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Complexity_C_Integer 2019-03-21 04.38 pair #429988896
details
property
value
status
complete
benchmark
textbook_ex4.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n101.star.cs.uiowa.edu
space
ABC
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.45234 seconds
cpu usage
2.42811
user time
2.24409
system time
0.184015
max virtual memory
1.8273644E7
max residence set size
183680.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
2.22/1.41 WORST_CASE(?, O(n^2)) 2.22/1.42 proof of /export/starexec/sandbox2/output/output_files/bench.koat 2.22/1.42 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.22/1.42 2.22/1.42 2.22/1.42 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 2.22/1.42 2.22/1.42 (0) CpxIntTrs 2.22/1.42 (1) Koat Proof [FINISHED, 67 ms] 2.22/1.42 (2) BOUNDS(1, n^2) 2.22/1.42 2.22/1.42 2.22/1.42 ---------------------------------------- 2.22/1.42 2.22/1.42 (0) 2.22/1.42 Obligation: 2.22/1.42 Complexity Int TRS consisting of the following rules: 2.22/1.42 eval_textbook_ex4_start(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_textbook_ex4_bb0_in(v_i.0, v_j.0, v_m, v_n)) :|: TRUE 2.22/1.42 eval_textbook_ex4_bb0_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_textbook_ex4_bb1_in(v_i.0, 1, v_m, v_n)) :|: TRUE 2.22/1.42 eval_textbook_ex4_bb1_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_textbook_ex4_bb2_in(1, v_j.0, v_m, v_n)) :|: v_j.0 <= v_n 2.22/1.42 eval_textbook_ex4_bb1_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_textbook_ex4_bb5_in(v_i.0, v_j.0, v_m, v_n)) :|: v_j.0 > v_n 2.22/1.42 eval_textbook_ex4_bb2_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_textbook_ex4_bb3_in(v_i.0, v_j.0, v_m, v_n)) :|: v_i.0 <= v_m 2.22/1.42 eval_textbook_ex4_bb2_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_textbook_ex4_bb4_in(v_i.0, v_j.0, v_m, v_n)) :|: v_i.0 > v_m 2.22/1.42 eval_textbook_ex4_bb3_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_textbook_ex4_bb2_in(v_i.0 + 1, v_j.0, v_m, v_n)) :|: TRUE 2.22/1.42 eval_textbook_ex4_bb4_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_textbook_ex4_bb1_in(v_i.0, v_j.0 + 1, v_m, v_n)) :|: TRUE 2.22/1.42 eval_textbook_ex4_bb5_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_textbook_ex4_stop(v_i.0, v_j.0, v_m, v_n)) :|: TRUE 2.22/1.42 2.22/1.42 The start-symbols are:[eval_textbook_ex4_start_4] 2.22/1.42 2.22/1.42 2.22/1.42 ---------------------------------------- 2.22/1.42 2.22/1.42 (1) Koat Proof (FINISHED) 2.22/1.42 YES(?, 9*ar_1 + 2*ar_1*ar_3 + 6) 2.22/1.42 2.22/1.42 2.22/1.42 2.22/1.42 Initial complexity problem: 2.22/1.42 2.22/1.42 1: T: 2.22/1.42 2.22/1.42 (Comp: ?, Cost: 1) evaltextbookex4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3)) 2.22/1.42 2.22/1.42 (Comp: ?, Cost: 1) evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(1, ar_1, ar_2, ar_3)) 2.22/1.42 2.22/1.42 (Comp: ?, Cost: 1) evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ] 2.22/1.42 2.22/1.42 (Comp: ?, Cost: 1) evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ] 2.22/1.42 2.22/1.42 (Comp: ?, Cost: 1) evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ] 2.22/1.42 2.22/1.42 (Comp: ?, Cost: 1) evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ] 2.22/1.42 2.22/1.42 (Comp: ?, Cost: 1) evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 2.22/1.42 2.22/1.42 (Comp: ?, Cost: 1) evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(ar_0 + 1, ar_1, ar_2, ar_3)) 2.22/1.42 2.22/1.42 (Comp: ?, Cost: 1) evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4stop(ar_0, ar_1, ar_2, ar_3)) 2.22/1.42 2.22/1.42 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 2.22/1.42 2.22/1.42 start location: koat_start 2.22/1.42 2.22/1.42 leaf cost: 0 2.22/1.42 2.22/1.42 2.22/1.42 2.22/1.42 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.22/1.42 2.22/1.42 2: T: 2.22/1.42 2.22/1.42 (Comp: 1, Cost: 1) evaltextbookex4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3)) 2.22/1.42 2.22/1.42 (Comp: 1, Cost: 1) evaltextbookex4bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(1, ar_1, ar_2, ar_3)) 2.22/1.42 2.22/1.42 (Comp: ?, Cost: 1) evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, 1, ar_3)) [ ar_1 >= ar_0 ] 2.22/1.42 2.22/1.42 (Comp: ?, Cost: 1) evaltextbookex4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ] 2.22/1.42 2.22/1.42 (Comp: ?, Cost: 1) evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ] 2.22/1.42 2.22/1.42 (Comp: ?, Cost: 1) evaltextbookex4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ] 2.22/1.42 2.22/1.42 (Comp: ?, Cost: 1) evaltextbookex4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 2.22/1.42 2.22/1.42 (Comp: ?, Cost: 1) evaltextbookex4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4bb1in(ar_0 + 1, ar_1, ar_2, ar_3)) 2.22/1.42 2.22/1.42 (Comp: ?, Cost: 1) evaltextbookex4bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4stop(ar_0, ar_1, ar_2, ar_3)) 2.22/1.42 2.22/1.42 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaltextbookex4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 2.22/1.42 2.22/1.42 start location: koat_start 2.22/1.42 2.22/1.42 leaf cost: 0 2.22/1.42 2.22/1.42 2.22/1.42 2.22/1.42 A polynomial rank function with 2.22/1.42 2.22/1.42 Pol(evaltextbookex4start) = 2
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