details

property	value
status	complete
benchmark	nested_loop.c
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n053.star.cs.uiowa.edu
space	WTC_V2

run statistics

property	value
solver	AProVE
configuration	c_complexity
runtime (wallclock)	11.0840940475 seconds
cpu usage	12.667637115
max memory	5.530624E8

stage attributes

key	value
output-size	1576985
starexec-result	WORST_CASE(?, O(n^3))

output

/export/starexec/sandbox/solver/bin/starexec_run_c_complexity /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^3)) proof of /export/starexec/sandbox/output/output_files/bench.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^3). (0) CpxIntTrs (1) Koat Proof [FINISHED, 9742 ms] (2) BOUNDS(1, n^3) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_nested_loop_start(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_bb0_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE eval_nested_loop_bb0_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_bb1_in(v_11, v_4, v_7, v_9, v_N, 0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: 0 <= v_n && 0 <= v_m && 0 <= v_N eval_nested_loop_bb0_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_.critedge_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: 0 > v_n eval_nested_loop_bb0_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_.critedge_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: 0 > v_m eval_nested_loop_bb0_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_.critedge_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: 0 > v_N eval_nested_loop_bb1_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_bb2_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: v_i.0 < v_n eval_nested_loop_bb1_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_.critedge_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: v_i.0 >= v_n eval_nested_loop_bb2_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_0(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE eval_nested_loop_0(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_2(eval_nondet_start(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n), eval_nested_loop_1(v_11, nondef.0, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE eval_nested_loop_1(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_.critedge3_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.0, 0, v_k.0, v_m, v_n)) :|: v_4 > 0 eval_nested_loop_1(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_.critedge_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: v_4 <= 0 eval_nested_loop_.critedge3_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_bb3_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: v_j.0 < v_m eval_nested_loop_.critedge3_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_.critedge2_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: v_j.0 >= v_m eval_nested_loop_bb3_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_2(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE eval_nested_loop_2(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_2(eval_nondet_start(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n), eval_nested_loop_3(v_11, v_4, nondef.1, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE eval_nested_loop_3(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_bb4_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: v_7 > 0 eval_nested_loop_3(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_.critedge2_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: v_7 <= 0 eval_nested_loop_bb4_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_bb5_in(v_11, v_4, v_7, v_j.0 + 1, v_N, v_i.0, v_i.1, v_j.0, v_i.1, v_m, v_n)) :|: TRUE eval_nested_loop_bb5_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_bb6_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: v_k.0 < v_N eval_nested_loop_bb5_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_.critedge3_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_k.0, v_9, v_k.0, v_m, v_n)) :|: v_k.0 >= v_N eval_nested_loop_bb6_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_6(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE eval_nested_loop_6(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_2(eval_nondet_start(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n), eval_nested_loop_7(nondef.2, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE eval_nested_loop_7(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_bb7_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: v_11 > 0 eval_nested_loop_7(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_.critedge3_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_k.0, v_9, v_k.0, v_m, v_n)) :|: v_11 <= 0 eval_nested_loop_bb7_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_bb5_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0 + 1, v_m, v_n)) :|: TRUE eval_nested_loop_.critedge2_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_bb1_in(v_11, v_4, v_7, v_9, v_N, v_i.1 + 1, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE eval_nested_loop_.critedge_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_stop(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE The start-symbols are:[eval_nested_loop_start_11] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 216*ar_0 + 31360*ar_0*ar_1*ar_2 + 7840*ar_0*ar_2 + 28224*ar_0^2*ar_1 + 7056*ar_0^2 + 576*ar_0*ar_1 + 11) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalnestedloopstart(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(evalnestedloopbb0in(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) evalnestedloopbb0in(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(evalnestedloopbb1in(ar_0, ar_1, ar_2, 0, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ ar_0 >= 0 /\ ar_1 >= 0 /\ ar_2 >= 0 ] (Comp: ?, Cost: 1) evalnestedloopbb0in(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(evalnestedloopcritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ 0 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalnestedloopbb0in(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(evalnestedloopcritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ 0 >= ar_1 + 1 ] (Comp: ?, Cost: 1) evalnestedloopbb0in(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(evalnestedloopcritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ 0 >= ar_2 + 1 ] (Comp: ?, Cost: 1) evalnestedloopbb1in(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(evalnestedloopbb2in(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 >= ar_3 + 1 ] (Comp: ?, Cost: 1) evalnestedloopbb1in(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(evalnestedloopcritedgein(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_3 >= ar_0 ] (Comp: ?, Cost: 1) evalnestedloopbb2in(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(evalnestedloop0(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) evalnestedloop00(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(evalnondetstart(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) evalnestedloop01(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(evalnestedloop1(ar_0, ar_1, ar_2, ar_3, ar_5, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) (Comp: ?, Cost: 1) evalnestedloop0(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_2(evalnestedloop00(ar_0, ar_1, ar_2, ar_3, ar_4, m, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11), evalnestedloop01(ar_0, ar_1, ar_2, ar_3, ar_4, m, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) (Comp: ?, Cost: 1) evalnestedloop1(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(evalnestedloopcritedge3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_3, 0, ar_8, ar_9, ar_10, ar_11)) [ ar_4 >= 1 ] (Comp: ?, Cost: 1) evalnestedloop1(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(evalnestedloopcritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ 0 >= ar_4 ] (Comp: ?, Cost: 1) evalnestedloopcritedge3in(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(evalnestedloopbb3in(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_1 >= ar_7 + 1 ] (Comp: ?, Cost: 1) evalnestedloopcritedge3in(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(evalnestedloopcritedge2in(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_7 >= ar_1 ] (Comp: ?, Cost: 1) evalnestedloopbb3in(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(evalnestedloop2(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) evalnestedloop20(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(evalnondetstart(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) evalnestedloop21(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(evalnestedloop3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_5, ar_9, ar_10, ar_11)) popout

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all output return to Compl C Integ Progr 85445