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Compl Integ Trans Syste 26843 pair #381744069
details
property
value
status
complete
benchmark
abstractions.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n020.star.cs.uiowa.edu
space
ESOP08
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
2.61397004128 seconds
cpu usage
5.283560695
max memory
3.73174272E8
stage attributes
key
value
output-size
3721
starexec-result
WORST_CASE(Omega(n^1), ?)
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, INF). (0) CpxIntTrs (1) Loat Proof [FINISHED, 466 ms] (2) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval(A, B) -> Com_1(eval(A - 1, C)) :|: A >= 1 && B >= 1 eval(A, B) -> Com_1(eval(A, B - 1)) :|: A >= 1 && B >= 1 start(A, B) -> Com_1(eval(A, B)) :|: TRUE The start-symbols are:[start_2] ---------------------------------------- (1) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: start 0: eval -> eval : A'=-1+A, B'=free, [ A>=1 && B>=1 ], cost: 1 1: eval -> eval : B'=-1+B, [ A>=1 && B>=1 ], cost: 1 2: start -> eval : [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 0. Accelerating the following rules: 0: eval -> eval : A'=-1+A, B'=free, [ A>=1 && B>=1 ], cost: 1 1: eval -> eval : B'=-1+B, [ A>=1 && B>=1 ], cost: 1 Accelerated rule 0 with metering function A (after strengthening guard), yielding the new rule 3. Accelerated rule 1 with metering function B, yielding the new rule 4. Removing the simple loops: 1. Accelerated all simple loops using metering functions (where possible): Start location: start 0: eval -> eval : A'=-1+A, B'=free, [ A>=1 && B>=1 ], cost: 1 3: eval -> eval : A'=0, B'=free, [ A>=1 && B>=1 && free>=1 ], cost: A 4: eval -> eval : B'=0, [ A>=1 && B>=1 ], cost: B 2: start -> eval : [], cost: 1 Chained accelerated rules (with incoming rules): Start location: start 2: start -> eval : [], cost: 1 5: start -> eval : A'=-1+A, B'=free, [ A>=1 && B>=1 ], cost: 2 6: start -> eval : A'=0, B'=free, [ A>=1 && B>=1 && free>=1 ], cost: 1+A 7: start -> eval : B'=0, [ A>=1 && B>=1 ], cost: 1+B
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