Complexity_ITS 2019-03-21 04.46 pair #429990940

details

property	value
status	complete
benchmark	poly3.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n019.star.cs.uiowa.edu
space	VMCAI05

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	4.00563 seconds
cpu usage	6.37882
user time	5.91887
system time	0.459951
max virtual memory	1.870986E7
max residence set size	247252.0

stage attributes

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

output

6.23/3.97	WORST_CASE(Omega(n^1), ?)
6.23/3.98	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
6.23/3.98	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.23/3.98	
6.23/3.98	
6.23/3.98	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, INF).
6.23/3.98	
6.23/3.98	(0) CpxIntTrs
6.23/3.98	(1) Loat Proof [FINISHED, 323 ms]
6.23/3.98	(2) BOUNDS(n^1, INF)
6.23/3.98	
6.23/3.98	
6.23/3.98	----------------------------------------
6.23/3.98	
6.23/3.98	(0)
6.23/3.98	Obligation:
6.23/3.98	Complexity Int TRS consisting of the following rules:
6.23/3.98	eval(A, B, C) -> Com_1(eval(A - 1, B, C - 1)) :|: A >= 0 && B * B * B >= C
6.23/3.98	eval(A, B, C) -> Com_1(eval(A, B + C, C - 1)) :|: A >= 0 && B * B * B >= C
6.23/3.98	start(A, B, C) -> Com_1(eval(A, B, C)) :|: TRUE
6.23/3.98	
6.23/3.98	The start-symbols are:[start_3]
6.23/3.98	
6.23/3.98	
6.23/3.98	----------------------------------------
6.23/3.98	
6.23/3.98	(1) Loat Proof (FINISHED)
6.23/3.98	
6.23/3.98	
6.23/3.98	### Pre-processing the ITS problem ###
6.23/3.98	
6.23/3.98	
6.23/3.98	
6.23/3.98	Initial linear ITS problem
6.23/3.98	
6.23/3.98	   Start location: start
6.23/3.98	
6.23/3.98	      0: eval -> eval : A'=-1+A, C'=-1+C, [ A>=0 && B^3>=C ], cost: 1
6.23/3.98	
6.23/3.98	      1: eval -> eval : B'=C+B, C'=-1+C, [ A>=0 && B^3>=C ], cost: 1
6.23/3.98	
6.23/3.98	      2: start -> eval : [], cost: 1
6.23/3.98	
6.23/3.98	
6.23/3.98	
6.23/3.98	### Simplification by acceleration and chaining ###
6.23/3.98	
6.23/3.98	
6.23/3.98	
6.23/3.98	Accelerating simple loops of location 0.
6.23/3.98	
6.23/3.98	   Accelerating the following rules:
6.23/3.98	
6.23/3.98	      0: eval -> eval : A'=-1+A, C'=-1+C, [ A>=0 && B^3>=C ], cost: 1
6.23/3.98	
6.23/3.98	      1: eval -> eval : B'=C+B, C'=-1+C, [ A>=0 && B^3>=C ], cost: 1
6.23/3.98	
6.23/3.98	
6.23/3.98	
6.23/3.98	   Accelerated rule 0 with metering function 1+A, yielding the new rule 3.
6.23/3.98	
6.23/3.98	   Found no metering function for rule 1 (rule is too complicated).
6.23/3.98	
6.23/3.98	   Removing the simple loops: 0.
6.23/3.98	
6.23/3.98	
6.23/3.98	
6.23/3.98	Accelerated all simple loops using metering functions (where possible):
6.23/3.98	
6.23/3.98	   Start location: start
6.23/3.98	
6.23/3.98	      1: eval -> eval : B'=C+B, C'=-1+C, [ A>=0 && B^3>=C ], cost: 1
6.23/3.98	
6.23/3.98	      3: eval -> eval : A'=-1, C'=-1+C-A, [ A>=0 && B^3>=C ], cost: 1+A
6.23/3.98	
6.23/3.98	      2: start -> eval : [], cost: 1
6.23/3.98	
6.23/3.98	
6.23/3.98	
6.23/3.98	Chained accelerated rules (with incoming rules):
6.23/3.98	
6.23/3.98	   Start location: start
6.23/3.98	
6.23/3.98	      2: start -> eval : [], cost: 1
6.23/3.98	
6.23/3.98	      4: start -> eval : B'=C+B, C'=-1+C, [ A>=0 && B^3>=C ], cost: 2
6.23/3.98	
6.23/3.98	      5: start -> eval : A'=-1, C'=-1+C-A, [ A>=0 && B^3>=C ], cost: 2+A
6.23/3.98	
6.23/3.98	
6.23/3.98	
6.23/3.98	Removed unreachable locations (and leaf rules with constant cost):
6.23/3.98	
6.23/3.98	   Start location: start
6.23/3.98	
6.23/3.98	      5: start -> eval : A'=-1, C'=-1+C-A, [ A>=0 && B^3>=C ], cost: 2+A
6.23/3.98	
6.23/3.98	
6.23/3.98	
6.23/3.98	### Computing asymptotic complexity ###

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