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Complexity_C_Integer 2019-03-21 04.38 pair #429989708
details
property
value
status
complete
benchmark
while2.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n103.star.cs.uiowa.edu
space
WTC_V2
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.36753 seconds
cpu usage
2.44202
user time
2.26397
system time
0.178055
max virtual memory
1.8273644E7
max residence set size
184652.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
2.25/1.33 WORST_CASE(?, O(n^2)) 2.25/1.34 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.25/1.34 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.25/1.34 2.25/1.34 2.25/1.34 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 2.25/1.34 2.25/1.34 (0) CpxIntTrs 2.25/1.34 (1) Koat Proof [FINISHED, 74 ms] 2.25/1.34 (2) BOUNDS(1, n^2) 2.25/1.34 2.25/1.34 2.25/1.34 ---------------------------------------- 2.25/1.34 2.25/1.34 (0) 2.25/1.34 Obligation: 2.25/1.34 Complexity Int TRS consisting of the following rules: 2.25/1.34 eval_while2_start(v_N, v_i.0, v_j.0) -> Com_1(eval_while2_bb0_in(v_N, v_i.0, v_j.0)) :|: TRUE 2.25/1.34 eval_while2_bb0_in(v_N, v_i.0, v_j.0) -> Com_1(eval_while2_bb1_in(v_N, v_N, v_j.0)) :|: TRUE 2.25/1.34 eval_while2_bb1_in(v_N, v_i.0, v_j.0) -> Com_1(eval_while2_bb2_in(v_N, v_i.0, v_N)) :|: v_i.0 > 0 2.25/1.34 eval_while2_bb1_in(v_N, v_i.0, v_j.0) -> Com_1(eval_while2_bb5_in(v_N, v_i.0, v_j.0)) :|: v_i.0 <= 0 2.25/1.34 eval_while2_bb2_in(v_N, v_i.0, v_j.0) -> Com_1(eval_while2_bb3_in(v_N, v_i.0, v_j.0)) :|: v_j.0 > 0 2.25/1.34 eval_while2_bb2_in(v_N, v_i.0, v_j.0) -> Com_1(eval_while2_bb4_in(v_N, v_i.0, v_j.0)) :|: v_j.0 <= 0 2.25/1.34 eval_while2_bb3_in(v_N, v_i.0, v_j.0) -> Com_1(eval_while2_bb2_in(v_N, v_i.0, v_j.0 - 1)) :|: TRUE 2.25/1.34 eval_while2_bb4_in(v_N, v_i.0, v_j.0) -> Com_1(eval_while2_bb1_in(v_N, v_i.0 - 1, v_j.0)) :|: TRUE 2.25/1.34 eval_while2_bb5_in(v_N, v_i.0, v_j.0) -> Com_1(eval_while2_stop(v_N, v_i.0, v_j.0)) :|: TRUE 2.25/1.34 2.25/1.34 The start-symbols are:[eval_while2_start_3] 2.25/1.34 2.25/1.34 2.25/1.34 ---------------------------------------- 2.25/1.34 2.25/1.34 (1) Koat Proof (FINISHED) 2.25/1.34 YES(?, 7*ar_1 + 2*ar_1^2 + 11) 2.25/1.34 2.25/1.34 2.25/1.34 2.25/1.34 Initial complexity problem: 2.25/1.34 2.25/1.34 1: T: 2.25/1.34 2.25/1.34 (Comp: ?, Cost: 1) evalwhile2start(ar_0, ar_1, ar_2) -> Com_1(evalwhile2bb0in(ar_0, ar_1, ar_2)) 2.25/1.34 2.25/1.34 (Comp: ?, Cost: 1) evalwhile2bb0in(ar_0, ar_1, ar_2) -> Com_1(evalwhile2bb1in(ar_1, ar_1, ar_2)) 2.25/1.34 2.25/1.34 (Comp: ?, Cost: 1) evalwhile2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_1)) [ ar_0 >= 1 ] 2.25/1.34 2.25/1.34 (Comp: ?, Cost: 1) evalwhile2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwhile2bb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ] 2.25/1.34 2.25/1.34 (Comp: ?, Cost: 1) evalwhile2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwhile2bb3in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ] 2.25/1.34 2.25/1.34 (Comp: ?, Cost: 1) evalwhile2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwhile2bb4in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ] 2.25/1.34 2.25/1.34 (Comp: ?, Cost: 1) evalwhile2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_2 - 1)) 2.25/1.34 2.25/1.34 (Comp: ?, Cost: 1) evalwhile2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwhile2bb1in(ar_0 - 1, ar_1, ar_2)) 2.25/1.34 2.25/1.34 (Comp: ?, Cost: 1) evalwhile2bb5in(ar_0, ar_1, ar_2) -> Com_1(evalwhile2stop(ar_0, ar_1, ar_2)) 2.25/1.34 2.25/1.34 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalwhile2start(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 2.25/1.34 2.25/1.34 start location: koat_start 2.25/1.34 2.25/1.34 leaf cost: 0 2.25/1.34 2.25/1.34 2.25/1.34 2.25/1.34 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.25/1.34 2.25/1.34 2: T: 2.25/1.34 2.25/1.34 (Comp: 1, Cost: 1) evalwhile2start(ar_0, ar_1, ar_2) -> Com_1(evalwhile2bb0in(ar_0, ar_1, ar_2)) 2.25/1.34 2.25/1.34 (Comp: 1, Cost: 1) evalwhile2bb0in(ar_0, ar_1, ar_2) -> Com_1(evalwhile2bb1in(ar_1, ar_1, ar_2)) 2.25/1.34 2.25/1.34 (Comp: ?, Cost: 1) evalwhile2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_1)) [ ar_0 >= 1 ] 2.25/1.34 2.25/1.34 (Comp: ?, Cost: 1) evalwhile2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwhile2bb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ] 2.25/1.34 2.25/1.34 (Comp: ?, Cost: 1) evalwhile2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwhile2bb3in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ] 2.25/1.34 2.25/1.34 (Comp: ?, Cost: 1) evalwhile2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwhile2bb4in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ] 2.25/1.34 2.25/1.34 (Comp: ?, Cost: 1) evalwhile2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwhile2bb2in(ar_0, ar_1, ar_2 - 1)) 2.25/1.34 2.25/1.34 (Comp: ?, Cost: 1) evalwhile2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwhile2bb1in(ar_0 - 1, ar_1, ar_2)) 2.25/1.34 2.25/1.34 (Comp: ?, Cost: 1) evalwhile2bb5in(ar_0, ar_1, ar_2) -> Com_1(evalwhile2stop(ar_0, ar_1, ar_2)) 2.25/1.34 2.25/1.34 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalwhile2start(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 2.25/1.34 2.25/1.34 start location: koat_start 2.25/1.34 2.25/1.34 leaf cost: 0 2.25/1.34 2.25/1.34 2.25/1.34 2.25/1.34 A polynomial rank function with 2.25/1.34 2.25/1.34 Pol(evalwhile2start) = 2
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