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Complexity_C_Integer 2019-03-21 04.38 pair #429989720
details
property
value
status
complete
benchmark
wcet0.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n148.star.cs.uiowa.edu
space
WTC_V2
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.99715 seconds
cpu usage
3.05306
user time
2.81265
system time
0.240413
max virtual memory
1.8495188E7
max residence set size
187396.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
2.91/1.95 WORST_CASE(?, O(n^1)) 2.91/1.96 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.91/1.96 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.91/1.96 2.91/1.96 2.91/1.96 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 2.91/1.96 2.91/1.96 (0) CpxIntTrs 2.91/1.96 (1) Koat Proof [FINISHED, 692 ms] 2.91/1.96 (2) BOUNDS(1, n^1) 2.91/1.96 2.91/1.96 2.91/1.96 ---------------------------------------- 2.91/1.96 2.91/1.96 (0) 2.91/1.96 Obligation: 2.91/1.96 Complexity Int TRS consisting of the following rules: 2.91/1.96 eval_wcet0_start(v_1, v_i.0, v_j.0, v_j.3, v_n) -> Com_1(eval_wcet0_bb0_in(v_1, v_i.0, v_j.0, v_j.3, v_n)) :|: TRUE 2.91/1.96 eval_wcet0_bb0_in(v_1, v_i.0, v_j.0, v_j.3, v_n) -> Com_1(eval_wcet0_bb1_in(v_1, v_n, 0, v_j.3, v_n)) :|: v_n >= 1 2.91/1.96 eval_wcet0_bb0_in(v_1, v_i.0, v_j.0, v_j.3, v_n) -> Com_1(eval_wcet0_bb5_in(v_1, v_i.0, v_j.0, v_j.3, v_n)) :|: v_n < 1 2.91/1.96 eval_wcet0_bb1_in(v_1, v_i.0, v_j.0, v_j.3, v_n) -> Com_1(eval_wcet0_0(v_1, v_i.0, v_j.0, v_j.3, v_n)) :|: TRUE 2.91/1.96 eval_wcet0_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_wcet0_1(nondef.0, v_i.0, v_j.0, v_j.3, v_n)) :|: TRUE 2.91/1.96 eval_wcet0_1(v_1, v_i.0, v_j.0, v_j.3, v_n) -> Com_1(eval_wcet0_bb2_in(v_1, v_i.0, v_j.0, v_j.3, v_n)) :|: v_1 > 0 2.91/1.96 eval_wcet0_1(v_1, v_i.0, v_j.0, v_j.3, v_n) -> Com_1(eval_wcet0_bb3_in(v_1, v_i.0, v_j.0, v_j.3, v_n)) :|: v_1 <= 0 2.91/1.96 eval_wcet0_bb2_in(v_1, v_i.0, v_j.0, v_j.3, v_n) -> Com_1(eval_wcet0_bb4_in(v_1, v_i.0, v_j.0, 0, v_n)) :|: v_j.0 + 1 >= v_n 2.91/1.96 eval_wcet0_bb2_in(v_1, v_i.0, v_j.0, v_j.3, v_n) -> Com_1(eval_wcet0_bb4_in(v_1, v_i.0, v_j.0, v_j.0 + 1, v_n)) :|: v_j.0 + 1 < v_n 2.91/1.96 eval_wcet0_bb3_in(v_1, v_i.0, v_j.0, v_j.3, v_n) -> Com_1(eval_wcet0_bb4_in(v_1, v_i.0, v_j.0, 0, v_n)) :|: v_j.0 - 1 <= -(v_n) 2.91/1.96 eval_wcet0_bb3_in(v_1, v_i.0, v_j.0, v_j.3, v_n) -> Com_1(eval_wcet0_bb4_in(v_1, v_i.0, v_j.0, v_j.0 - 1, v_n)) :|: v_j.0 - 1 > -(v_n) 2.91/1.96 eval_wcet0_bb4_in(v_1, v_i.0, v_j.0, v_j.3, v_n) -> Com_1(eval_wcet0_bb1_in(v_1, v_i.0 - 1, v_j.3, v_j.3, v_n)) :|: v_i.0 - 1 > 0 2.91/1.96 eval_wcet0_bb4_in(v_1, v_i.0, v_j.0, v_j.3, v_n) -> Com_1(eval_wcet0_bb5_in(v_1, v_i.0, v_j.0, v_j.3, v_n)) :|: v_i.0 - 1 <= 0 2.91/1.96 eval_wcet0_bb5_in(v_1, v_i.0, v_j.0, v_j.3, v_n) -> Com_1(eval_wcet0_stop(v_1, v_i.0, v_j.0, v_j.3, v_n)) :|: TRUE 2.91/1.96 2.91/1.96 The start-symbols are:[eval_wcet0_start_5] 2.91/1.96 2.91/1.96 2.91/1.96 ---------------------------------------- 2.91/1.96 2.91/1.96 (1) Koat Proof (FINISHED) 2.91/1.96 YES(?, 77*ar_0 + 73) 2.91/1.96 2.91/1.96 2.91/1.96 2.91/1.96 Initial complexity problem: 2.91/1.96 2.91/1.96 1: T: 2.91/1.96 2.91/1.96 (Comp: ?, Cost: 1) evalwcet0start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet0bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.91/1.96 2.91/1.96 (Comp: ?, Cost: 1) evalwcet0bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet0bb1in(ar_0, ar_0, 0, ar_3, ar_4, ar_5)) [ ar_0 >= 1 ] 2.91/1.96 2.91/1.96 (Comp: ?, Cost: 1) evalwcet0bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet0bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 ] 2.91/1.96 2.91/1.96 (Comp: ?, Cost: 1) evalwcet0bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet00(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.91/1.96 2.91/1.96 (Comp: ?, Cost: 1) evalwcet000(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)) 2.91/1.96 2.91/1.96 (Comp: ?, Cost: 1) evalwcet001(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet01(ar_0, ar_1, ar_2, ar_4, ar_4, ar_5)) 2.91/1.96 2.91/1.96 (Comp: ?, Cost: 1) evalwcet00(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_2(evalwcet000(ar_0, ar_1, ar_2, ar_3, g, ar_5), evalwcet001(ar_0, ar_1, ar_2, ar_3, g, ar_5)) 2.91/1.96 2.91/1.96 (Comp: ?, Cost: 1) evalwcet01(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet0bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_3 >= 1 ] 2.91/1.96 2.91/1.96 (Comp: ?, Cost: 1) evalwcet01(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet0bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_3 ] 2.91/1.96 2.91/1.96 (Comp: ?, Cost: 1) evalwcet0bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet0bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, 0)) [ ar_2 + 1 >= ar_0 ] 2.91/1.96 2.91/1.96 (Comp: ?, Cost: 1) evalwcet0bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet0bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_2 + 1)) [ ar_0 >= ar_2 + 2 ] 2.91/1.96 2.91/1.96 (Comp: ?, Cost: 1) evalwcet0bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet0bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, 0)) [ 1 >= ar_0 + ar_2 ] 2.91/1.96 2.91/1.96 (Comp: ?, Cost: 1) evalwcet0bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet0bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_2 - 1)) [ ar_2 + ar_0 >= 2 ] 2.91/1.96 2.91/1.96 (Comp: ?, Cost: 1) evalwcet0bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet0bb1in(ar_0, ar_1 - 1, ar_5, ar_3, ar_4, ar_5)) [ ar_1 >= 2 ] 2.91/1.96 2.91/1.96 (Comp: ?, Cost: 1) evalwcet0bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet0bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 1 >= ar_1 ] 2.91/1.96 2.91/1.96 (Comp: ?, Cost: 1) evalwcet0bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet0stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.91/1.96 2.91/1.96 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet0start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 2.91/1.96 2.91/1.96 start location: koat_start 2.91/1.96 2.91/1.96 leaf cost: 0 2.91/1.96 2.91/1.96 2.91/1.96 2.91/1.96 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.91/1.96 2.91/1.96 2: T: 2.91/1.96 2.91/1.96 (Comp: 1, Cost: 1) evalwcet0start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet0bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.91/1.96 2.91/1.96 (Comp: 1, Cost: 1) evalwcet0bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet0bb1in(ar_0, ar_0, 0, ar_3, ar_4, ar_5)) [ ar_0 >= 1 ] 2.91/1.96 2.91/1.96 (Comp: 1, Cost: 1) evalwcet0bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet0bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 ] 2.91/1.96 2.91/1.96 (Comp: ?, Cost: 1) evalwcet0bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalwcet00(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.91/1.96 2.91/1.96 (Comp: ?, Cost: 1) evalwcet000(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)) 2.91/1.96
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return to Complexity_C_Integer 2019-03-21 04.38