Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307966

details

property	value
status	complete
benchmark	18.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n033.star.cs.uiowa.edu
space	Various_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	5.38306 seconds
cpu usage	17.6078
user time	16.5655
system time	1.04221
max virtual memory	1.8878116E7
max residence set size	2888336.0

stage attributes

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

output

17.34/5.32	WORST_CASE(Omega(n^1), O(n^1))
17.53/5.34	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
17.53/5.34	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
17.53/5.34	
17.53/5.34	
17.53/5.34	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
17.53/5.34	
17.53/5.34	(0) CpxTRS
17.53/5.34	(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms]
17.53/5.34	(2) CpxTRS
17.53/5.34	    (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
17.53/5.34	    (4) CpxTRS
17.53/5.34	    (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
17.53/5.34	    (6) CpxWeightedTrs
17.53/5.34	    (7) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
17.53/5.34	    (8) CpxWeightedTrs
17.53/5.34	    (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
17.53/5.34	    (10) CpxTypedWeightedTrs
17.53/5.34	    (11) CompletionProof [UPPER BOUND(ID), 0 ms]
17.53/5.34	    (12) CpxTypedWeightedCompleteTrs
17.53/5.34	    (13) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
17.53/5.34	    (14) CpxTypedWeightedCompleteTrs
17.53/5.34	    (15) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
17.53/5.34	    (16) CpxRNTS
17.53/5.34	    (17) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
17.53/5.34	    (18) CpxRNTS
17.53/5.34	    (19) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
17.53/5.34	    (20) CpxRNTS
17.53/5.34	    (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
17.53/5.34	    (22) CpxRNTS
17.53/5.34	    (23) IntTrsBoundProof [UPPER BOUND(ID), 240 ms]
17.53/5.34	    (24) CpxRNTS
17.53/5.34	    (25) IntTrsBoundProof [UPPER BOUND(ID), 86 ms]
17.53/5.34	    (26) CpxRNTS
17.53/5.34	    (27) FinalProof [FINISHED, 0 ms]
17.53/5.34	    (28) BOUNDS(1, n^1)
17.53/5.34	(29) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
17.53/5.34	(30) TRS for Loop Detection
17.53/5.34	    (31) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
17.53/5.34	    (32) BEST
17.53/5.34	        (33) proven lower bound
17.53/5.34	            (34) LowerBoundPropagationProof [FINISHED, 0 ms]
17.53/5.34	            (35) BOUNDS(n^1, INF)
17.53/5.34	        (36) TRS for Loop Detection
17.53/5.34	
17.53/5.34	
17.53/5.34	----------------------------------------
17.53/5.34	
17.53/5.34	(0)
17.53/5.34	Obligation:
17.53/5.34	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
17.53/5.34	
17.53/5.34	
17.53/5.34	The TRS R consists of the following rules:
17.53/5.34	
17.53/5.34	   +(*(x, y), *(x, z)) -> *(x, +(y, z))
17.53/5.34	   +(+(x, y), z) -> +(x, +(y, z))
17.53/5.34	   +(*(x, y), +(*(x, z), u)) -> +(*(x, +(y, z)), u)
17.53/5.34	
17.53/5.34	S is empty.
17.53/5.34	Rewrite Strategy: FULL
17.53/5.34	----------------------------------------
17.53/5.34	
17.53/5.34	(1) NestedDefinedSymbolProof (UPPER BOUND(ID))
17.53/5.34	The TRS does not nest defined symbols.
17.53/5.34	Hence, the left-hand sides of the following rules are not basic-reachable and can be removed:
17.53/5.34	+(+(x, y), z) -> +(x, +(y, z))
17.53/5.34	+(*(x, y), +(*(x, z), u)) -> +(*(x, +(y, z)), u)
17.53/5.34	
17.53/5.34	----------------------------------------
17.53/5.34	
17.53/5.34	(2)
17.53/5.34	Obligation:
17.53/5.34	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
17.53/5.34	
17.53/5.34	
17.53/5.34	The TRS R consists of the following rules:
17.53/5.34	
17.53/5.34	   +(*(x, y), *(x, z)) -> *(x, +(y, z))
17.53/5.34	
17.53/5.34	S is empty.
17.53/5.34	Rewrite Strategy: FULL
17.53/5.34	----------------------------------------
17.53/5.34	
17.53/5.34	(3) RcToIrcProof (BOTH BOUNDS(ID, ID))
17.53/5.34	Converted rc-obligation to irc-obligation.
17.53/5.34	
17.53/5.34	As the TRS does not nest defined symbols, we have rc = irc.
17.53/5.34	----------------------------------------
17.53/5.34	
17.53/5.34	(4)
17.53/5.34	Obligation:
17.53/5.34	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
17.53/5.34	
17.53/5.34	
17.53/5.34	The TRS R consists of the following rules:
17.53/5.34	
17.53/5.34	   +(*(x, y), *(x, z)) -> *(x, +(y, z))
17.53/5.34	
17.53/5.34	S is empty.

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