Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307628

details

property	value
status	complete
benchmark	append.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n125.star.cs.uiowa.edu
space	CiME_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	8.25333 seconds
cpu usage	20.469
user time	18.9519
system time	1.51713
max virtual memory	1.9075044E7
max residence set size	3529348.0

stage attributes

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

output

20.19/8.18	WORST_CASE(Omega(n^1), O(n^1))
20.36/8.20	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
20.36/8.20	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
20.36/8.20	
20.36/8.20	
20.36/8.20	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
20.36/8.20	
20.36/8.20	(0) CpxTRS
20.36/8.20	(1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
20.36/8.20	(2) CpxTRS
20.36/8.20	    (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
20.36/8.20	    (4) CpxWeightedTrs
20.36/8.20	    (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
20.36/8.20	    (6) CpxTypedWeightedTrs
20.36/8.20	    (7) CompletionProof [UPPER BOUND(ID), 0 ms]
20.36/8.20	    (8) CpxTypedWeightedCompleteTrs
20.36/8.20	    (9) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
20.36/8.20	    (10) CpxTypedWeightedCompleteTrs
20.36/8.20	    (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
20.36/8.20	    (12) CpxRNTS
20.36/8.20	    (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
20.36/8.20	    (14) CpxRNTS
20.36/8.20	    (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
20.36/8.20	    (16) CpxRNTS
20.36/8.20	    (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
20.36/8.20	    (18) CpxRNTS
20.36/8.20	    (19) IntTrsBoundProof [UPPER BOUND(ID), 157 ms]
20.36/8.20	    (20) CpxRNTS
20.36/8.20	    (21) IntTrsBoundProof [UPPER BOUND(ID), 55 ms]
20.36/8.20	    (22) CpxRNTS
20.36/8.20	    (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
20.36/8.20	    (24) CpxRNTS
20.36/8.20	    (25) IntTrsBoundProof [UPPER BOUND(ID), 653 ms]
20.36/8.20	    (26) CpxRNTS
20.36/8.20	    (27) IntTrsBoundProof [UPPER BOUND(ID), 181 ms]
20.36/8.20	    (28) CpxRNTS
20.36/8.20	    (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
20.36/8.20	    (30) CpxRNTS
20.36/8.20	    (31) IntTrsBoundProof [UPPER BOUND(ID), 147 ms]
20.36/8.20	    (32) CpxRNTS
20.36/8.20	    (33) IntTrsBoundProof [UPPER BOUND(ID), 42 ms]
20.36/8.20	    (34) CpxRNTS
20.36/8.20	    (35) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
20.36/8.20	    (36) CpxRNTS
20.36/8.20	    (37) IntTrsBoundProof [UPPER BOUND(ID), 127 ms]
20.36/8.20	    (38) CpxRNTS
20.36/8.20	    (39) IntTrsBoundProof [UPPER BOUND(ID), 43 ms]
20.36/8.20	    (40) CpxRNTS
20.36/8.20	    (41) FinalProof [FINISHED, 0 ms]
20.36/8.20	    (42) BOUNDS(1, n^1)
20.36/8.20	(43) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
20.36/8.20	(44) TRS for Loop Detection
20.36/8.20	    (45) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
20.36/8.20	    (46) BEST
20.36/8.20	        (47) proven lower bound
20.36/8.20	            (48) LowerBoundPropagationProof [FINISHED, 0 ms]
20.36/8.20	            (49) BOUNDS(n^1, INF)
20.36/8.20	        (50) TRS for Loop Detection
20.36/8.20	
20.36/8.20	
20.36/8.20	----------------------------------------
20.36/8.20	
20.36/8.20	(0)
20.36/8.20	Obligation:
20.36/8.20	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
20.36/8.20	
20.36/8.20	
20.36/8.20	The TRS R consists of the following rules:
20.36/8.20	
20.36/8.20	   is_empty(nil) -> true
20.36/8.20	   is_empty(cons(x, l)) -> false
20.36/8.20	   hd(cons(x, l)) -> x
20.36/8.20	   tl(cons(x, l)) -> l
20.36/8.20	   append(l1, l2) -> ifappend(l1, l2, l1)
20.36/8.20	   ifappend(l1, l2, nil) -> l2
20.36/8.20	   ifappend(l1, l2, cons(x, l)) -> cons(x, append(l, l2))
20.36/8.20	
20.36/8.20	S is empty.
20.36/8.20	Rewrite Strategy: FULL
20.36/8.20	----------------------------------------
20.36/8.20	
20.36/8.20	(1) RcToIrcProof (BOTH BOUNDS(ID, ID))
20.36/8.20	Converted rc-obligation to irc-obligation.
20.36/8.20	
20.36/8.20	As the TRS does not nest defined symbols, we have rc = irc.
20.36/8.20	----------------------------------------
20.36/8.20	
20.36/8.20	(2)
20.36/8.20	Obligation:
20.36/8.20	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
20.36/8.20	
20.36/8.20	
20.36/8.20	The TRS R consists of the following rules:
20.36/8.20	
20.36/8.20	   is_empty(nil) -> true
20.36/8.20	   is_empty(cons(x, l)) -> false
20.36/8.20	   hd(cons(x, l)) -> x
20.36/8.20	   tl(cons(x, l)) -> l
20.36/8.20	   append(l1, l2) -> ifappend(l1, l2, l1)
20.36/8.20	   ifappend(l1, l2, nil) -> l2

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actions all output return to Runtime_Complexity_Full_Rewriting 2019-04-01 06.11