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Complexity_C_Integer 2019-03-21 04.38 pair #429988884
details
property
value
status
complete
benchmark
textbook_ex2.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n061.star.cs.uiowa.edu
space
ABC
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.43007 seconds
cpu usage
2.19611
user time
2.01918
system time
0.176935
max virtual memory
1.8273644E7
max residence set size
177852.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
2.00/1.39 WORST_CASE(?, O(n^2)) 2.00/1.40 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.00/1.40 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.00/1.40 2.00/1.40 2.00/1.40 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 2.00/1.40 2.00/1.40 (0) CpxIntTrs 2.00/1.40 (1) Koat Proof [FINISHED, 76 ms] 2.00/1.40 (2) BOUNDS(1, n^2) 2.00/1.40 2.00/1.40 2.00/1.40 ---------------------------------------- 2.00/1.40 2.00/1.40 (0) 2.00/1.40 Obligation: 2.00/1.40 Complexity Int TRS consisting of the following rules: 2.00/1.40 eval_textbook_ex2_start(v_i.0, v_j.0, v_n) -> Com_1(eval_textbook_ex2_bb0_in(v_i.0, v_j.0, v_n)) :|: TRUE 2.00/1.40 eval_textbook_ex2_bb0_in(v_i.0, v_j.0, v_n) -> Com_1(eval_textbook_ex2_bb1_in(0, v_j.0, v_n)) :|: TRUE 2.00/1.40 eval_textbook_ex2_bb1_in(v_i.0, v_j.0, v_n) -> Com_1(eval_textbook_ex2_bb2_in(v_i.0, 0, v_n)) :|: v_i.0 <= v_n - 1 2.00/1.40 eval_textbook_ex2_bb1_in(v_i.0, v_j.0, v_n) -> Com_1(eval_textbook_ex2_bb5_in(v_i.0, v_j.0, v_n)) :|: v_i.0 > v_n - 1 2.00/1.40 eval_textbook_ex2_bb2_in(v_i.0, v_j.0, v_n) -> Com_1(eval_textbook_ex2_bb3_in(v_i.0, v_j.0, v_n)) :|: v_j.0 <= v_i.0 2.00/1.40 eval_textbook_ex2_bb2_in(v_i.0, v_j.0, v_n) -> Com_1(eval_textbook_ex2_bb4_in(v_i.0, v_j.0, v_n)) :|: v_j.0 > v_i.0 2.00/1.40 eval_textbook_ex2_bb3_in(v_i.0, v_j.0, v_n) -> Com_1(eval_textbook_ex2_bb2_in(v_i.0, v_j.0 + 1, v_n)) :|: TRUE 2.00/1.40 eval_textbook_ex2_bb4_in(v_i.0, v_j.0, v_n) -> Com_1(eval_textbook_ex2_bb1_in(v_i.0 + 1, v_j.0, v_n)) :|: TRUE 2.00/1.40 eval_textbook_ex2_bb5_in(v_i.0, v_j.0, v_n) -> Com_1(eval_textbook_ex2_stop(v_i.0, v_j.0, v_n)) :|: TRUE 2.00/1.40 2.00/1.40 The start-symbols are:[eval_textbook_ex2_start_3] 2.00/1.40 2.00/1.40 2.00/1.40 ---------------------------------------- 2.00/1.40 2.00/1.40 (1) Koat Proof (FINISHED) 2.00/1.40 YES(?, 27*ar_1 + 4*ar_1^2 + 29) 2.00/1.40 2.00/1.40 2.00/1.40 2.00/1.40 Initial complexity problem: 2.00/1.40 2.00/1.40 1: T: 2.00/1.40 2.00/1.40 (Comp: ?, Cost: 1) evaltextbookex2start(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2bb0in(ar_0, ar_1, ar_2)) 2.00/1.40 2.00/1.40 (Comp: ?, Cost: 1) evaltextbookex2bb0in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2bb1in(0, ar_1, ar_2)) 2.00/1.40 2.00/1.40 (Comp: ?, Cost: 1) evaltextbookex2bb1in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2bb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 + 1 ] 2.00/1.40 2.00/1.40 (Comp: ?, Cost: 1) evaltextbookex2bb1in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ] 2.00/1.40 2.00/1.40 (Comp: ?, Cost: 1) evaltextbookex2bb2in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 ] 2.00/1.40 2.00/1.40 (Comp: ?, Cost: 1) evaltextbookex2bb2in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ] 2.00/1.40 2.00/1.40 (Comp: ?, Cost: 1) evaltextbookex2bb3in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2bb2in(ar_0, ar_1, ar_2 + 1)) 2.00/1.40 2.00/1.40 (Comp: ?, Cost: 1) evaltextbookex2bb4in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2bb1in(ar_0 + 1, ar_1, ar_2)) 2.00/1.40 2.00/1.40 (Comp: ?, Cost: 1) evaltextbookex2bb5in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2stop(ar_0, ar_1, ar_2)) 2.00/1.40 2.00/1.40 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2start(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 2.00/1.40 2.00/1.40 start location: koat_start 2.00/1.40 2.00/1.40 leaf cost: 0 2.00/1.40 2.00/1.40 2.00/1.40 2.00/1.40 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.00/1.40 2.00/1.40 2: T: 2.00/1.40 2.00/1.40 (Comp: 1, Cost: 1) evaltextbookex2start(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2bb0in(ar_0, ar_1, ar_2)) 2.00/1.40 2.00/1.40 (Comp: 1, Cost: 1) evaltextbookex2bb0in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2bb1in(0, ar_1, ar_2)) 2.00/1.40 2.00/1.40 (Comp: ?, Cost: 1) evaltextbookex2bb1in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2bb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 + 1 ] 2.00/1.40 2.00/1.40 (Comp: ?, Cost: 1) evaltextbookex2bb1in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ] 2.00/1.40 2.00/1.40 (Comp: ?, Cost: 1) evaltextbookex2bb2in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 ] 2.00/1.40 2.00/1.40 (Comp: ?, Cost: 1) evaltextbookex2bb2in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ] 2.00/1.40 2.00/1.40 (Comp: ?, Cost: 1) evaltextbookex2bb3in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2bb2in(ar_0, ar_1, ar_2 + 1)) 2.00/1.40 2.00/1.40 (Comp: ?, Cost: 1) evaltextbookex2bb4in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2bb1in(ar_0 + 1, ar_1, ar_2)) 2.00/1.40 2.00/1.40 (Comp: ?, Cost: 1) evaltextbookex2bb5in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2stop(ar_0, ar_1, ar_2)) 2.00/1.40 2.00/1.40 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex2start(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 2.00/1.40 2.00/1.40 start location: koat_start 2.00/1.40 2.00/1.40 leaf cost: 0 2.00/1.40 2.00/1.40 2.00/1.40 2.00/1.40 A polynomial rank function with 2.00/1.40 2.00/1.40 Pol(evaltextbookex2start) = 2
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