details

property	value
status	complete
benchmark	textbook_ex3.c
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n178.star.cs.uiowa.edu
space	ABC

run statistics

property	value
solver	AProVE
configuration	c_complexity
runtime (wallclock)	1.68134 seconds
cpu usage	2.58047
user time	2.38159
system time	0.198881
max virtual memory	1.8273644E7
max residence set size	181576.0

stage attributes

key	value
starexec-result	WORST_CASE(?, O(n^6))

output

2.15/1.63 WORST_CASE(?, O(n^6)) 2.15/1.64 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.15/1.64 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.15/1.64 2.15/1.64 2.15/1.64 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^6). 2.15/1.64 2.15/1.64 (0) CpxIntTrs 2.15/1.64 (1) Koat Proof [FINISHED, 332 ms] 2.15/1.64 (2) BOUNDS(1, n^6) 2.15/1.64 2.15/1.64 2.15/1.64 ---------------------------------------- 2.15/1.64 2.15/1.64 (0) 2.15/1.64 Obligation: 2.15/1.64 Complexity Int TRS consisting of the following rules: 2.15/1.64 eval_textbook_ex3_start(v_i.0, v_j.0, v_k.0, v_l.0, v_m) -> Com_1(eval_textbook_ex3_bb0_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m)) :|: TRUE 2.15/1.64 eval_textbook_ex3_bb0_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m) -> Com_1(eval_textbook_ex3_bb1_in(1, v_j.0, v_k.0, v_l.0, v_m)) :|: TRUE 2.15/1.64 eval_textbook_ex3_bb1_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m) -> Com_1(eval_textbook_ex3_bb2_in(v_i.0, 1, v_k.0, v_l.0, v_m)) :|: v_i.0 <= v_m 2.15/1.64 eval_textbook_ex3_bb1_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m) -> Com_1(eval_textbook_ex3_bb8_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m)) :|: v_i.0 > v_m 2.15/1.64 eval_textbook_ex3_bb2_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m) -> Com_1(eval_textbook_ex3_bb3_in(v_i.0, v_j.0, v_i.0 + 1, v_l.0, v_m)) :|: v_j.0 <= v_i.0 2.15/1.64 eval_textbook_ex3_bb2_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m) -> Com_1(eval_textbook_ex3_bb1_in(v_i.0 + 1, v_j.0, v_k.0, v_l.0, v_m)) :|: v_j.0 > v_i.0 2.15/1.64 eval_textbook_ex3_bb3_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m) -> Com_1(eval_textbook_ex3_bb4_in(v_i.0, v_j.0, v_k.0, 1, v_m)) :|: v_k.0 <= v_m 2.15/1.64 eval_textbook_ex3_bb3_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m) -> Com_1(eval_textbook_ex3_bb7_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m)) :|: v_k.0 > v_m 2.15/1.64 eval_textbook_ex3_bb4_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m) -> Com_1(eval_textbook_ex3_bb5_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m)) :|: v_l.0 <= v_k.0 2.15/1.64 eval_textbook_ex3_bb4_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m) -> Com_1(eval_textbook_ex3_bb6_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m)) :|: v_l.0 > v_k.0 2.15/1.64 eval_textbook_ex3_bb5_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m) -> Com_1(eval_textbook_ex3_bb4_in(v_i.0, v_j.0, v_k.0, v_l.0 + 1, v_m)) :|: TRUE 2.15/1.64 eval_textbook_ex3_bb6_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m) -> Com_1(eval_textbook_ex3_bb3_in(v_i.0, v_j.0, v_k.0 + 1, v_l.0, v_m)) :|: TRUE 2.15/1.64 eval_textbook_ex3_bb7_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m) -> Com_1(eval_textbook_ex3_bb2_in(v_i.0, v_j.0 + 1, v_k.0, v_l.0, v_m)) :|: TRUE 2.15/1.64 eval_textbook_ex3_bb8_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m) -> Com_1(eval_textbook_ex3_stop(v_i.0, v_j.0, v_k.0, v_l.0, v_m)) :|: TRUE 2.15/1.64 2.15/1.64 The start-symbols are:[eval_textbook_ex3_start_5] 2.15/1.64 2.15/1.64 2.15/1.64 ---------------------------------------- 2.15/1.64 2.15/1.64 (1) Koat Proof (FINISHED) 2.15/1.64 YES(?, 134*ar_1 + 464*ar_1^2 + 692*ar_1^3 + 472*ar_1^4 + 16*ar_1^6 + 144*ar_1^5 + 6) 2.15/1.64 2.15/1.64 2.15/1.64 2.15/1.64 Initial complexity problem: 2.15/1.64 2.15/1.64 1: T: 2.15/1.64 2.15/1.64 (Comp: ?, Cost: 1) evaltextbookex3start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.15/1.64 2.15/1.64 (Comp: ?, Cost: 1) evaltextbookex3bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb1in(1, ar_1, ar_2, ar_3, ar_4)) 2.15/1.64 2.15/1.64 (Comp: ?, Cost: 1) evaltextbookex3bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb2in(ar_0, ar_1, 1, ar_3, ar_4)) [ ar_1 >= ar_0 ] 2.15/1.64 2.15/1.64 (Comp: ?, Cost: 1) evaltextbookex3bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb8in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 + 1 ] 2.15/1.64 2.15/1.64 (Comp: ?, Cost: 1) evaltextbookex3bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb3in(ar_0, ar_1, ar_2, ar_0 + 1, ar_4)) [ ar_0 >= ar_2 ] 2.15/1.64 2.15/1.64 (Comp: ?, Cost: 1) evaltextbookex3bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 ] 2.15/1.64 2.15/1.64 (Comp: ?, Cost: 1) evaltextbookex3bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb4in(ar_0, ar_1, ar_2, ar_3, 1)) [ ar_1 >= ar_3 ] 2.15/1.64 2.15/1.64 (Comp: ?, Cost: 1) evaltextbookex3bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 ] 2.15/1.64 2.15/1.64 (Comp: ?, Cost: 1) evaltextbookex3bb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ] 2.15/1.64 2.15/1.64 (Comp: ?, Cost: 1) evaltextbookex3bb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ] 2.15/1.64 2.15/1.64 (Comp: ?, Cost: 1) evaltextbookex3bb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb4in(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) 2.15/1.64 2.15/1.64 (Comp: ?, Cost: 1) evaltextbookex3bb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb3in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) 2.15/1.64 2.15/1.64 (Comp: ?, Cost: 1) evaltextbookex3bb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) 2.15/1.64 2.15/1.64 (Comp: ?, Cost: 1) evaltextbookex3bb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3stop(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.15/1.64 2.15/1.64 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 2.15/1.64 2.15/1.64 start location: koat_start 2.15/1.64 2.15/1.64 leaf cost: 0 2.15/1.64 2.15/1.64 2.15/1.64 2.15/1.64 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.15/1.64 2.15/1.64 2: T: 2.15/1.64 2.15/1.64 (Comp: 1, Cost: 1) evaltextbookex3start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.15/1.64 2.15/1.64 (Comp: 1, Cost: 1) evaltextbookex3bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb1in(1, ar_1, ar_2, ar_3, ar_4)) 2.15/1.64 2.15/1.64 (Comp: ?, Cost: 1) evaltextbookex3bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb2in(ar_0, ar_1, 1, ar_3, ar_4)) [ ar_1 >= ar_0 ] 2.15/1.64 2.15/1.64 (Comp: ?, Cost: 1) evaltextbookex3bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb8in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 + 1 ] 2.15/1.64 2.15/1.64 (Comp: ?, Cost: 1) evaltextbookex3bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb3in(ar_0, ar_1, ar_2, ar_0 + 1, ar_4)) [ ar_0 >= ar_2 ] 2.15/1.64 2.15/1.64 (Comp: ?, Cost: 1) evaltextbookex3bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 ] 2.15/1.64 2.15/1.64 (Comp: ?, Cost: 1) evaltextbookex3bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb4in(ar_0, ar_1, ar_2, ar_3, 1)) [ ar_1 >= ar_3 ] 2.15/1.64 popout

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all output return to Complexity_C_Integer 2019-03-21 04.38