evalrealheapsortstep131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4)) (Comp: ?, Cost: 1) evalrealheapsortstep13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_2(evalrealheapsortstep130(ar_0, ar_1, ar_2, ar_3, g, ar_5), evalrealheapsortstep131(ar_0, ar_1, ar_2, ar_3, g, ar_5)) (Comp: ?, Cost: 1) evalrealheapsortstep14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_3 >= ar_5 + 1 ] (Comp: ?, Cost: 1) evalrealheapsortstep14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= ar_3 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep15(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: ?, Cost: 1) evalrealheapsortstep15(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_2(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5), evalrealheapsortstep16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: ?, Cost: 1) evalrealheapsortstep16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3, ar_4, ar_5)) [ ar_2 + 1 = 0 ] (Comp: ?, Cost: 1) evalrealheapsortstep16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, g - 1, ar_3, ar_4, ar_5)) [ ar_2 >= 0 /\ g >= 0 /\ ar_2 >= g ] (Comp: ?, Cost: 1) evalrealheapsortstep16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, g - 1, ar_3, ar_4, ar_5)) [ 0 >= ar_2 + 2 /\ 0 >= g /\ g >= ar_2 + 2 ] (Comp: ?, Cost: 1) evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_1 + 1, ar_2, ar_3, ar_4, ar_5))
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