Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307837

details

property	value
status	complete
benchmark	bn122.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n136.star.cs.uiowa.edu
space	Rubio_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	5.44444 seconds
cpu usage	16.447
user time	15.3567
system time	1.09033
max virtual memory	1.8942632E7
max residence set size	3356480.0

stage attributes

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

output

16.36/5.40	WORST_CASE(Omega(n^1), O(n^1))
16.36/5.41	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
16.36/5.41	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
16.36/5.41	
16.36/5.41	
16.36/5.41	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
16.36/5.41	
16.36/5.41	(0) CpxTRS
16.36/5.41	(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms]
16.36/5.41	(2) CpxTRS
16.36/5.41	    (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
16.36/5.41	    (4) CpxTRS
16.36/5.41	    (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
16.36/5.41	    (6) CpxWeightedTrs
16.36/5.41	    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
16.36/5.41	    (8) CpxTypedWeightedTrs
16.36/5.41	    (9) CompletionProof [UPPER BOUND(ID), 0 ms]
16.36/5.41	    (10) CpxTypedWeightedCompleteTrs
16.36/5.41	    (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
16.36/5.41	    (12) CpxTypedWeightedCompleteTrs
16.36/5.41	    (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
16.36/5.41	    (14) CpxRNTS
16.36/5.41	    (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
16.36/5.41	    (16) CpxRNTS
16.36/5.41	    (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
16.36/5.41	    (18) CpxRNTS
16.36/5.41	    (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
16.36/5.41	    (20) CpxRNTS
16.36/5.41	    (21) IntTrsBoundProof [UPPER BOUND(ID), 209 ms]
16.36/5.41	    (22) CpxRNTS
16.36/5.41	    (23) IntTrsBoundProof [UPPER BOUND(ID), 65 ms]
16.36/5.41	    (24) CpxRNTS
16.36/5.41	    (25) FinalProof [FINISHED, 0 ms]
16.36/5.41	    (26) BOUNDS(1, n^1)
16.36/5.41	(27) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
16.36/5.41	(28) TRS for Loop Detection
16.36/5.41	    (29) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
16.36/5.41	    (30) BEST
16.36/5.41	        (31) proven lower bound
16.36/5.41	            (32) LowerBoundPropagationProof [FINISHED, 0 ms]
16.36/5.41	            (33) BOUNDS(n^1, INF)
16.36/5.41	        (34) TRS for Loop Detection
16.36/5.41	
16.36/5.41	
16.36/5.41	----------------------------------------
16.36/5.41	
16.36/5.41	(0)
16.36/5.41	Obligation:
16.36/5.41	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
16.36/5.41	
16.36/5.41	
16.36/5.41	The TRS R consists of the following rules:
16.36/5.41	
16.36/5.41	   plus(plus(X, Y), Z) -> plus(X, plus(Y, Z))
16.36/5.41	   times(X, s(Y)) -> plus(X, times(Y, X))
16.36/5.41	
16.36/5.41	S is empty.
16.36/5.41	Rewrite Strategy: FULL
16.36/5.41	----------------------------------------
16.36/5.41	
16.36/5.41	(1) NestedDefinedSymbolProof (UPPER BOUND(ID))
16.36/5.41	The following defined symbols can occur below the 1th argument of plus: times
16.36/5.41	
16.36/5.41	Hence, the left-hand sides of the following rules are not basic-reachable and can be removed:
16.36/5.41	plus(plus(X, Y), Z) -> plus(X, plus(Y, Z))
16.36/5.41	
16.36/5.41	----------------------------------------
16.36/5.41	
16.36/5.41	(2)
16.36/5.41	Obligation:
16.36/5.41	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
16.36/5.41	
16.36/5.41	
16.36/5.41	The TRS R consists of the following rules:
16.36/5.41	
16.36/5.41	   times(X, s(Y)) -> plus(X, times(Y, X))
16.36/5.41	
16.36/5.41	S is empty.
16.36/5.41	Rewrite Strategy: FULL
16.36/5.41	----------------------------------------
16.36/5.41	
16.36/5.41	(3) RcToIrcProof (BOTH BOUNDS(ID, ID))
16.36/5.41	Converted rc-obligation to irc-obligation.
16.36/5.41	
16.36/5.41	As the TRS does not nest defined symbols, we have rc = irc.
16.36/5.41	----------------------------------------
16.36/5.41	
16.36/5.41	(4)
16.36/5.41	Obligation:
16.36/5.41	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
16.36/5.41	
16.36/5.41	
16.36/5.41	The TRS R consists of the following rules:
16.36/5.41	
16.36/5.41	   times(X, s(Y)) -> plus(X, times(Y, X))
16.36/5.41	
16.36/5.41	S is empty.
16.36/5.41	Rewrite Strategy: INNERMOST
16.36/5.41	----------------------------------------
16.36/5.41

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