Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313435

details

property	value
status	complete
benchmark	Ex1_GL02a_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n144.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	4.75814 seconds
cpu usage	14.8127
user time	13.843
system time	0.969753
max virtual memory	1.9179012E7
max residence set size	3349688.0

stage attributes

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

output

14.65/4.70	WORST_CASE(Omega(n^1), O(n^1))
14.65/4.71	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
14.65/4.71	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
14.65/4.71	
14.65/4.71	
14.65/4.71	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
14.65/4.71	
14.65/4.71	(0) CpxTRS
14.65/4.71	(1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
14.65/4.71	(2) CdtProblem
14.65/4.71	    (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
14.65/4.71	    (4) CdtProblem
14.65/4.71	    (5) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
14.65/4.71	    (6) CdtProblem
14.65/4.71	    (7) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
14.65/4.71	    (8) CdtProblem
14.65/4.71	    (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 54 ms]
14.65/4.71	    (10) CdtProblem
14.65/4.71	    (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 9 ms]
14.65/4.71	    (12) CdtProblem
14.65/4.71	    (13) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms]
14.65/4.71	    (14) BOUNDS(1, 1)
14.65/4.71	(15) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
14.65/4.71	(16) CpxTRS
14.65/4.71	    (17) SlicingProof [LOWER BOUND(ID), 0 ms]
14.65/4.71	    (18) CpxTRS
14.65/4.71	    (19) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
14.65/4.71	    (20) typed CpxTrs
14.65/4.71	    (21) OrderProof [LOWER BOUND(ID), 0 ms]
14.65/4.71	    (22) typed CpxTrs
14.65/4.71	    (23) RewriteLemmaProof [LOWER BOUND(ID), 289 ms]
14.65/4.71	    (24) BEST
14.65/4.71	        (25) proven lower bound
14.65/4.71	            (26) LowerBoundPropagationProof [FINISHED, 0 ms]
14.65/4.71	            (27) BOUNDS(n^1, INF)
14.65/4.71	        (28) typed CpxTrs
14.65/4.71	
14.65/4.71	
14.65/4.71	----------------------------------------
14.65/4.71	
14.65/4.71	(0)
14.65/4.71	Obligation:
14.65/4.71	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
14.65/4.71	
14.65/4.71	
14.65/4.71	The TRS R consists of the following rules:
14.65/4.71	
14.65/4.71	   a__eq(0, 0) -> true
14.65/4.71	   a__eq(s(X), s(Y)) -> a__eq(X, Y)
14.65/4.71	   a__eq(X, Y) -> false
14.65/4.71	   a__inf(X) -> cons(X, inf(s(X)))
14.65/4.71	   a__take(0, X) -> nil
14.65/4.71	   a__take(s(X), cons(Y, L)) -> cons(Y, take(X, L))
14.65/4.71	   a__length(nil) -> 0
14.65/4.71	   a__length(cons(X, L)) -> s(length(L))
14.65/4.71	   mark(eq(X1, X2)) -> a__eq(X1, X2)
14.65/4.71	   mark(inf(X)) -> a__inf(mark(X))
14.65/4.71	   mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
14.65/4.71	   mark(length(X)) -> a__length(mark(X))
14.65/4.71	   mark(0) -> 0
14.65/4.71	   mark(true) -> true
14.65/4.71	   mark(s(X)) -> s(X)
14.65/4.71	   mark(false) -> false
14.65/4.71	   mark(cons(X1, X2)) -> cons(X1, X2)
14.65/4.71	   mark(nil) -> nil
14.65/4.71	   a__eq(X1, X2) -> eq(X1, X2)
14.65/4.71	   a__inf(X) -> inf(X)
14.65/4.71	   a__take(X1, X2) -> take(X1, X2)
14.65/4.71	   a__length(X) -> length(X)
14.65/4.71	
14.65/4.71	S is empty.
14.65/4.71	Rewrite Strategy: INNERMOST
14.65/4.71	----------------------------------------
14.65/4.71	
14.65/4.71	(1) CpxTrsToCdtProof (UPPER BOUND(ID))
14.65/4.71	Converted Cpx (relative) TRS to CDT
14.65/4.71	----------------------------------------
14.65/4.71	
14.65/4.71	(2)
14.65/4.71	Obligation:
14.65/4.71	Complexity Dependency Tuples Problem
14.65/4.71	
14.65/4.71	Rules:
14.65/4.71	   a__eq(0, 0) -> true
14.65/4.71	   a__eq(s(z0), s(z1)) -> a__eq(z0, z1)
14.65/4.71	   a__eq(z0, z1) -> false
14.65/4.71	   a__eq(z0, z1) -> eq(z0, z1)
14.65/4.71	   a__inf(z0) -> cons(z0, inf(s(z0)))
14.65/4.71	   a__inf(z0) -> inf(z0)
14.65/4.71	   a__take(0, z0) -> nil
14.65/4.71	   a__take(s(z0), cons(z1, z2)) -> cons(z1, take(z0, z2))
14.65/4.71	   a__take(z0, z1) -> take(z0, z1)
14.65/4.71	   a__length(nil) -> 0
14.65/4.71	   a__length(cons(z0, z1)) -> s(length(z1))
14.65/4.71	   a__length(z0) -> length(z0)
14.65/4.71	   mark(eq(z0, z1)) -> a__eq(z0, z1)
14.65/4.71	   mark(inf(z0)) -> a__inf(mark(z0))
14.65/4.71	   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
14.65/4.71	   mark(length(z0)) -> a__length(mark(z0))
14.65/4.71	   mark(0) -> 0

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