details

property	value
status	complete
benchmark	t13.c
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n031.star.cs.uiowa.edu
space	C4B_examples

run statistics

property	value
solver	AProVE
configuration	c_complexity
runtime (wallclock)	2.2111 seconds
cpu usage	3.27498
user time	3.02514
system time	0.249836
max virtual memory	1.8473324E7
max residence set size	187712.0

stage attributes

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

output

3.16/2.17 WORST_CASE(?, O(n^2)) 3.16/2.19 proof of /export/starexec/sandbox/output/output_files/bench.koat 3.16/2.19 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.16/2.19 3.16/2.19 3.16/2.19 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 3.16/2.19 3.16/2.19 (0) CpxIntTrs 3.16/2.19 (1) Koat Proof [FINISHED, 882 ms] 3.16/2.19 (2) BOUNDS(1, n^2) 3.16/2.19 3.16/2.19 3.16/2.19 ---------------------------------------- 3.16/2.19 3.16/2.19 (0) 3.16/2.19 Obligation: 3.16/2.19 Complexity Int TRS consisting of the following rules: 3.16/2.19 eval_t13_start(v_.0, v_.01, v_.1, v_1, v_2, v_x, v_y) -> Com_1(eval_t13_bb0_in(v_.0, v_.01, v_.1, v_1, v_2, v_x, v_y)) :|: TRUE 3.16/2.19 eval_t13_bb0_in(v_.0, v_.01, v_.1, v_1, v_2, v_x, v_y) -> Com_1(eval_t13_bb1_in(v_x, v_y, v_.1, v_1, v_2, v_x, v_y)) :|: TRUE 3.16/2.19 eval_t13_bb1_in(v_.0, v_.01, v_.1, v_1, v_2, v_x, v_y) -> Com_1(eval_t13_bb2_in(v_.0, v_.01, v_.1, v_1, v_2, v_x, v_y)) :|: v_.0 > 0 3.16/2.19 eval_t13_bb1_in(v_.0, v_.01, v_.1, v_1, v_2, v_x, v_y) -> Com_1(eval_t13_bb6_in(v_.0, v_.01, v_.1, v_1, v_2, v_x, v_y)) :|: v_.0 <= 0 3.16/2.19 eval_t13_bb2_in(v_.0, v_.01, v_.1, v_1, v_2, v_x, v_y) -> Com_1(eval_t13_1(v_.0, v_.01, v_.1, v_.0 - 1, v_2, v_x, v_y)) :|: TRUE 3.16/2.19 eval_t13_1(v_.0, v_.01, v_.1, v_1, v_2, v_x, v_y) -> Com_2(eval_nondet_start(v_.0, v_.01, v_.1, v_1, v_2, v_x, v_y), eval_t13_2(v_.0, v_.01, v_.1, v_1, nondef.0, v_x, v_y)) :|: TRUE 3.16/2.19 eval_t13_2(v_.0, v_.01, v_.1, v_1, v_2, v_x, v_y) -> Com_1(eval_t13_bb3_in(v_.0, v_.01, v_.1, v_1, v_2, v_x, v_y)) :|: v_2 > 0 3.16/2.19 eval_t13_2(v_.0, v_.01, v_.1, v_1, v_2, v_x, v_y) -> Com_1(eval_t13_bb4_in(v_.0, v_.01, v_.01, v_1, v_2, v_x, v_y)) :|: v_2 <= 0 3.16/2.19 eval_t13_bb3_in(v_.0, v_.01, v_.1, v_1, v_2, v_x, v_y) -> Com_1(eval_t13_bb1_in(v_1, v_.01 + 1, v_.1, v_1, v_2, v_x, v_y)) :|: TRUE 3.16/2.19 eval_t13_bb4_in(v_.0, v_.01, v_.1, v_1, v_2, v_x, v_y) -> Com_1(eval_t13_bb5_in(v_.0, v_.01, v_.1, v_1, v_2, v_x, v_y)) :|: v_.1 > 0 3.16/2.19 eval_t13_bb4_in(v_.0, v_.01, v_.1, v_1, v_2, v_x, v_y) -> Com_1(eval_t13_bb1_in(v_1, v_.1, v_.1, v_1, v_2, v_x, v_y)) :|: v_.1 <= 0 3.16/2.19 eval_t13_bb5_in(v_.0, v_.01, v_.1, v_1, v_2, v_x, v_y) -> Com_1(eval_t13_bb4_in(v_.0, v_.01, v_.1 - 1, v_1, v_2, v_x, v_y)) :|: TRUE 3.16/2.19 eval_t13_bb6_in(v_.0, v_.01, v_.1, v_1, v_2, v_x, v_y) -> Com_1(eval_t13_stop(v_.0, v_.01, v_.1, v_1, v_2, v_x, v_y)) :|: TRUE 3.16/2.19 3.16/2.19 The start-symbols are:[eval_t13_start_7] 3.16/2.19 3.16/2.19 3.16/2.19 ---------------------------------------- 3.16/2.19 3.16/2.19 (1) Koat Proof (FINISHED) 3.16/2.19 YES(?, 224*ar_1^2 + 224*ar_1*ar_3 + 63*ar_1 + 6) 3.16/2.19 3.16/2.19 3.16/2.19 3.16/2.19 Initial complexity problem: 3.16/2.19 3.16/2.19 1: T: 3.16/2.19 3.16/2.19 (Comp: ?, Cost: 1) evalt13start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalt13bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 3.16/2.19 3.16/2.19 (Comp: ?, Cost: 1) evalt13bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalt13bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7)) 3.16/2.19 3.16/2.19 (Comp: ?, Cost: 1) evalt13bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalt13bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 ] 3.16/2.19 3.16/2.19 (Comp: ?, Cost: 1) evalt13bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalt13bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_0 ] 3.16/2.19 3.16/2.19 (Comp: ?, Cost: 1) evalt13bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalt131(ar_0, ar_1, ar_2, ar_3, ar_0 - 1, ar_5, ar_6, ar_7)) 3.16/2.19 3.16/2.19 (Comp: ?, Cost: 1) evalt1310(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 3.16/2.19 3.16/2.19 (Comp: ?, Cost: 1) evalt1311(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalt132(ar_0, ar_1, ar_2, ar_3, ar_4, ar_6, ar_6, ar_7)) 3.16/2.19 3.16/2.19 (Comp: ?, Cost: 1) evalt131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_2(evalt1310(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, i, ar_7), evalt1311(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, i, ar_7)) 3.16/2.19 3.16/2.19 (Comp: ?, Cost: 1) evalt132(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalt13bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_5 >= 1 ] 3.16/2.19 3.16/2.19 (Comp: ?, Cost: 1) evalt132(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalt13bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_2)) [ 0 >= ar_5 ] 3.16/2.19 3.16/2.19 (Comp: ?, Cost: 1) evalt13bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalt13bb1in(ar_4, ar_1, ar_2 + 1, ar_3, ar_4, ar_5, ar_6, ar_7)) 3.16/2.19 3.16/2.19 (Comp: ?, Cost: 1) evalt13bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalt13bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_7 >= 1 ] 3.16/2.19 3.16/2.19 (Comp: ?, Cost: 1) evalt13bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalt13bb1in(ar_4, ar_1, ar_7, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_7 ] 3.16/2.19 3.16/2.19 (Comp: ?, Cost: 1) evalt13bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalt13bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7 - 1)) 3.16/2.19 3.16/2.19 (Comp: ?, Cost: 1) evalt13bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalt13stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 3.16/2.19 3.16/2.19 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalt13start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] 3.16/2.19 3.16/2.19 start location: koat_start 3.16/2.19 3.16/2.19 leaf cost: 0 3.16/2.19 3.16/2.19 3.16/2.19 3.16/2.19 Repeatedly propagating knowledge in problem 1 produces the following problem: 3.16/2.19 3.16/2.19 2: T: 3.16/2.19 3.16/2.19 (Comp: 1, Cost: 1) evalt13start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalt13bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 3.16/2.19 3.16/2.19 (Comp: 1, Cost: 1) evalt13bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalt13bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7)) 3.16/2.19 3.16/2.19 (Comp: ?, Cost: 1) evalt13bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalt13bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 ] 3.16/2.19 3.16/2.19 (Comp: ?, Cost: 1) evalt13bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalt13bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_0 ] 3.16/2.19 3.16/2.19 (Comp: ?, Cost: 1) evalt13bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalt131(ar_0, ar_1, ar_2, ar_3, ar_0 - 1, ar_5, ar_6, ar_7)) 3.16/2.19 3.16/2.19 (Comp: ?, Cost: 1) evalt1310(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 3.16/2.19 3.16/2.19 (Comp: ?, Cost: 1) evalt1311(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalt132(ar_0, ar_1, ar_2, ar_3, ar_4, ar_6, ar_6, ar_7)) popout

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all output return to Complexity_C_Integer 2019-03-21 04.38