Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308346

details

property	value
status	complete
benchmark	Ex2_Luc03b_Z.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	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	12.9381 seconds
cpu usage	33.4571
user time	30.8944
system time	2.56272
max virtual memory	3.8368264E7
max residence set size	3917792.0

stage attributes

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

output

33.29/12.88	WORST_CASE(Omega(n^1), O(n^1))
33.29/12.89	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
33.29/12.89	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
33.29/12.89	
33.29/12.89	
33.29/12.89	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
33.29/12.89	
33.29/12.89	(0) CpxTRS
33.29/12.89	(1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
33.29/12.89	(2) CpxTRS
33.29/12.89	    (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
33.29/12.89	    (4) CpxWeightedTrs
33.29/12.89	    (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
33.29/12.89	    (6) CpxTypedWeightedTrs
33.29/12.89	    (7) CompletionProof [UPPER BOUND(ID), 0 ms]
33.29/12.89	    (8) CpxTypedWeightedCompleteTrs
33.29/12.89	    (9) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
33.29/12.89	    (10) CpxTypedWeightedCompleteTrs
33.29/12.89	    (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
33.29/12.89	    (12) CpxRNTS
33.29/12.89	    (13) InliningProof [UPPER BOUND(ID), 76 ms]
33.29/12.89	    (14) CpxRNTS
33.29/12.89	    (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
33.29/12.89	    (16) CpxRNTS
33.29/12.89	    (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
33.29/12.89	    (18) CpxRNTS
33.29/12.89	    (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
33.29/12.89	    (20) CpxRNTS
33.29/12.89	    (21) IntTrsBoundProof [UPPER BOUND(ID), 264 ms]
33.29/12.89	    (22) CpxRNTS
33.29/12.89	    (23) IntTrsBoundProof [UPPER BOUND(ID), 45 ms]
33.29/12.89	    (24) CpxRNTS
33.29/12.89	    (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
33.29/12.89	    (26) CpxRNTS
33.29/12.89	    (27) IntTrsBoundProof [UPPER BOUND(ID), 5257 ms]
33.29/12.89	    (28) CpxRNTS
33.29/12.89	    (29) IntTrsBoundProof [UPPER BOUND(ID), 518 ms]
33.29/12.89	    (30) CpxRNTS
33.29/12.89	    (31) FinalProof [FINISHED, 0 ms]
33.29/12.89	    (32) BOUNDS(1, n^1)
33.29/12.89	(33) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
33.29/12.89	(34) TRS for Loop Detection
33.29/12.89	    (35) DecreasingLoopProof [LOWER BOUND(ID), 38 ms]
33.29/12.89	    (36) BEST
33.29/12.89	        (37) proven lower bound
33.29/12.89	            (38) LowerBoundPropagationProof [FINISHED, 0 ms]
33.29/12.89	            (39) BOUNDS(n^1, INF)
33.29/12.89	        (40) TRS for Loop Detection
33.29/12.89	
33.29/12.89	
33.29/12.89	----------------------------------------
33.29/12.89	
33.29/12.89	(0)
33.29/12.89	Obligation:
33.29/12.89	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
33.29/12.89	
33.29/12.89	
33.29/12.89	The TRS R consists of the following rules:
33.29/12.89	
33.29/12.89	   fst(0, Z) -> nil
33.29/12.89	   fst(s(X), cons(Y, Z)) -> cons(Y, n__fst(activate(X), activate(Z)))
33.29/12.89	   from(X) -> cons(X, n__from(s(X)))
33.29/12.89	   add(0, X) -> X
33.29/12.89	   add(s(X), Y) -> s(n__add(activate(X), Y))
33.29/12.89	   len(nil) -> 0
33.29/12.89	   len(cons(X, Z)) -> s(n__len(activate(Z)))
33.29/12.89	   fst(X1, X2) -> n__fst(X1, X2)
33.29/12.89	   from(X) -> n__from(X)
33.29/12.89	   add(X1, X2) -> n__add(X1, X2)
33.29/12.89	   len(X) -> n__len(X)
33.29/12.89	   activate(n__fst(X1, X2)) -> fst(X1, X2)
33.29/12.89	   activate(n__from(X)) -> from(X)
33.29/12.89	   activate(n__add(X1, X2)) -> add(X1, X2)
33.29/12.89	   activate(n__len(X)) -> len(X)
33.29/12.89	   activate(X) -> X
33.29/12.89	
33.29/12.89	S is empty.
33.29/12.89	Rewrite Strategy: FULL
33.29/12.89	----------------------------------------
33.29/12.89	
33.29/12.89	(1) RcToIrcProof (BOTH BOUNDS(ID, ID))
33.29/12.89	Converted rc-obligation to irc-obligation.
33.29/12.89	
33.29/12.89	As the TRS does not nest defined symbols, we have rc = irc.
33.29/12.89	----------------------------------------
33.29/12.89	
33.29/12.89	(2)
33.29/12.89	Obligation:
33.29/12.89	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
33.29/12.89	
33.29/12.89	
33.29/12.89	The TRS R consists of the following rules:
33.29/12.89	
33.29/12.89	   fst(0, Z) -> nil
33.29/12.89	   fst(s(X), cons(Y, Z)) -> cons(Y, n__fst(activate(X), activate(Z)))
33.29/12.89	   from(X) -> cons(X, n__from(s(X)))
33.29/12.89	   add(0, X) -> X
33.29/12.89	   add(s(X), Y) -> s(n__add(activate(X), Y))
33.29/12.89	   len(nil) -> 0
33.29/12.89	   len(cons(X, Z)) -> s(n__len(activate(Z)))

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