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Complexity_C_Integer 2019-03-21 04.38 pair #429989582
details
property
value
status
complete
benchmark
cBench_noiseTickSize.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n082.star.cs.uiowa.edu
space
Sinn_2016
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
3.21737 seconds
cpu usage
4.57549
user time
4.2348
system time
0.340691
max virtual memory
1.8508904E7
max residence set size
200488.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
4.39/3.15 WORST_CASE(?, O(n^2)) 4.39/3.17 proof of /export/starexec/sandbox/output/output_files/bench.koat 4.39/3.17 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.39/3.17 4.39/3.17 4.39/3.17 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 4.39/3.17 4.39/3.17 (0) CpxIntTrs 4.39/3.17 (1) Koat Proof [FINISHED, 1901 ms] 4.39/3.17 (2) BOUNDS(1, n^2) 4.39/3.17 4.39/3.17 4.39/3.17 ---------------------------------------- 4.39/3.17 4.39/3.17 (0) 4.39/3.17 Obligation: 4.39/3.17 Complexity Int TRS consisting of the following rules: 4.39/3.17 eval_noiseTickSize_start(v_0, v_DELTAS, v_i.0, v_j.0) -> Com_1(eval_noiseTickSize_bb0_in(v_0, v_DELTAS, v_i.0, v_j.0)) :|: TRUE 4.39/3.17 eval_noiseTickSize_bb0_in(v_0, v_DELTAS, v_i.0, v_j.0) -> Com_1(eval_noiseTickSize_bb1_in(v_0, v_DELTAS, 0, 0)) :|: TRUE 4.39/3.17 eval_noiseTickSize_bb1_in(v_0, v_DELTAS, v_i.0, v_j.0) -> Com_1(eval_noiseTickSize_0(v_0, v_DELTAS, v_i.0, v_j.0)) :|: TRUE 4.39/3.17 eval_noiseTickSize_0(v_0, v_DELTAS, v_i.0, v_j.0) -> Com_2(eval_nondet_start(v_0, v_DELTAS, v_i.0, v_j.0), eval_noiseTickSize_1(nondef.0, v_DELTAS, v_i.0, v_j.0)) :|: TRUE 4.39/3.17 eval_noiseTickSize_1(v_0, v_DELTAS, v_i.0, v_j.0) -> Com_1(eval_noiseTickSize_bb1_in(v_0, v_DELTAS, v_i.0 + 1, 1)) :|: v_0 < 0 && v_i.0 + 1 < v_DELTAS 4.39/3.17 eval_noiseTickSize_1(v_0, v_DELTAS, v_i.0, v_j.0) -> Com_1(eval_noiseTickSize_bb1_in(v_0, v_DELTAS, v_i.0 + 1, 1)) :|: v_0 < 0 && v_0 > 0 && v_i.0 + 1 < v_DELTAS 4.39/3.17 eval_noiseTickSize_1(v_0, v_DELTAS, v_i.0, v_j.0) -> Com_1(eval_noiseTickSize_bb1_in(v_0, v_DELTAS, v_i.0 + 1, 1)) :|: v_0 > 0 && v_i.0 + 1 < v_DELTAS 4.39/3.17 eval_noiseTickSize_1(v_0, v_DELTAS, v_i.0, v_j.0) -> Com_1(eval_noiseTickSize_bb2_in(v_0, v_DELTAS, v_i.0, v_j.0)) :|: v_0 < 0 && v_i.0 + 1 >= v_DELTAS 4.39/3.17 eval_noiseTickSize_1(v_0, v_DELTAS, v_i.0, v_j.0) -> Com_1(eval_noiseTickSize_bb2_in(v_0, v_DELTAS, v_i.0, v_j.0)) :|: v_0 < 0 && v_0 > 0 && v_i.0 + 1 >= v_DELTAS 4.39/3.17 eval_noiseTickSize_1(v_0, v_DELTAS, v_i.0, v_j.0) -> Com_1(eval_noiseTickSize_bb2_in(v_0, v_DELTAS, v_i.0, v_j.0)) :|: v_0 > 0 && v_i.0 + 1 >= v_DELTAS 4.39/3.17 eval_noiseTickSize_1(v_0, v_DELTAS, v_i.0, v_j.0) -> Com_1(eval_noiseTickSize_bb1_in(v_0, v_DELTAS, v_i.0, 1)) :|: v_0 < 0 && v_0 >= 0 && v_0 <= 0 && v_i.0 < v_DELTAS 4.39/3.17 eval_noiseTickSize_1(v_0, v_DELTAS, v_i.0, v_j.0) -> Com_1(eval_noiseTickSize_bb1_in(v_0, v_DELTAS, v_i.0, 1)) :|: v_0 > 0 && v_0 >= 0 && v_0 <= 0 && v_i.0 < v_DELTAS 4.39/3.17 eval_noiseTickSize_1(v_0, v_DELTAS, v_i.0, v_j.0) -> Com_1(eval_noiseTickSize_bb2_in(v_0, v_DELTAS, v_i.0, v_j.0)) :|: v_0 < 0 && v_0 >= 0 && v_0 <= 0 && v_i.0 >= v_DELTAS 4.39/3.17 eval_noiseTickSize_1(v_0, v_DELTAS, v_i.0, v_j.0) -> Com_1(eval_noiseTickSize_bb2_in(v_0, v_DELTAS, v_i.0, v_j.0)) :|: v_0 > 0 && v_0 >= 0 && v_0 <= 0 && v_i.0 >= v_DELTAS 4.39/3.17 eval_noiseTickSize_1(v_0, v_DELTAS, v_i.0, v_j.0) -> Com_1(eval_noiseTickSize_bb1_in(v_0, v_DELTAS, v_i.0 + 1, v_j.0 + 1)) :|: v_0 >= 0 && v_0 <= 0 && v_0 < 0 && v_j.0 <= 10000 && v_i.0 + 1 < v_DELTAS 4.39/3.17 eval_noiseTickSize_1(v_0, v_DELTAS, v_i.0, v_j.0) -> Com_1(eval_noiseTickSize_bb1_in(v_0, v_DELTAS, v_i.0 + 1, v_j.0 + 1)) :|: v_0 >= 0 && v_0 <= 0 && v_0 > 0 && v_j.0 <= 10000 && v_i.0 + 1 < v_DELTAS 4.39/3.17 eval_noiseTickSize_1(v_0, v_DELTAS, v_i.0, v_j.0) -> Com_1(eval_noiseTickSize_bb2_in(v_0, v_DELTAS, v_i.0, v_j.0)) :|: v_0 >= 0 && v_0 <= 0 && v_0 < 0 && v_j.0 > 10000 4.39/3.17 eval_noiseTickSize_1(v_0, v_DELTAS, v_i.0, v_j.0) -> Com_1(eval_noiseTickSize_bb2_in(v_0, v_DELTAS, v_i.0, v_j.0)) :|: v_0 >= 0 && v_0 <= 0 && v_0 < 0 && v_i.0 + 1 >= v_DELTAS 4.39/3.17 eval_noiseTickSize_1(v_0, v_DELTAS, v_i.0, v_j.0) -> Com_1(eval_noiseTickSize_bb2_in(v_0, v_DELTAS, v_i.0, v_j.0)) :|: v_0 >= 0 && v_0 <= 0 && v_0 > 0 && v_j.0 > 10000 4.39/3.17 eval_noiseTickSize_1(v_0, v_DELTAS, v_i.0, v_j.0) -> Com_1(eval_noiseTickSize_bb2_in(v_0, v_DELTAS, v_i.0, v_j.0)) :|: v_0 >= 0 && v_0 <= 0 && v_0 > 0 && v_i.0 + 1 >= v_DELTAS 4.39/3.17 eval_noiseTickSize_1(v_0, v_DELTAS, v_i.0, v_j.0) -> Com_1(eval_noiseTickSize_bb1_in(v_0, v_DELTAS, v_i.0, v_j.0 + 1)) :|: v_0 >= 0 && v_0 <= 0 && v_j.0 <= 10000 && v_i.0 < v_DELTAS 4.39/3.17 eval_noiseTickSize_1(v_0, v_DELTAS, v_i.0, v_j.0) -> Com_1(eval_noiseTickSize_bb2_in(v_0, v_DELTAS, v_i.0, v_j.0)) :|: v_0 >= 0 && v_0 <= 0 && v_j.0 > 10000 4.39/3.17 eval_noiseTickSize_1(v_0, v_DELTAS, v_i.0, v_j.0) -> Com_1(eval_noiseTickSize_bb2_in(v_0, v_DELTAS, v_i.0, v_j.0)) :|: v_0 >= 0 && v_0 <= 0 && v_i.0 >= v_DELTAS 4.39/3.17 eval_noiseTickSize_bb2_in(v_0, v_DELTAS, v_i.0, v_j.0) -> Com_1(eval_noiseTickSize_stop(v_0, v_DELTAS, v_i.0, v_j.0)) :|: TRUE 4.39/3.17 4.39/3.17 The start-symbols are:[eval_noiseTickSize_start_4] 4.39/3.17 4.39/3.17 4.39/3.17 ---------------------------------------- 4.39/3.17 4.39/3.17 (1) Koat Proof (FINISHED) 4.39/3.17 YES(?, 300068*ar_4 + 200020*ar_4^2 + 64) 4.39/3.17 4.39/3.17 4.39/3.17 4.39/3.17 Initial complexity problem: 4.39/3.17 4.39/3.17 1: T: 4.39/3.17 4.39/3.17 (Comp: ?, Cost: 1) evalnoiseTickSizestart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalnoiseTickSizebb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) 4.39/3.17 4.39/3.17 (Comp: ?, Cost: 1) evalnoiseTickSizebb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalnoiseTickSizebb1in(0, 0, ar_2, ar_3, ar_4)) 4.39/3.17 4.39/3.17 (Comp: ?, Cost: 1) evalnoiseTickSizebb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalnoiseTickSize0(ar_0, ar_1, ar_2, ar_3, ar_4)) 4.39/3.17 4.39/3.17 (Comp: ?, Cost: 1) evalnoiseTickSize00(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4)) 4.39/3.17 4.39/3.17 (Comp: ?, Cost: 1) evalnoiseTickSize01(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalnoiseTickSize1(ar_0, ar_1, ar_3, ar_3, ar_4)) 4.39/3.17 4.39/3.17 (Comp: ?, Cost: 1) evalnoiseTickSize0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_2(evalnoiseTickSize00(ar_0, ar_1, ar_2, f, ar_4), evalnoiseTickSize01(ar_0, ar_1, ar_2, f, ar_4)) 4.39/3.17 4.39/3.17 (Comp: ?, Cost: 1) evalnoiseTickSize1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalnoiseTickSizebb1in(ar_0 + 1, 1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 /\ ar_4 >= ar_0 + 2 ] 4.39/3.17 4.39/3.17 (Comp: ?, Cost: 1) evalnoiseTickSize1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalnoiseTickSizebb1in(ar_0 + 1, 1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 /\ ar_2 >= 1 /\ ar_4 >= ar_0 + 2 ] 4.39/3.17 4.39/3.17 (Comp: ?, Cost: 1) evalnoiseTickSize1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalnoiseTickSizebb1in(ar_0 + 1, 1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 /\ ar_4 >= ar_0 + 2 ] 4.39/3.17 4.39/3.17 (Comp: ?, Cost: 1) evalnoiseTickSize1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalnoiseTickSizebb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 /\ ar_0 + 1 >= ar_4 ] 4.39/3.17 4.39/3.17 (Comp: ?, Cost: 1) evalnoiseTickSize1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalnoiseTickSizebb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 /\ ar_2 >= 1 /\ ar_0 + 1 >= ar_4 ] 4.39/3.17 4.39/3.17 (Comp: ?, Cost: 1) evalnoiseTickSize1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalnoiseTickSizebb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 /\ ar_0 + 1 >= ar_4 ] 4.39/3.17 4.39/3.17 (Comp: ?, Cost: 1) evalnoiseTickSize1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalnoiseTickSizebb1in(ar_0, 1, ar_2, ar_3, ar_4)) [ 0 >= 1 /\ ar_4 >= ar_0 + 1 /\ ar_2 = 0 ] 4.39/3.17 4.39/3.17 (Comp: ?, Cost: 1) evalnoiseTickSize1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalnoiseTickSizebb1in(ar_0, 1, ar_2, ar_3, ar_4)) [ 0 >= 1 /\ ar_4 >= ar_0 + 1 /\ ar_2 = 0 ] 4.39/3.17 4.39/3.17 (Comp: ?, Cost: 1) evalnoiseTickSize1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalnoiseTickSizebb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= 1 /\ ar_0 >= ar_4 /\ ar_2 = 0 ] 4.39/3.17 4.39/3.17 (Comp: ?, Cost: 1) evalnoiseTickSize1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalnoiseTickSizebb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= 1 /\ ar_0 >= ar_4 /\ ar_2 = 0 ] 4.39/3.17 4.39/3.17 (Comp: ?, Cost: 1) evalnoiseTickSize1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalnoiseTickSizebb1in(ar_0 + 1, ar_1 + 1, ar_2, ar_3, ar_4)) [ 0 >= 1 /\ 10000 >= ar_1 /\ ar_4 >= ar_0 + 2 /\ ar_2 = 0 ] 4.39/3.17 4.39/3.17 (Comp: ?, Cost: 1) evalnoiseTickSize1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalnoiseTickSizebb1in(ar_0 + 1, ar_1 + 1, ar_2, ar_3, ar_4)) [ 0 >= 1 /\ 10000 >= ar_1 /\ ar_4 >= ar_0 + 2 /\ ar_2 = 0 ] 4.39/3.17 4.39/3.17 (Comp: ?, Cost: 1) evalnoiseTickSize1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalnoiseTickSizebb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= 1 /\ ar_1 >= 10001 /\ ar_2 = 0 ] 4.39/3.17 4.39/3.17 (Comp: ?, Cost: 1) evalnoiseTickSize1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalnoiseTickSizebb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= 1 /\ ar_0 + 1 >= ar_4 /\ ar_2 = 0 ] 4.39/3.17 4.39/3.17 (Comp: ?, Cost: 1) evalnoiseTickSize1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalnoiseTickSizebb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= 1 /\ ar_1 >= 10001 /\ ar_2 = 0 ] 4.39/3.17 4.39/3.17 (Comp: ?, Cost: 1) evalnoiseTickSize1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalnoiseTickSizebb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= 1 /\ ar_0 + 1 >= ar_4 /\ ar_2 = 0 ] 4.39/3.17
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