Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308380

details

property	value
status	complete
benchmark	ExSec4_2_DLMMU04_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n170.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	11.09 seconds
cpu usage	38.5407
user time	36.4441
system time	2.09662
max virtual memory	1.9408156E7
max residence set size	4199552.0

stage attributes

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

output

38.10/11.00	WORST_CASE(Omega(n^1), O(n^1))
38.34/11.02	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
38.34/11.02	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
38.34/11.02	
38.34/11.02	
38.34/11.02	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
38.34/11.02	
38.34/11.02	(0) CpxTRS
38.34/11.02	(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms]
38.34/11.02	(2) CpxTRS
38.34/11.02	    (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
38.34/11.02	    (4) CpxTRS
38.34/11.02	    (5) CpxTrsMatchBoundsTAProof [FINISHED, 342 ms]
38.34/11.02	    (6) BOUNDS(1, n^1)
38.34/11.02	(7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
38.34/11.02	(8) CpxTRS
38.34/11.02	    (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
38.34/11.02	    (10) typed CpxTrs
38.34/11.02	    (11) OrderProof [LOWER BOUND(ID), 0 ms]
38.34/11.02	    (12) typed CpxTrs
38.34/11.02	    (13) RewriteLemmaProof [LOWER BOUND(ID), 488 ms]
38.34/11.02	    (14) BEST
38.34/11.02	        (15) proven lower bound
38.34/11.02	            (16) LowerBoundPropagationProof [FINISHED, 0 ms]
38.34/11.02	            (17) BOUNDS(n^1, INF)
38.34/11.02	        (18) typed CpxTrs
38.34/11.02	            (19) RewriteLemmaProof [LOWER BOUND(ID), 118 ms]
38.34/11.02	            (20) typed CpxTrs
38.34/11.02	            (21) RewriteLemmaProof [LOWER BOUND(ID), 65 ms]
38.34/11.02	            (22) typed CpxTrs
38.34/11.02	            (23) RewriteLemmaProof [LOWER BOUND(ID), 62 ms]
38.34/11.02	            (24) typed CpxTrs
38.34/11.02	            (25) RewriteLemmaProof [LOWER BOUND(ID), 125 ms]
38.34/11.02	            (26) typed CpxTrs
38.34/11.02	            (27) RewriteLemmaProof [LOWER BOUND(ID), 94 ms]
38.34/11.02	            (28) typed CpxTrs
38.34/11.02	            (29) RewriteLemmaProof [LOWER BOUND(ID), 92 ms]
38.34/11.02	            (30) typed CpxTrs
38.34/11.02	            (31) RewriteLemmaProof [LOWER BOUND(ID), 70 ms]
38.34/11.02	            (32) typed CpxTrs
38.34/11.02	            (33) RewriteLemmaProof [LOWER BOUND(ID), 114 ms]
38.34/11.02	            (34) typed CpxTrs
38.34/11.02	            (35) RewriteLemmaProof [LOWER BOUND(ID), 123 ms]
38.34/11.02	            (36) typed CpxTrs
38.34/11.02	            (37) RewriteLemmaProof [LOWER BOUND(ID), 135 ms]
38.34/11.02	            (38) typed CpxTrs
38.34/11.02	            (39) RewriteLemmaProof [LOWER BOUND(ID), 134 ms]
38.34/11.02	            (40) typed CpxTrs
38.34/11.02	            (41) RewriteLemmaProof [LOWER BOUND(ID), 159 ms]
38.34/11.02	            (42) typed CpxTrs
38.34/11.02	
38.34/11.02	
38.34/11.02	----------------------------------------
38.34/11.02	
38.34/11.02	(0)
38.34/11.02	Obligation:
38.34/11.02	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
38.34/11.02	
38.34/11.02	
38.34/11.02	The TRS R consists of the following rules:
38.34/11.02	
38.34/11.02	   active(natsFrom(N)) -> mark(cons(N, natsFrom(s(N))))
38.34/11.02	   active(fst(pair(XS, YS))) -> mark(XS)
38.34/11.02	   active(snd(pair(XS, YS))) -> mark(YS)
38.34/11.02	   active(splitAt(0, XS)) -> mark(pair(nil, XS))
38.34/11.02	   active(splitAt(s(N), cons(X, XS))) -> mark(u(splitAt(N, XS), N, X, XS))
38.34/11.02	   active(u(pair(YS, ZS), N, X, XS)) -> mark(pair(cons(X, YS), ZS))
38.34/11.02	   active(head(cons(N, XS))) -> mark(N)
38.34/11.02	   active(tail(cons(N, XS))) -> mark(XS)
38.34/11.02	   active(sel(N, XS)) -> mark(head(afterNth(N, XS)))
38.34/11.02	   active(take(N, XS)) -> mark(fst(splitAt(N, XS)))
38.34/11.02	   active(afterNth(N, XS)) -> mark(snd(splitAt(N, XS)))
38.34/11.02	   active(natsFrom(X)) -> natsFrom(active(X))
38.34/11.02	   active(cons(X1, X2)) -> cons(active(X1), X2)
38.34/11.02	   active(s(X)) -> s(active(X))
38.34/11.02	   active(fst(X)) -> fst(active(X))
38.34/11.02	   active(pair(X1, X2)) -> pair(active(X1), X2)
38.34/11.02	   active(pair(X1, X2)) -> pair(X1, active(X2))
38.34/11.02	   active(snd(X)) -> snd(active(X))
38.34/11.02	   active(splitAt(X1, X2)) -> splitAt(active(X1), X2)
38.34/11.02	   active(splitAt(X1, X2)) -> splitAt(X1, active(X2))
38.34/11.02	   active(u(X1, X2, X3, X4)) -> u(active(X1), X2, X3, X4)
38.34/11.02	   active(head(X)) -> head(active(X))
38.34/11.02	   active(tail(X)) -> tail(active(X))
38.34/11.02	   active(sel(X1, X2)) -> sel(active(X1), X2)
38.34/11.02	   active(sel(X1, X2)) -> sel(X1, active(X2))
38.34/11.02	   active(afterNth(X1, X2)) -> afterNth(active(X1), X2)
38.34/11.02	   active(afterNth(X1, X2)) -> afterNth(X1, active(X2))
38.34/11.02	   active(take(X1, X2)) -> take(active(X1), X2)
38.34/11.02	   active(take(X1, X2)) -> take(X1, active(X2))
38.34/11.02	   natsFrom(mark(X)) -> mark(natsFrom(X))
38.34/11.02	   cons(mark(X1), X2) -> mark(cons(X1, X2))
38.34/11.02	   s(mark(X)) -> mark(s(X))
38.34/11.02	   fst(mark(X)) -> mark(fst(X))
38.34/11.02	   pair(mark(X1), X2) -> mark(pair(X1, X2))
38.34/11.02	   pair(X1, mark(X2)) -> mark(pair(X1, X2))
38.34/11.02	   snd(mark(X)) -> mark(snd(X))
38.34/11.02	   splitAt(mark(X1), X2) -> mark(splitAt(X1, X2))
38.34/11.02	   splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2))
38.34/11.02	   u(mark(X1), X2, X3, X4) -> mark(u(X1, X2, X3, X4))

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