details

property	value
status	complete
benchmark	realbubble.c.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n113.star.cs.uiowa.edu
space	Flores-Montoya_16

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	3.13397 seconds
cpu usage	7.37425
user time	7.0197
system time	0.354552
max virtual memory	1.8537364E7
max residence set size	236760.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^2), O(n^2))

output

7.26/3.09 WORST_CASE(Omega(n^2), O(n^2)) 7.26/3.10 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 7.26/3.10 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 7.26/3.10 7.26/3.10 7.26/3.10 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2). 7.26/3.10 7.26/3.10 (0) CpxIntTrs 7.26/3.10 (1) Koat Proof [FINISHED, 638 ms] 7.26/3.10 (2) BOUNDS(1, n^2) 7.26/3.10 (3) Loat Proof [FINISHED, 1308 ms] 7.26/3.10 (4) BOUNDS(n^2, INF) 7.26/3.10 7.26/3.10 7.26/3.10 ---------------------------------------- 7.26/3.10 7.26/3.10 (0) 7.26/3.10 Obligation: 7.26/3.10 Complexity Int TRS consisting of the following rules: 7.26/3.10 eval_realbubble_start(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_bb0_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: TRUE 7.26/3.10 eval_realbubble_bb0_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_1(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: TRUE 7.26/3.10 eval_realbubble_1(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_2(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: TRUE 7.26/3.10 eval_realbubble_2(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_3(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: TRUE 7.26/3.10 eval_realbubble_3(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_4(v_length - 1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: TRUE 7.26/3.10 eval_realbubble_4(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_5(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: TRUE 7.26/3.10 eval_realbubble_5(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_6(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: TRUE 7.26/3.10 eval_realbubble_6(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_7(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: TRUE 7.26/3.10 eval_realbubble_7(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_8(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: TRUE 7.26/3.10 eval_realbubble_8(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_9(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: TRUE 7.26/3.10 eval_realbubble_9(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_10(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: TRUE 7.26/3.10 eval_realbubble_10(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_bb1_in(v_1, v_26, v_1, v_j_0, v_length, v_test_0, v_test_1)) :|: TRUE 7.26/3.10 eval_realbubble_bb1_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_bb2_in(v_1, v_26, v_i_0, 0, v_length, 0, v_test_1)) :|: v_i_0 > 0 7.26/3.10 eval_realbubble_bb1_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_bb8_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: v_i_0 <= 0 7.26/3.10 eval_realbubble_bb2_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_bb3_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: v_j_0 < v_i_0 7.26/3.10 eval_realbubble_bb2_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_bb6_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: v_j_0 >= v_i_0 7.26/3.10 eval_realbubble_bb3_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_bb4_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: nondef_1 > nondef_2 7.26/3.10 eval_realbubble_bb3_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_bb5_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_0)) :|: nondef_1 <= nondef_2 7.26/3.10 eval_realbubble_bb4_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_bb5_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, 1)) :|: TRUE 7.26/3.10 eval_realbubble_bb5_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_bb2_in(v_1, v_26, v_i_0, v_j_0 + 1, v_length, v_test_1, v_test_1)) :|: TRUE 7.26/3.10 eval_realbubble_bb6_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_bb8_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: v_test_0 >= 0 && v_test_0 <= 0 7.26/3.10 eval_realbubble_bb6_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_bb7_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: v_test_0 < 0 7.26/3.10 eval_realbubble_bb6_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_bb7_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: v_test_0 > 0 7.26/3.10 eval_realbubble_bb7_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_31(v_1, v_i_0 - 1, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: TRUE 7.26/3.10 eval_realbubble_31(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_32(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: TRUE 7.26/3.10 eval_realbubble_32(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_bb1_in(v_1, v_26, v_26, v_j_0, v_length, v_test_0, v_test_1)) :|: TRUE 7.26/3.10 eval_realbubble_bb8_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_stop(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: TRUE 7.26/3.10 7.26/3.10 The start-symbols are:[eval_realbubble_start_7] 7.26/3.10 7.26/3.10 7.26/3.10 ---------------------------------------- 7.26/3.10 7.26/3.10 (1) Koat Proof (FINISHED) 7.26/3.10 YES(?, 253*ar_1 + 36*ar_1^2 + 18) 7.26/3.10 7.26/3.10 7.26/3.10 7.26/3.10 Initial complexity problem: 7.26/3.10 7.26/3.10 1: T: 7.26/3.10 7.26/3.10 (Comp: ?, Cost: 1) evalrealbubblestart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubblebb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 7.26/3.10 7.26/3.10 (Comp: ?, Cost: 1) evalrealbubblebb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubble1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 7.26/3.10 7.26/3.10 (Comp: ?, Cost: 1) evalrealbubble1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubble2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 7.26/3.10 7.26/3.10 (Comp: ?, Cost: 1) evalrealbubble2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubble3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 7.26/3.10 7.26/3.10 (Comp: ?, Cost: 1) evalrealbubble3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubble4(ar_1 - 1, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 7.26/3.10 7.26/3.10 (Comp: ?, Cost: 1) evalrealbubble4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubble5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 7.26/3.10 7.26/3.10 (Comp: ?, Cost: 1) evalrealbubble5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubble6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 7.26/3.10 7.26/3.10 (Comp: ?, Cost: 1) evalrealbubble6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubble7(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 7.26/3.10 7.26/3.10 (Comp: ?, Cost: 1) evalrealbubble7(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubble8(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 7.26/3.10 7.26/3.10 (Comp: ?, Cost: 1) evalrealbubble8(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubble9(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 7.26/3.10 7.26/3.10 (Comp: ?, Cost: 1) evalrealbubble9(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubble10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 7.26/3.10 7.26/3.10 (Comp: ?, Cost: 1) evalrealbubble10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubblebb1in(ar_0, ar_1, ar_0, ar_3, ar_4, ar_5, ar_6)) 7.26/3.10 7.26/3.10 (Comp: ?, Cost: 1) evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubblebb2in(ar_0, ar_1, ar_2, 0, 0, ar_5, ar_6)) [ ar_2 >= 1 ] 7.26/3.10 7.26/3.10 (Comp: ?, Cost: 1) evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubblebb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_2 ] 7.26/3.10 7.26/3.10 (Comp: ?, Cost: 1) evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_2 >= ar_3 + 1 ] 7.26/3.10 7.26/3.10 (Comp: ?, Cost: 1) evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_3 >= ar_2 ] 7.26/3.10 7.26/3.10 (Comp: ?, Cost: 1) evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ h >= i + 1 ] 7.26/3.10 7.26/3.10 (Comp: ?, Cost: 1) evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4, ar_6)) [ i >= h ] 7.26/3.10 7.26/3.10 (Comp: ?, Cost: 1) evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3, ar_4, 1, ar_6)) 7.26/3.10 7.26/3.10 (Comp: ?, Cost: 1) evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_5, ar_5, ar_6)) popout

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all output return to Complexity_ITS 2019-03-21 04.46