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Complexity_C_Integer 2019-03-21 04.38 pair #429989738
details
property
value
status
complete
benchmark
wcet1.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n139.star.cs.uiowa.edu
space
WTC_V2
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
2.10405 seconds
cpu usage
3.00895
user time
2.7724
system time
0.236552
max virtual memory
1.846816E7
max residence set size
184264.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
2.83/2.06 WORST_CASE(?, O(n^1)) 2.83/2.07 proof of /export/starexec/sandbox2/output/output_files/bench.koat 2.83/2.07 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.83/2.07 2.83/2.07 2.83/2.07 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 2.83/2.07 2.83/2.07 (0) CpxIntTrs 2.83/2.07 (1) Koat Proof [FINISHED, 784 ms] 2.83/2.07 (2) BOUNDS(1, n^1) 2.83/2.07 2.83/2.07 2.83/2.07 ---------------------------------------- 2.83/2.07 2.83/2.07 (0) 2.83/2.07 Obligation: 2.83/2.07 Complexity Int TRS consisting of the following rules: 2.83/2.07 eval_wcet1_start(v_1, v_i.0, v_j.0, v_j.3, v_n) -> Com_1(eval_wcet1_bb0_in(v_1, v_i.0, v_j.0, v_j.3, v_n)) :|: TRUE 2.83/2.07 eval_wcet1_bb0_in(v_1, v_i.0, v_j.0, v_j.3, v_n) -> Com_1(eval_wcet1_bb1_in(v_1, v_n, 0, v_j.3, v_n)) :|: v_n >= 1 2.83/2.07 eval_wcet1_bb0_in(v_1, v_i.0, v_j.0, v_j.3, v_n) -> Com_1(eval_wcet1_bb5_in(v_1, v_i.0, v_j.0, v_j.3, v_n)) :|: v_n < 1 2.83/2.07 eval_wcet1_bb1_in(v_1, v_i.0, v_j.0, v_j.3, v_n) -> Com_1(eval_wcet1_0(v_1, v_i.0, v_j.0, v_j.3, v_n)) :|: TRUE 2.83/2.07 eval_wcet1_0(v_1, v_i.0, v_j.0, v_j.3, v_n) -> Com_2(eval_nondet_start(v_1, v_i.0, v_j.0, v_j.3, v_n), eval_wcet1_1(nondef.0, v_i.0, v_j.0, v_j.3, v_n)) :|: TRUE 2.83/2.07 eval_wcet1_1(v_1, v_i.0, v_j.0, v_j.3, v_n) -> Com_1(eval_wcet1_bb2_in(v_1, v_i.0, v_j.0, v_j.3, v_n)) :|: v_1 > 0 2.83/2.07 eval_wcet1_1(v_1, v_i.0, v_j.0, v_j.3, v_n) -> Com_1(eval_wcet1_bb3_in(v_1, v_i.0, v_j.0, v_j.3, v_n)) :|: v_1 <= 0 2.83/2.07 eval_wcet1_bb2_in(v_1, v_i.0, v_j.0, v_j.3, v_n) -> Com_1(eval_wcet1_bb4_in(v_1, v_i.0, v_j.0, 0, v_n)) :|: v_j.0 + 1 >= v_n 2.83/2.07 eval_wcet1_bb2_in(v_1, v_i.0, v_j.0, v_j.3, v_n) -> Com_1(eval_wcet1_bb4_in(v_1, v_i.0, v_j.0, v_j.0 + 1, v_n)) :|: v_j.0 + 1 < v_n 2.83/2.07 eval_wcet1_bb3_in(v_1, v_i.0, v_j.0, v_j.3, v_n) -> Com_1(eval_wcet1_bb4_in(v_1, v_i.0, v_j.0, 0, v_n)) :|: v_j.0 - 1 <= 0 2.83/2.07 eval_wcet1_bb3_in(v_1, v_i.0, v_j.0, v_j.3, v_n) -> Com_1(eval_wcet1_bb4_in(v_1, v_i.0, v_j.0, v_j.0 - 1, v_n)) :|: v_j.0 - 1 > 0 2.83/2.07 eval_wcet1_bb4_in(v_1, v_i.0, v_j.0, v_j.3, v_n) -> Com_1(eval_wcet1_bb1_in(v_1, v_i.0 - 1, v_j.3, v_j.3, v_n)) :|: v_i.0 - 1 > 0 2.83/2.07 eval_wcet1_bb4_in(v_1, v_i.0, v_j.0, v_j.3, v_n) -> Com_1(eval_wcet1_bb5_in(v_1, v_i.0, v_j.0, v_j.3, v_n)) :|: v_i.0 - 1 <= 0 2.83/2.07 eval_wcet1_bb5_in(v_1, v_i.0, v_j.0, v_j.3, v_n) -> Com_1(eval_wcet1_stop(v_1, v_i.0, v_j.0, v_j.3, v_n)) :|: TRUE 2.83/2.07 2.83/2.07 The start-symbols are:[eval_wcet1_start_5] 2.83/2.07 2.83/2.07 2.83/2.07 ---------------------------------------- 2.83/2.07 2.83/2.07 (1) Koat Proof (FINISHED) 2.83/2.07 YES(?, 77*ar_0 + 18) 2.83/2.07 2.83/2.07 2.83/2.07 2.83/2.07 Initial complexity problem: 2.83/2.07 2.83/2.07 1: T: 2.83/2.07 2.83/2.07 (Comp: ?, Cost: 1) evalwcet1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.83/2.07 2.83/2.07 (Comp: ?, Cost: 1) evalwcet1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet1bb1in(ar_0, ar_0, 0, ar_3, ar_4, ar_5)) [ ar_0 >= 1 ] 2.83/2.07 2.83/2.07 (Comp: ?, Cost: 1) evalwcet1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet1bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 ] 2.83/2.07 2.83/2.07 (Comp: ?, Cost: 1) evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.83/2.07 2.83/2.07 (Comp: ?, Cost: 1) evalwcet100(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.83/2.07 2.83/2.07 (Comp: ?, Cost: 1) evalwcet101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet11(ar_0, ar_1, ar_2, ar_4, ar_4, ar_5)) 2.83/2.07 2.83/2.07 (Comp: ?, Cost: 1) evalwcet10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_2(evalwcet100(ar_0, ar_1, ar_2, ar_3, g, ar_5), evalwcet101(ar_0, ar_1, ar_2, ar_3, g, ar_5)) 2.83/2.07 2.83/2.07 (Comp: ?, Cost: 1) evalwcet11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_3 >= 1 ] 2.83/2.07 2.83/2.07 (Comp: ?, Cost: 1) evalwcet11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_3 ] 2.83/2.07 2.83/2.07 (Comp: ?, Cost: 1) evalwcet1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, 0)) [ ar_2 + 1 >= ar_0 ] 2.83/2.07 2.83/2.07 (Comp: ?, Cost: 1) evalwcet1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_2 + 1)) [ ar_0 >= ar_2 + 2 ] 2.83/2.07 2.83/2.07 (Comp: ?, Cost: 1) evalwcet1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, 0)) [ 1 >= ar_2 ] 2.83/2.07 2.83/2.07 (Comp: ?, Cost: 1) evalwcet1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_2 - 1)) [ ar_2 >= 2 ] 2.83/2.07 2.83/2.07 (Comp: ?, Cost: 1) evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet1bb1in(ar_0, ar_1 - 1, ar_5, ar_3, ar_4, ar_5)) [ ar_1 >= 2 ] 2.83/2.07 2.83/2.07 (Comp: ?, Cost: 1) evalwcet1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet1bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 1 >= ar_1 ] 2.83/2.07 2.83/2.07 (Comp: ?, Cost: 1) evalwcet1bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet1stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.83/2.07 2.83/2.07 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 2.83/2.07 2.83/2.07 start location: koat_start 2.83/2.07 2.83/2.07 leaf cost: 0 2.83/2.07 2.83/2.07 2.83/2.07 2.83/2.07 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.83/2.07 2.83/2.07 2: T: 2.83/2.07 2.83/2.07 (Comp: 1, Cost: 1) evalwcet1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.83/2.07 2.83/2.07 (Comp: 1, Cost: 1) evalwcet1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet1bb1in(ar_0, ar_0, 0, ar_3, ar_4, ar_5)) [ ar_0 >= 1 ] 2.83/2.07 2.83/2.07 (Comp: 1, Cost: 1) evalwcet1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet1bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 ] 2.83/2.07 2.83/2.07 (Comp: ?, Cost: 1) evalwcet1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.83/2.07 2.83/2.07 (Comp: ?, Cost: 1) evalwcet100(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.83/2.07
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