Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313622

details

property	value
status	complete
benchmark	test77.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n151.star.cs.uiowa.edu
space	Strategy_removed_mixed_05

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	5.15819 seconds
cpu usage	15.543
user time	14.0811
system time	1.46189
max virtual memory	1.9134464E7
max residence set size	4139516.0

stage attributes

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

output

15.18/5.09	WORST_CASE(Omega(n^1), O(n^1))
15.18/5.11	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
15.18/5.11	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
15.18/5.11	
15.18/5.11	
15.18/5.11	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
15.18/5.11	
15.18/5.11	(0) CpxTRS
15.18/5.11	(1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
15.18/5.11	(2) CpxWeightedTrs
15.18/5.11	    (3) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
15.18/5.11	    (4) CpxWeightedTrs
15.18/5.11	    (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
15.18/5.11	    (6) CpxTypedWeightedTrs
15.18/5.11	    (7) CompletionProof [UPPER BOUND(ID), 0 ms]
15.18/5.11	    (8) CpxTypedWeightedCompleteTrs
15.18/5.11	    (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
15.18/5.11	    (10) CpxRNTS
15.18/5.11	    (11) CompleteCoflocoProof [FINISHED, 179 ms]
15.18/5.11	    (12) BOUNDS(1, n^1)
15.18/5.11	(13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
15.18/5.11	(14) TRS for Loop Detection
15.18/5.11	    (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
15.18/5.11	    (16) BEST
15.18/5.11	        (17) proven lower bound
15.18/5.11	            (18) LowerBoundPropagationProof [FINISHED, 0 ms]
15.18/5.11	            (19) BOUNDS(n^1, INF)
15.18/5.11	        (20) TRS for Loop Detection
15.18/5.11	
15.18/5.11	
15.18/5.11	----------------------------------------
15.18/5.11	
15.18/5.11	(0)
15.18/5.11	Obligation:
15.18/5.11	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
15.18/5.11	
15.18/5.11	
15.18/5.11	The TRS R consists of the following rules:
15.18/5.11	
15.18/5.11	   +(X, 0) -> X
15.18/5.11	   +(X, s(Y)) -> s(+(X, Y))
15.18/5.11	   double(X) -> +(X, X)
15.18/5.11	   f(0, s(0), X) -> f(X, double(X), X)
15.18/5.11	   g(X, Y) -> X
15.18/5.11	   g(X, Y) -> Y
15.18/5.11	
15.18/5.11	S is empty.
15.18/5.11	Rewrite Strategy: INNERMOST
15.18/5.11	----------------------------------------
15.18/5.11	
15.18/5.11	(1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
15.18/5.11	Transformed relative TRS to weighted TRS
15.18/5.11	----------------------------------------
15.18/5.11	
15.18/5.11	(2)
15.18/5.11	Obligation:
15.18/5.11	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).
15.18/5.11	
15.18/5.11	
15.18/5.11	The TRS R consists of the following rules:
15.18/5.11	
15.18/5.11	   +(X, 0) -> X [1]
15.18/5.11	   +(X, s(Y)) -> s(+(X, Y)) [1]
15.18/5.11	   double(X) -> +(X, X) [1]
15.18/5.11	   f(0, s(0), X) -> f(X, double(X), X) [1]
15.18/5.11	   g(X, Y) -> X [1]
15.18/5.11	   g(X, Y) -> Y [1]
15.18/5.11	
15.18/5.11	Rewrite Strategy: INNERMOST
15.18/5.11	----------------------------------------
15.18/5.11	
15.18/5.11	(3) CpxWeightedTrsRenamingProof (BOTH BOUNDS(ID, ID))
15.18/5.11	Renamed defined symbols to avoid conflicts with arithmetic symbols:
15.18/5.11	
15.18/5.11	+ => plus
15.18/5.11	
15.18/5.11	----------------------------------------
15.18/5.11	
15.18/5.11	(4)
15.18/5.11	Obligation:
15.18/5.11	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).
15.18/5.11	
15.18/5.11	
15.18/5.11	The TRS R consists of the following rules:
15.18/5.11	
15.18/5.11	   plus(X, 0) -> X [1]
15.18/5.11	   plus(X, s(Y)) -> s(plus(X, Y)) [1]
15.18/5.11	   double(X) -> plus(X, X) [1]
15.18/5.11	   f(0, s(0), X) -> f(X, double(X), X) [1]
15.18/5.11	   g(X, Y) -> X [1]
15.18/5.11	   g(X, Y) -> Y [1]
15.18/5.11	
15.18/5.11	Rewrite Strategy: INNERMOST
15.18/5.11	----------------------------------------
15.18/5.11	
15.18/5.11	(5) TypeInferenceProof (BOTH BOUNDS(ID, ID))
15.18/5.11	Infered types.
15.18/5.11	----------------------------------------
15.18/5.11	
15.18/5.11	(6)

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