details

property	value
status	complete
benchmark	speed_pldi09_fig4_5.c
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n056.star.cs.uiowa.edu
space	C4B_examples

run statistics

property	value
solver	AProVE
configuration	c_complexity
runtime (wallclock)	2.0216550827 seconds
cpu usage	3.094373287
max memory	3.02985216E8

stage attributes

key	value
output-size	72989
starexec-result	WORST_CASE(?, O(n^2))

output

/export/starexec/sandbox2/solver/bin/starexec_run_c_complexity /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^2)) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 882 ms] (2) BOUNDS(1, n^2) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_peed_pldi09_fig4_5_start(v_dir, v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_5_bb0_in(v_dir, v_i.0, v_m, v_n)) :|: TRUE eval_peed_pldi09_fig4_5_bb0_in(v_dir, v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_5_bb3_in(v_dir, v_i.0, v_m, v_n)) :|: 0 >= v_m eval_peed_pldi09_fig4_5_bb0_in(v_dir, v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_5_bb3_in(v_dir, v_i.0, v_m, v_n)) :|: v_m >= v_n eval_peed_pldi09_fig4_5_bb0_in(v_dir, v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_5_bb1_in(v_dir, v_m, v_m, v_n)) :|: 0 < v_m && v_m < v_n eval_peed_pldi09_fig4_5_bb1_in(v_dir, v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_5_bb2_in(v_dir, v_i.0, v_m, v_n)) :|: 0 < v_i.0 && v_i.0 < v_n eval_peed_pldi09_fig4_5_bb1_in(v_dir, v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_5_bb3_in(v_dir, v_i.0, v_m, v_n)) :|: 0 >= v_i.0 eval_peed_pldi09_fig4_5_bb1_in(v_dir, v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_5_bb3_in(v_dir, v_i.0, v_m, v_n)) :|: v_i.0 >= v_n eval_peed_pldi09_fig4_5_bb2_in(v_dir, v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_5_bb1_in(v_dir, v_i.0 + 1, v_m, v_n)) :|: v_dir >= 1 && v_dir <= 1 eval_peed_pldi09_fig4_5_bb2_in(v_dir, v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_5_bb1_in(v_dir, v_i.0 - 1, v_m, v_n)) :|: v_dir < 1 eval_peed_pldi09_fig4_5_bb2_in(v_dir, v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_5_bb1_in(v_dir, v_i.0 - 1, v_m, v_n)) :|: v_dir > 1 eval_peed_pldi09_fig4_5_bb3_in(v_dir, v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_5_stop(v_dir, v_i.0, v_m, v_n)) :|: TRUE The start-symbols are:[eval_peed_pldi09_fig4_5_start_4] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 10*ar_0 + 4*ar_1 + 4*ar_0*ar_1 + 4*ar_0^2 + 17) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalpeedpldi09fig45start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] (Comp: ?, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] (Comp: ?, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] (Comp: ?, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 ] (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 = 1 ] (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ 0 >= ar_3 ] (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_3 >= 2 ] (Comp: ?, Cost: 1) evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (Comp: 1, Cost: 1) evalpeedpldi09fig45start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] (Comp: 1, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] (Comp: 1, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] (Comp: ?, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 ] (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 = 1 ] (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ 0 >= ar_3 ] popout

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actions

all output return to Compl C Integ Progr 85445