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Complexity_ITS 2019-03-21 04.46 pair #429989766
details
property
value
status
complete
benchmark
a.11.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n176.star.cs.uiowa.edu
space
pasta
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
2.42689 seconds
cpu usage
5.06476
user time
4.79261
system time
0.272147
max virtual memory
1.8526608E7
max residence set size
218720.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
4.95/2.39 WORST_CASE(Omega(n^1), O(n^1)) 4.95/2.40 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 4.95/2.40 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.95/2.40 4.95/2.40 4.95/2.40 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, max(1, 1 + Arg_0 + -1 * Arg_1) + nat(Arg_0 + -1 * Arg_0 * Arg_1 + -1 * Arg_2 * Arg_0 + Arg_0^2 + Arg_2 * Arg_1 + -1 * Arg_2) + nat(Arg_0 + -1 * Arg_2) + nat(Arg_0 + -1 * Arg_1) + nat(1 + Arg_0 + -1 * Arg_1)). 4.95/2.40 4.95/2.40 (0) CpxIntTrs 4.95/2.40 (1) Loat Proof [FINISHED, 654 ms] 4.95/2.40 (2) BOUNDS(n^1, INF) 4.95/2.40 4.95/2.40 4.95/2.40 ---------------------------------------- 4.95/2.40 4.95/2.40 (0) 4.95/2.40 Obligation: 4.95/2.40 Complexity Int TRS consisting of the following rules: 4.95/2.40 eval1(A, B, C) -> Com_1(eval2(A, B, C)) :|: A >= B + 1 4.95/2.40 eval2(A, B, C) -> Com_1(eval1(A, B + 1, C)) :|: A >= C + 1 4.95/2.40 eval2(A, B, C) -> Com_1(eval1(A, B, C + 1)) :|: A >= C + 1 4.95/2.40 eval2(A, B, C) -> Com_1(eval1(A - 1, B, C)) :|: C >= A 4.95/2.40 start(A, B, C) -> Com_1(eval1(A, B, C)) :|: TRUE 4.95/2.40 4.95/2.40 The start-symbols are:[start_3] 4.95/2.40 4.95/2.40 4.95/2.40 ---------------------------------------- 4.95/2.40 4.95/2.40 (1) Loat Proof (FINISHED) 4.95/2.40 4.95/2.40 4.95/2.40 ### Pre-processing the ITS problem ### 4.95/2.40 4.95/2.40 4.95/2.40 4.95/2.40 Initial linear ITS problem 4.95/2.40 4.95/2.40 Start location: start 4.95/2.40 4.95/2.40 0: eval1 -> eval2 : [ A>=1+B ], cost: 1 4.95/2.40 4.95/2.40 1: eval2 -> eval1 : B'=1+B, [ A>=1+C ], cost: 1 4.95/2.40 4.95/2.40 2: eval2 -> eval1 : C'=1+C, [ A>=1+C ], cost: 1 4.95/2.40 4.95/2.40 3: eval2 -> eval1 : A'=-1+A, [ C>=A ], cost: 1 4.95/2.40 4.95/2.40 4: start -> eval1 : [], cost: 1 4.95/2.40 4.95/2.40 4.95/2.40 4.95/2.40 ### Simplification by acceleration and chaining ### 4.95/2.40 4.95/2.40 4.95/2.40 4.95/2.40 Eliminated locations (on tree-shaped paths): 4.95/2.40 4.95/2.40 Start location: start 4.95/2.40 4.95/2.40 5: eval1 -> eval1 : B'=1+B, [ A>=1+B && A>=1+C ], cost: 2 4.95/2.40 4.95/2.40 6: eval1 -> eval1 : C'=1+C, [ A>=1+B && A>=1+C ], cost: 2 4.95/2.40 4.95/2.40 7: eval1 -> eval1 : A'=-1+A, [ A>=1+B && C>=A ], cost: 2 4.95/2.40 4.95/2.40 4: start -> eval1 : [], cost: 1 4.95/2.40 4.95/2.40 4.95/2.40 4.95/2.40 Accelerating simple loops of location 0. 4.95/2.40 4.95/2.40 Accelerating the following rules: 4.95/2.40 4.95/2.40 5: eval1 -> eval1 : B'=1+B, [ A>=1+B && A>=1+C ], cost: 2 4.95/2.40 4.95/2.40 6: eval1 -> eval1 : C'=1+C, [ A>=1+B && A>=1+C ], cost: 2 4.95/2.40 4.95/2.40 7: eval1 -> eval1 : A'=-1+A, [ A>=1+B && C>=A ], cost: 2 4.95/2.40 4.95/2.40 4.95/2.40 4.95/2.40 Accelerated rule 5 with metering function A-B, yielding the new rule 8. 4.95/2.40 4.95/2.40 Accelerated rule 6 with metering function -C+A, yielding the new rule 9. 4.95/2.40 4.95/2.40 Accelerated rule 7 with metering function A-B, yielding the new rule 10. 4.95/2.40 4.95/2.40 Removing the simple loops: 5 6 7. 4.95/2.40 4.95/2.40 4.95/2.40 4.95/2.40 Accelerated all simple loops using metering functions (where possible): 4.95/2.40 4.95/2.40 Start location: start 4.95/2.40 4.95/2.40 8: eval1 -> eval1 : B'=A, [ A>=1+B && A>=1+C ], cost: 2*A-2*B 4.95/2.40 4.95/2.40 9: eval1 -> eval1 : C'=A, [ A>=1+B && A>=1+C ], cost: -2*C+2*A 4.95/2.40 4.95/2.40 10: eval1 -> eval1 : A'=B, [ A>=1+B && C>=A ], cost: 2*A-2*B
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