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Complexity_C_Integer 2019-03-21 04.38 pair #429989534
details
property
value
status
complete
benchmark
ex_paper3.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n149.star.cs.uiowa.edu
space
Other
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
7.21674 seconds
cpu usage
7.00104
user time
6.56297
system time
0.438073
max virtual memory
1.8720748E7
max residence set size
280564.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
6.91/5.64 WORST_CASE(?, O(n^2)) 6.91/5.65 proof of /export/starexec/sandbox/output/output_files/bench.koat 6.91/5.65 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 6.91/5.65 6.91/5.65 6.91/5.65 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 6.91/5.65 6.91/5.65 (0) CpxIntTrs 6.91/5.65 (1) Koat Proof [FINISHED, 4309 ms] 6.91/5.65 (2) BOUNDS(1, n^2) 6.91/5.65 6.91/5.65 6.91/5.65 ---------------------------------------- 6.91/5.65 6.91/5.65 (0) 6.91/5.65 Obligation: 6.91/5.65 Complexity Int TRS consisting of the following rules: 6.91/5.65 eval_exp_paper3_start(v_.0, v_.01, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z) -> Com_1(eval_exp_paper3_bb0_in(v_.0, v_.01, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z)) :|: TRUE 6.91/5.65 eval_exp_paper3_bb0_in(v_.0, v_.01, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z) -> Com_1(eval_exp_paper3_bb1_in(v_x, v_y, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z)) :|: TRUE 6.91/5.65 eval_exp_paper3_bb1_in(v_.0, v_.01, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z) -> Com_1(eval_exp_paper3_bb2_in(v_.0, v_.01, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z)) :|: v_.0 > 0 6.91/5.65 eval_exp_paper3_bb1_in(v_.0, v_.01, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z) -> Com_1(eval_exp_paper3_bb7_in(v_.0, v_.01, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z)) :|: v_.0 <= 0 6.91/5.65 eval_exp_paper3_bb2_in(v_.0, v_.01, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z) -> Com_1(eval_exp_paper3_0(v_.0, v_.01, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z)) :|: TRUE 6.91/5.65 eval_exp_paper3_0(v_.0, v_.01, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z) -> Com_2(eval_nondet_start(v_.0, v_.01, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z), eval_exp_paper3_1(v_.0, v_.01, v_.1, v_.3, nondef.0, v_3, v_8, v_x, v_y, v_z)) :|: TRUE 6.91/5.65 eval_exp_paper3_1(v_.0, v_.01, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z) -> Com_1(eval_exp_paper3_bb3_in(v_.0, v_.01, v_.01, v_.3, v_1, v_3, v_8, v_x, v_y, v_z)) :|: v_1 > 0 6.91/5.65 eval_exp_paper3_1(v_.0, v_.01, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z) -> Com_1(eval_exp_paper3_bb5_in(v_.0, v_.01, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z)) :|: v_1 <= 0 6.91/5.65 eval_exp_paper3_bb3_in(v_.0, v_.01, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z) -> Com_1(eval_exp_paper3_2(v_.0, v_.01, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z)) :|: TRUE 6.91/5.65 eval_exp_paper3_2(v_.0, v_.01, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z) -> Com_2(eval_nondet_start(v_.0, v_.01, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z), eval_exp_paper3_3(v_.0, v_.01, v_.1, v_.3, v_1, nondef.1, v_8, v_x, v_y, v_z)) :|: TRUE 6.91/5.65 eval_exp_paper3_3(v_.0, v_.01, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z) -> Com_1(eval_exp_paper3_bb4_in(v_.0, v_.01, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z)) :|: v_3 > 0 && v_.1 > 0 6.91/5.65 eval_exp_paper3_3(v_.0, v_.01, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z) -> Com_1(eval_exp_paper3_bb6_in(v_.0, v_.01, v_.1, v_.1, v_1, v_3, v_8, v_x, v_y, v_z)) :|: v_3 <= 0 6.91/5.65 eval_exp_paper3_3(v_.0, v_.01, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z) -> Com_1(eval_exp_paper3_bb6_in(v_.0, v_.01, v_.1, v_.1, v_1, v_3, v_8, v_x, v_y, v_z)) :|: v_.1 <= 0 6.91/5.65 eval_exp_paper3_bb4_in(v_.0, v_.01, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z) -> Com_1(eval_exp_paper3_bb3_in(v_.0, v_.01, v_.1 - 1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z)) :|: TRUE 6.91/5.65 eval_exp_paper3_bb5_in(v_.0, v_.01, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z) -> Com_1(eval_exp_paper3_6(v_.0, v_.01, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z)) :|: TRUE 6.91/5.65 eval_exp_paper3_6(v_.0, v_.01, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z) -> Com_2(eval_nondet_start(v_.0, v_.01, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z), eval_exp_paper3_7(v_.0, v_.01, v_.1, v_.3, v_1, v_3, nondef.2, v_x, v_y, v_z)) :|: TRUE 6.91/5.65 eval_exp_paper3_7(v_.0, v_.01, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z) -> Com_1(eval_exp_paper3_bb6_in(v_.0, v_.01, v_.1, v_.01 + 1, v_1, v_3, v_8, v_x, v_y, v_z)) :|: v_8 > 0 6.91/5.65 eval_exp_paper3_7(v_.0, v_.01, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z) -> Com_1(eval_exp_paper3_bb6_in(v_.0, v_.01, v_.1, v_z, v_1, v_3, v_8, v_x, v_y, v_z)) :|: v_8 <= 0 6.91/5.65 eval_exp_paper3_bb6_in(v_.0, v_.01, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z) -> Com_1(eval_exp_paper3_bb1_in(v_.0 - 1, v_.3, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z)) :|: TRUE 6.91/5.65 eval_exp_paper3_bb7_in(v_.0, v_.01, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z) -> Com_1(eval_exp_paper3_stop(v_.0, v_.01, v_.1, v_.3, v_1, v_3, v_8, v_x, v_y, v_z)) :|: TRUE 6.91/5.65 6.91/5.65 The start-symbols are:[eval_exp_paper3_start_10] 6.91/5.65 6.91/5.65 6.91/5.65 ---------------------------------------- 6.91/5.65 6.91/5.65 (1) Koat Proof (FINISHED) 6.91/5.65 YES(?, 2808*ar_1^2 + 2808*ar_1*ar_3 + 2808*ar_1*ar_10 + 404418*ar_1 + 2574*ar_3 + 2574*ar_10 + 368363) 6.91/5.65 6.91/5.65 6.91/5.65 6.91/5.65 Initial complexity problem: 6.91/5.65 6.91/5.65 1: T: 6.91/5.65 6.91/5.65 (Comp: ?, Cost: 1) evalexppaper3start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(evalexppaper3bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10)) 6.91/5.65 6.91/5.65 (Comp: ?, Cost: 1) evalexppaper3bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(evalexppaper3bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10)) 6.91/5.65 6.91/5.65 (Comp: ?, Cost: 1) evalexppaper3bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(evalexppaper3bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10)) [ ar_0 >= 1 ] 6.91/5.65 6.91/5.65 (Comp: ?, Cost: 1) evalexppaper3bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(evalexppaper3bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10)) [ 0 >= ar_0 ] 6.91/5.65 6.91/5.65 (Comp: ?, Cost: 1) evalexppaper3bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(evalexppaper30(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10)) 6.91/5.65 6.91/5.65 (Comp: ?, Cost: 1) evalexppaper300(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10)) 6.91/5.65 6.91/5.65 (Comp: ?, Cost: 1) evalexppaper301(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(evalexppaper31(ar_0, ar_1, ar_2, ar_3, ar_5, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10)) 6.91/5.65 6.91/5.65 (Comp: ?, Cost: 1) evalexppaper30(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_2(evalexppaper300(ar_0, ar_1, ar_2, ar_3, ar_4, l, ar_6, ar_7, ar_8, ar_9, ar_10), evalexppaper301(ar_0, ar_1, ar_2, ar_3, ar_4, l, ar_6, ar_7, ar_8, ar_9, ar_10)) 6.91/5.65 6.91/5.65 (Comp: ?, Cost: 1) evalexppaper31(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(evalexppaper3bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_2, ar_7, ar_8, ar_9, ar_10)) [ ar_4 >= 1 ] 6.91/5.65 6.91/5.65 (Comp: ?, Cost: 1) evalexppaper31(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(evalexppaper3bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10)) [ 0 >= ar_4 ] 6.91/5.65 6.91/5.65 (Comp: ?, Cost: 1) evalexppaper3bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(evalexppaper32(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10)) 6.91/5.65 6.91/5.65 (Comp: ?, Cost: 1) evalexppaper320(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10)) 6.91/5.65 6.91/5.65 (Comp: ?, Cost: 1) evalexppaper321(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(evalexppaper33(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_5, ar_8, ar_9, ar_10)) 6.91/5.65 6.91/5.65 (Comp: ?, Cost: 1) evalexppaper32(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_2(evalexppaper320(ar_0, ar_1, ar_2, ar_3, ar_4, l, ar_6, ar_7, ar_8, ar_9, ar_10), evalexppaper321(ar_0, ar_1, ar_2, ar_3, ar_4, l, ar_6, ar_7, ar_8, ar_9, ar_10)) 6.91/5.65 6.91/5.65 (Comp: ?, Cost: 1) evalexppaper33(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(evalexppaper3bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10)) [ ar_7 >= 1 /\ ar_6 >= 1 ] 6.91/5.65 6.91/5.65 (Comp: ?, Cost: 1) evalexppaper33(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(evalexppaper3bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_6, ar_9, ar_10)) [ 0 >= ar_7 ] 6.91/5.65 6.91/5.65 (Comp: ?, Cost: 1) evalexppaper33(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(evalexppaper3bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_6, ar_9, ar_10)) [ 0 >= ar_6 ] 6.91/5.65 6.91/5.65 (Comp: ?, Cost: 1) evalexppaper3bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(evalexppaper3bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7, ar_8, ar_9, ar_10)) 6.91/5.65 6.91/5.65 (Comp: ?, Cost: 1) evalexppaper3bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(evalexppaper36(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10)) 6.91/5.65 6.91/5.65 (Comp: ?, Cost: 1) evalexppaper360(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10)) 6.91/5.65 6.91/5.65 (Comp: ?, Cost: 1) evalexppaper361(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(evalexppaper37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_5, ar_10)) 6.91/5.65 6.91/5.65 (Comp: ?, Cost: 1) evalexppaper36(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_2(evalexppaper360(ar_0, ar_1, ar_2, ar_3, ar_4, l, ar_6, ar_7, ar_8, ar_9, ar_10), evalexppaper361(ar_0, ar_1, ar_2, ar_3, ar_4, l, ar_6, ar_7, ar_8, ar_9, ar_10)) 6.91/5.65 6.91/5.65 (Comp: ?, Cost: 1) evalexppaper37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(evalexppaper3bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_2 + 1, ar_9, ar_10)) [ ar_9 >= 1 ] 6.91/5.65 6.91/5.65 (Comp: ?, Cost: 1) evalexppaper37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(evalexppaper3bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_10, ar_9, ar_10)) [ 0 >= ar_9 ] 6.91/5.65
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