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Complexity_C_Integer 2019-03-21 04.38 pair #429989560
details
property
value
status
complete
benchmark
CPU2006_local_alloc.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n100.star.cs.uiowa.edu
space
Sinn_2016
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.48366 seconds
cpu usage
2.55853
user time
2.38172
system time
0.176818
max virtual memory
1.8273644E7
max residence set size
184616.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
2.26/1.37 WORST_CASE(?, O(n^2)) 2.26/1.38 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.26/1.38 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.26/1.38 2.26/1.38 2.26/1.38 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 2.26/1.38 2.26/1.38 (0) CpxIntTrs 2.26/1.38 (1) Koat Proof [FINISHED, 179 ms] 2.26/1.38 (2) BOUNDS(1, n^2) 2.26/1.38 2.26/1.38 2.26/1.38 ---------------------------------------- 2.26/1.38 2.26/1.38 (0) 2.26/1.38 Obligation: 2.26/1.38 Complexity Int TRS consisting of the following rules: 2.26/1.38 eval_local_alloc_start(v_b.0, v_i.0, v_limit, v_max_qty, v_n_basic_blocks, v_next_qty.0) -> Com_1(eval_local_alloc_bb0_in(v_b.0, v_i.0, v_limit, v_max_qty, v_n_basic_blocks, v_next_qty.0)) :|: TRUE 2.26/1.38 eval_local_alloc_bb0_in(v_b.0, v_i.0, v_limit, v_max_qty, v_n_basic_blocks, v_next_qty.0) -> Com_1(eval_local_alloc_bb1_in(0, v_i.0, v_limit, v_max_qty, v_n_basic_blocks, v_max_qty)) :|: TRUE 2.26/1.38 eval_local_alloc_bb1_in(v_b.0, v_i.0, v_limit, v_max_qty, v_n_basic_blocks, v_next_qty.0) -> Com_1(eval_local_alloc_bb2_in(v_b.0, v_i.0, v_limit, v_max_qty, v_n_basic_blocks, v_next_qty.0)) :|: v_b.0 < v_n_basic_blocks 2.26/1.38 eval_local_alloc_bb1_in(v_b.0, v_i.0, v_limit, v_max_qty, v_n_basic_blocks, v_next_qty.0) -> Com_1(eval_local_alloc_bb6_in(v_b.0, v_i.0, v_limit, v_max_qty, v_n_basic_blocks, v_next_qty.0)) :|: v_b.0 >= v_n_basic_blocks 2.26/1.38 eval_local_alloc_bb2_in(v_b.0, v_i.0, v_limit, v_max_qty, v_n_basic_blocks, v_next_qty.0) -> Com_1(eval_local_alloc_bb3_in(v_b.0, 0, v_limit, v_max_qty, v_n_basic_blocks, v_next_qty.0)) :|: v_next_qty.0 < v_limit 2.26/1.38 eval_local_alloc_bb2_in(v_b.0, v_i.0, v_limit, v_max_qty, v_n_basic_blocks, v_next_qty.0) -> Com_1(eval_local_alloc_bb5_in(v_b.0, v_i.0, v_limit, v_max_qty, v_n_basic_blocks, v_next_qty.0)) :|: v_next_qty.0 >= v_limit 2.26/1.38 eval_local_alloc_bb3_in(v_b.0, v_i.0, v_limit, v_max_qty, v_n_basic_blocks, v_next_qty.0) -> Com_1(eval_local_alloc_bb4_in(v_b.0, v_i.0, v_limit, v_max_qty, v_n_basic_blocks, v_next_qty.0)) :|: v_i.0 < v_next_qty.0 2.26/1.38 eval_local_alloc_bb3_in(v_b.0, v_i.0, v_limit, v_max_qty, v_n_basic_blocks, v_next_qty.0) -> Com_1(eval_local_alloc_bb5_in(v_b.0, v_i.0, v_limit, v_max_qty, v_n_basic_blocks, v_next_qty.0)) :|: v_i.0 >= v_next_qty.0 2.26/1.38 eval_local_alloc_bb4_in(v_b.0, v_i.0, v_limit, v_max_qty, v_n_basic_blocks, v_next_qty.0) -> Com_1(eval_local_alloc_bb3_in(v_b.0, v_i.0 + 1, v_limit, v_max_qty, v_n_basic_blocks, v_next_qty.0)) :|: TRUE 2.26/1.38 eval_local_alloc_bb5_in(v_b.0, v_i.0, v_limit, v_max_qty, v_n_basic_blocks, v_next_qty.0) -> Com_1(eval_local_alloc_bb1_in(v_b.0 + 1, v_i.0, v_limit, v_max_qty, v_n_basic_blocks, 0)) :|: TRUE 2.26/1.38 eval_local_alloc_bb6_in(v_b.0, v_i.0, v_limit, v_max_qty, v_n_basic_blocks, v_next_qty.0) -> Com_1(eval_local_alloc_stop(v_b.0, v_i.0, v_limit, v_max_qty, v_n_basic_blocks, v_next_qty.0)) :|: TRUE 2.26/1.38 2.26/1.38 The start-symbols are:[eval_local_alloc_start_6] 2.26/1.38 2.26/1.38 2.26/1.38 ---------------------------------------- 2.26/1.38 2.26/1.38 (1) Koat Proof (FINISHED) 2.26/1.38 YES(?, 9*ar_3 + 2*ar_2*ar_3 + 2*ar_2 + 15) 2.26/1.38 2.26/1.38 2.26/1.38 2.26/1.38 Initial complexity problem: 2.26/1.38 2.26/1.38 1: T: 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evallocalallocstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evallocalallocbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evallocalallocbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evallocalallocbb1in(0, ar_2, ar_2, ar_3, ar_4, ar_5)) 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evallocalallocbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evallocalallocbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_3 >= ar_0 + 1 ] 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evallocalallocbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evallocalallocbb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_3 ] 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evallocalallocbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evallocalallocbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, 0)) [ ar_4 >= ar_1 + 1 ] 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evallocalallocbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evallocalallocbb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= ar_4 ] 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evallocalallocbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evallocalallocbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= ar_5 + 1 ] 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evallocalallocbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evallocalallocbb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= ar_1 ] 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evallocalallocbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evallocalallocbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1)) 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evallocalallocbb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evallocalallocbb1in(ar_0 + 1, 0, ar_2, ar_3, ar_4, ar_5)) 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evallocalallocbb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evallocalallocstop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.26/1.38 2.26/1.38 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evallocalallocstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 2.26/1.38 2.26/1.38 start location: koat_start 2.26/1.38 2.26/1.38 leaf cost: 0 2.26/1.38 2.26/1.38 2.26/1.38 2.26/1.38 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.26/1.38 2.26/1.38 2: T: 2.26/1.38 2.26/1.38 (Comp: 1, Cost: 1) evallocalallocstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evallocalallocbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.26/1.38 2.26/1.38 (Comp: 1, Cost: 1) evallocalallocbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evallocalallocbb1in(0, ar_2, ar_2, ar_3, ar_4, ar_5)) 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evallocalallocbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evallocalallocbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_3 >= ar_0 + 1 ] 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evallocalallocbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evallocalallocbb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_3 ] 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evallocalallocbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evallocalallocbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, 0)) [ ar_4 >= ar_1 + 1 ] 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evallocalallocbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evallocalallocbb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= ar_4 ] 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evallocalallocbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evallocalallocbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= ar_5 + 1 ] 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evallocalallocbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evallocalallocbb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= ar_1 ] 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evallocalallocbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evallocalallocbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1)) 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evallocalallocbb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evallocalallocbb1in(ar_0 + 1, 0, ar_2, ar_3, ar_4, ar_5)) 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evallocalallocbb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evallocalallocstop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.26/1.38 2.26/1.38 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evallocalallocstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
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return to Complexity_C_Integer 2019-03-21 04.38