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Complexity_C_Integer 2019-03-21 04.38 pair #429989608
details
property
value
status
complete
benchmark
wcet2.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n090.star.cs.uiowa.edu
space
WTC_V2
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.37845 seconds
cpu usage
2.37521
user time
2.18932
system time
0.185889
max virtual memory
1.8273644E7
max residence set size
181828.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
2.18/1.33 WORST_CASE(?, O(n^1)) 2.18/1.34 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.18/1.34 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.18/1.34 2.18/1.34 2.18/1.34 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 2.18/1.34 2.18/1.34 (0) CpxIntTrs 2.18/1.34 (1) Koat Proof [FINISHED, 77 ms] 2.18/1.34 (2) BOUNDS(1, n^1) 2.18/1.34 2.18/1.34 2.18/1.34 ---------------------------------------- 2.18/1.34 2.18/1.34 (0) 2.18/1.34 Obligation: 2.18/1.34 Complexity Int TRS consisting of the following rules: 2.18/1.34 eval_wcet2_start(v_.0, v_i, v_j.0) -> Com_1(eval_wcet2_bb0_in(v_.0, v_i, v_j.0)) :|: TRUE 2.18/1.34 eval_wcet2_bb0_in(v_.0, v_i, v_j.0) -> Com_1(eval_wcet2_bb1_in(v_i, v_i, v_j.0)) :|: TRUE 2.18/1.34 eval_wcet2_bb1_in(v_.0, v_i, v_j.0) -> Com_1(eval_wcet2_bb2_in(v_.0, v_i, 0)) :|: v_.0 < 5 2.18/1.34 eval_wcet2_bb1_in(v_.0, v_i, v_j.0) -> Com_1(eval_wcet2_bb5_in(v_.0, v_i, v_j.0)) :|: v_.0 >= 5 2.18/1.34 eval_wcet2_bb2_in(v_.0, v_i, v_j.0) -> Com_1(eval_wcet2_bb3_in(v_.0, v_i, v_j.0)) :|: v_.0 > 2 && v_j.0 <= 9 2.18/1.34 eval_wcet2_bb2_in(v_.0, v_i, v_j.0) -> Com_1(eval_wcet2_bb4_in(v_.0, v_i, v_j.0)) :|: v_.0 <= 2 2.18/1.34 eval_wcet2_bb2_in(v_.0, v_i, v_j.0) -> Com_1(eval_wcet2_bb4_in(v_.0, v_i, v_j.0)) :|: v_j.0 > 9 2.18/1.34 eval_wcet2_bb3_in(v_.0, v_i, v_j.0) -> Com_1(eval_wcet2_bb2_in(v_.0, v_i, v_j.0 + 1)) :|: TRUE 2.18/1.34 eval_wcet2_bb4_in(v_.0, v_i, v_j.0) -> Com_1(eval_wcet2_bb1_in(v_.0 + 1, v_i, v_j.0)) :|: TRUE 2.18/1.34 eval_wcet2_bb5_in(v_.0, v_i, v_j.0) -> Com_1(eval_wcet2_stop(v_.0, v_i, v_j.0)) :|: TRUE 2.18/1.34 2.18/1.34 The start-symbols are:[eval_wcet2_start_3] 2.18/1.34 2.18/1.34 2.18/1.34 ---------------------------------------- 2.18/1.34 2.18/1.34 (1) Koat Proof (FINISHED) 2.18/1.34 YES(?, 56*ar_1 + 258) 2.18/1.34 2.18/1.34 2.18/1.34 2.18/1.34 Initial complexity problem: 2.18/1.34 2.18/1.34 1: T: 2.18/1.34 2.18/1.34 (Comp: ?, Cost: 1) evalwcet2start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2)) 2.18/1.34 2.18/1.34 (Comp: ?, Cost: 1) evalwcet2bb0in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2)) 2.18/1.34 2.18/1.34 (Comp: ?, Cost: 1) evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ] 2.18/1.34 2.18/1.34 (Comp: ?, Cost: 1) evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ] 2.18/1.34 2.18/1.34 (Comp: ?, Cost: 1) evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\ 9 >= ar_2 ] 2.18/1.34 2.18/1.34 (Comp: ?, Cost: 1) evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ] 2.18/1.34 2.18/1.34 (Comp: ?, Cost: 1) evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ] 2.18/1.34 2.18/1.34 (Comp: ?, Cost: 1) evalwcet2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1)) 2.18/1.34 2.18/1.34 (Comp: ?, Cost: 1) evalwcet2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_0 + 1, ar_1, ar_2)) 2.18/1.34 2.18/1.34 (Comp: ?, Cost: 1) evalwcet2bb5in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2)) 2.18/1.34 2.18/1.34 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 2.18/1.34 2.18/1.34 start location: koat_start 2.18/1.34 2.18/1.34 leaf cost: 0 2.18/1.34 2.18/1.34 2.18/1.34 2.18/1.34 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.18/1.34 2.18/1.34 2: T: 2.18/1.34 2.18/1.34 (Comp: 1, Cost: 1) evalwcet2start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2)) 2.18/1.34 2.18/1.34 (Comp: 1, Cost: 1) evalwcet2bb0in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2)) 2.18/1.34 2.18/1.34 (Comp: ?, Cost: 1) evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ] 2.18/1.34 2.18/1.34 (Comp: ?, Cost: 1) evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ] 2.18/1.34 2.18/1.34 (Comp: ?, Cost: 1) evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\ 9 >= ar_2 ] 2.18/1.34 2.18/1.34 (Comp: ?, Cost: 1) evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ] 2.18/1.34 2.18/1.34 (Comp: ?, Cost: 1) evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ] 2.18/1.34 2.18/1.34 (Comp: ?, Cost: 1) evalwcet2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1)) 2.18/1.34 2.18/1.34 (Comp: ?, Cost: 1) evalwcet2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_0 + 1, ar_1, ar_2)) 2.18/1.34 2.18/1.34 (Comp: ?, Cost: 1) evalwcet2bb5in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2)) 2.18/1.34 2.18/1.34 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 2.18/1.34 2.18/1.34 start location: koat_start 2.18/1.34 2.18/1.34 leaf cost: 0 2.18/1.34
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