details

property	value
status	complete
benchmark	p-43.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n101.star.cs.uiowa.edu
space	T2

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.98528695107 seconds
cpu usage	5.428947056
max memory	3.68881664E8

stage attributes

key	value
output-size	5331
starexec-result	WORST_CASE(Omega(n^1), ?)

output

/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, INF).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, 975 ms] (2) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: f2(A, B, C, D) -> Com_1(f300(A, B, C, D)) :|: TRUE f300(A, B, C, D) -> Com_1(f300(-(1) + B, -(1) + B, E, D)) :|: A >= 1 && B >= 1 && E >= 1 && B + A >= 1 f300(A, B, C, D) -> Com_1(f300(-(1) + B, -(1) + B, E, D)) :|: A >= 1 && B >= 1 && 0 >= E + 1 && B + A >= 1 f300(A, B, C, D) -> Com_1(f300(-(1) + A, -(2) + A, 0, D)) :|: A >= 1 && B + A >= 1 && B >= 1 f300(A, B, C, D) -> Com_1(f1(A, B, C, E)) :|: A >= 1 && 0 >= B + A && B >= 1 f300(A, B, C, D) -> Com_1(f1(A, B, C, E)) :|: B >= 1 && 0 >= A f300(A, B, C, D) -> Com_1(f1(A, B, C, E)) :|: 0 >= B The start-symbols are:[f2_4] ---------------------------------------- (1) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: f2 0: f2 -> f300 : [], cost: 1 1: f300 -> f300 : A'=-1+B, B'=-1+B, C'=free, [ A>=1 && B>=1 && free>=1 && A+B>=1 ], cost: 1 2: f300 -> f300 : A'=-1+B, B'=-1+B, C'=free_1, [ A>=1 && B>=1 && 0>=1+free_1 && A+B>=1 ], cost: 1 3: f300 -> f300 : A'=-1+A, B'=-2+A, C'=0, [ A>=1 && A+B>=1 && B>=1 ], cost: 1 4: f300 -> f1 : D'=free_2, [ A>=1 && 0>=A+B && B>=1 ], cost: 1 5: f300 -> f1 : D'=free_3, [ B>=1 && 0>=A ], cost: 1 6: f300 -> f1 : D'=free_4, [ 0>=B ], cost: 1 Removed unreachable and leaf rules: Start location: f2 0: f2 -> f300 : [], cost: 1 1: f300 -> f300 : A'=-1+B, B'=-1+B, C'=free, [ A>=1 && B>=1 && free>=1 && A+B>=1 ], cost: 1 2: f300 -> f300 : A'=-1+B, B'=-1+B, C'=free_1, [ A>=1 && B>=1 && 0>=1+free_1 && A+B>=1 ], cost: 1 3: f300 -> f300 : A'=-1+A, B'=-2+A, C'=0, [ A>=1 && A+B>=1 && B>=1 ], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 1: f300 -> f300 : A'=-1+B, B'=-1+B, C'=free, [ A>=1 && B>=1 && free>=1 ], cost: 1 2: f300 -> f300 : A'=-1+B, B'=-1+B, C'=free_1, [ A>=1 && B>=1 && 0>=1+free_1 ], cost: 1 3: f300 -> f300 : A'=-1+A, B'=-2+A, C'=0, [ A>=1 && A+B>=1 && B>=1 ], cost: 1 Accelerated rule 1 with backward acceleration, yielding the new rule 7. Accelerated rule 1 with backward acceleration, yielding the new rule 8. Accelerated rule 2 with backward acceleration, yielding the new rule 9. Accelerated rule 2 with backward acceleration, yielding the new rule 10. popout

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job log

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actions

all output return to Compl Integ Trans Syste 26843