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	n112.star.cs.uiowa.edu
space	ESOP08

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.63155 seconds
cpu usage	5.2785
user time	4.96669
system time	0.311816
max virtual memory	1.862074E7
max residence set size	216424.0

stage attributes

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

output

5.21/2.59 WORST_CASE(Omega(n^1), ?) 5.21/2.60 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 5.21/2.60 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.21/2.60 5.21/2.60 5.21/2.60 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, INF). 5.21/2.60 5.21/2.60 (0) CpxIntTrs 5.21/2.60 (1) Loat Proof [FINISHED, 526 ms] 5.21/2.60 (2) BOUNDS(n^1, INF) 5.21/2.60 5.21/2.60 5.21/2.60 ---------------------------------------- 5.21/2.60 5.21/2.60 (0) 5.21/2.60 Obligation: 5.21/2.60 Complexity Int TRS consisting of the following rules: 5.21/2.60 eval(A, B) -> Com_1(eval(A - 1, C)) :|: A >= 1 && B >= 1 5.21/2.60 eval(A, B) -> Com_1(eval(A, B - 1)) :|: A >= 1 && B >= 1 5.21/2.60 start(A, B) -> Com_1(eval(A, B)) :|: TRUE 5.21/2.60 5.21/2.60 The start-symbols are:[start_2] 5.21/2.60 5.21/2.60 5.21/2.60 ---------------------------------------- 5.21/2.60 5.21/2.60 (1) Loat Proof (FINISHED) 5.21/2.60 5.21/2.60 5.21/2.60 ### Pre-processing the ITS problem ### 5.21/2.60 5.21/2.60 5.21/2.60 5.21/2.60 Initial linear ITS problem 5.21/2.60 5.21/2.60 Start location: start 5.21/2.60 5.21/2.60 0: eval -> eval : A'=-1+A, B'=free, [ A>=1 && B>=1 ], cost: 1 5.21/2.60 5.21/2.60 1: eval -> eval : B'=-1+B, [ A>=1 && B>=1 ], cost: 1 5.21/2.60 5.21/2.60 2: start -> eval : [], cost: 1 5.21/2.60 5.21/2.60 5.21/2.60 5.21/2.60 ### Simplification by acceleration and chaining ### 5.21/2.60 5.21/2.60 5.21/2.60 5.21/2.60 Accelerating simple loops of location 0. 5.21/2.60 5.21/2.60 Accelerating the following rules: 5.21/2.60 5.21/2.60 0: eval -> eval : A'=-1+A, B'=free, [ A>=1 && B>=1 ], cost: 1 5.21/2.60 5.21/2.60 1: eval -> eval : B'=-1+B, [ A>=1 && B>=1 ], cost: 1 5.21/2.60 5.21/2.60 5.21/2.60 5.21/2.60 Accelerated rule 0 with metering function A (after strengthening guard), yielding the new rule 3. 5.21/2.60 5.21/2.60 Accelerated rule 1 with metering function B, yielding the new rule 4. 5.21/2.60 5.21/2.60 Removing the simple loops: 1. 5.21/2.60 5.21/2.60 5.21/2.60 5.21/2.60 Accelerated all simple loops using metering functions (where possible): 5.21/2.60 5.21/2.60 Start location: start 5.21/2.60 5.21/2.60 0: eval -> eval : A'=-1+A, B'=free, [ A>=1 && B>=1 ], cost: 1 5.21/2.60 5.21/2.60 3: eval -> eval : A'=0, B'=free, [ A>=1 && B>=1 && free>=1 ], cost: A 5.21/2.60 5.21/2.60 4: eval -> eval : B'=0, [ A>=1 && B>=1 ], cost: B 5.21/2.60 5.21/2.60 2: start -> eval : [], cost: 1 5.21/2.60 5.21/2.60 5.21/2.60 5.21/2.60 Chained accelerated rules (with incoming rules): 5.21/2.60 5.21/2.60 Start location: start 5.21/2.60 5.21/2.60 2: start -> eval : [], cost: 1 5.21/2.60 5.21/2.60 5: start -> eval : A'=-1+A, B'=free, [ A>=1 && B>=1 ], cost: 2 5.21/2.60 5.21/2.60 6: start -> eval : A'=0, B'=free, [ A>=1 && B>=1 && free>=1 ], cost: 1+A 5.21/2.60 5.21/2.60 7: start -> eval : B'=0, [ A>=1 && B>=1 ], cost: 1+B 5.21/2.60 5.21/2.60 5.21/2.60 5.21/2.60 Removed unreachable locations (and leaf rules with constant cost): 5.21/2.60 5.21/2.60 Start location: start 5.21/2.60 5.21/2.60 6: start -> eval : A'=0, B'=free, [ A>=1 && B>=1 && free>=1 ], cost: 1+A popout

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job log

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actions

all output return to Complexity_ITS 2019-03-21 04.46