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Complexity_C_Integer 2019-03-21 04.38 pair #429989726
details
property
value
status
complete
benchmark
complex.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n143.star.cs.uiowa.edu
space
WTC_V2
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.74181 seconds
cpu usage
2.64102
user time
2.40754
system time
0.233481
max virtual memory
1.8273644E7
max residence set size
182296.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
2.08/1.71 WORST_CASE(?, O(n^1)) 2.08/1.72 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.08/1.72 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.08/1.72 2.08/1.72 2.08/1.72 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 2.08/1.72 2.08/1.72 (0) CpxIntTrs 2.08/1.72 (1) Koat Proof [FINISHED, 489 ms] 2.08/1.72 (2) BOUNDS(1, n^1) 2.08/1.72 2.08/1.72 2.08/1.72 ---------------------------------------- 2.08/1.72 2.08/1.72 (0) 2.08/1.72 Obligation: 2.08/1.72 Complexity Int TRS consisting of the following rules: 2.08/1.72 eval_complex_start(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_complex_bb0_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b)) :|: TRUE 2.08/1.72 eval_complex_bb0_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_complex_bb1_in(v_a, v_b, v_.1, v_.12, v_a, v_b)) :|: TRUE 2.08/1.72 eval_complex_bb1_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_complex_bb2_in(v_.0, v_.01, v_.0, v_.01, v_a, v_b)) :|: v_.0 < 30 2.08/1.72 eval_complex_bb1_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_complex_bb5_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b)) :|: v_.0 >= 30 2.08/1.72 eval_complex_bb2_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_complex_bb3_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b)) :|: v_.12 < v_.1 2.08/1.72 eval_complex_bb2_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_complex_bb4_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b)) :|: v_.12 >= v_.1 2.08/1.72 eval_complex_bb3_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_complex_bb2_in(v_.0, v_.01, v_.1 + 10, v_.12 + 7, v_a, v_b)) :|: v_.12 > 5 && v_.12 + 7 >= 10 && v_.12 + 7 <= 12 2.08/1.72 eval_complex_bb3_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_complex_bb2_in(v_.0, v_.01, v_.1 + 1, v_.12 + 7, v_a, v_b)) :|: v_.12 > 5 && v_.12 + 7 < 10 2.08/1.72 eval_complex_bb3_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_complex_bb2_in(v_.0, v_.01, v_.1 + 1, v_.12 + 7, v_a, v_b)) :|: v_.12 > 5 && v_.12 + 7 > 12 2.08/1.72 eval_complex_bb3_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_complex_bb2_in(v_.0, v_.01, v_.1 + 10, v_.12 + 2, v_a, v_b)) :|: v_.12 <= 5 && v_.12 + 2 >= 10 && v_.12 + 2 <= 12 2.08/1.72 eval_complex_bb3_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_complex_bb2_in(v_.0, v_.01, v_.1 + 1, v_.12 + 2, v_a, v_b)) :|: v_.12 <= 5 && v_.12 + 2 < 10 2.08/1.72 eval_complex_bb3_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_complex_bb2_in(v_.0, v_.01, v_.1 + 1, v_.12 + 2, v_a, v_b)) :|: v_.12 <= 5 && v_.12 + 2 > 12 2.08/1.72 eval_complex_bb4_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_complex_bb1_in(v_.1 + 2, v_.12 - 10, v_.1, v_.12, v_a, v_b)) :|: TRUE 2.08/1.72 eval_complex_bb5_in(v_.0, v_.01, v_.1, v_.12, v_a, v_b) -> Com_1(eval_complex_stop(v_.0, v_.01, v_.1, v_.12, v_a, v_b)) :|: TRUE 2.08/1.72 2.08/1.72 The start-symbols are:[eval_complex_start_6] 2.08/1.72 2.08/1.72 2.08/1.72 ---------------------------------------- 2.08/1.72 2.08/1.72 (1) Koat Proof (FINISHED) 2.08/1.72 YES(?, 35*ar_1 + 6*ar_3 + 1200) 2.08/1.72 2.08/1.72 2.08/1.72 2.08/1.72 Initial complexity problem: 2.08/1.72 2.08/1.72 1: T: 2.08/1.72 2.08/1.72 (Comp: ?, Cost: 1) evalcomplexstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalcomplexbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.08/1.72 2.08/1.72 (Comp: ?, Cost: 1) evalcomplexbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalcomplexbb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) 2.08/1.72 2.08/1.72 (Comp: ?, Cost: 1) evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalcomplexbb2in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_2)) [ 29 >= ar_0 ] 2.08/1.72 2.08/1.72 (Comp: ?, Cost: 1) evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalcomplexbb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 30 ] 2.08/1.72 2.08/1.72 (Comp: ?, Cost: 1) evalcomplexbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalcomplexbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= ar_5 + 1 ] 2.08/1.72 2.08/1.72 (Comp: ?, Cost: 1) evalcomplexbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalcomplexbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= ar_4 ] 2.08/1.72 2.08/1.72 (Comp: ?, Cost: 1) evalcomplexbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalcomplexbb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 10, ar_5 + 7)) [ ar_5 >= 6 /\ ar_5 >= 3 /\ 5 >= ar_5 ] 2.08/1.72 2.08/1.72 (Comp: ?, Cost: 1) evalcomplexbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalcomplexbb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5 + 7)) [ ar_5 >= 6 /\ 2 >= ar_5 ] 2.08/1.72 2.08/1.72 (Comp: ?, Cost: 1) evalcomplexbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalcomplexbb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5 + 7)) [ ar_5 >= 6 ] 2.08/1.72 2.08/1.72 (Comp: ?, Cost: 1) evalcomplexbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalcomplexbb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 10, ar_5 + 2)) [ 5 >= ar_5 /\ ar_5 >= 8 /\ 10 >= ar_5 ] 2.08/1.72 2.08/1.72 (Comp: ?, Cost: 1) evalcomplexbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalcomplexbb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5 + 2)) [ 5 >= ar_5 /\ 7 >= ar_5 ] 2.08/1.72 2.08/1.72 (Comp: ?, Cost: 1) evalcomplexbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalcomplexbb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5 + 2)) [ 5 >= ar_5 /\ ar_5 >= 11 ] 2.08/1.72 2.08/1.72 (Comp: ?, Cost: 1) evalcomplexbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalcomplexbb1in(ar_4 + 2, ar_1, ar_5 - 10, ar_3, ar_4, ar_5)) 2.08/1.72 2.08/1.72 (Comp: ?, Cost: 1) evalcomplexbb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalcomplexstop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.08/1.72 2.08/1.72 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalcomplexstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 2.08/1.72 2.08/1.72 start location: koat_start 2.08/1.72 2.08/1.72 leaf cost: 0 2.08/1.72 2.08/1.72 2.08/1.72 2.08/1.72 Testing for reachability in the complexity graph removes the following transitions from problem 1: 2.08/1.72 2.08/1.72 evalcomplexbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalcomplexbb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 10, ar_5 + 7)) [ ar_5 >= 6 /\ ar_5 >= 3 /\ 5 >= ar_5 ] 2.08/1.72 2.08/1.72 evalcomplexbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalcomplexbb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5 + 7)) [ ar_5 >= 6 /\ 2 >= ar_5 ] 2.08/1.72 2.08/1.72 evalcomplexbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalcomplexbb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 10, ar_5 + 2)) [ 5 >= ar_5 /\ ar_5 >= 8 /\ 10 >= ar_5 ] 2.08/1.72 2.08/1.72 evalcomplexbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalcomplexbb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5 + 2)) [ 5 >= ar_5 /\ ar_5 >= 11 ] 2.08/1.72 2.08/1.72 We thus obtain the following problem: 2.08/1.72 2.08/1.72 2: T: 2.08/1.72 2.08/1.72 (Comp: ?, Cost: 1) evalcomplexbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalcomplexbb1in(ar_4 + 2, ar_1, ar_5 - 10, ar_3, ar_4, ar_5)) 2.08/1.72 2.08/1.72 (Comp: ?, Cost: 1) evalcomplexbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalcomplexbb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5 + 2)) [ 5 >= ar_5 /\ 7 >= ar_5 ] 2.08/1.72
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