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Complexity_C_Integer 2019-03-21 04.38 pair #429989644
details
property
value
status
complete
benchmark
speedSimpleMultipleDep.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n175.star.cs.uiowa.edu
space
WTC_V2
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.58032 seconds
cpu usage
2.48993
user time
2.28441
system time
0.205522
max virtual memory
1.8273644E7
max residence set size
181584.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
2.15/1.55 WORST_CASE(?, O(n^2)) 2.15/1.56 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.15/1.56 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.15/1.56 2.15/1.56 2.15/1.56 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 2.15/1.56 2.15/1.56 (0) CpxIntTrs 2.15/1.56 (1) Koat Proof [FINISHED, 280 ms] 2.15/1.56 (2) BOUNDS(1, n^2) 2.15/1.56 2.15/1.56 2.15/1.56 ---------------------------------------- 2.15/1.56 2.15/1.56 (0) 2.15/1.56 Obligation: 2.15/1.56 Complexity Int TRS consisting of the following rules: 2.15/1.56 eval_speedSimpleMultipleDep_start(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedSimpleMultipleDep_bb0_in(v_m, v_n, v_x.0, v_y.0)) :|: TRUE 2.15/1.56 eval_speedSimpleMultipleDep_bb0_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(v_m, v_n, 0, 0)) :|: TRUE 2.15/1.56 eval_speedSimpleMultipleDep_bb1_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedSimpleMultipleDep_bb2_in(v_m, v_n, v_x.0, v_y.0)) :|: v_x.0 < v_n 2.15/1.56 eval_speedSimpleMultipleDep_bb1_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedSimpleMultipleDep_bb3_in(v_m, v_n, v_x.0, v_y.0)) :|: v_x.0 >= v_n 2.15/1.56 eval_speedSimpleMultipleDep_bb2_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(v_m, v_n, v_x.0, v_y.0 + 1)) :|: v_y.0 < v_m 2.15/1.56 eval_speedSimpleMultipleDep_bb2_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(v_m, v_n, v_x.0 + 1, v_y.0 + 1)) :|: v_y.0 < v_m && v_y.0 >= v_m 2.15/1.56 eval_speedSimpleMultipleDep_bb2_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(v_m, v_n, v_x.0, 0)) :|: v_y.0 >= v_m && v_y.0 < v_m 2.15/1.56 eval_speedSimpleMultipleDep_bb2_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(v_m, v_n, v_x.0 + 1, 0)) :|: v_y.0 >= v_m 2.15/1.56 eval_speedSimpleMultipleDep_bb3_in(v_m, v_n, v_x.0, v_y.0) -> Com_1(eval_speedSimpleMultipleDep_stop(v_m, v_n, v_x.0, v_y.0)) :|: TRUE 2.15/1.56 2.15/1.56 The start-symbols are:[eval_speedSimpleMultipleDep_start_4] 2.15/1.56 2.15/1.56 2.15/1.56 ---------------------------------------- 2.15/1.56 2.15/1.56 (1) Koat Proof (FINISHED) 2.15/1.56 YES(?, 2*ar_2 + 2*ar_2*ar_3 + 2*ar_3 + 7) 2.15/1.56 2.15/1.56 2.15/1.56 2.15/1.56 Initial complexity problem: 2.15/1.56 2.15/1.56 1: T: 2.15/1.56 2.15/1.56 (Comp: ?, Cost: 1) evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3)) 2.15/1.56 2.15/1.56 (Comp: ?, Cost: 1) evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(0, 0, ar_2, ar_3)) 2.15/1.56 2.15/1.56 (Comp: ?, Cost: 1) evalspeedSimpleMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ] 2.15/1.56 2.15/1.56 (Comp: ?, Cost: 1) evalspeedSimpleMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ] 2.15/1.56 2.15/1.56 (Comp: ?, Cost: 1) evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ] 2.15/1.56 2.15/1.56 (Comp: ?, Cost: 1) evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0 + 1, ar_1 + 1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 /\ ar_1 >= ar_3 ] 2.15/1.56 2.15/1.56 (Comp: ?, Cost: 1) evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0, 0, ar_2, ar_3)) [ ar_1 >= ar_3 /\ ar_3 >= ar_1 + 1 ] 2.15/1.56 2.15/1.56 (Comp: ?, Cost: 1) evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0 + 1, 0, ar_2, ar_3)) [ ar_1 >= ar_3 ] 2.15/1.56 2.15/1.56 (Comp: ?, Cost: 1) evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstop(ar_0, ar_1, ar_2, ar_3)) 2.15/1.56 2.15/1.56 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 2.15/1.56 2.15/1.56 start location: koat_start 2.15/1.56 2.15/1.56 leaf cost: 0 2.15/1.56 2.15/1.56 2.15/1.56 2.15/1.56 Testing for reachability in the complexity graph removes the following transitions from problem 1: 2.15/1.56 2.15/1.56 evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0 + 1, ar_1 + 1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 /\ ar_1 >= ar_3 ] 2.15/1.56 2.15/1.56 evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0, 0, ar_2, ar_3)) [ ar_1 >= ar_3 /\ ar_3 >= ar_1 + 1 ] 2.15/1.56 2.15/1.56 We thus obtain the following problem: 2.15/1.56 2.15/1.56 2: T: 2.15/1.56 2.15/1.56 (Comp: ?, Cost: 1) evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstop(ar_0, ar_1, ar_2, ar_3)) 2.15/1.56 2.15/1.56 (Comp: ?, Cost: 1) evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0 + 1, 0, ar_2, ar_3)) [ ar_1 >= ar_3 ] 2.15/1.56 2.15/1.56 (Comp: ?, Cost: 1) evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ] 2.15/1.56 2.15/1.56 (Comp: ?, Cost: 1) evalspeedSimpleMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ] 2.15/1.56 2.15/1.56 (Comp: ?, Cost: 1) evalspeedSimpleMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ] 2.15/1.56 2.15/1.56 (Comp: ?, Cost: 1) evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb1in(0, 0, ar_2, ar_3)) 2.15/1.56 2.15/1.56 (Comp: ?, Cost: 1) evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepbb0in(ar_0, ar_1, ar_2, ar_3)) 2.15/1.56 2.15/1.56 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalspeedSimpleMultipleDepstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 2.15/1.56 2.15/1.56 start location: koat_start 2.15/1.56 2.15/1.56 leaf cost: 0 2.15/1.56 2.15/1.56 2.15/1.56 2.15/1.56 Repeatedly propagating knowledge in problem 2 produces the following problem:
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return to Complexity_C_Integer 2019-03-21 04.38