Complexity_ITS 2019-03-21 04.46 pair #429989772

details

property	value
status	complete
benchmark	a.02.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n152.star.cs.uiowa.edu
space	pasta

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	8.43928 seconds
cpu usage	22.8312
user time	22.0509
system time	0.780338
max virtual memory	1.8559656E7
max residence set size	220060.0

stage attributes

key	value
starexec-result	MAYBE

output

11.33/8.39	MAYBE
11.33/8.40	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
11.33/8.40	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
11.33/8.40	
11.33/8.40	
11.33/8.40	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF).
11.33/8.40	
11.33/8.40	(0) CpxIntTrs
11.33/8.40	(1) Loat Proof [FINISHED, 487 ms]
11.33/8.40	(2) BOUNDS(1, INF)
11.33/8.40	
11.33/8.40	
11.33/8.40	----------------------------------------
11.33/8.40	
11.33/8.40	(0)
11.33/8.40	Obligation:
11.33/8.40	Complexity Int TRS consisting of the following rules:
11.33/8.40	eval(A, B) -> Com_1(eval(D, B)) :|: A >= 0 && B >= 0 && B >= A + 1 && A + B >= 2 * C && 3 * C >= A + B + 1 && D >= C + 1 && A + B >= 2 * E && 3 * E >= A + B + 1 && E + 1 >= D
11.33/8.40	eval(A, B) -> Com_1(eval(A, D)) :|: A >= 0 && B >= 0 && B >= A + 1 && A + B >= 2 * C && 3 * C >= A + B + 1 && D >= C && A + B >= 2 * E && 3 * E >= A + B + 1 && E >= D
11.33/8.40	start(A, B) -> Com_1(eval(A, B)) :|: TRUE
11.33/8.40	
11.33/8.40	The start-symbols are:[start_2]
11.33/8.40	
11.33/8.40	
11.33/8.40	----------------------------------------
11.33/8.40	
11.33/8.40	(1) Loat Proof (FINISHED)
11.33/8.40	
11.33/8.40	
11.33/8.40	### Pre-processing the ITS problem ###
11.33/8.40	
11.33/8.40	
11.33/8.40	
11.33/8.40	Initial linear ITS problem
11.33/8.40	
11.33/8.40	   Start location: start
11.33/8.40	
11.33/8.40	      0: eval -> eval : A'=free_1, [ A>=0 && B>=0 && B>=1+A && A+B>=2*free && 3*free>=1+A+B && free_1>=1+free && A+B>=2*free_2 && 3*free_2>=1+A+B && 1+free_2>=free_1 ], cost: 1
11.33/8.40	
11.33/8.40	      1: eval -> eval : B'=free_4, [ A>=0 && B>=0 && B>=1+A && A+B>=2*free_3 && 3*free_3>=1+A+B && free_4>=free_3 && A+B>=2*free_5 && 3*free_5>=1+A+B && free_5>=free_4 ], cost: 1
11.33/8.40	
11.33/8.40	      2: start -> eval : [], cost: 1
11.33/8.40	
11.33/8.40	
11.33/8.40	
11.33/8.40	Simplified all rules, resulting in:
11.33/8.40	
11.33/8.40	   Start location: start
11.33/8.40	
11.33/8.40	      0: eval -> eval : A'=free_1, [ A>=0 && B>=1+A && 3*free>=1+A+B && free_1>=1+free && A+B>=2*free_2 && 3*free_2>=1+A+B && 1+free_2>=free_1 ], cost: 1
11.33/8.40	
11.33/8.40	      1: eval -> eval : B'=free_4, [ A>=0 && B>=1+A && 3*free_3>=1+A+B && free_4>=free_3 && A+B>=2*free_5 && 3*free_5>=1+A+B && free_5>=free_4 ], cost: 1
11.33/8.40	
11.33/8.40	      2: start -> eval : [], cost: 1
11.33/8.40	
11.33/8.40	
11.33/8.40	
11.33/8.40	### Simplification by acceleration and chaining ###
11.33/8.40	
11.33/8.40	
11.33/8.40	
11.33/8.40	Accelerating simple loops of location 0.
11.33/8.40	
11.33/8.40	   Accelerating the following rules:
11.33/8.40	
11.33/8.40	      0: eval -> eval : A'=free_1, [ A>=0 && B>=1+A && 3*free>=1+A+B && free_1>=1+free && A+B>=2*free_2 && 3*free_2>=1+A+B && 1+free_2>=free_1 ], cost: 1
11.33/8.40	
11.33/8.40	      1: eval -> eval : B'=free_4, [ A>=0 && B>=1+A && 3*free_3>=1+A+B && free_4>=free_3 && A+B>=2*free_5 && 3*free_5>=1+A+B && free_5>=free_4 ], cost: 1
11.33/8.40	
11.33/8.40	
11.33/8.40	
11.33/8.40	      During metering: Instantiating temporary variables by {free==-1+free_1,free_1==1+free_2,free_2==-1+free_1}
11.33/8.40	
11.33/8.40	   Accelerated rule 0 with metering function -1+free_1-free_2, yielding the new rule 3.
11.33/8.40	
11.33/8.40	      During metering: Instantiating temporary variables by {free_3==free_4,free_4==free_3,free_5==free_4}
11.33/8.40	
11.33/8.40	   Accelerated rule 1 with metering function free_3-free_4, yielding the new rule 4.
11.33/8.40	
11.33/8.40	   Removing the simple loops: 0 1.
11.33/8.40	
11.33/8.40	
11.33/8.40	
11.33/8.40	Accelerated all simple loops using metering functions (where possible):
11.33/8.40	
11.33/8.40	   Start location: start
11.33/8.40	
11.33/8.40	      3: eval -> eval : A'=1+free_2, [ A>=0 && B>=1+A && -3+3*free_1>=1+A+B && 1+free_2>=free_1 && A+B>=-2+2*free_1 && -1+free_1-free_2>=1 ], cost: -1+free_1-free_2
11.33/8.40	
11.33/8.40	      4: eval -> eval : B'=free_3, [ A>=0 && B>=1+A && 3*free_4>=1+A+B && A+B>=2*free_4 && free_4>=free_3 && free_3-free_4>=1 ], cost: free_3-free_4
11.33/8.40	
11.33/8.40	      2: start -> eval : [], cost: 1
11.33/8.40	
11.33/8.40	
11.33/8.40	
11.33/8.40	Chained accelerated rules (with incoming rules):
11.33/8.40	
11.33/8.40	   Start location: start
11.33/8.40	
11.33/8.40	      2: start -> eval : [], cost: 1

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