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Complexity_C_Integer 2019-03-21 04.38 pair #429988876
details
property
value
status
complete
benchmark
jama_ex5.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n041.star.cs.uiowa.edu
space
ABC
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.40188 seconds
cpu usage
2.32276
user time
2.15257
system time
0.170187
max virtual memory
1.8273644E7
max residence set size
181472.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
2.26/1.37 WORST_CASE(?, O(n^2)) 2.26/1.38 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.26/1.38 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.26/1.38 2.26/1.38 2.26/1.38 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 2.26/1.38 2.26/1.38 (0) CpxIntTrs 2.26/1.38 (1) Koat Proof [FINISHED, 75 ms] 2.26/1.38 (2) BOUNDS(1, n^2) 2.26/1.38 2.26/1.38 2.26/1.38 ---------------------------------------- 2.26/1.38 2.26/1.38 (0) 2.26/1.38 Obligation: 2.26/1.38 Complexity Int TRS consisting of the following rules: 2.26/1.38 eval_jama_ex5_start(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex5_bb0_in(v_i.0, v_j.0, v_n)) :|: TRUE 2.26/1.38 eval_jama_ex5_bb0_in(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex5_bb1_in(0, v_j.0, v_n)) :|: TRUE 2.26/1.38 eval_jama_ex5_bb1_in(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex5_bb2_in(v_i.0, 0, v_n)) :|: v_i.0 <= v_n 2.26/1.38 eval_jama_ex5_bb1_in(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex5_bb5_in(v_i.0, v_j.0, v_n)) :|: v_i.0 > v_n 2.26/1.38 eval_jama_ex5_bb2_in(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex5_bb3_in(v_i.0, v_j.0, v_n)) :|: v_j.0 <= v_n 2.26/1.38 eval_jama_ex5_bb2_in(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex5_bb4_in(v_i.0, v_j.0, v_n)) :|: v_j.0 > v_n 2.26/1.38 eval_jama_ex5_bb3_in(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex5_bb2_in(v_i.0, v_j.0 + 2, v_n)) :|: TRUE 2.26/1.38 eval_jama_ex5_bb4_in(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex5_bb1_in(v_i.0 + 2, v_j.0, v_n)) :|: TRUE 2.26/1.38 eval_jama_ex5_bb5_in(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex5_stop(v_i.0, v_j.0, v_n)) :|: TRUE 2.26/1.38 2.26/1.38 The start-symbols are:[eval_jama_ex5_start_3] 2.26/1.38 2.26/1.38 2.26/1.38 ---------------------------------------- 2.26/1.38 2.26/1.38 (1) Koat Proof (FINISHED) 2.26/1.38 YES(?, 13*ar_1 + 2*ar_1^2 + 24) 2.26/1.38 2.26/1.38 2.26/1.38 2.26/1.38 Initial complexity problem: 2.26/1.38 2.26/1.38 1: T: 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evaljamaex5start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb0in(ar_0, ar_1, ar_2)) 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evaljamaex5bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb1in(0, ar_1, ar_2)) 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evaljamaex5bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 ] 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evaljamaex5bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ] 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ] 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ] 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evaljamaex5bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, ar_2 + 2)) 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evaljamaex5bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb1in(ar_0 + 2, ar_1, ar_2)) 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evaljamaex5bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5stop(ar_0, ar_1, ar_2)) 2.26/1.38 2.26/1.38 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5start(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 2.26/1.38 2.26/1.38 start location: koat_start 2.26/1.38 2.26/1.38 leaf cost: 0 2.26/1.38 2.26/1.38 2.26/1.38 2.26/1.38 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.26/1.38 2.26/1.38 2: T: 2.26/1.38 2.26/1.38 (Comp: 1, Cost: 1) evaljamaex5start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb0in(ar_0, ar_1, ar_2)) 2.26/1.38 2.26/1.38 (Comp: 1, Cost: 1) evaljamaex5bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb1in(0, ar_1, ar_2)) 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evaljamaex5bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 ] 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evaljamaex5bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ] 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ] 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ] 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evaljamaex5bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, ar_2 + 2)) 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evaljamaex5bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb1in(ar_0 + 2, ar_1, ar_2)) 2.26/1.38 2.26/1.38 (Comp: ?, Cost: 1) evaljamaex5bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5stop(ar_0, ar_1, ar_2)) 2.26/1.38 2.26/1.38 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5start(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 2.26/1.38 2.26/1.38 start location: koat_start 2.26/1.38 2.26/1.38 leaf cost: 0 2.26/1.38 2.26/1.38 2.26/1.38 2.26/1.38 A polynomial rank function with 2.26/1.38 2.26/1.38 Pol(evaljamaex5start) = 2
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return to Complexity_C_Integer 2019-03-21 04.38