Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313920

details

property	value
status	complete
benchmark	gcdhard.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n057.star.cs.uiowa.edu
space	AProVE_09_Inductive

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	14.066 seconds
cpu usage	49.7799
user time	47.341
system time	2.43893
max virtual memory	5.5806188E7
max residence set size	4170980.0

stage attributes

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

output

49.43/14.02	WORST_CASE(Omega(n^1), O(n^1))
49.43/14.02	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
49.43/14.02	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
49.43/14.02	
49.43/14.02	
49.43/14.02	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
49.43/14.02	
49.43/14.02	(0) CpxTRS
49.43/14.02	(1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
49.43/14.02	(2) CpxWeightedTrs
49.43/14.02	    (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
49.43/14.02	    (4) CpxTypedWeightedTrs
49.43/14.02	    (5) CompletionProof [UPPER BOUND(ID), 0 ms]
49.43/14.02	    (6) CpxTypedWeightedCompleteTrs
49.43/14.02	    (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 3 ms]
49.43/14.02	    (8) CpxRNTS
49.43/14.02	    (9) CompleteCoflocoProof [FINISHED, 1332 ms]
49.43/14.02	    (10) BOUNDS(1, n^1)
49.43/14.02	(11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
49.43/14.02	(12) TRS for Loop Detection
49.43/14.02	    (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
49.43/14.02	    (14) BEST
49.43/14.02	        (15) proven lower bound
49.43/14.02	            (16) LowerBoundPropagationProof [FINISHED, 0 ms]
49.43/14.02	            (17) BOUNDS(n^1, INF)
49.43/14.02	        (18) TRS for Loop Detection
49.43/14.02	
49.43/14.02	
49.43/14.02	----------------------------------------
49.43/14.03	
49.43/14.03	(0)
49.43/14.03	Obligation:
49.43/14.03	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
49.43/14.03	
49.43/14.03	
49.43/14.03	The TRS R consists of the following rules:
49.43/14.03	
49.43/14.03	   minus(0, x) -> 0
49.43/14.03	   minus(s(x), 0) -> s(x)
49.43/14.03	   minus(s(x), s(y)) -> minus(x, y)
49.43/14.03	   mod(x, 0) -> 0
49.43/14.03	   mod(x, s(y)) -> if(lt(x, s(y)), x, s(y))
49.43/14.03	   if(true, x, y) -> x
49.43/14.03	   if(false, x, y) -> mod(minus(x, y), y)
49.43/14.03	   gcd(x, 0) -> x
49.43/14.03	   gcd(0, s(y)) -> s(y)
49.43/14.03	   gcd(s(x), s(y)) -> gcd(mod(s(x), s(y)), mod(s(y), s(x)))
49.43/14.03	   lt(x, 0) -> false
49.43/14.03	   lt(0, s(x)) -> true
49.43/14.03	   lt(s(x), s(y)) -> lt(x, y)
49.43/14.03	
49.43/14.03	S is empty.
49.43/14.03	Rewrite Strategy: INNERMOST
49.43/14.03	----------------------------------------
49.43/14.03	
49.43/14.03	(1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
49.43/14.03	Transformed relative TRS to weighted TRS
49.43/14.03	----------------------------------------
49.43/14.03	
49.43/14.03	(2)
49.43/14.03	Obligation:
49.43/14.03	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).
49.43/14.03	
49.43/14.03	
49.43/14.03	The TRS R consists of the following rules:
49.43/14.03	
49.43/14.03	   minus(0, x) -> 0 [1]
49.43/14.03	   minus(s(x), 0) -> s(x) [1]
49.43/14.03	   minus(s(x), s(y)) -> minus(x, y) [1]
49.43/14.03	   mod(x, 0) -> 0 [1]
49.43/14.03	   mod(x, s(y)) -> if(lt(x, s(y)), x, s(y)) [1]
49.43/14.03	   if(true, x, y) -> x [1]
49.43/14.03	   if(false, x, y) -> mod(minus(x, y), y) [1]
49.43/14.03	   gcd(x, 0) -> x [1]
49.43/14.03	   gcd(0, s(y)) -> s(y) [1]
49.43/14.03	   gcd(s(x), s(y)) -> gcd(mod(s(x), s(y)), mod(s(y), s(x))) [1]
49.43/14.03	   lt(x, 0) -> false [1]
49.43/14.03	   lt(0, s(x)) -> true [1]
49.43/14.03	   lt(s(x), s(y)) -> lt(x, y) [1]
49.43/14.03	
49.43/14.03	Rewrite Strategy: INNERMOST
49.43/14.03	----------------------------------------
49.43/14.03	
49.43/14.03	(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
49.43/14.03	Infered types.
49.43/14.03	----------------------------------------
49.43/14.03	
49.43/14.03	(4)
49.43/14.03	Obligation:
49.43/14.03	Runtime Complexity Weighted TRS with Types.
49.43/14.03	The TRS R consists of the following rules:
49.43/14.03	
49.43/14.03	   minus(0, x) -> 0 [1]
49.43/14.03	   minus(s(x), 0) -> s(x) [1]
49.43/14.03	   minus(s(x), s(y)) -> minus(x, y) [1]
49.43/14.03	   mod(x, 0) -> 0 [1]
49.43/14.03	   mod(x, s(y)) -> if(lt(x, s(y)), x, s(y)) [1]
49.43/14.03	   if(true, x, y) -> x [1]
49.43/14.03	   if(false, x, y) -> mod(minus(x, y), y) [1]
49.43/14.03	   gcd(x, 0) -> x [1]

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actions all output return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40