Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308025

details

property	value
status	complete
benchmark	Ex4_DLMMU04_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n127.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	293.208 seconds
cpu usage	1151.4
user time	1136.47
system time	14.9268
max virtual memory	5.7793888E7
max residence set size	1.5113804E7

stage attributes

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

output

1145.15/291.58	WORST_CASE(Omega(n^1), ?)
1151.24/293.11	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
1151.24/293.11	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
1151.24/293.11	
1151.24/293.11	
1151.24/293.11	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1151.24/293.11	
1151.24/293.11	(0) CpxTRS
1151.24/293.11	(1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
1151.24/293.11	(2) CpxTRS
1151.24/293.11	(3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
1151.24/293.11	(4) typed CpxTrs
1151.24/293.11	(5) OrderProof [LOWER BOUND(ID), 0 ms]
1151.24/293.11	(6) typed CpxTrs
1151.24/293.11	(7) RewriteLemmaProof [LOWER BOUND(ID), 467 ms]
1151.24/293.11	(8) BEST
1151.24/293.11	    (9) proven lower bound
1151.24/293.11	        (10) LowerBoundPropagationProof [FINISHED, 0 ms]
1151.24/293.11	        (11) BOUNDS(n^1, INF)
1151.24/293.11	    (12) typed CpxTrs
1151.24/293.11	        (13) RewriteLemmaProof [LOWER BOUND(ID), 164 ms]
1151.24/293.11	        (14) typed CpxTrs
1151.24/293.11	        (15) RewriteLemmaProof [LOWER BOUND(ID), 109 ms]
1151.24/293.11	        (16) typed CpxTrs
1151.24/293.11	        (17) RewriteLemmaProof [LOWER BOUND(ID), 154 ms]
1151.24/293.11	        (18) typed CpxTrs
1151.24/293.11	        (19) RewriteLemmaProof [LOWER BOUND(ID), 95 ms]
1151.24/293.11	        (20) typed CpxTrs
1151.24/293.11	        (21) RewriteLemmaProof [LOWER BOUND(ID), 156 ms]
1151.24/293.11	        (22) typed CpxTrs
1151.24/293.11	        (23) RewriteLemmaProof [LOWER BOUND(ID), 118 ms]
1151.24/293.11	        (24) typed CpxTrs
1151.24/293.11	        (25) RewriteLemmaProof [LOWER BOUND(ID), 83 ms]
1151.24/293.11	        (26) typed CpxTrs
1151.24/293.11	
1151.24/293.11	
1151.24/293.11	----------------------------------------
1151.24/293.11	
1151.24/293.11	(0)
1151.24/293.11	Obligation:
1151.24/293.11	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1151.24/293.11	
1151.24/293.11	
1151.24/293.11	The TRS R consists of the following rules:
1151.24/293.11	
1151.24/293.11	   active(and(tt, T)) -> mark(T)
1151.24/293.11	   active(isNatIList(IL)) -> mark(isNatList(IL))
1151.24/293.11	   active(isNat(0)) -> mark(tt)
1151.24/293.11	   active(isNat(s(N))) -> mark(isNat(N))
1151.24/293.11	   active(isNat(length(L))) -> mark(isNatList(L))
1151.24/293.11	   active(isNatIList(zeros)) -> mark(tt)
1151.24/293.11	   active(isNatIList(cons(N, IL))) -> mark(and(isNat(N), isNatIList(IL)))
1151.24/293.11	   active(isNatList(nil)) -> mark(tt)
1151.24/293.11	   active(isNatList(cons(N, L))) -> mark(and(isNat(N), isNatList(L)))
1151.24/293.11	   active(isNatList(take(N, IL))) -> mark(and(isNat(N), isNatIList(IL)))
1151.24/293.11	   active(zeros) -> mark(cons(0, zeros))
1151.24/293.11	   active(take(0, IL)) -> mark(uTake1(isNatIList(IL)))
1151.24/293.11	   active(uTake1(tt)) -> mark(nil)
1151.24/293.11	   active(take(s(M), cons(N, IL))) -> mark(uTake2(and(isNat(M), and(isNat(N), isNatIList(IL))), M, N, IL))
1151.24/293.11	   active(uTake2(tt, M, N, IL)) -> mark(cons(N, take(M, IL)))
1151.24/293.11	   active(length(cons(N, L))) -> mark(uLength(and(isNat(N), isNatList(L)), L))
1151.24/293.11	   active(uLength(tt, L)) -> mark(s(length(L)))
1151.24/293.11	   active(and(X1, X2)) -> and(active(X1), X2)
1151.24/293.11	   active(and(X1, X2)) -> and(X1, active(X2))
1151.24/293.11	   active(s(X)) -> s(active(X))
1151.24/293.11	   active(length(X)) -> length(active(X))
1151.24/293.11	   active(cons(X1, X2)) -> cons(active(X1), X2)
1151.24/293.11	   active(take(X1, X2)) -> take(active(X1), X2)
1151.24/293.11	   active(take(X1, X2)) -> take(X1, active(X2))
1151.24/293.11	   active(uTake1(X)) -> uTake1(active(X))
1151.24/293.11	   active(uTake2(X1, X2, X3, X4)) -> uTake2(active(X1), X2, X3, X4)
1151.24/293.11	   active(uLength(X1, X2)) -> uLength(active(X1), X2)
1151.24/293.11	   and(mark(X1), X2) -> mark(and(X1, X2))
1151.24/293.11	   and(X1, mark(X2)) -> mark(and(X1, X2))
1151.24/293.11	   s(mark(X)) -> mark(s(X))
1151.24/293.11	   length(mark(X)) -> mark(length(X))
1151.24/293.11	   cons(mark(X1), X2) -> mark(cons(X1, X2))
1151.24/293.11	   take(mark(X1), X2) -> mark(take(X1, X2))
1151.24/293.11	   take(X1, mark(X2)) -> mark(take(X1, X2))
1151.24/293.11	   uTake1(mark(X)) -> mark(uTake1(X))
1151.24/293.11	   uTake2(mark(X1), X2, X3, X4) -> mark(uTake2(X1, X2, X3, X4))
1151.24/293.11	   uLength(mark(X1), X2) -> mark(uLength(X1, X2))
1151.24/293.11	   proper(and(X1, X2)) -> and(proper(X1), proper(X2))
1151.24/293.11	   proper(tt) -> ok(tt)
1151.24/293.11	   proper(isNatIList(X)) -> isNatIList(proper(X))
1151.24/293.11	   proper(isNatList(X)) -> isNatList(proper(X))
1151.24/293.11	   proper(isNat(X)) -> isNat(proper(X))
1151.24/293.11	   proper(0) -> ok(0)
1151.24/293.11	   proper(s(X)) -> s(proper(X))
1151.24/293.11	   proper(length(X)) -> length(proper(X))
1151.24/293.11	   proper(zeros) -> ok(zeros)
1151.24/293.11	   proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
1151.24/293.11	   proper(nil) -> ok(nil)
1151.24/293.11	   proper(take(X1, X2)) -> take(proper(X1), proper(X2))
1151.24/293.11	   proper(uTake1(X)) -> uTake1(proper(X))
1151.24/293.11	   proper(uTake2(X1, X2, X3, X4)) -> uTake2(proper(X1), proper(X2), proper(X3), proper(X4))
1151.24/293.11	   proper(uLength(X1, X2)) -> uLength(proper(X1), proper(X2))
1151.24/293.11	   and(ok(X1), ok(X2)) -> ok(and(X1, X2))
1151.24/293.11	   isNatIList(ok(X)) -> ok(isNatIList(X))
1151.24/293.11	   isNatList(ok(X)) -> ok(isNatList(X))

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