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Complexity_C_Integer 2019-03-21 04.38 pair #429989704
details
property
value
status
complete
benchmark
realbubble.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n100.star.cs.uiowa.edu
space
WTC_V2
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
3.19856 seconds
cpu usage
4.55767
user time
4.17398
system time
0.383682
max virtual memory
1.8549624E7
max residence set size
210744.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
4.39/3.15 WORST_CASE(?, O(n^2)) 4.39/3.16 proof of /export/starexec/sandbox/output/output_files/bench.koat 4.39/3.16 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.39/3.16 4.39/3.16 4.39/3.16 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 4.39/3.16 4.39/3.16 (0) CpxIntTrs 4.39/3.16 (1) Koat Proof [FINISHED, 1989 ms] 4.39/3.16 (2) BOUNDS(1, n^2) 4.39/3.16 4.39/3.16 4.39/3.16 ---------------------------------------- 4.39/3.16 4.39/3.16 (0) 4.39/3.16 Obligation: 4.39/3.16 Complexity Int TRS consisting of the following rules: 4.39/3.16 eval_realbubble_start(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1) -> Com_1(eval_realbubble_bb0_in(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1)) :|: TRUE 4.39/3.16 eval_realbubble_bb0_in(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1) -> Com_1(eval_realbubble_bb1_in(v_3, v_4, v_length - 1, v_j.0, v_length, v_test.0, v_test.1)) :|: TRUE 4.39/3.16 eval_realbubble_bb1_in(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1) -> Com_1(eval_realbubble_bb2_in(v_3, v_4, v_i.0, 0, v_length, 0, v_test.1)) :|: v_i.0 > 0 4.39/3.16 eval_realbubble_bb1_in(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1) -> Com_1(eval_realbubble_bb8_in(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1)) :|: v_i.0 <= 0 4.39/3.16 eval_realbubble_bb2_in(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1) -> Com_1(eval_realbubble_bb3_in(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1)) :|: v_j.0 < v_i.0 4.39/3.16 eval_realbubble_bb2_in(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1) -> Com_1(eval_realbubble_bb6_in(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1)) :|: v_j.0 >= v_i.0 4.39/3.16 eval_realbubble_bb3_in(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1) -> Com_1(eval_realbubble_2(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1)) :|: TRUE 4.39/3.16 eval_realbubble_2(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1) -> Com_2(eval_nondet_start(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1), eval_realbubble_3(nondef.0, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1)) :|: TRUE 4.39/3.16 eval_realbubble_3(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1) -> Com_2(eval_nondet_start(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1), eval_realbubble_4(v_3, nondef.1, v_i.0, v_j.0, v_length, v_test.0, v_test.1)) :|: TRUE 4.39/3.16 eval_realbubble_4(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1) -> Com_1(eval_realbubble_bb4_in(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1)) :|: v_3 > v_4 4.39/3.16 eval_realbubble_4(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1) -> Com_1(eval_realbubble_bb5_in(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.0)) :|: v_3 <= v_4 4.39/3.16 eval_realbubble_bb4_in(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1) -> Com_1(eval_realbubble_5(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1)) :|: TRUE 4.39/3.16 eval_realbubble_5(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1) -> Com_2(eval_nondet_start(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1), eval_realbubble_6(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1)) :|: TRUE 4.39/3.16 eval_realbubble_6(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1) -> Com_1(eval_realbubble_bb5_in(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, 1)) :|: TRUE 4.39/3.16 eval_realbubble_bb5_in(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1) -> Com_1(eval_realbubble_bb2_in(v_3, v_4, v_i.0, v_j.0 + 1, v_length, v_test.1, v_test.1)) :|: TRUE 4.39/3.16 eval_realbubble_bb6_in(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1) -> Com_1(eval_realbubble_bb8_in(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1)) :|: v_test.0 >= 0 && v_test.0 <= 0 4.39/3.16 eval_realbubble_bb6_in(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1) -> Com_1(eval_realbubble_bb7_in(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1)) :|: v_test.0 < 0 4.39/3.16 eval_realbubble_bb6_in(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1) -> Com_1(eval_realbubble_bb7_in(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1)) :|: v_test.0 > 0 4.39/3.16 eval_realbubble_bb7_in(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1) -> Com_1(eval_realbubble_bb1_in(v_3, v_4, v_i.0 - 1, v_j.0, v_length, v_test.0, v_test.1)) :|: TRUE 4.39/3.16 eval_realbubble_bb8_in(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1) -> Com_1(eval_realbubble_stop(v_3, v_4, v_i.0, v_j.0, v_length, v_test.0, v_test.1)) :|: TRUE 4.39/3.16 4.39/3.16 The start-symbols are:[eval_realbubble_start_7] 4.39/3.16 4.39/3.16 4.39/3.16 ---------------------------------------- 4.39/3.16 4.39/3.16 (1) Koat Proof (FINISHED) 4.39/3.16 YES(?, 744*ar_1 + 728*ar_1^2 + 8) 4.39/3.16 4.39/3.16 4.39/3.16 4.39/3.16 Initial complexity problem: 4.39/3.16 4.39/3.16 1: T: 4.39/3.16 4.39/3.16 (Comp: ?, Cost: 1) evalrealbubblestart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalrealbubblebb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 4.39/3.16 4.39/3.16 (Comp: ?, Cost: 1) evalrealbubblebb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalrealbubblebb1in(ar_1 - 1, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 4.39/3.16 4.39/3.16 (Comp: ?, Cost: 1) evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalrealbubblebb2in(ar_0, ar_1, 0, 0, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 ] 4.39/3.16 4.39/3.16 (Comp: ?, Cost: 1) evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalrealbubblebb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_0 ] 4.39/3.16 4.39/3.16 (Comp: ?, Cost: 1) evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_2 + 1 ] 4.39/3.16 4.39/3.16 (Comp: ?, Cost: 1) evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_2 >= ar_0 ] 4.39/3.16 4.39/3.16 (Comp: ?, Cost: 1) evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalrealbubble2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 4.39/3.16 4.39/3.16 (Comp: ?, Cost: 1) evalrealbubble20(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 4.39/3.16 4.39/3.16 (Comp: ?, Cost: 1) evalrealbubble21(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalrealbubble3(ar_0, ar_1, ar_2, ar_3, ar_5, ar_5, ar_6, ar_7)) 4.39/3.16 4.39/3.16 (Comp: ?, Cost: 1) evalrealbubble2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_2(evalrealbubble20(ar_0, ar_1, ar_2, ar_3, ar_4, i, ar_6, ar_7), evalrealbubble21(ar_0, ar_1, ar_2, ar_3, ar_4, i, ar_6, ar_7)) 4.39/3.16 4.39/3.16 (Comp: ?, Cost: 1) evalrealbubble30(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 4.39/3.16 4.39/3.16 (Comp: ?, Cost: 1) evalrealbubble31(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalrealbubble4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_5, ar_7)) 4.39/3.16 4.39/3.16 (Comp: ?, Cost: 1) evalrealbubble3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_2(evalrealbubble30(ar_0, ar_1, ar_2, ar_3, ar_4, i, ar_6, ar_7), evalrealbubble31(ar_0, ar_1, ar_2, ar_3, ar_4, i, ar_6, ar_7)) 4.39/3.16 4.39/3.16 (Comp: ?, Cost: 1) evalrealbubble4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_4 >= ar_6 + 1 ] 4.39/3.16 4.39/3.16 (Comp: ?, Cost: 1) evalrealbubble4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_3)) [ ar_6 >= ar_4 ] 4.39/3.16 4.39/3.16 (Comp: ?, Cost: 1) evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalrealbubble5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 4.39/3.16 4.39/3.16 (Comp: ?, Cost: 1) evalrealbubble5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_2(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7), evalrealbubble6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 4.39/3.16 4.39/3.16 (Comp: ?, Cost: 1) evalrealbubble6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, 1)) 4.39/3.16 4.39/3.16 (Comp: ?, Cost: 1) evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalrealbubblebb2in(ar_0, ar_1, ar_2 + 1, ar_7, ar_4, ar_5, ar_6, ar_7)) 4.39/3.16 4.39/3.16 (Comp: ?, Cost: 1) evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalrealbubblebb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 = 0 ] 4.39/3.16 4.39/3.16 (Comp: ?, Cost: 1) evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_3 + 1 ] 4.39/3.16 4.39/3.16 (Comp: ?, Cost: 1) evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 >= 1 ] 4.39/3.16 4.39/3.16 (Comp: ?, Cost: 1) evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalrealbubblebb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 4.39/3.16 4.39/3.16 (Comp: ?, Cost: 1) evalrealbubblebb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalrealbubblestop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 4.39/3.16
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