details

property	value
status	complete
benchmark	Loopus2014_ex1.c.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n108.star.cs.uiowa.edu
space	Flores-Montoya_16

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	7.29209780693 seconds
cpu usage	19.28436722
max memory	6.47548928E8

stage attributes

key	value
output-size	556184
starexec-result	WORST_CASE(Omega(n^2), O(n^2))

output

/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^2), O(n^2)) proof of /export/starexec/sandbox/benchmark/theBenchmark.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 5257 ms] (2) BOUNDS(1, n^2) (3) Loat Proof [FINISHED, 4366 ms] (4) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_start_start(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n) -> Com_1(eval_start_bb0_in(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n)) :|: TRUE eval_start_bb0_in(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n) -> Com_1(eval_start_0(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n)) :|: TRUE eval_start_0(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n) -> Com_1(eval_start_1(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n)) :|: TRUE eval_start_1(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n) -> Com_1(eval_start_2(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n)) :|: TRUE eval_start_2(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n) -> Com_1(eval_start_3(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n)) :|: TRUE eval_start_3(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n) -> Com_1(eval_start_4(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n)) :|: TRUE eval_start_4(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n) -> Com_1(eval_start_5(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n)) :|: TRUE eval_start_5(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n) -> Com_1(eval_start_6(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n)) :|: TRUE eval_start_6(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n) -> Com_1(eval_start_7(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n)) :|: TRUE eval_start_7(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n) -> Com_1(eval_start_8(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n)) :|: TRUE eval_start_8(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n) -> Com_1(eval_start_9(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n)) :|: TRUE eval_start_9(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n) -> Com_1(eval_start_10(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n)) :|: TRUE eval_start_10(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n) -> Com_1(eval_start_bb1_in(v_4, v_8, v_n, v_a_1, v_a_2, v_a_3, 0, v_b_1, v_b_2, v_b_3, v_i_0, v_n)) :|: TRUE eval_start_bb1_in(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n) -> Com_1(eval_start_bb2_in(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n)) :|: v_a_0 > 0 eval_start_bb1_in(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n) -> Com_1(eval_start_bb10_in(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n)) :|: v_a_0 <= 0 eval_start_bb2_in(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n) -> Com_1(eval_start_bb3_in(v_4, v_8, v_a_0, v_a_0 - 1, v_a_2, v_a_3, v_b_0, v_b_0 + 1, v_b_2, v_b_3, v_i_0, v_n)) :|: TRUE eval_start_bb3_in(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n) -> Com_1(eval_start_bb4_in(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n)) :|: v_b_1 > 0 eval_start_bb3_in(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n) -> Com_1(eval_start_bb1_in(v_4, v_8, v_a_1, v_a_1, v_a_2, v_a_3, v_b_1, v_b_1, v_b_2, v_b_3, v_i_0, v_n)) :|: v_b_1 <= 0 eval_start_bb4_in(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n) -> Com_1(eval_start_15(v_b_1 - 1, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n)) :|: TRUE eval_start_15(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n) -> Com_1(eval_start_16(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n)) :|: TRUE eval_start_16(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n) -> Com_1(eval_start_bb5_in(v_4, v_8, v_a_0, v_a_1, v_a_1, v_a_3, v_b_0, v_b_1, v_4, v_b_3, v_n - 1, v_n)) :|: TRUE eval_start_bb5_in(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n) -> Com_1(eval_start_bb6_in(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n)) :|: v_i_0 > 0 eval_start_bb5_in(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n) -> Com_1(eval_start_bb3_in(v_4, v_8, v_a_0, v_a_2, v_a_2, v_a_3, v_b_0, v_b_2, v_b_2, v_b_3, v_i_0, v_n)) :|: v_i_0 <= 0 eval_start_bb6_in(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n) -> Com_1(eval_start_bb7_in(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n)) :|: v_a_2 > 0 eval_start_bb6_in(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n) -> Com_1(eval_start_bb9_in(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_2, v_b_0, v_b_1, v_b_2, v_b_2, v_i_0, v_n)) :|: v_a_2 <= 0 eval_start_bb7_in(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n) -> Com_1(eval_start_18(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n)) :|: TRUE eval_start_18(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n) -> Com_1(eval_start_19(v_4, nondef_0, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n)) :|: TRUE eval_start_19(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n) -> Com_1(eval_start_bb8_in(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n)) :|: v_8 > 0 eval_start_19(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n) -> Com_1(eval_start_bb9_in(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_2, v_b_0, v_b_1, v_b_2, v_b_2, v_i_0, v_n)) :|: v_8 <= 0 eval_start_bb8_in(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n) -> Com_1(eval_start_bb9_in(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_2 - 1, v_b_0, v_b_1, v_b_2, v_b_2 + 1, v_i_0, v_n)) :|: TRUE eval_start_bb9_in(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n) -> Com_1(eval_start_bb5_in(v_4, v_8, v_a_0, v_a_1, v_a_3, v_a_3, v_b_0, v_b_1, v_b_3, v_b_3, v_i_0 - 1, v_n)) :|: TRUE eval_start_bb10_in(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n) -> Com_1(eval_start_stop(v_4, v_8, v_a_0, v_a_1, v_a_2, v_a_3, v_b_0, v_b_1, v_b_2, v_b_3, v_i_0, v_n)) :|: TRUE The start-symbols are:[eval_start_start_12] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 672*ar_1^2 + 339*ar_1 + 17) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) (Comp: ?, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) (Comp: ?, Cost: 1) evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) (Comp: ?, Cost: 1) evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) (Comp: ?, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) (Comp: ?, Cost: 1) evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) (Comp: ?, Cost: 1) evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) (Comp: ?, Cost: 1) evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalstart6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) (Comp: ?, Cost: 1) evalstart6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalstart7(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) (Comp: ?, Cost: 1) evalstart7(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) (Comp: ?, Cost: 1) evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) (Comp: ?, Cost: 1) evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalstart10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) (Comp: ?, Cost: 1) evalstart10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalstartbb1in(ar_1, ar_1, 0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) (Comp: ?, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ ar_0 >= 1 ] popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to Compl Integ Trans Syste 26843