Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308085

details

property	value
status	complete
benchmark	Ex5_DLMMU04_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n047.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	292.138 seconds
cpu usage	1128.61
user time	1112.73
system time	15.8797
max virtual memory	5.6805712E7
max residence set size	1.5076716E7

stage attributes

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

output

1126.45/291.58	WORST_CASE(Omega(n^1), ?)
1128.44/292.07	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
1128.44/292.07	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
1128.44/292.07	
1128.44/292.07	
1128.44/292.07	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1128.44/292.07	
1128.44/292.07	(0) CpxTRS
1128.44/292.07	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
1128.44/292.07	(2) TRS for Loop Detection
1128.44/292.07	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
1128.44/292.07	(4) BEST
1128.44/292.07	    (5) proven lower bound
1128.44/292.07	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
1128.44/292.07	        (7) BOUNDS(n^1, INF)
1128.44/292.07	    (8) TRS for Loop Detection
1128.44/292.07	
1128.44/292.07	
1128.44/292.07	----------------------------------------
1128.44/292.07	
1128.44/292.07	(0)
1128.44/292.07	Obligation:
1128.44/292.07	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1128.44/292.07	
1128.44/292.07	
1128.44/292.07	The TRS R consists of the following rules:
1128.44/292.07	
1128.44/292.07	   active(pairNs) -> mark(cons(0, incr(oddNs)))
1128.44/292.07	   active(oddNs) -> mark(incr(pairNs))
1128.44/292.07	   active(incr(cons(X, XS))) -> mark(cons(s(X), incr(XS)))
1128.44/292.07	   active(take(0, XS)) -> mark(nil)
1128.44/292.07	   active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS)))
1128.44/292.07	   active(zip(nil, XS)) -> mark(nil)
1128.44/292.07	   active(zip(X, nil)) -> mark(nil)
1128.44/292.07	   active(zip(cons(X, XS), cons(Y, YS))) -> mark(cons(pair(X, Y), zip(XS, YS)))
1128.44/292.07	   active(tail(cons(X, XS))) -> mark(XS)
1128.44/292.07	   active(repItems(nil)) -> mark(nil)
1128.44/292.07	   active(repItems(cons(X, XS))) -> mark(cons(X, cons(X, repItems(XS))))
1128.44/292.07	   active(cons(X1, X2)) -> cons(active(X1), X2)
1128.44/292.07	   active(incr(X)) -> incr(active(X))
1128.44/292.07	   active(s(X)) -> s(active(X))
1128.44/292.07	   active(take(X1, X2)) -> take(active(X1), X2)
1128.44/292.07	   active(take(X1, X2)) -> take(X1, active(X2))
1128.44/292.07	   active(zip(X1, X2)) -> zip(active(X1), X2)
1128.44/292.07	   active(zip(X1, X2)) -> zip(X1, active(X2))
1128.44/292.07	   active(pair(X1, X2)) -> pair(active(X1), X2)
1128.44/292.07	   active(pair(X1, X2)) -> pair(X1, active(X2))
1128.44/292.07	   active(tail(X)) -> tail(active(X))
1128.44/292.07	   active(repItems(X)) -> repItems(active(X))
1128.44/292.07	   cons(mark(X1), X2) -> mark(cons(X1, X2))
1128.44/292.07	   incr(mark(X)) -> mark(incr(X))
1128.44/292.07	   s(mark(X)) -> mark(s(X))
1128.44/292.07	   take(mark(X1), X2) -> mark(take(X1, X2))
1128.44/292.07	   take(X1, mark(X2)) -> mark(take(X1, X2))
1128.44/292.07	   zip(mark(X1), X2) -> mark(zip(X1, X2))
1128.44/292.07	   zip(X1, mark(X2)) -> mark(zip(X1, X2))
1128.44/292.07	   pair(mark(X1), X2) -> mark(pair(X1, X2))
1128.44/292.07	   pair(X1, mark(X2)) -> mark(pair(X1, X2))
1128.44/292.07	   tail(mark(X)) -> mark(tail(X))
1128.44/292.07	   repItems(mark(X)) -> mark(repItems(X))
1128.44/292.07	   proper(pairNs) -> ok(pairNs)
1128.44/292.07	   proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
1128.44/292.07	   proper(0) -> ok(0)
1128.44/292.07	   proper(incr(X)) -> incr(proper(X))
1128.44/292.07	   proper(oddNs) -> ok(oddNs)
1128.44/292.07	   proper(s(X)) -> s(proper(X))
1128.44/292.07	   proper(take(X1, X2)) -> take(proper(X1), proper(X2))
1128.44/292.07	   proper(nil) -> ok(nil)
1128.44/292.07	   proper(zip(X1, X2)) -> zip(proper(X1), proper(X2))
1128.44/292.07	   proper(pair(X1, X2)) -> pair(proper(X1), proper(X2))
1128.44/292.07	   proper(tail(X)) -> tail(proper(X))
1128.44/292.07	   proper(repItems(X)) -> repItems(proper(X))
1128.44/292.07	   cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
1128.44/292.07	   incr(ok(X)) -> ok(incr(X))
1128.44/292.07	   s(ok(X)) -> ok(s(X))
1128.44/292.07	   take(ok(X1), ok(X2)) -> ok(take(X1, X2))
1128.44/292.07	   zip(ok(X1), ok(X2)) -> ok(zip(X1, X2))
1128.44/292.07	   pair(ok(X1), ok(X2)) -> ok(pair(X1, X2))
1128.44/292.07	   tail(ok(X)) -> ok(tail(X))
1128.44/292.07	   repItems(ok(X)) -> ok(repItems(X))
1128.44/292.07	   top(mark(X)) -> top(proper(X))
1128.44/292.07	   top(ok(X)) -> top(active(X))
1128.44/292.07	
1128.44/292.07	S is empty.
1128.44/292.07	Rewrite Strategy: FULL
1128.44/292.07	----------------------------------------
1128.44/292.07	
1128.44/292.07	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
1128.44/292.07	Transformed a relative TRS into a decreasing-loop problem.
1128.44/292.07	----------------------------------------
1128.44/292.07	
1128.44/292.07	(2)
1128.44/292.07	Obligation:
1128.44/292.07	Analyzing the following TRS for decreasing loops:
1128.44/292.07	
1128.44/292.07	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1128.44/292.07	
1128.44/292.07	
1128.44/292.07	The TRS R consists of the following rules:
1128.44/292.07

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