Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308361

details

property	value
status	complete
benchmark	LISTUTILITIES_nosorts_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n161.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	10.9671 seconds
cpu usage	36.8947
user time	34.8635
system time	2.03121
max virtual memory	3.6577168E7
max residence set size	4193712.0

stage attributes

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

output

36.78/10.90	WORST_CASE(Omega(n^1), O(n^1))
36.78/10.91	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
36.78/10.91	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
36.78/10.91	
36.78/10.91	
36.78/10.91	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
36.78/10.91	
36.78/10.91	(0) CpxTRS
36.78/10.91	(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms]
36.78/10.91	(2) CpxTRS
36.78/10.91	    (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
36.78/10.91	    (4) CpxTRS
36.78/10.91	    (5) CpxTrsMatchBoundsTAProof [FINISHED, 430 ms]
36.78/10.91	    (6) BOUNDS(1, n^1)
36.78/10.91	(7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
36.78/10.91	(8) TRS for Loop Detection
36.78/10.91	    (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
36.78/10.91	    (10) BEST
36.78/10.91	        (11) proven lower bound
36.78/10.91	            (12) LowerBoundPropagationProof [FINISHED, 0 ms]
36.78/10.91	            (13) BOUNDS(n^1, INF)
36.78/10.91	        (14) TRS for Loop Detection
36.78/10.91	
36.78/10.91	
36.78/10.91	----------------------------------------
36.78/10.91	
36.78/10.91	(0)
36.78/10.91	Obligation:
36.78/10.91	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
36.78/10.91	
36.78/10.91	
36.78/10.91	The TRS R consists of the following rules:
36.78/10.91	
36.78/10.91	   active(U11(tt, N, X, XS)) -> mark(U12(splitAt(N, XS), X))
36.78/10.92	   active(U12(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS))
36.78/10.92	   active(afterNth(N, XS)) -> mark(snd(splitAt(N, XS)))
36.78/10.92	   active(and(tt, X)) -> mark(X)
36.78/10.92	   active(fst(pair(X, Y))) -> mark(X)
36.78/10.92	   active(head(cons(N, XS))) -> mark(N)
36.78/10.92	   active(natsFrom(N)) -> mark(cons(N, natsFrom(s(N))))
36.78/10.92	   active(sel(N, XS)) -> mark(head(afterNth(N, XS)))
36.78/10.92	   active(snd(pair(X, Y))) -> mark(Y)
36.78/10.92	   active(splitAt(0, XS)) -> mark(pair(nil, XS))
36.78/10.92	   active(splitAt(s(N), cons(X, XS))) -> mark(U11(tt, N, X, XS))
36.78/10.92	   active(tail(cons(N, XS))) -> mark(XS)
36.78/10.92	   active(take(N, XS)) -> mark(fst(splitAt(N, XS)))
36.78/10.92	   active(U11(X1, X2, X3, X4)) -> U11(active(X1), X2, X3, X4)
36.78/10.92	   active(U12(X1, X2)) -> U12(active(X1), X2)
36.78/10.92	   active(splitAt(X1, X2)) -> splitAt(active(X1), X2)
36.78/10.92	   active(splitAt(X1, X2)) -> splitAt(X1, active(X2))
36.78/10.92	   active(pair(X1, X2)) -> pair(active(X1), X2)
36.78/10.92	   active(pair(X1, X2)) -> pair(X1, active(X2))
36.78/10.92	   active(cons(X1, X2)) -> cons(active(X1), X2)
36.78/10.92	   active(afterNth(X1, X2)) -> afterNth(active(X1), X2)
36.78/10.92	   active(afterNth(X1, X2)) -> afterNth(X1, active(X2))
36.78/10.92	   active(snd(X)) -> snd(active(X))
36.78/10.92	   active(and(X1, X2)) -> and(active(X1), X2)
36.78/10.92	   active(fst(X)) -> fst(active(X))
36.78/10.92	   active(head(X)) -> head(active(X))
36.78/10.92	   active(natsFrom(X)) -> natsFrom(active(X))
36.78/10.92	   active(s(X)) -> s(active(X))
36.78/10.92	   active(sel(X1, X2)) -> sel(active(X1), X2)
36.78/10.92	   active(sel(X1, X2)) -> sel(X1, active(X2))
36.78/10.92	   active(tail(X)) -> tail(active(X))
36.78/10.92	   active(take(X1, X2)) -> take(active(X1), X2)
36.78/10.92	   active(take(X1, X2)) -> take(X1, active(X2))
36.78/10.92	   U11(mark(X1), X2, X3, X4) -> mark(U11(X1, X2, X3, X4))
36.78/10.92	   U12(mark(X1), X2) -> mark(U12(X1, X2))
36.78/10.92	   splitAt(mark(X1), X2) -> mark(splitAt(X1, X2))
36.78/10.92	   splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2))
36.78/10.92	   pair(mark(X1), X2) -> mark(pair(X1, X2))
36.78/10.92	   pair(X1, mark(X2)) -> mark(pair(X1, X2))
36.78/10.92	   cons(mark(X1), X2) -> mark(cons(X1, X2))
36.78/10.92	   afterNth(mark(X1), X2) -> mark(afterNth(X1, X2))
36.78/10.92	   afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2))
36.78/10.92	   snd(mark(X)) -> mark(snd(X))
36.78/10.92	   and(mark(X1), X2) -> mark(and(X1, X2))
36.78/10.92	   fst(mark(X)) -> mark(fst(X))
36.78/10.92	   head(mark(X)) -> mark(head(X))
36.78/10.92	   natsFrom(mark(X)) -> mark(natsFrom(X))
36.78/10.92	   s(mark(X)) -> mark(s(X))
36.78/10.92	   sel(mark(X1), X2) -> mark(sel(X1, X2))
36.78/10.92	   sel(X1, mark(X2)) -> mark(sel(X1, X2))
36.78/10.92	   tail(mark(X)) -> mark(tail(X))
36.78/10.92	   take(mark(X1), X2) -> mark(take(X1, X2))
36.78/10.92	   take(X1, mark(X2)) -> mark(take(X1, X2))
36.78/10.92	   proper(U11(X1, X2, X3, X4)) -> U11(proper(X1), proper(X2), proper(X3), proper(X4))
36.78/10.92	   proper(tt) -> ok(tt)
36.78/10.92	   proper(U12(X1, X2)) -> U12(proper(X1), proper(X2))
36.78/10.92	   proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2))
36.78/10.92	   proper(pair(X1, X2)) -> pair(proper(X1), proper(X2))
36.78/10.92	   proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
36.78/10.92	   proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2))
36.78/10.92	   proper(snd(X)) -> snd(proper(X))
36.78/10.92	   proper(and(X1, X2)) -> and(proper(X1), proper(X2))
36.78/10.92	   proper(fst(X)) -> fst(proper(X))
36.78/10.92	   proper(head(X)) -> head(proper(X))
36.78/10.92	   proper(natsFrom(X)) -> natsFrom(proper(X))
36.78/10.92	   proper(s(X)) -> s(proper(X))
36.78/10.92	   proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))

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