Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313295

details

property	value
status	complete
benchmark	polo2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n106.star.cs.uiowa.edu
space	Rubio_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	5.05416 seconds
cpu usage	16.1001
user time	15.1301
system time	0.969991
max virtual memory	1.900464E7
max residence set size	3397440.0

stage attributes

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

output

15.71/4.95	WORST_CASE(Omega(n^1), O(n^1))
15.71/4.96	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
15.71/4.96	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
15.71/4.96	
15.71/4.96	
15.71/4.96	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
15.71/4.96	
15.71/4.96	(0) CpxTRS
15.71/4.96	(1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
15.71/4.96	(2) CpxWeightedTrs
15.71/4.96	    (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
15.71/4.96	    (4) CpxTypedWeightedTrs
15.71/4.96	    (5) CompletionProof [UPPER BOUND(ID), 0 ms]
15.71/4.96	    (6) CpxTypedWeightedCompleteTrs
15.71/4.96	    (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
15.71/4.96	    (8) CpxRNTS
15.71/4.96	    (9) CompleteCoflocoProof [FINISHED, 255 ms]
15.71/4.96	    (10) BOUNDS(1, n^1)
15.71/4.96	(11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
15.71/4.96	(12) TRS for Loop Detection
15.71/4.96	    (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
15.71/4.96	    (14) BEST
15.71/4.96	        (15) proven lower bound
15.71/4.96	            (16) LowerBoundPropagationProof [FINISHED, 0 ms]
15.71/4.96	            (17) BOUNDS(n^1, INF)
15.71/4.96	        (18) TRS for Loop Detection
15.71/4.96	
15.71/4.96	
15.71/4.96	----------------------------------------
15.71/4.96	
15.71/4.96	(0)
15.71/4.96	Obligation:
15.71/4.96	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
15.71/4.96	
15.71/4.96	
15.71/4.96	The TRS R consists of the following rules:
15.71/4.96	
15.71/4.96	   dx(X) -> one
15.71/4.96	   dx(a) -> zero
15.71/4.96	   dx(plus(ALPHA, BETA)) -> plus(dx(ALPHA), dx(BETA))
15.71/4.96	   dx(times(ALPHA, BETA)) -> plus(times(BETA, dx(ALPHA)), times(ALPHA, dx(BETA)))
15.71/4.96	   dx(minus(ALPHA, BETA)) -> minus(dx(ALPHA), dx(BETA))
15.71/4.96	   dx(neg(ALPHA)) -> neg(dx(ALPHA))
15.71/4.96	   dx(div(ALPHA, BETA)) -> minus(div(dx(ALPHA), BETA), times(ALPHA, div(dx(BETA), exp(BETA, two))))
15.71/4.96	   dx(ln(ALPHA)) -> div(dx(ALPHA), ALPHA)
15.71/4.96	   dx(exp(ALPHA, BETA)) -> plus(times(BETA, times(exp(ALPHA, minus(BETA, one)), dx(ALPHA))), times(exp(ALPHA, BETA), times(ln(ALPHA), dx(BETA))))
15.71/4.96	
15.71/4.96	S is empty.
15.71/4.96	Rewrite Strategy: INNERMOST
15.71/4.96	----------------------------------------
15.71/4.96	
15.71/4.96	(1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
15.71/4.96	Transformed relative TRS to weighted TRS
15.71/4.96	----------------------------------------
15.71/4.96	
15.71/4.96	(2)
15.71/4.96	Obligation:
15.71/4.96	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).
15.71/4.96	
15.71/4.96	
15.71/4.96	The TRS R consists of the following rules:
15.71/4.96	
15.71/4.96	   dx(X) -> one [1]
15.71/4.96	   dx(a) -> zero [1]
15.71/4.96	   dx(plus(ALPHA, BETA)) -> plus(dx(ALPHA), dx(BETA)) [1]
15.71/4.96	   dx(times(ALPHA, BETA)) -> plus(times(BETA, dx(ALPHA)), times(ALPHA, dx(BETA))) [1]
15.71/4.96	   dx(minus(ALPHA, BETA)) -> minus(dx(ALPHA), dx(BETA)) [1]
15.71/4.96	   dx(neg(ALPHA)) -> neg(dx(ALPHA)) [1]
15.71/4.96	   dx(div(ALPHA, BETA)) -> minus(div(dx(ALPHA), BETA), times(ALPHA, div(dx(BETA), exp(BETA, two)))) [1]
15.71/4.96	   dx(ln(ALPHA)) -> div(dx(ALPHA), ALPHA) [1]
15.71/4.96	   dx(exp(ALPHA, BETA)) -> plus(times(BETA, times(exp(ALPHA, minus(BETA, one)), dx(ALPHA))), times(exp(ALPHA, BETA), times(ln(ALPHA), dx(BETA)))) [1]
15.71/4.96	
15.71/4.96	Rewrite Strategy: INNERMOST
15.71/4.96	----------------------------------------
15.71/4.96	
15.71/4.96	(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
15.71/4.96	Infered types.
15.71/4.96	----------------------------------------
15.71/4.96	
15.71/4.96	(4)
15.71/4.96	Obligation:
15.71/4.96	Runtime Complexity Weighted TRS with Types.
15.71/4.96	The TRS R consists of the following rules:
15.71/4.96	
15.71/4.96	   dx(X) -> one [1]
15.71/4.96	   dx(a) -> zero [1]
15.71/4.96	   dx(plus(ALPHA, BETA)) -> plus(dx(ALPHA), dx(BETA)) [1]
15.71/4.96	   dx(times(ALPHA, BETA)) -> plus(times(BETA, dx(ALPHA)), times(ALPHA, dx(BETA))) [1]
15.71/4.96	   dx(minus(ALPHA, BETA)) -> minus(dx(ALPHA), dx(BETA)) [1]
15.71/4.96	   dx(neg(ALPHA)) -> neg(dx(ALPHA)) [1]
15.71/4.96	   dx(div(ALPHA, BETA)) -> minus(div(dx(ALPHA), BETA), times(ALPHA, div(dx(BETA), exp(BETA, two)))) [1]
15.71/4.96	   dx(ln(ALPHA)) -> div(dx(ALPHA), ALPHA) [1]
15.71/4.96	   dx(exp(ALPHA, BETA)) -> plus(times(BETA, times(exp(ALPHA, minus(BETA, one)), dx(ALPHA))), times(exp(ALPHA, BETA), times(ln(ALPHA), dx(BETA)))) [1]
15.71/4.96	
15.71/4.96	The TRS has the following type information:
15.71/4.96	dx :: one:a:zero:plus:times:minus:neg:div:two:exp:ln -> one:a:zero:plus:times:minus:neg:div:two:exp:ln
15.71/4.96	one :: one:a:zero:plus:times:minus:neg:div:two:exp:ln
15.71/4.96	a :: one:a:zero:plus:times:minus:neg:div:two:exp:ln
15.71/4.96	zero :: one:a:zero:plus:times:minus:neg:div:two:exp:ln
15.71/4.96	plus :: one:a:zero:plus:times:minus:neg:div:two:exp:ln -> one:a:zero:plus:times:minus:neg:div:two:exp:ln -> one:a:zero:plus:times:minus:neg:div:two:exp:ln

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