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Complexity_C_Integer 2019-03-21 04.38 pair #429989648
details
property
value
status
complete
benchmark
cousot9.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n056.star.cs.uiowa.edu
space
WTC_V2
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.4865 seconds
cpu usage
2.59517
user time
2.38245
system time
0.212725
max virtual memory
1.8548924E7
max residence set size
184632.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
2.49/1.44 WORST_CASE(?, O(n^2)) 2.49/1.45 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.49/1.45 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.49/1.45 2.49/1.45 2.49/1.45 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 2.49/1.45 2.49/1.45 (0) CpxIntTrs 2.49/1.45 (1) Koat Proof [FINISHED, 179 ms] 2.49/1.45 (2) BOUNDS(1, n^2) 2.49/1.45 2.49/1.45 2.49/1.45 ---------------------------------------- 2.49/1.45 2.49/1.45 (0) 2.49/1.45 Obligation: 2.49/1.45 Complexity Int TRS consisting of the following rules: 2.49/1.45 eval_cousot9_start(v_.0, v_N, v_i.0, v_j) -> Com_1(eval_cousot9_bb0_in(v_.0, v_N, v_i.0, v_j)) :|: TRUE 2.49/1.45 eval_cousot9_bb0_in(v_.0, v_N, v_i.0, v_j) -> Com_1(eval_cousot9_bb1_in(v_j, v_N, v_N, v_j)) :|: TRUE 2.49/1.45 eval_cousot9_bb1_in(v_.0, v_N, v_i.0, v_j) -> Com_1(eval_cousot9_bb2_in(v_.0, v_N, v_i.0, v_j)) :|: v_i.0 > 0 2.49/1.45 eval_cousot9_bb1_in(v_.0, v_N, v_i.0, v_j) -> Com_1(eval_cousot9_bb3_in(v_.0, v_N, v_i.0, v_j)) :|: v_i.0 <= 0 2.49/1.45 eval_cousot9_bb2_in(v_.0, v_N, v_i.0, v_j) -> Com_1(eval_cousot9_bb1_in(v_.0 - 1, v_N, v_i.0, v_j)) :|: v_.0 > 0 2.49/1.45 eval_cousot9_bb2_in(v_.0, v_N, v_i.0, v_j) -> Com_1(eval_cousot9_bb1_in(v_N, v_N, v_i.0, v_j)) :|: v_.0 > 0 && v_.0 <= 0 2.49/1.45 eval_cousot9_bb2_in(v_.0, v_N, v_i.0, v_j) -> Com_1(eval_cousot9_bb1_in(v_.0 - 1, v_N, v_i.0 - 1, v_j)) :|: v_.0 <= 0 && v_.0 > 0 2.49/1.45 eval_cousot9_bb2_in(v_.0, v_N, v_i.0, v_j) -> Com_1(eval_cousot9_bb1_in(v_N, v_N, v_i.0 - 1, v_j)) :|: v_.0 <= 0 2.49/1.45 eval_cousot9_bb3_in(v_.0, v_N, v_i.0, v_j) -> Com_1(eval_cousot9_stop(v_.0, v_N, v_i.0, v_j)) :|: TRUE 2.49/1.45 2.49/1.45 The start-symbols are:[eval_cousot9_start_4] 2.49/1.45 2.49/1.45 2.49/1.45 ---------------------------------------- 2.49/1.45 2.49/1.45 (1) Koat Proof (FINISHED) 2.49/1.45 YES(?, 2*ar_3 + 2*ar_3^2 + 2*ar_1 + 7) 2.49/1.45 2.49/1.45 2.49/1.45 2.49/1.45 Initial complexity problem: 2.49/1.45 2.49/1.45 1: T: 2.49/1.45 2.49/1.45 (Comp: ?, Cost: 1) evalcousot9start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb0in(ar_0, ar_1, ar_2, ar_3)) 2.49/1.45 2.49/1.45 (Comp: ?, Cost: 1) evalcousot9bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_1, ar_1, ar_3, ar_3)) 2.49/1.45 2.49/1.45 (Comp: ?, Cost: 1) evalcousot9bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ] 2.49/1.45 2.49/1.45 (Comp: ?, Cost: 1) evalcousot9bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ] 2.49/1.45 2.49/1.45 (Comp: ?, Cost: 1) evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 2.49/1.45 2.49/1.45 (Comp: ?, Cost: 1) evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_3, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\ 0 >= ar_0 ] 2.49/1.45 2.49/1.45 (Comp: ?, Cost: 1) evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3)) [ 0 >= ar_0 /\ ar_0 >= 1 ] 2.49/1.45 2.49/1.45 (Comp: ?, Cost: 1) evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_3, ar_1, ar_2 - 1, ar_3)) [ 0 >= ar_0 ] 2.49/1.45 2.49/1.45 (Comp: ?, Cost: 1) evalcousot9bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9stop(ar_0, ar_1, ar_2, ar_3)) 2.49/1.45 2.49/1.45 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 2.49/1.45 2.49/1.45 start location: koat_start 2.49/1.45 2.49/1.45 leaf cost: 0 2.49/1.45 2.49/1.45 2.49/1.45 2.49/1.45 Testing for reachability in the complexity graph removes the following transitions from problem 1: 2.49/1.45 2.49/1.45 evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_3, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\ 0 >= ar_0 ] 2.49/1.45 2.49/1.45 evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3)) [ 0 >= ar_0 /\ ar_0 >= 1 ] 2.49/1.45 2.49/1.45 We thus obtain the following problem: 2.49/1.45 2.49/1.45 2: T: 2.49/1.45 2.49/1.45 (Comp: ?, Cost: 1) evalcousot9bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9stop(ar_0, ar_1, ar_2, ar_3)) 2.49/1.45 2.49/1.45 (Comp: ?, Cost: 1) evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_3, ar_1, ar_2 - 1, ar_3)) [ 0 >= ar_0 ] 2.49/1.45 2.49/1.45 (Comp: ?, Cost: 1) evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_0 >= 1 ] 2.49/1.45 2.49/1.45 (Comp: ?, Cost: 1) evalcousot9bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ] 2.49/1.45 2.49/1.45 (Comp: ?, Cost: 1) evalcousot9bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ] 2.49/1.45 2.49/1.45 (Comp: ?, Cost: 1) evalcousot9bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb1in(ar_1, ar_1, ar_3, ar_3)) 2.49/1.45 2.49/1.45 (Comp: ?, Cost: 1) evalcousot9start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9bb0in(ar_0, ar_1, ar_2, ar_3)) 2.49/1.45 2.49/1.45 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalcousot9start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 2.49/1.45 2.49/1.45 start location: koat_start 2.49/1.45 2.49/1.45 leaf cost: 0 2.49/1.45 2.49/1.45 2.49/1.45 2.49/1.45 Repeatedly propagating knowledge in problem 2 produces the following problem:
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return to Complexity_C_Integer 2019-03-21 04.38