details

property	value
status	complete
benchmark	textbook_ex2.c
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n080.star.cs.uiowa.edu
space	ABC

run statistics

property	value
solver	AProVE
configuration	c_complexity
runtime (wallclock)	1.24617385864 seconds
cpu usage	2.32135686
max memory	2.12672512E8

stage attributes

key	value
output-size	21091
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2).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, 74 ms] (2) BOUNDS(1, n^2) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_textbook_ex2_start(v_i.0, v_j.0, v_n) -> Com_1(eval_textbook_ex2_bb0_in(v_i.0, v_j.0, v_n)) :|: TRUE eval_textbook_ex2_bb0_in(v_i.0, v_j.0, v_n) -> Com_1(eval_textbook_ex2_bb1_in(0, v_j.0, v_n)) :|: TRUE eval_textbook_ex2_bb1_in(v_i.0, v_j.0, v_n) -> Com_1(eval_textbook_ex2_bb2_in(v_i.0, 0, v_n)) :|: v_i.0 <= v_n - 1 eval_textbook_ex2_bb1_in(v_i.0, v_j.0, v_n) -> Com_1(eval_textbook_ex2_bb5_in(v_i.0, v_j.0, v_n)) :|: v_i.0 > v_n - 1 eval_textbook_ex2_bb2_in(v_i.0, v_j.0, v_n) -> Com_1(eval_textbook_ex2_bb3_in(v_i.0, v_j.0, v_n)) :|: v_j.0 <= v_i.0 eval_textbook_ex2_bb2_in(v_i.0, v_j.0, v_n) -> Com_1(eval_textbook_ex2_bb4_in(v_i.0, v_j.0, v_n)) :|: v_j.0 > v_i.0 eval_textbook_ex2_bb3_in(v_i.0, v_j.0, v_n) -> Com_1(eval_textbook_ex2_bb2_in(v_i.0, v_j.0 + 1, v_n)) :|: TRUE eval_textbook_ex2_bb4_in(v_i.0, v_j.0, v_n) -> Com_1(eval_textbook_ex2_bb1_in(v_i.0 + 1, v_j.0, v_n)) :|: TRUE eval_textbook_ex2_bb5_in(v_i.0, v_j.0, v_n) -> Com_1(eval_textbook_ex2_stop(v_i.0, v_j.0, v_n)) :|: TRUE The start-symbols are:[eval_textbook_ex2_start_3] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 27*ar_1 + 4*ar_1^2 + 29) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evaltextbookex2start(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2bb0in(ar_0, ar_1, ar_2)) (Comp: ?, Cost: 1) evaltextbookex2bb0in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2bb1in(0, ar_1, ar_2)) (Comp: ?, Cost: 1) evaltextbookex2bb1in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2bb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evaltextbookex2bb1in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ] (Comp: ?, Cost: 1) evaltextbookex2bb2in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 ] (Comp: ?, Cost: 1) evaltextbookex2bb2in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evaltextbookex2bb3in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2bb2in(ar_0, ar_1, ar_2 + 1)) (Comp: ?, Cost: 1) evaltextbookex2bb4in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2bb1in(ar_0 + 1, ar_1, ar_2)) (Comp: ?, Cost: 1) evaltextbookex2bb5in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2stop(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2start(ar_0, ar_1, ar_2)) [ 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) evaltextbookex2start(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2bb0in(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 1) evaltextbookex2bb0in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2bb1in(0, ar_1, ar_2)) (Comp: ?, Cost: 1) evaltextbookex2bb1in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2bb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evaltextbookex2bb1in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ] (Comp: ?, Cost: 1) evaltextbookex2bb2in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 ] (Comp: ?, Cost: 1) evaltextbookex2bb2in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evaltextbookex2bb3in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2bb2in(ar_0, ar_1, ar_2 + 1)) (Comp: ?, Cost: 1) evaltextbookex2bb4in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2bb1in(ar_0 + 1, ar_1, ar_2)) (Comp: ?, Cost: 1) evaltextbookex2bb5in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2stop(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2start(ar_0, ar_1, ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 popout

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actions

all output return to Compl C Integ Progr 85445