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Complexity_C_Integer 2019-03-21 04.38 pair #429989638
details
property
value
status
complete
benchmark
rsd.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n019.star.cs.uiowa.edu
space
WTC_V2
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.82122 seconds
cpu usage
2.78145
user time
2.55224
system time
0.229213
max virtual memory
1.833918E7
max residence set size
184276.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
2.15/1.76 WORST_CASE(?, O(n^1)) 2.15/1.77 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.15/1.77 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.15/1.77 2.15/1.77 2.15/1.77 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 2.15/1.77 2.15/1.77 (0) CpxIntTrs 2.15/1.77 (1) Koat Proof [FINISHED, 583 ms] 2.15/1.77 (2) BOUNDS(1, n^1) 2.15/1.77 2.15/1.77 2.15/1.77 ---------------------------------------- 2.15/1.77 2.15/1.77 (0) 2.15/1.77 Obligation: 2.15/1.77 Complexity Int TRS consisting of the following rules: 2.15/1.77 eval_rsd_start(v_4, v_da.0, v_db.0, v_r) -> Com_1(eval_rsd_bb0_in(v_4, v_da.0, v_db.0, v_r)) :|: TRUE 2.15/1.77 eval_rsd_bb0_in(v_4, v_da.0, v_db.0, v_r) -> Com_1(eval_rsd_bb1_in(v_4, v_da.0, v_db.0, v_r)) :|: v_r >= 0 2.15/1.77 eval_rsd_bb0_in(v_4, v_da.0, v_db.0, v_r) -> Com_1(eval_rsd_bb4_in(v_4, v_da.0, v_db.0, v_r)) :|: v_r < 0 2.15/1.77 eval_rsd_bb1_in(v_4, v_da.0, v_db.0, v_r) -> Com_1(eval_rsd_bb2_in(v_4, 2 * v_r, 2 * v_r, v_r)) :|: TRUE 2.15/1.77 eval_rsd_bb2_in(v_4, v_da.0, v_db.0, v_r) -> Com_1(eval_rsd_bb3_in(v_4, v_da.0, v_db.0, v_r)) :|: v_da.0 >= v_r 2.15/1.77 eval_rsd_bb2_in(v_4, v_da.0, v_db.0, v_r) -> Com_1(eval_rsd_bb4_in(v_4, v_da.0, v_db.0, v_r)) :|: v_da.0 < v_r 2.15/1.77 eval_rsd_bb3_in(v_4, v_da.0, v_db.0, v_r) -> Com_1(eval_rsd_3(v_4, v_da.0, v_db.0, v_r)) :|: TRUE 2.15/1.77 eval_rsd_3(v_4, v_da.0, v_db.0, v_r) -> Com_2(eval_nondet_start(v_4, v_da.0, v_db.0, v_r), eval_rsd_4(nondef.0, v_da.0, v_db.0, v_r)) :|: TRUE 2.15/1.77 eval_rsd_4(v_4, v_da.0, v_db.0, v_r) -> Com_1(eval_rsd_bb2_in(v_4, v_da.0 - 1, v_db.0, v_r)) :|: v_4 > 0 2.15/1.77 eval_rsd_4(v_4, v_da.0, v_db.0, v_r) -> Com_1(eval_rsd_bb2_in(v_4, v_db.0 - 1, v_db.0, v_r)) :|: v_4 > 0 && v_4 <= 0 2.15/1.77 eval_rsd_4(v_4, v_da.0, v_db.0, v_r) -> Com_1(eval_rsd_bb2_in(v_4, v_da.0 - 1, v_da.0, v_r)) :|: v_4 <= 0 && v_4 > 0 2.15/1.77 eval_rsd_4(v_4, v_da.0, v_db.0, v_r) -> Com_1(eval_rsd_bb2_in(v_4, v_db.0 - 1, v_da.0, v_r)) :|: v_4 <= 0 2.15/1.77 eval_rsd_bb4_in(v_4, v_da.0, v_db.0, v_r) -> Com_1(eval_rsd_stop(v_4, v_da.0, v_db.0, v_r)) :|: TRUE 2.15/1.77 2.15/1.77 The start-symbols are:[eval_rsd_start_4] 2.15/1.77 2.15/1.77 2.15/1.77 ---------------------------------------- 2.15/1.77 2.15/1.77 (1) Koat Proof (FINISHED) 2.15/1.77 YES(?, 168*ar_0 + 50) 2.15/1.77 2.15/1.77 2.15/1.77 2.15/1.77 Initial complexity problem: 2.15/1.77 2.15/1.77 1: T: 2.15/1.77 2.15/1.77 (Comp: ?, Cost: 1) evalrsdstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrsdbb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.15/1.77 2.15/1.77 (Comp: ?, Cost: 1) evalrsdbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrsdbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= 0 ] 2.15/1.77 2.15/1.77 (Comp: ?, Cost: 1) evalrsdbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ] 2.15/1.77 2.15/1.77 (Comp: ?, Cost: 1) evalrsdbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrsdbb2in(ar_0, 2*ar_0, 2*ar_0, ar_3, ar_4)) 2.15/1.77 2.15/1.77 (Comp: ?, Cost: 1) evalrsdbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrsdbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ] 2.15/1.77 2.15/1.77 (Comp: ?, Cost: 1) evalrsdbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 + 1 ] 2.15/1.77 2.15/1.77 (Comp: ?, Cost: 1) evalrsdbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrsd3(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.15/1.77 2.15/1.77 (Comp: ?, Cost: 1) evalrsd30(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.15/1.77 2.15/1.77 (Comp: ?, Cost: 1) evalrsd31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrsd4(ar_0, ar_1, ar_2, ar_4, ar_4)) 2.15/1.77 2.15/1.77 (Comp: ?, Cost: 1) evalrsd3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_2(evalrsd30(ar_0, ar_1, ar_2, ar_3, f), evalrsd31(ar_0, ar_1, ar_2, ar_3, f)) 2.15/1.77 2.15/1.77 (Comp: ?, Cost: 1) evalrsd4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrsdbb2in(ar_0, ar_1 - 1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ] 2.15/1.77 2.15/1.77 (Comp: ?, Cost: 1) evalrsd4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrsdbb2in(ar_0, ar_2 - 1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 /\ 0 >= ar_3 ] 2.15/1.77 2.15/1.77 (Comp: ?, Cost: 1) evalrsd4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrsdbb2in(ar_0, ar_1 - 1, ar_1, ar_3, ar_4)) [ 0 >= ar_3 /\ ar_3 >= 1 ] 2.15/1.77 2.15/1.77 (Comp: ?, Cost: 1) evalrsd4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrsdbb2in(ar_0, ar_2 - 1, ar_1, ar_3, ar_4)) [ 0 >= ar_3 ] 2.15/1.77 2.15/1.77 (Comp: ?, Cost: 1) evalrsdbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.15/1.77 2.15/1.77 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrsdstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 2.15/1.77 2.15/1.77 start location: koat_start 2.15/1.77 2.15/1.77 leaf cost: 0 2.15/1.77 2.15/1.77 2.15/1.77 2.15/1.77 Testing for reachability in the complexity graph removes the following transitions from problem 1: 2.15/1.77 2.15/1.77 evalrsd4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrsdbb2in(ar_0, ar_2 - 1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 /\ 0 >= ar_3 ] 2.15/1.77 2.15/1.77 evalrsd4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrsdbb2in(ar_0, ar_1 - 1, ar_1, ar_3, ar_4)) [ 0 >= ar_3 /\ ar_3 >= 1 ] 2.15/1.77 2.15/1.77 We thus obtain the following problem: 2.15/1.77 2.15/1.77 2: T: 2.15/1.77 2.15/1.77 (Comp: ?, Cost: 1) evalrsd4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrsdbb2in(ar_0, ar_2 - 1, ar_1, ar_3, ar_4)) [ 0 >= ar_3 ] 2.15/1.77 2.15/1.77 (Comp: ?, Cost: 1) evalrsd4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrsdbb2in(ar_0, ar_1 - 1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ] 2.15/1.77 2.15/1.77 (Comp: ?, Cost: 1) evalrsd31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrsd4(ar_0, ar_1, ar_2, ar_4, ar_4)) 2.15/1.77 2.15/1.77 (Comp: ?, Cost: 1) evalrsd30(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4))
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