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Complexity_C_Integer 2019-03-21 04.38 pair #429988878
details
property
value
status
complete
benchmark
jama_ex7.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n032.star.cs.uiowa.edu
space
ABC
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.87877 seconds
cpu usage
2.46847
user time
2.28371
system time
0.184761
max virtual memory
1.833918E7
max residence set size
183292.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
2.40/1.33 WORST_CASE(?, O(n^2)) 2.40/1.34 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.40/1.34 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.40/1.34 2.40/1.34 2.40/1.34 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 2.40/1.34 2.40/1.34 (0) CpxIntTrs 2.40/1.34 (1) Koat Proof [FINISHED, 75 ms] 2.40/1.34 (2) BOUNDS(1, n^2) 2.40/1.34 2.40/1.34 2.40/1.34 ---------------------------------------- 2.40/1.34 2.40/1.34 (0) 2.40/1.34 Obligation: 2.40/1.34 Complexity Int TRS consisting of the following rules: 2.40/1.34 eval_jama_ex7_start(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_jama_ex7_bb0_in(v_i.0, v_j.0, v_m, v_n)) :|: TRUE 2.40/1.34 eval_jama_ex7_bb0_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_jama_ex7_bb1_in(v_n, v_j.0, v_m, v_n)) :|: TRUE 2.40/1.34 eval_jama_ex7_bb1_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_jama_ex7_bb2_in(v_i.0, v_m, v_m, v_n)) :|: v_i.0 >= 1 2.40/1.34 eval_jama_ex7_bb1_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_jama_ex7_bb5_in(v_i.0, v_j.0, v_m, v_n)) :|: v_i.0 < 1 2.40/1.34 eval_jama_ex7_bb2_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_jama_ex7_bb3_in(v_i.0, v_j.0, v_m, v_n)) :|: v_j.0 >= 1 2.40/1.34 eval_jama_ex7_bb2_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_jama_ex7_bb4_in(v_i.0, v_j.0, v_m, v_n)) :|: v_j.0 < 1 2.40/1.34 eval_jama_ex7_bb3_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_jama_ex7_bb2_in(v_i.0, v_j.0 - 1, v_m, v_n)) :|: TRUE 2.40/1.34 eval_jama_ex7_bb4_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_jama_ex7_bb1_in(v_i.0 - 1, v_j.0, v_m, v_n)) :|: TRUE 2.40/1.34 eval_jama_ex7_bb5_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_jama_ex7_stop(v_i.0, v_j.0, v_m, v_n)) :|: TRUE 2.40/1.34 2.40/1.34 The start-symbols are:[eval_jama_ex7_start_4] 2.40/1.34 2.40/1.34 2.40/1.34 ---------------------------------------- 2.40/1.34 2.40/1.34 (1) Koat Proof (FINISHED) 2.40/1.34 YES(?, 5*ar_1 + 2*ar_1*ar_3 + 2*ar_3 + 11) 2.40/1.34 2.40/1.34 2.40/1.34 2.40/1.34 Initial complexity problem: 2.40/1.34 2.40/1.34 1: T: 2.40/1.34 2.40/1.34 (Comp: ?, Cost: 1) evaljamaex7start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaljamaex7bb0in(ar_0, ar_1, ar_2, ar_3)) 2.40/1.34 2.40/1.34 (Comp: ?, Cost: 1) evaljamaex7bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaljamaex7bb1in(ar_1, ar_1, ar_2, ar_3)) 2.40/1.34 2.40/1.34 (Comp: ?, Cost: 1) evaljamaex7bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaljamaex7bb2in(ar_0, ar_1, ar_3, ar_3)) [ ar_0 >= 1 ] 2.40/1.34 2.40/1.34 (Comp: ?, Cost: 1) evaljamaex7bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaljamaex7bb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 2.40/1.34 2.40/1.34 (Comp: ?, Cost: 1) evaljamaex7bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaljamaex7bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ] 2.40/1.34 2.40/1.34 (Comp: ?, Cost: 1) evaljamaex7bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaljamaex7bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ] 2.40/1.34 2.40/1.34 (Comp: ?, Cost: 1) evaljamaex7bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaljamaex7bb2in(ar_0, ar_1, ar_2 - 1, ar_3)) 2.40/1.34 2.40/1.34 (Comp: ?, Cost: 1) evaljamaex7bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaljamaex7bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) 2.40/1.34 2.40/1.34 (Comp: ?, Cost: 1) evaljamaex7bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaljamaex7stop(ar_0, ar_1, ar_2, ar_3)) 2.40/1.34 2.40/1.34 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaljamaex7start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 2.40/1.34 2.40/1.34 start location: koat_start 2.40/1.34 2.40/1.34 leaf cost: 0 2.40/1.34 2.40/1.34 2.40/1.34 2.40/1.34 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.40/1.34 2.40/1.34 2: T: 2.40/1.34 2.40/1.34 (Comp: 1, Cost: 1) evaljamaex7start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaljamaex7bb0in(ar_0, ar_1, ar_2, ar_3)) 2.40/1.34 2.40/1.34 (Comp: 1, Cost: 1) evaljamaex7bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaljamaex7bb1in(ar_1, ar_1, ar_2, ar_3)) 2.40/1.34 2.40/1.34 (Comp: ?, Cost: 1) evaljamaex7bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaljamaex7bb2in(ar_0, ar_1, ar_3, ar_3)) [ ar_0 >= 1 ] 2.40/1.34 2.40/1.34 (Comp: ?, Cost: 1) evaljamaex7bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaljamaex7bb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 2.40/1.34 2.40/1.34 (Comp: ?, Cost: 1) evaljamaex7bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaljamaex7bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ] 2.40/1.34 2.40/1.34 (Comp: ?, Cost: 1) evaljamaex7bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaljamaex7bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ] 2.40/1.34 2.40/1.34 (Comp: ?, Cost: 1) evaljamaex7bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaljamaex7bb2in(ar_0, ar_1, ar_2 - 1, ar_3)) 2.40/1.34 2.40/1.34 (Comp: ?, Cost: 1) evaljamaex7bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaljamaex7bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) 2.40/1.34 2.40/1.34 (Comp: ?, Cost: 1) evaljamaex7bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaljamaex7stop(ar_0, ar_1, ar_2, ar_3)) 2.40/1.34 2.40/1.34 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evaljamaex7start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 2.40/1.34 2.40/1.34 start location: koat_start 2.40/1.34 2.40/1.34 leaf cost: 0 2.40/1.34 2.40/1.34 2.40/1.34 2.40/1.34 A polynomial rank function with 2.40/1.34 2.40/1.34 Pol(evaljamaex7start) = 2
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