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Complexity_C_Integer 2019-03-21 04.38 pair #429988886
details
property
value
status
complete
benchmark
textbook_ex1.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n087.star.cs.uiowa.edu
space
ABC
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.3035 seconds
cpu usage
2.09502
user time
1.94239
system time
0.152637
max virtual memory
1.8273644E7
max residence set size
180916.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
1.97/1.25 WORST_CASE(?, O(n^1)) 1.97/1.26 proof of /export/starexec/sandbox/output/output_files/bench.koat 1.97/1.26 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1.97/1.26 1.97/1.26 1.97/1.26 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 1.97/1.26 1.97/1.26 (0) CpxIntTrs 1.97/1.26 (1) Koat Proof [FINISHED, 72 ms] 1.97/1.26 (2) BOUNDS(1, n^1) 1.97/1.26 1.97/1.26 1.97/1.26 ---------------------------------------- 1.97/1.26 1.97/1.26 (0) 1.97/1.26 Obligation: 1.97/1.26 Complexity Int TRS consisting of the following rules: 1.97/1.26 eval_textbook_ex1_start(v_a, v_b, v_i.0) -> Com_1(eval_textbook_ex1_bb0_in(v_a, v_b, v_i.0)) :|: TRUE 1.97/1.26 eval_textbook_ex1_bb0_in(v_a, v_b, v_i.0) -> Com_1(eval_textbook_ex1_bb1_in(v_a, v_b, v_a)) :|: TRUE 1.97/1.26 eval_textbook_ex1_bb1_in(v_a, v_b, v_i.0) -> Com_1(eval_textbook_ex1_bb2_in(v_a, v_b, v_i.0)) :|: v_i.0 <= v_b 1.97/1.26 eval_textbook_ex1_bb1_in(v_a, v_b, v_i.0) -> Com_1(eval_textbook_ex1_bb3_in(v_a, v_b, v_i.0)) :|: v_i.0 > v_b 1.97/1.26 eval_textbook_ex1_bb2_in(v_a, v_b, v_i.0) -> Com_1(eval_textbook_ex1_bb1_in(v_a, v_b, v_i.0 + 1)) :|: TRUE 1.97/1.26 eval_textbook_ex1_bb3_in(v_a, v_b, v_i.0) -> Com_1(eval_textbook_ex1_stop(v_a, v_b, v_i.0)) :|: TRUE 1.97/1.26 1.97/1.26 The start-symbols are:[eval_textbook_ex1_start_3] 1.97/1.26 1.97/1.26 1.97/1.26 ---------------------------------------- 1.97/1.26 1.97/1.26 (1) Koat Proof (FINISHED) 1.97/1.26 YES(?, 2*ar_1 + 2*ar_2 + 8) 1.97/1.26 1.97/1.26 1.97/1.26 1.97/1.26 Initial complexity problem: 1.97/1.26 1.97/1.26 1: T: 1.97/1.26 1.97/1.26 (Comp: ?, Cost: 1) evaltextbookex1start(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex1bb0in(ar_0, ar_1, ar_2)) 1.97/1.26 1.97/1.26 (Comp: ?, Cost: 1) evaltextbookex1bb0in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex1bb1in(ar_1, ar_1, ar_2)) 1.97/1.26 1.97/1.26 (Comp: ?, Cost: 1) evaltextbookex1bb1in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex1bb2in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 ] 1.97/1.26 1.97/1.26 (Comp: ?, Cost: 1) evaltextbookex1bb1in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex1bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ] 1.97/1.26 1.97/1.26 (Comp: ?, Cost: 1) evaltextbookex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex1bb1in(ar_0 + 1, ar_1, ar_2)) 1.97/1.26 1.97/1.26 (Comp: ?, Cost: 1) evaltextbookex1bb3in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex1stop(ar_0, ar_1, ar_2)) 1.97/1.26 1.97/1.26 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex1start(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 1.97/1.26 1.97/1.26 start location: koat_start 1.97/1.26 1.97/1.26 leaf cost: 0 1.97/1.26 1.97/1.26 1.97/1.26 1.97/1.26 Repeatedly propagating knowledge in problem 1 produces the following problem: 1.97/1.26 1.97/1.26 2: T: 1.97/1.26 1.97/1.26 (Comp: 1, Cost: 1) evaltextbookex1start(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex1bb0in(ar_0, ar_1, ar_2)) 1.97/1.26 1.97/1.26 (Comp: 1, Cost: 1) evaltextbookex1bb0in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex1bb1in(ar_1, ar_1, ar_2)) 1.97/1.26 1.97/1.26 (Comp: ?, Cost: 1) evaltextbookex1bb1in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex1bb2in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 ] 1.97/1.26 1.97/1.26 (Comp: ?, Cost: 1) evaltextbookex1bb1in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex1bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ] 1.97/1.26 1.97/1.26 (Comp: ?, Cost: 1) evaltextbookex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex1bb1in(ar_0 + 1, ar_1, ar_2)) 1.97/1.26 1.97/1.26 (Comp: ?, Cost: 1) evaltextbookex1bb3in(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex1stop(ar_0, ar_1, ar_2)) 1.97/1.26 1.97/1.26 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evaltextbookex1start(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 1.97/1.26 1.97/1.26 start location: koat_start 1.97/1.26 1.97/1.26 leaf cost: 0 1.97/1.26 1.97/1.26 1.97/1.26 1.97/1.26 A polynomial rank function with 1.97/1.26 1.97/1.26 Pol(evaltextbookex1start) = 2 1.97/1.26 1.97/1.26 Pol(evaltextbookex1bb0in) = 2 1.97/1.26 1.97/1.26 Pol(evaltextbookex1bb1in) = 2 1.97/1.26 1.97/1.26 Pol(evaltextbookex1bb2in) = 2 1.97/1.26 1.97/1.26 Pol(evaltextbookex1bb3in) = 1 1.97/1.26 1.97/1.26 Pol(evaltextbookex1stop) = 0 1.97/1.26 1.97/1.26 Pol(koat_start) = 2 1.97/1.26 1.97/1.26 orients all transitions weakly and the transitions 1.97/1.26
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