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Complexity_C_Integer 2019-03-21 04.38 pair #429989610
details
property
value
status
complete
benchmark
speedNestedMultipleDep.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n103.star.cs.uiowa.edu
space
WTC_V2
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.34484 seconds
cpu usage
2.40914
user time
2.22847
system time
0.180669
max virtual memory
1.8273644E7
max residence set size
181372.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
2.20/1.31 WORST_CASE(?, O(n^2)) 2.20/1.32 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.20/1.32 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.20/1.32 2.20/1.32 2.20/1.32 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 2.20/1.32 2.20/1.32 (0) CpxIntTrs 2.20/1.32 (1) Koat Proof [FINISHED, 83 ms] 2.20/1.32 (2) BOUNDS(1, n^2) 2.20/1.32 2.20/1.32 2.20/1.32 ---------------------------------------- 2.20/1.32 2.20/1.32 (0) 2.20/1.32 Obligation: 2.20/1.32 Complexity Int TRS consisting of the following rules: 2.20/1.32 eval_speedNestedMultipleDep_start(v_1, v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedNestedMultipleDep_bb0_in(v_1, v_m, v_n, v_x.0, v_y.0)) :|: TRUE 2.20/1.32 eval_speedNestedMultipleDep_bb0_in(v_1, v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedNestedMultipleDep_bb1_in(v_1, v_m, v_n, 0, v_y.0)) :|: TRUE 2.20/1.32 eval_speedNestedMultipleDep_bb1_in(v_1, v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedNestedMultipleDep_bb2_in(v_1, v_m, v_n, v_x.0, v_y.0)) :|: v_x.0 < v_n 2.20/1.32 eval_speedNestedMultipleDep_bb1_in(v_1, v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedNestedMultipleDep_bb5_in(v_1, v_m, v_n, v_x.0, v_y.0)) :|: v_x.0 >= v_n 2.20/1.32 eval_speedNestedMultipleDep_bb2_in(v_1, v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedNestedMultipleDep_bb3_in(v_x.0 + 1, v_m, v_n, v_x.0, 0)) :|: TRUE 2.20/1.32 eval_speedNestedMultipleDep_bb3_in(v_1, v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedNestedMultipleDep_bb4_in(v_1, v_m, v_n, v_x.0, v_y.0)) :|: v_y.0 < v_m 2.20/1.32 eval_speedNestedMultipleDep_bb3_in(v_1, v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedNestedMultipleDep_bb1_in(v_1, v_m, v_n, v_1, v_y.0)) :|: v_y.0 >= v_m 2.20/1.32 eval_speedNestedMultipleDep_bb4_in(v_1, v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedNestedMultipleDep_bb3_in(v_1, v_m, v_n, v_x.0, v_y.0 + 1)) :|: TRUE 2.20/1.32 eval_speedNestedMultipleDep_bb5_in(v_1, v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedNestedMultipleDep_stop(v_1, v_m, v_n, v_x.0, v_y.0)) :|: TRUE 2.20/1.32 2.20/1.32 The start-symbols are:[eval_speedNestedMultipleDep_start_5] 2.20/1.32 2.20/1.32 2.20/1.32 ---------------------------------------- 2.20/1.32 2.20/1.32 (1) Koat Proof (FINISHED) 2.20/1.32 YES(?, 3*ar_1 + 2*ar_1*ar_4 + 6) 2.20/1.32 2.20/1.32 2.20/1.32 2.20/1.32 Initial complexity problem: 2.20/1.32 2.20/1.32 1: T: 2.20/1.32 2.20/1.32 (Comp: ?, Cost: 1) evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.20/1.32 2.20/1.32 (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, ar_1, ar_2, ar_3, ar_4)) 2.20/1.32 2.20/1.32 (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ] 2.20/1.32 2.20/1.32 (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ] 2.20/1.32 2.20/1.32 (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_0 + 1, 0, ar_4)) 2.20/1.32 2.20/1.32 (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ] 2.20/1.32 2.20/1.32 (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ] 2.20/1.32 2.20/1.32 (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) 2.20/1.32 2.20/1.32 (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.20/1.32 2.20/1.32 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 2.20/1.32 2.20/1.32 start location: koat_start 2.20/1.32 2.20/1.32 leaf cost: 0 2.20/1.32 2.20/1.32 2.20/1.32 2.20/1.32 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.20/1.32 2.20/1.32 2: T: 2.20/1.32 2.20/1.32 (Comp: 1, Cost: 1) evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.20/1.32 2.20/1.32 (Comp: 1, Cost: 1) evalspeedNestedMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, ar_1, ar_2, ar_3, ar_4)) 2.20/1.32 2.20/1.32 (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ] 2.20/1.32 2.20/1.32 (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ] 2.20/1.32 2.20/1.32 (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_0 + 1, 0, ar_4)) 2.20/1.32 2.20/1.32 (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ] 2.20/1.32 2.20/1.32 (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ] 2.20/1.32 2.20/1.32 (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) 2.20/1.32 2.20/1.32 (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.20/1.32 2.20/1.32 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 2.20/1.32 2.20/1.32 start location: koat_start 2.20/1.32 2.20/1.32 leaf cost: 0 2.20/1.32 2.20/1.32 2.20/1.32 2.20/1.32 A polynomial rank function with 2.20/1.32 2.20/1.32 Pol(evalspeedNestedMultipleDepstart) = 2
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