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Complexity_C_Integer 2019-03-21 04.38 pair #429989698
details
property
value
status
complete
benchmark
speedpldi3.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n082.star.cs.uiowa.edu
space
WTC_V2
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.59311 seconds
cpu usage
2.57743
user time
2.36394
system time
0.213495
max virtual memory
1.8273644E7
max residence set size
181864.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
2.16/1.56 WORST_CASE(?, O(n^2)) 2.16/1.57 proof of /export/starexec/sandbox2/output/output_files/bench.koat 2.16/1.57 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.16/1.57 2.16/1.57 2.16/1.57 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 2.16/1.57 2.16/1.57 (0) CpxIntTrs 2.16/1.57 (1) Koat Proof [FINISHED, 271 ms] 2.16/1.57 (2) BOUNDS(1, n^2) 2.16/1.57 2.16/1.57 2.16/1.57 ---------------------------------------- 2.16/1.57 2.16/1.57 (0) 2.16/1.57 Obligation: 2.16/1.57 Complexity Int TRS consisting of the following rules: 2.16/1.57 eval_speedpldi3_start(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_speedpldi3_bb0_in(v_i.0, v_j.0, v_m, v_n)) :|: TRUE 2.16/1.57 eval_speedpldi3_bb0_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_speedpldi3_bb3_in(v_i.0, v_j.0, v_m, v_n)) :|: v_m <= 0 2.16/1.57 eval_speedpldi3_bb0_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_speedpldi3_bb3_in(v_i.0, v_j.0, v_m, v_n)) :|: v_n <= v_m 2.16/1.57 eval_speedpldi3_bb0_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_speedpldi3_bb1_in(0, 0, v_m, v_n)) :|: v_m > 0 && v_n > v_m 2.16/1.57 eval_speedpldi3_bb1_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_speedpldi3_bb2_in(v_i.0, v_j.0, v_m, v_n)) :|: v_i.0 < v_n 2.16/1.57 eval_speedpldi3_bb1_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_speedpldi3_bb3_in(v_i.0, v_j.0, v_m, v_n)) :|: v_i.0 >= v_n 2.16/1.57 eval_speedpldi3_bb2_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_speedpldi3_bb1_in(v_i.0, v_j.0 + 1, v_m, v_n)) :|: v_j.0 < v_m 2.16/1.57 eval_speedpldi3_bb2_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_speedpldi3_bb1_in(v_i.0 + 1, v_j.0 + 1, v_m, v_n)) :|: v_j.0 < v_m && v_j.0 >= v_m 2.16/1.57 eval_speedpldi3_bb2_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_speedpldi3_bb1_in(v_i.0, 0, v_m, v_n)) :|: v_j.0 >= v_m && v_j.0 < v_m 2.16/1.57 eval_speedpldi3_bb2_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_speedpldi3_bb1_in(v_i.0 + 1, 0, v_m, v_n)) :|: v_j.0 >= v_m 2.16/1.57 eval_speedpldi3_bb3_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_speedpldi3_stop(v_i.0, v_j.0, v_m, v_n)) :|: TRUE 2.16/1.57 2.16/1.57 The start-symbols are:[eval_speedpldi3_start_4] 2.16/1.57 2.16/1.57 2.16/1.57 ---------------------------------------- 2.16/1.57 2.16/1.57 (1) Koat Proof (FINISHED) 2.16/1.57 YES(?, 2*ar_1 + 2*ar_0*ar_1 + 2*ar_0 + 9) 2.16/1.57 2.16/1.57 2.16/1.57 2.16/1.57 Initial complexity problem: 2.16/1.57 2.16/1.57 1: T: 2.16/1.57 2.16/1.57 (Comp: ?, Cost: 1) evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3)) 2.16/1.57 2.16/1.57 (Comp: ?, Cost: 1) evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 2.16/1.57 2.16/1.57 (Comp: ?, Cost: 1) evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] 2.16/1.57 2.16/1.57 (Comp: ?, Cost: 1) evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ] 2.16/1.57 2.16/1.57 (Comp: ?, Cost: 1) evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 + 1 ] 2.16/1.57 2.16/1.57 (Comp: ?, Cost: 1) evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 ] 2.16/1.57 2.16/1.57 (Comp: ?, Cost: 1) evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_0 >= ar_3 + 1 ] 2.16/1.57 2.16/1.57 (Comp: ?, Cost: 1) evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2 + 1, ar_3 + 1)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_0 ] 2.16/1.57 2.16/1.57 (Comp: ?, Cost: 1) evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= ar_0 /\ ar_0 >= ar_3 + 1 ] 2.16/1.57 2.16/1.57 (Comp: ?, Cost: 1) evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= ar_0 ] 2.16/1.57 2.16/1.57 (Comp: ?, Cost: 1) evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3stop(ar_0, ar_1, ar_2, ar_3)) 2.16/1.57 2.16/1.57 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 2.16/1.57 2.16/1.57 start location: koat_start 2.16/1.57 2.16/1.57 leaf cost: 0 2.16/1.57 2.16/1.57 2.16/1.57 2.16/1.57 Testing for reachability in the complexity graph removes the following transitions from problem 1: 2.16/1.57 2.16/1.57 evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2 + 1, ar_3 + 1)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_0 ] 2.16/1.57 2.16/1.57 evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2, 0)) [ ar_3 >= ar_0 /\ ar_0 >= ar_3 + 1 ] 2.16/1.57 2.16/1.57 We thus obtain the following problem: 2.16/1.57 2.16/1.57 2: T: 2.16/1.57 2.16/1.57 (Comp: ?, Cost: 1) evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 ] 2.16/1.57 2.16/1.57 (Comp: ?, Cost: 1) evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2 + 1, 0)) [ ar_3 >= ar_0 ] 2.16/1.57 2.16/1.57 (Comp: ?, Cost: 1) evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_0 >= ar_3 + 1 ] 2.16/1.57 2.16/1.57 (Comp: ?, Cost: 1) evalspeedpldi3bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 + 1 ] 2.16/1.57 2.16/1.57 (Comp: ?, Cost: 1) evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3stop(ar_0, ar_1, ar_2, ar_3)) 2.16/1.57 2.16/1.57 (Comp: ?, Cost: 1) evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb1in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ] 2.16/1.57 2.16/1.57 (Comp: ?, Cost: 1) evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] 2.16/1.57 2.16/1.57 (Comp: ?, Cost: 1) evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 2.16/1.57 2.16/1.57 (Comp: ?, Cost: 1) evalspeedpldi3start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedpldi3bb0in(ar_0, ar_1, ar_2, ar_3))
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