Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313288

details

property	value
status	complete
benchmark	prov.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n078.star.cs.uiowa.edu
space	Rubio_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	4.72365 seconds
cpu usage	12.1488
user time	11.1524
system time	0.996401
max virtual memory	1.8478756E7
max residence set size	3370664.0

stage attributes

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

output

11.97/4.65	WORST_CASE(Omega(n^1), O(n^1))
11.97/4.67	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
11.97/4.67	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
11.97/4.67	
11.97/4.67	
11.97/4.67	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
11.97/4.67	
11.97/4.67	(0) CpxTRS
11.97/4.67	(1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
11.97/4.67	(2) CpxWeightedTrs
11.97/4.67	    (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
11.97/4.67	    (4) CpxTypedWeightedTrs
11.97/4.67	    (5) CompletionProof [UPPER BOUND(ID), 0 ms]
11.97/4.67	    (6) CpxTypedWeightedCompleteTrs
11.97/4.67	    (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
11.97/4.67	    (8) CpxRNTS
11.97/4.67	    (9) CompleteCoflocoProof [FINISHED, 40 ms]
11.97/4.67	    (10) BOUNDS(1, n^1)
11.97/4.67	(11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
11.97/4.67	(12) TRS for Loop Detection
11.97/4.67	    (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
11.97/4.67	    (14) BEST
11.97/4.67	        (15) proven lower bound
11.97/4.67	            (16) LowerBoundPropagationProof [FINISHED, 0 ms]
11.97/4.67	            (17) BOUNDS(n^1, INF)
11.97/4.67	        (18) TRS for Loop Detection
11.97/4.67	
11.97/4.67	
11.97/4.67	----------------------------------------
11.97/4.67	
11.97/4.67	(0)
11.97/4.67	Obligation:
11.97/4.67	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
11.97/4.67	
11.97/4.67	
11.97/4.67	The TRS R consists of the following rules:
11.97/4.67	
11.97/4.67	   ackin(s(X), s(Y)) -> u21(ackin(s(X), Y), X)
11.97/4.67	   u21(ackout(X), Y) -> u22(ackin(Y, X))
11.97/4.67	
11.97/4.67	S is empty.
11.97/4.67	Rewrite Strategy: INNERMOST
11.97/4.67	----------------------------------------
11.97/4.67	
11.97/4.67	(1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
11.97/4.67	Transformed relative TRS to weighted TRS
11.97/4.67	----------------------------------------
11.97/4.67	
11.97/4.67	(2)
11.97/4.67	Obligation:
11.97/4.67	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).
11.97/4.67	
11.97/4.67	
11.97/4.67	The TRS R consists of the following rules:
11.97/4.67	
11.97/4.67	   ackin(s(X), s(Y)) -> u21(ackin(s(X), Y), X) [1]
11.97/4.67	   u21(ackout(X), Y) -> u22(ackin(Y, X)) [1]
11.97/4.67	
11.97/4.67	Rewrite Strategy: INNERMOST
11.97/4.67	----------------------------------------
11.97/4.67	
11.97/4.67	(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
11.97/4.67	Infered types.
11.97/4.67	----------------------------------------
11.97/4.67	
11.97/4.67	(4)
11.97/4.67	Obligation:
11.97/4.67	Runtime Complexity Weighted TRS with Types.
11.97/4.67	The TRS R consists of the following rules:
11.97/4.67	
11.97/4.67	   ackin(s(X), s(Y)) -> u21(ackin(s(X), Y), X) [1]
11.97/4.67	   u21(ackout(X), Y) -> u22(ackin(Y, X)) [1]
11.97/4.67	
11.97/4.67	The TRS has the following type information:
11.97/4.67	ackin :: s -> s -> ackout:u22
11.97/4.67	s :: s -> s
11.97/4.67	u21 :: ackout:u22 -> s -> ackout:u22
11.97/4.67	ackout :: s -> ackout:u22
11.97/4.67	u22 :: ackout:u22 -> ackout:u22
11.97/4.67	
11.97/4.67	Rewrite Strategy: INNERMOST
11.97/4.67	----------------------------------------
11.97/4.67	
11.97/4.67	(5) CompletionProof (UPPER BOUND(ID))
11.97/4.67	The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added:
11.97/4.67	
11.97/4.67	   ackin(v0, v1) -> null_ackin [0]
11.97/4.67	   u21(v0, v1) -> null_u21 [0]
11.97/4.67	
11.97/4.67	And the following fresh constants:    null_ackin, null_u21, const
11.97/4.67	
11.97/4.67	----------------------------------------
11.97/4.67	
11.97/4.67	(6)
11.97/4.67	Obligation:
11.97/4.67	Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is:
11.97/4.67	
11.97/4.67	Runtime Complexity Weighted TRS with Types.
11.97/4.67	The TRS R consists of the following rules:
11.97/4.67

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