details

property	value
status	complete
benchmark	ax.c
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n104.star.cs.uiowa.edu
space	WTC_V2

run statistics

property	value
solver	AProVE
configuration	c_complexity
runtime (wallclock)	1.33044886589 seconds
cpu usage	2.434970581
max memory	2.17223168E8

stage attributes

key	value
output-size	21581
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2).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, 68 ms] (2) BOUNDS(1, n^2) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_ax_start(v_.0, v_.01, v_i, v_j, v_n) -> Com_1(eval_ax_bb0_in(v_.0, v_.01, v_i, v_j, v_n)) :|: TRUE eval_ax_bb0_in(v_.0, v_.01, v_i, v_j, v_n) -> Com_1(eval_ax_bb1_in(0, v_.01, v_i, v_j, v_n)) :|: TRUE eval_ax_bb1_in(v_.0, v_.01, v_i, v_j, v_n) -> Com_1(eval_ax_bb2_in(v_.0, 0, v_i, v_j, v_n)) :|: TRUE eval_ax_bb2_in(v_.0, v_.01, v_i, v_j, v_n) -> Com_1(eval_ax_bb3_in(v_.0, v_.01, v_i, v_j, v_n)) :|: v_.01 < v_n - 1 eval_ax_bb2_in(v_.0, v_.01, v_i, v_j, v_n) -> Com_1(eval_ax_bb4_in(v_.0, v_.01, v_i, v_j, v_n)) :|: v_.01 >= v_n - 1 eval_ax_bb3_in(v_.0, v_.01, v_i, v_j, v_n) -> Com_1(eval_ax_bb2_in(v_.0, v_.01 + 1, v_i, v_j, v_n)) :|: TRUE eval_ax_bb4_in(v_.0, v_.01, v_i, v_j, v_n) -> Com_1(eval_ax_bb1_in(v_.0 + 1, v_.01, v_i, v_j, v_n)) :|: v_.01 >= v_n - 1 && v_.0 + 1 < v_n - 1 eval_ax_bb4_in(v_.0, v_.01, v_i, v_j, v_n) -> Com_1(eval_ax_.critedge_in(v_.0, v_.01, v_i, v_j, v_n)) :|: v_.01 < v_n - 1 eval_ax_bb4_in(v_.0, v_.01, v_i, v_j, v_n) -> Com_1(eval_ax_.critedge_in(v_.0, v_.01, v_i, v_j, v_n)) :|: v_.0 + 1 >= v_n - 1 eval_ax_.critedge_in(v_.0, v_.01, v_i, v_j, v_n) -> Com_1(eval_ax_stop(v_.0, v_.01, v_i, v_j, v_n)) :|: TRUE The start-symbols are:[eval_ax_start_5] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 7*ar_2 + 2*ar_2^2 + 10) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalaxstart(ar_0, ar_1, ar_2) -> Com_1(evalaxbb0in(ar_0, ar_1, ar_2)) (Comp: ?, Cost: 1) evalaxbb0in(ar_0, ar_1, ar_2) -> Com_1(evalaxbb1in(0, ar_1, ar_2)) (Comp: ?, Cost: 1) evalaxbb1in(ar_0, ar_1, ar_2) -> Com_1(evalaxbb2in(ar_0, 0, ar_2)) (Comp: ?, Cost: 1) evalaxbb2in(ar_0, ar_1, ar_2) -> Com_1(evalaxbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 2 ] (Comp: ?, Cost: 1) evalaxbb2in(ar_0, ar_1, ar_2) -> Com_1(evalaxbb4in(ar_0, ar_1, ar_2)) [ ar_1 + 1 >= ar_2 ] (Comp: ?, Cost: 1) evalaxbb3in(ar_0, ar_1, ar_2) -> Com_1(evalaxbb2in(ar_0, ar_1 + 1, ar_2)) (Comp: ?, Cost: 1) evalaxbb4in(ar_0, ar_1, ar_2) -> Com_1(evalaxbb1in(ar_0 + 1, ar_1, ar_2)) [ ar_1 + 1 >= ar_2 /\ ar_2 >= ar_0 + 3 ] (Comp: ?, Cost: 1) evalaxbb4in(ar_0, ar_1, ar_2) -> Com_1(evalaxcritedgein(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 2 ] (Comp: ?, Cost: 1) evalaxbb4in(ar_0, ar_1, ar_2) -> Com_1(evalaxcritedgein(ar_0, ar_1, ar_2)) [ ar_0 + 2 >= ar_2 ] (Comp: ?, Cost: 1) evalaxcritedgein(ar_0, ar_1, ar_2) -> Com_1(evalaxstop(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalaxstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 1: evalaxbb4in(ar_0, ar_1, ar_2) -> Com_1(evalaxcritedgein(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 2 ] We thus obtain the following problem: 2: T: (Comp: ?, Cost: 1) evalaxcritedgein(ar_0, ar_1, ar_2) -> Com_1(evalaxstop(ar_0, ar_1, ar_2)) (Comp: ?, Cost: 1) evalaxbb4in(ar_0, ar_1, ar_2) -> Com_1(evalaxcritedgein(ar_0, ar_1, ar_2)) [ ar_0 + 2 >= ar_2 ] (Comp: ?, Cost: 1) evalaxbb4in(ar_0, ar_1, ar_2) -> Com_1(evalaxbb1in(ar_0 + 1, ar_1, ar_2)) [ ar_1 + 1 >= ar_2 /\ ar_2 >= ar_0 + 3 ] (Comp: ?, Cost: 1) evalaxbb3in(ar_0, ar_1, ar_2) -> Com_1(evalaxbb2in(ar_0, ar_1 + 1, ar_2)) (Comp: ?, Cost: 1) evalaxbb2in(ar_0, ar_1, ar_2) -> Com_1(evalaxbb4in(ar_0, ar_1, ar_2)) [ ar_1 + 1 >= ar_2 ] (Comp: ?, Cost: 1) evalaxbb2in(ar_0, ar_1, ar_2) -> Com_1(evalaxbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 2 ] (Comp: ?, Cost: 1) evalaxbb1in(ar_0, ar_1, ar_2) -> Com_1(evalaxbb2in(ar_0, 0, ar_2)) (Comp: ?, Cost: 1) evalaxbb0in(ar_0, ar_1, ar_2) -> Com_1(evalaxbb1in(0, ar_1, ar_2)) popout

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

job log

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actions

all output return to Compl C Integ Progr 85445