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Complexity_C_Integer 2019-03-21 04.38 pair #429989630
details
property
value
status
complete
benchmark
realselect.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n089.star.cs.uiowa.edu
space
WTC_V2
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.85475 seconds
cpu usage
2.64438
user time
2.43497
system time
0.209419
max virtual memory
1.8435304E7
max residence set size
180004.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
2.53/1.82 WORST_CASE(?, O(n^2)) 2.59/1.83 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.59/1.83 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.59/1.83 2.59/1.83 2.59/1.83 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 2.59/1.83 2.59/1.83 (0) CpxIntTrs 2.59/1.83 (1) Koat Proof [FINISHED, 479 ms] 2.59/1.83 (2) BOUNDS(1, n^2) 2.59/1.83 2.59/1.83 2.59/1.83 ---------------------------------------- 2.59/1.83 2.59/1.83 (0) 2.59/1.83 Obligation: 2.59/1.83 Complexity Int TRS consisting of the following rules: 2.59/1.83 eval_realselect_start(v_array_size, v_i.0, v_j.0) -> Com_1(eval_realselect_bb0_in(v_array_size, v_i.0, v_j.0)) :|: TRUE 2.59/1.83 eval_realselect_bb0_in(v_array_size, v_i.0, v_j.0) -> Com_1(eval_realselect_bb1_in(v_array_size, 0, v_j.0)) :|: TRUE 2.59/1.83 eval_realselect_bb1_in(v_array_size, v_i.0, v_j.0) -> Com_1(eval_realselect_bb2_in(v_array_size, v_i.0, v_j.0)) :|: v_i.0 < v_array_size - 1 2.59/1.83 eval_realselect_bb1_in(v_array_size, v_i.0, v_j.0) -> Com_1(eval_realselect_bb6_in(v_array_size, v_i.0, v_j.0)) :|: v_i.0 >= v_array_size - 1 2.59/1.83 eval_realselect_bb2_in(v_array_size, v_i.0, v_j.0) -> Com_1(eval_realselect_bb3_in(v_array_size, v_i.0, v_i.0 + 1)) :|: TRUE 2.59/1.83 eval_realselect_bb3_in(v_array_size, v_i.0, v_j.0) -> Com_1(eval_realselect_bb4_in(v_array_size, v_i.0, v_j.0)) :|: v_j.0 < v_array_size 2.59/1.83 eval_realselect_bb3_in(v_array_size, v_i.0, v_j.0) -> Com_1(eval_realselect_bb5_in(v_array_size, v_i.0, v_j.0)) :|: v_j.0 >= v_array_size 2.59/1.83 eval_realselect_bb4_in(v_array_size, v_i.0, v_j.0) -> Com_1(eval_realselect_4(v_array_size, v_i.0, v_j.0)) :|: TRUE 2.59/1.83 eval_realselect_4(v_array_size, v_i.0, v_j.0) -> Com_2(eval_nondet_start(v_array_size, v_i.0, v_j.0), eval_realselect_5(v_array_size, v_i.0, v_j.0)) :|: TRUE 2.59/1.83 eval_realselect_5(v_array_size, v_i.0, v_j.0) -> Com_2(eval_nondet_start(v_array_size, v_i.0, v_j.0), eval_realselect_6(v_array_size, v_i.0, v_j.0)) :|: TRUE 2.59/1.83 eval_realselect_6(v_array_size, v_i.0, v_j.0) -> Com_1(eval_realselect_bb3_in(v_array_size, v_i.0, v_j.0 + 1)) :|: TRUE 2.59/1.83 eval_realselect_bb5_in(v_array_size, v_i.0, v_j.0) -> Com_1(eval_realselect_bb1_in(v_array_size, v_i.0 + 1, v_j.0)) :|: TRUE 2.59/1.83 eval_realselect_bb6_in(v_array_size, v_i.0, v_j.0) -> Com_1(eval_realselect_stop(v_array_size, v_i.0, v_j.0)) :|: TRUE 2.59/1.83 2.59/1.83 The start-symbols are:[eval_realselect_start_3] 2.59/1.83 2.59/1.83 2.59/1.83 ---------------------------------------- 2.59/1.83 2.59/1.83 (1) Koat Proof (FINISHED) 2.59/1.83 YES(?, 16*ar_1 + 200*ar_1^2 + 6) 2.59/1.83 2.59/1.83 2.59/1.83 2.59/1.83 Initial complexity problem: 2.59/1.83 2.59/1.83 1: T: 2.59/1.83 2.59/1.83 (Comp: ?, Cost: 1) evalrealselectstart(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb0in(ar_0, ar_1, ar_2)) 2.59/1.83 2.59/1.83 (Comp: ?, Cost: 1) evalrealselectbb0in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb1in(0, ar_1, ar_2)) 2.59/1.83 2.59/1.83 (Comp: ?, Cost: 1) evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb2in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_0 + 2 ] 2.59/1.83 2.59/1.83 (Comp: ?, Cost: 1) evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(ar_0, ar_1, ar_2)) [ ar_0 + 1 >= ar_1 ] 2.59/1.83 2.59/1.83 (Comp: ?, Cost: 1) evalrealselectbb2in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb3in(ar_0, ar_1, ar_0 + 1)) 2.59/1.83 2.59/1.83 (Comp: ?, Cost: 1) evalrealselectbb3in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ] 2.59/1.83 2.59/1.83 (Comp: ?, Cost: 1) evalrealselectbb3in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ] 2.59/1.83 2.59/1.83 (Comp: ?, Cost: 1) evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselect4(ar_0, ar_1, ar_2)) 2.59/1.83 2.59/1.83 (Comp: ?, Cost: 1) evalrealselect4(ar_0, ar_1, ar_2) -> Com_2(evalnondetstart(ar_0, ar_1, ar_2), evalrealselect5(ar_0, ar_1, ar_2)) 2.59/1.83 2.59/1.83 (Comp: ?, Cost: 1) evalrealselect5(ar_0, ar_1, ar_2) -> Com_2(evalnondetstart(ar_0, ar_1, ar_2), evalrealselect6(ar_0, ar_1, ar_2)) 2.59/1.83 2.59/1.83 (Comp: ?, Cost: 1) evalrealselect6(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb3in(ar_0, ar_1, ar_2 + 1)) 2.59/1.83 2.59/1.83 (Comp: ?, Cost: 1) evalrealselectbb5in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb1in(ar_0 + 1, ar_1, ar_2)) 2.59/1.83 2.59/1.83 (Comp: ?, Cost: 1) evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstop(ar_0, ar_1, ar_2)) 2.59/1.83 2.59/1.83 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 2.59/1.83 2.59/1.83 start location: koat_start 2.59/1.83 2.59/1.83 leaf cost: 0 2.59/1.83 2.59/1.83 2.59/1.83 2.59/1.83 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.59/1.83 2.59/1.83 2: T: 2.59/1.83 2.59/1.83 (Comp: 1, Cost: 1) evalrealselectstart(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb0in(ar_0, ar_1, ar_2)) 2.59/1.83 2.59/1.83 (Comp: 1, Cost: 1) evalrealselectbb0in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb1in(0, ar_1, ar_2)) 2.59/1.83 2.59/1.83 (Comp: ?, Cost: 1) evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb2in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_0 + 2 ] 2.59/1.83 2.59/1.83 (Comp: ?, Cost: 1) evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(ar_0, ar_1, ar_2)) [ ar_0 + 1 >= ar_1 ] 2.59/1.83 2.59/1.83 (Comp: ?, Cost: 1) evalrealselectbb2in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb3in(ar_0, ar_1, ar_0 + 1)) 2.59/1.83 2.59/1.83 (Comp: ?, Cost: 1) evalrealselectbb3in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ] 2.59/1.83 2.59/1.83 (Comp: ?, Cost: 1) evalrealselectbb3in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ] 2.59/1.83 2.59/1.83 (Comp: ?, Cost: 1) evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselect4(ar_0, ar_1, ar_2)) 2.59/1.83 2.59/1.83 (Comp: ?, Cost: 1) evalrealselect4(ar_0, ar_1, ar_2) -> Com_2(evalnondetstart(ar_0, ar_1, ar_2), evalrealselect5(ar_0, ar_1, ar_2))
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