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Complexity_C_Integer 2019-03-21 04.38 pair #429988880
details
property
value
status
complete
benchmark
jama_ex4.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)
1.42517 seconds
cpu usage
2.51711
user time
2.32106
system time
0.196052
max virtual memory
1.8273644E7
max residence set size
184816.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
2.27/1.39 WORST_CASE(?, O(n^2)) 2.46/1.40 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.46/1.40 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.46/1.40 2.46/1.40 2.46/1.40 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 2.46/1.40 2.46/1.40 (0) CpxIntTrs 2.46/1.40 (1) Koat Proof [FINISHED, 167 ms] 2.46/1.40 (2) BOUNDS(1, n^2) 2.46/1.40 2.46/1.40 2.46/1.40 ---------------------------------------- 2.46/1.40 2.46/1.40 (0) 2.46/1.40 Obligation: 2.46/1.40 Complexity Int TRS consisting of the following rules: 2.46/1.40 eval_jama_ex4_start(v_a, v_b, v_c, v_d, v_i.0, v_j.0) -> Com_1(eval_jama_ex4_bb0_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0)) :|: TRUE 2.46/1.40 eval_jama_ex4_bb0_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0) -> Com_1(eval_jama_ex4_bb1_in(v_a, v_b, v_c, v_d, v_a, v_j.0)) :|: TRUE 2.46/1.40 eval_jama_ex4_bb1_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0) -> Com_1(eval_jama_ex4_bb2_in(v_a, v_b, v_c, v_d, v_i.0, v_c)) :|: v_i.0 <= v_b 2.46/1.40 eval_jama_ex4_bb1_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0) -> Com_1(eval_jama_ex4_bb5_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0)) :|: v_i.0 > v_b 2.46/1.40 eval_jama_ex4_bb2_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0) -> Com_1(eval_jama_ex4_bb3_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0)) :|: v_j.0 <= v_d 2.46/1.40 eval_jama_ex4_bb2_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0) -> Com_1(eval_jama_ex4_bb4_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0)) :|: v_j.0 > v_d 2.46/1.40 eval_jama_ex4_bb3_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0) -> Com_1(eval_jama_ex4_bb2_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0 + 1)) :|: TRUE 2.46/1.40 eval_jama_ex4_bb4_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0) -> Com_1(eval_jama_ex4_bb1_in(v_a, v_b, v_c, v_d, v_i.0 + 1, v_j.0)) :|: TRUE 2.46/1.40 eval_jama_ex4_bb5_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0) -> Com_1(eval_jama_ex4_stop(v_a, v_b, v_c, v_d, v_i.0, v_j.0)) :|: TRUE 2.46/1.40 2.46/1.40 The start-symbols are:[eval_jama_ex4_start_6] 2.46/1.40 2.46/1.40 2.46/1.40 ---------------------------------------- 2.46/1.40 2.46/1.40 (1) Koat Proof (FINISHED) 2.46/1.40 YES(?, 7*ar_1 + 7*ar_2 + 2*ar_1*ar_4 + 2*ar_2*ar_4 + 2*ar_1*ar_5 + 2*ar_2*ar_5 + 2*ar_4 + 2*ar_5 + 13) 2.46/1.40 2.46/1.40 2.46/1.40 2.46/1.40 Initial complexity problem: 2.46/1.40 2.46/1.40 1: T: 2.46/1.40 2.46/1.40 (Comp: ?, Cost: 1) evaljamaex4start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evaljamaex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.46/1.40 2.46/1.40 (Comp: ?, Cost: 1) evaljamaex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evaljamaex4bb1in(ar_1, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.46/1.40 2.46/1.40 (Comp: ?, Cost: 1) evaljamaex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evaljamaex4bb2in(ar_0, ar_1, ar_2, ar_4, ar_4, ar_5)) [ ar_2 >= ar_0 ] 2.46/1.40 2.46/1.40 (Comp: ?, Cost: 1) evaljamaex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evaljamaex4bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 1 ] 2.46/1.40 2.46/1.40 (Comp: ?, Cost: 1) evaljamaex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evaljamaex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= ar_3 ] 2.46/1.40 2.46/1.40 (Comp: ?, Cost: 1) evaljamaex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evaljamaex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_3 >= ar_5 + 1 ] 2.46/1.40 2.46/1.40 (Comp: ?, Cost: 1) evaljamaex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evaljamaex4bb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5)) 2.46/1.40 2.46/1.40 (Comp: ?, Cost: 1) evaljamaex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evaljamaex4bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.46/1.40 2.46/1.40 (Comp: ?, Cost: 1) evaljamaex4bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evaljamaex4stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.46/1.40 2.46/1.40 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evaljamaex4start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 2.46/1.40 2.46/1.40 start location: koat_start 2.46/1.40 2.46/1.40 leaf cost: 0 2.46/1.40 2.46/1.40 2.46/1.40 2.46/1.40 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.46/1.40 2.46/1.40 2: T: 2.46/1.40 2.46/1.40 (Comp: 1, Cost: 1) evaljamaex4start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evaljamaex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.46/1.40 2.46/1.40 (Comp: 1, Cost: 1) evaljamaex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evaljamaex4bb1in(ar_1, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.46/1.40 2.46/1.40 (Comp: ?, Cost: 1) evaljamaex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evaljamaex4bb2in(ar_0, ar_1, ar_2, ar_4, ar_4, ar_5)) [ ar_2 >= ar_0 ] 2.46/1.40 2.46/1.40 (Comp: ?, Cost: 1) evaljamaex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evaljamaex4bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 1 ] 2.46/1.40 2.46/1.40 (Comp: ?, Cost: 1) evaljamaex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evaljamaex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= ar_3 ] 2.46/1.40 2.46/1.40 (Comp: ?, Cost: 1) evaljamaex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evaljamaex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_3 >= ar_5 + 1 ] 2.46/1.40 2.46/1.40 (Comp: ?, Cost: 1) evaljamaex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evaljamaex4bb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5)) 2.46/1.40 2.46/1.40 (Comp: ?, Cost: 1) evaljamaex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evaljamaex4bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.46/1.40 2.46/1.40 (Comp: ?, Cost: 1) evaljamaex4bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evaljamaex4stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.46/1.40 2.46/1.40 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evaljamaex4start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 2.46/1.40 2.46/1.40 start location: koat_start 2.46/1.40 2.46/1.40 leaf cost: 0 2.46/1.40 2.46/1.40 2.46/1.40 2.46/1.40 A polynomial rank function with 2.46/1.40 2.46/1.40 Pol(evaljamaex4start) = 2
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