Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Compl Integ Trans Syste 26843 pair #381744080
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
n007.star.cs.uiowa.edu
space
pasta
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
2.32090115547 seconds
cpu usage
4.916356355
max memory
3.0388224E8
stage attributes
key
value
output-size
4709
starexec-result
WORST_CASE(Omega(n^1), O(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), O(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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, max(1, 1 + Arg_0 + -1 * Arg_1) + nat(Arg_0 + -1 * Arg_0 * Arg_1 + -1 *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)). (0) CpxIntTrs (1) Loat Proof [FINISHED, 609 ms] (2) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval1(A, B, C) -> Com_1(eval2(A, B, C)) :|: A >= B + 1 eval2(A, B, C) -> Com_1(eval1(A, B + 1, C)) :|: A >= C + 1 eval2(A, B, C) -> Com_1(eval1(A, B, C + 1)) :|: A >= C + 1 eval2(A, B, C) -> Com_1(eval1(A - 1, B, C)) :|: C >= A start(A, B, C) -> Com_1(eval1(A, B, C)) :|: TRUE The start-symbols are:[start_3] ---------------------------------------- (1) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: start 0: eval1 -> eval2 : [ A>=1+B ], cost: 1 1: eval2 -> eval1 : B'=1+B, [ A>=1+C ], cost: 1 2: eval2 -> eval1 : C'=1+C, [ A>=1+C ], cost: 1 3: eval2 -> eval1 : A'=-1+A, [ C>=A ], cost: 1 4: start -> eval1 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on tree-shaped paths): Start location: start 5: eval1 -> eval1 : B'=1+B, [ A>=1+B && A>=1+C ], cost: 2 6: eval1 -> eval1 : C'=1+C, [ A>=1+B && A>=1+C ], cost: 2 7: eval1 -> eval1 : A'=-1+A, [ A>=1+B && C>=A ], cost: 2 4: start -> eval1 : [], cost: 1 Accelerating simple loops of location 0. Accelerating the following rules: 5: eval1 -> eval1 : B'=1+B, [ A>=1+B && A>=1+C ], cost: 2 6: eval1 -> eval1 : C'=1+C, [ A>=1+B && A>=1+C ], cost: 2 7: eval1 -> eval1 : A'=-1+A, [ A>=1+B && C>=A ], cost: 2 Accelerated rule 5 with metering function A-B, yielding the new rule 8. Accelerated rule 6 with metering function -C+A, yielding the new rule 9. Accelerated rule 7 with metering function A-B, yielding the new rule 10. Removing the simple loops: 5 6 7. Accelerated all simple loops using metering functions (where possible): Start location: start
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Compl Integ Trans Syste 26843