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Complexity_C_Integer 2019-03-21 04.38 pair #429989532
details
property
value
status
complete
benchmark
ex_paper1.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n181.star.cs.uiowa.edu
space
Other
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
12.7797 seconds
cpu usage
14.299
user time
13.577
system time
0.722056
max virtual memory
1.8794784E7
max residence set size
351516.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
14.14/12.71 WORST_CASE(?, O(n^2)) 14.14/12.72 proof of /export/starexec/sandbox/output/output_files/bench.koat 14.14/12.72 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 14.14/12.72 14.14/12.72 14.14/12.72 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 14.14/12.72 14.14/12.72 (0) CpxIntTrs 14.14/12.72 (1) Koat Proof [FINISHED, 11.4 s] 14.14/12.72 (2) BOUNDS(1, n^2) 14.14/12.72 14.14/12.72 14.14/12.72 ---------------------------------------- 14.14/12.72 14.14/12.72 (0) 14.14/12.72 Obligation: 14.14/12.72 Complexity Int TRS consisting of the following rules: 14.14/12.72 eval_ex_paper1_start(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z) -> Com_1(eval_ex_paper1_bb0_in(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z)) :|: TRUE 14.14/12.72 eval_ex_paper1_bb0_in(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z) -> Com_1(eval_ex_paper1_bb9_in(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z)) :|: v_x <= 0 14.14/12.72 eval_ex_paper1_bb0_in(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z) -> Com_1(eval_ex_paper1_bb9_in(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z)) :|: v_y <= 0 14.14/12.72 eval_ex_paper1_bb0_in(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z) -> Com_1(eval_ex_paper1_bb1_in(v_x, v_y, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z)) :|: v_x > 0 && v_y > 0 14.14/12.72 eval_ex_paper1_bb1_in(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z) -> Com_1(eval_ex_paper1_bb2_in(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z)) :|: v_.0 > 0 14.14/12.72 eval_ex_paper1_bb1_in(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z) -> Com_1(eval_ex_paper1_bb5_in(v_.0, v_.01, v_.1, v_.01, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z)) :|: v_.0 <= 0 14.14/12.72 eval_ex_paper1_bb2_in(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z) -> Com_1(eval_ex_paper1_bb3_in(v_.0, v_.01, v_.01 + 1, v_.2, v_11, v_.0 - 1, v_5, v_9, v_i.0, v_x, v_y, v_z)) :|: TRUE 14.14/12.72 eval_ex_paper1_bb3_in(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z) -> Com_1(eval_ex_paper1_3(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z)) :|: TRUE 14.14/12.72 eval_ex_paper1_3(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z) -> Com_2(eval_nondet_start(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z), eval_ex_paper1_4(v_.0, v_.01, v_.1, v_.2, v_11, v_3, nondef.0, v_9, v_i.0, v_x, v_y, v_z)) :|: TRUE 14.14/12.72 eval_ex_paper1_4(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z) -> Com_1(eval_ex_paper1_bb4_in(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z)) :|: v_5 < 0 && v_.1 > 0 14.14/12.72 eval_ex_paper1_4(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z) -> Com_1(eval_ex_paper1_bb4_in(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z)) :|: v_5 > 0 && v_.1 > 0 14.14/12.72 eval_ex_paper1_4(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z) -> Com_1(eval_ex_paper1_bb1_in(v_3, v_.1, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z)) :|: v_5 >= 0 && v_5 <= 0 14.14/12.72 eval_ex_paper1_4(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z) -> Com_1(eval_ex_paper1_bb1_in(v_3, v_.1, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z)) :|: v_.1 <= 0 14.14/12.72 eval_ex_paper1_bb4_in(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z) -> Com_1(eval_ex_paper1_6(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_.1 - 1, v_i.0, v_x, v_y, v_z)) :|: TRUE 14.14/12.72 eval_ex_paper1_6(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z) -> Com_2(eval_tick_start(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z), eval_ex_paper1_7(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z)) :|: TRUE 14.14/12.72 eval_ex_paper1_7(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z) -> Com_1(eval_ex_paper1_bb3_in(v_.0, v_.01, v_9, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z)) :|: TRUE 14.14/12.72 eval_ex_paper1_bb5_in(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z) -> Com_1(eval_ex_paper1_bb6_in(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z)) :|: v_.2 > 0 14.14/12.72 eval_ex_paper1_bb5_in(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z) -> Com_1(eval_ex_paper1_bb9_in(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z)) :|: v_.2 <= 0 14.14/12.72 eval_ex_paper1_bb6_in(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z) -> Com_1(eval_ex_paper1_bb7_in(v_.0, v_.01, v_.1, v_.2, v_.2 - 1, v_3, v_5, v_9, 0, v_x, v_y, v_z)) :|: TRUE 14.14/12.72 eval_ex_paper1_bb7_in(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z) -> Com_1(eval_ex_paper1_bb8_in(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z)) :|: v_i.0 < v_z 14.14/12.72 eval_ex_paper1_bb7_in(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z) -> Com_1(eval_ex_paper1_bb5_in(v_.0, v_.01, v_.1, v_11, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z)) :|: v_i.0 >= v_z 14.14/12.72 eval_ex_paper1_bb8_in(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z) -> Com_1(eval_ex_paper1_10(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z)) :|: TRUE 14.14/12.72 eval_ex_paper1_10(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z) -> Com_2(eval_tick_start(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z), eval_ex_paper1_11(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z)) :|: TRUE 14.14/12.72 eval_ex_paper1_11(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z) -> Com_1(eval_ex_paper1_bb7_in(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0 + 1, v_x, v_y, v_z)) :|: TRUE 14.14/12.72 eval_ex_paper1_bb9_in(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z) -> Com_1(eval_ex_paper1_stop(v_.0, v_.01, v_.1, v_.2, v_11, v_3, v_5, v_9, v_i.0, v_x, v_y, v_z)) :|: TRUE 14.14/12.72 14.14/12.72 The start-symbols are:[eval_ex_paper1_start_12] 14.14/12.72 14.14/12.72 14.14/12.72 ---------------------------------------- 14.14/12.72 14.14/12.72 (1) Koat Proof (FINISHED) 14.14/12.72 YES(?, 594*ar_0^2 + 540*ar_0*ar_1 + 156*ar_0 + 576*ar_0*ar_12 + 576*ar_1*ar_12 + 108*ar_1 + 13) 14.14/12.72 14.14/12.72 14.14/12.72 14.14/12.72 Initial complexity problem: 14.14/12.72 14.14/12.72 1: T: 14.14/12.72 14.14/12.72 (Comp: ?, Cost: 1) evalexpaper1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12) -> Com_1(evalexpaper1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12)) 14.14/12.72 14.14/12.72 (Comp: ?, Cost: 1) evalexpaper1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12) -> Com_1(evalexpaper1bb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12)) [ 0 >= ar_0 ] 14.14/12.72 14.14/12.72 (Comp: ?, Cost: 1) evalexpaper1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12) -> Com_1(evalexpaper1bb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12)) [ 0 >= ar_1 ] 14.14/12.72 14.14/12.72 (Comp: ?, Cost: 1) evalexpaper1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12) -> Com_1(evalexpaper1bb1in(ar_0, ar_1, ar_0, ar_1, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12)) [ ar_0 >= 1 /\ ar_1 >= 1 ] 14.14/12.72 14.14/12.72 (Comp: ?, Cost: 1) evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12) -> Com_1(evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12)) [ ar_2 >= 1 ] 14.14/12.72 14.14/12.72 (Comp: ?, Cost: 1) evalexpaper1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12) -> Com_1(evalexpaper1bb5in(ar_0, ar_1, ar_2, ar_3, ar_3, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12)) [ 0 >= ar_2 ] 14.14/12.72 14.14/12.72 (Comp: ?, Cost: 1) evalexpaper1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12) -> Com_1(evalexpaper1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_3 + 1, ar_2 - 1, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12)) 14.14/12.72 14.14/12.72 (Comp: ?, Cost: 1) evalexpaper1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12) -> Com_1(evalexpaper13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12)) 14.14/12.72 14.14/12.72 (Comp: ?, Cost: 1) evalexpaper130(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12)) 14.14/12.72 14.14/12.72 (Comp: ?, Cost: 1) evalexpaper131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12) -> Com_1(evalexpaper14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_8, ar_8, ar_9, ar_10, ar_11, ar_12)) 14.14/12.72 14.14/12.72 (Comp: ?, Cost: 1) evalexpaper13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12) -> Com_2(evalexpaper130(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, n, ar_9, ar_10, ar_11, ar_12), evalexpaper131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, n, ar_9, ar_10, ar_11, ar_12)) 14.14/12.72 14.14/12.72 (Comp: ?, Cost: 1) evalexpaper14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12) -> Com_1(evalexpaper1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12)) [ 0 >= ar_7 + 1 /\ ar_5 >= 1 ] 14.14/12.72 14.14/12.72 (Comp: ?, Cost: 1) evalexpaper14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12) -> Com_1(evalexpaper1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12)) [ ar_7 >= 1 /\ ar_5 >= 1 ] 14.14/12.72 14.14/12.72 (Comp: ?, Cost: 1) evalexpaper14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12) -> Com_1(evalexpaper1bb1in(ar_0, ar_1, ar_6, ar_5, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12)) [ ar_7 = 0 ] 14.14/12.72 14.14/12.72 (Comp: ?, Cost: 1) evalexpaper14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12) -> Com_1(evalexpaper1bb1in(ar_0, ar_1, ar_6, ar_5, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12)) [ 0 >= ar_5 ] 14.14/12.72 14.14/12.72 (Comp: ?, Cost: 1) evalexpaper1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12) -> Com_1(evalexpaper16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_5 - 1, ar_10, ar_11, ar_12)) 14.14/12.72 14.14/12.72 (Comp: ?, Cost: 1) evalexpaper16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12) -> Com_2(evaltickstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12), evalexpaper17(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12)) 14.14/12.72 14.14/12.72 (Comp: ?, Cost: 1) evalexpaper17(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12) -> Com_1(evalexpaper1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_9, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12)) 14.14/12.72 14.14/12.72 (Comp: ?, Cost: 1) evalexpaper1bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12) -> Com_1(evalexpaper1bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12)) [ ar_4 >= 1 ] 14.14/12.72 14.14/12.72 (Comp: ?, Cost: 1) evalexpaper1bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12) -> Com_1(evalexpaper1bb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12)) [ 0 >= ar_4 ] 14.14/12.72 14.14/12.72 (Comp: ?, Cost: 1) evalexpaper1bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12) -> Com_1(evalexpaper1bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_4 - 1, 0, ar_12)) 14.14/12.72 14.14/12.72 (Comp: ?, Cost: 1) evalexpaper1bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12) -> Com_1(evalexpaper1bb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12)) [ ar_12 >= ar_11 + 1 ]
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