details

property	value
status	complete
benchmark	mc91.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n129.star.cs.uiowa.edu
space	T2

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.58853 seconds
cpu usage	5.35255
user time	5.0195
system time	0.333044
max virtual memory	1.8572108E7
max residence set size	213188.0

stage attributes

key	value
starexec-result	WORST_CASE(NON_POLY, ?)

output

5.22/2.55 WORST_CASE(NON_POLY, ?) 5.22/2.55 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 5.22/2.55 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.22/2.55 5.22/2.55 5.22/2.55 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF). 5.22/2.55 5.22/2.55 (0) CpxIntTrs 5.22/2.55 (1) Loat Proof [FINISHED, 836 ms] 5.22/2.55 (2) BOUNDS(INF, INF) 5.22/2.55 5.22/2.55 5.22/2.55 ---------------------------------------- 5.22/2.55 5.22/2.55 (0) 5.22/2.55 Obligation: 5.22/2.55 Complexity Int TRS consisting of the following rules: 5.22/2.55 f0(A, B) -> Com_1(f1(C, 1)) :|: TRUE 5.22/2.55 f1(A, B) -> Com_1(f1(A - 10, B - 1)) :|: B >= 1 && A >= 101 5.22/2.55 f1(A, B) -> Com_1(f1(A + 11, B + 1)) :|: B >= 1 && 100 >= A 5.22/2.55 5.22/2.55 The start-symbols are:[f0_2] 5.22/2.55 5.22/2.55 5.22/2.55 ---------------------------------------- 5.22/2.55 5.22/2.55 (1) Loat Proof (FINISHED) 5.22/2.55 5.22/2.55 5.22/2.55 ### Pre-processing the ITS problem ### 5.22/2.55 5.22/2.55 5.22/2.55 5.22/2.55 Initial linear ITS problem 5.22/2.55 5.22/2.55 Start location: f0 5.22/2.55 5.22/2.55 0: f0 -> f1 : A'=free, B'=1, [], cost: 1 5.22/2.55 5.22/2.55 1: f1 -> f1 : A'=-10+A, B'=-1+B, [ B>=1 && A>=101 ], cost: 1 5.22/2.55 5.22/2.55 2: f1 -> f1 : A'=11+A, B'=1+B, [ B>=1 && 100>=A ], cost: 1 5.22/2.55 5.22/2.55 5.22/2.55 5.22/2.55 ### Simplification by acceleration and chaining ### 5.22/2.55 5.22/2.55 5.22/2.55 5.22/2.55 Accelerating simple loops of location 1. 5.22/2.55 5.22/2.55 Accelerating the following rules: 5.22/2.55 5.22/2.55 1: f1 -> f1 : A'=-10+A, B'=-1+B, [ B>=1 && A>=101 ], cost: 1 5.22/2.55 5.22/2.55 2: f1 -> f1 : A'=11+A, B'=1+B, [ B>=1 && 100>=A ], cost: 1 5.22/2.55 5.22/2.55 5.22/2.55 5.22/2.55 Accelerated rule 1 with metering function meter (where 10*meter==-100+A) (after adding A<=B), yielding the new rule 3. 5.22/2.55 5.22/2.55 Accelerated rule 1 with backward acceleration, yielding the new rule 4. 5.22/2.55 5.22/2.55 Accelerated rule 2 with metering function meter_1 (where 11*meter_1==100-A), yielding the new rule 5. 5.22/2.55 5.22/2.55 During metering: Instantiating temporary variables by {meter==1} 5.22/2.55 5.22/2.55 Nested simple loops 2 (outer loop) and 3 (inner loop) with metering function 89+10*meter-A, resulting in the new rules: 6. 5.22/2.55 5.22/2.55 During metering: Instantiating temporary variables by {k==-1+B} 5.22/2.55 5.22/2.55 During metering: Instantiating temporary variables by {k==1} 5.22/2.55 5.22/2.55 Removing the simple loops: 1 2. 5.22/2.55 5.22/2.55 5.22/2.55 5.22/2.55 Accelerated all simple loops using metering functions (where possible): 5.22/2.55 5.22/2.55 Start location: f0 5.22/2.55 5.22/2.55 0: f0 -> f1 : A'=free, B'=1, [], cost: 1 5.22/2.55 5.22/2.55 3: f1 -> f1 : A'=-10*meter+A, B'=-meter+B, [ B>=1 && A>=101 && A<=B && 10*meter==-100+A && meter>=1 ], cost: meter 5.22/2.55 5.22/2.55 4: f1 -> f1 : A'=A-10*k, B'=-k+B, [ B>=1 && A>=101 && k>0 && 1-k+B>=1 && 10+A-10*k>=101 ], cost: k 5.22/2.55 5.22/2.55 5: f1 -> f1 : A'=11*meter_1+A, B'=meter_1+B, [ B>=1 && 100>=A && 11*meter_1==100-A && meter_1>=1 ], cost: meter_1 5.22/2.55 5.22/2.55 6: f1 -> f1 : A'=979-10*(89+10*meter-A)*meter+110*meter-10*A, B'=89-(89+10*meter-A)*meter+10*meter-A+B, [ B>=1 && 100>=A && 11+A>=101 && 11+A<=1+B && 10*meter==-89+A && meter>=1 && 89+10*meter-A>=1 ], cost: 89+(89+10*meter-A)*meter+10*meter-A 5.22/2.55 5.22/2.55 5.22/2.55 5.22/2.55 Chained accelerated rules (with incoming rules): 5.22/2.55 5.22/2.55 Start location: f0 5.22/2.55 5.22/2.55 0: f0 -> f1 : A'=free, B'=1, [], cost: 1 5.22/2.55 5.22/2.55 7: f0 -> f1 : A'=-10+free, B'=0, [ free>=101 ], cost: 2 popout

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all output return to Complexity_ITS 2019-03-21 04.46