Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308104

details

property	value
status	complete
benchmark	LengthOfFiniteLists_nokinds_noand_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n138.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.666 seconds
cpu usage	1144.36
user time	1128.83
system time	15.534
max virtual memory	3.8433144E7
max residence set size	1.5093876E7

stage attributes

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

output

1144.16/291.57	WORST_CASE(Omega(n^1), ?)
1144.16/291.59	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
1144.16/291.59	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
1144.16/291.59	
1144.16/291.59	
1144.16/291.59	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1144.16/291.59	
1144.16/291.59	(0) CpxTRS
1144.16/291.59	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
1144.16/291.59	(2) TRS for Loop Detection
1144.16/291.59	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
1144.16/291.59	(4) BEST
1144.16/291.59	    (5) proven lower bound
1144.16/291.59	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
1144.16/291.59	        (7) BOUNDS(n^1, INF)
1144.16/291.59	    (8) TRS for Loop Detection
1144.16/291.59	
1144.16/291.59	
1144.16/291.59	----------------------------------------
1144.16/291.59	
1144.16/291.59	(0)
1144.16/291.59	Obligation:
1144.16/291.59	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1144.16/291.59	
1144.16/291.59	
1144.16/291.59	The TRS R consists of the following rules:
1144.16/291.59	
1144.16/291.59	   active(zeros) -> mark(cons(0, zeros))
1144.16/291.59	   active(U11(tt)) -> mark(tt)
1144.16/291.59	   active(U21(tt)) -> mark(tt)
1144.16/291.59	   active(U31(tt)) -> mark(tt)
1144.16/291.59	   active(U41(tt, V2)) -> mark(U42(isNatIList(V2)))
1144.16/291.59	   active(U42(tt)) -> mark(tt)
1144.16/291.59	   active(U51(tt, V2)) -> mark(U52(isNatList(V2)))
1144.16/291.59	   active(U52(tt)) -> mark(tt)
1144.16/291.59	   active(U61(tt, L, N)) -> mark(U62(isNat(N), L))
1144.16/291.59	   active(U62(tt, L)) -> mark(s(length(L)))
1144.16/291.59	   active(isNat(0)) -> mark(tt)
1144.16/291.59	   active(isNat(length(V1))) -> mark(U11(isNatList(V1)))
1144.16/291.59	   active(isNat(s(V1))) -> mark(U21(isNat(V1)))
1144.16/291.59	   active(isNatIList(V)) -> mark(U31(isNatList(V)))
1144.16/291.59	   active(isNatIList(zeros)) -> mark(tt)
1144.16/291.59	   active(isNatIList(cons(V1, V2))) -> mark(U41(isNat(V1), V2))
1144.16/291.59	   active(isNatList(nil)) -> mark(tt)
1144.16/291.59	   active(isNatList(cons(V1, V2))) -> mark(U51(isNat(V1), V2))
1144.16/291.59	   active(length(nil)) -> mark(0)
1144.16/291.59	   active(length(cons(N, L))) -> mark(U61(isNatList(L), L, N))
1144.16/291.59	   active(cons(X1, X2)) -> cons(active(X1), X2)
1144.16/291.59	   active(U11(X)) -> U11(active(X))
1144.16/291.59	   active(U21(X)) -> U21(active(X))
1144.16/291.59	   active(U31(X)) -> U31(active(X))
1144.16/291.59	   active(U41(X1, X2)) -> U41(active(X1), X2)
1144.16/291.59	   active(U42(X)) -> U42(active(X))
1144.16/291.59	   active(U51(X1, X2)) -> U51(active(X1), X2)
1144.16/291.59	   active(U52(X)) -> U52(active(X))
1144.16/291.59	   active(U61(X1, X2, X3)) -> U61(active(X1), X2, X3)
1144.16/291.59	   active(U62(X1, X2)) -> U62(active(X1), X2)
1144.16/291.59	   active(s(X)) -> s(active(X))
1144.16/291.59	   active(length(X)) -> length(active(X))
1144.16/291.59	   cons(mark(X1), X2) -> mark(cons(X1, X2))
1144.16/291.59	   U11(mark(X)) -> mark(U11(X))
1144.16/291.59	   U21(mark(X)) -> mark(U21(X))
1144.16/291.59	   U31(mark(X)) -> mark(U31(X))
1144.16/291.59	   U41(mark(X1), X2) -> mark(U41(X1, X2))
1144.16/291.59	   U42(mark(X)) -> mark(U42(X))
1144.16/291.59	   U51(mark(X1), X2) -> mark(U51(X1, X2))
1144.16/291.59	   U52(mark(X)) -> mark(U52(X))
1144.16/291.59	   U61(mark(X1), X2, X3) -> mark(U61(X1, X2, X3))
1144.16/291.59	   U62(mark(X1), X2) -> mark(U62(X1, X2))
1144.16/291.59	   s(mark(X)) -> mark(s(X))
1144.16/291.59	   length(mark(X)) -> mark(length(X))
1144.16/291.59	   proper(zeros) -> ok(zeros)
1144.16/291.59	   proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
1144.16/291.59	   proper(0) -> ok(0)
1144.16/291.59	   proper(U11(X)) -> U11(proper(X))
1144.16/291.59	   proper(tt) -> ok(tt)
1144.16/291.59	   proper(U21(X)) -> U21(proper(X))
1144.16/291.59	   proper(U31(X)) -> U31(proper(X))
1144.16/291.59	   proper(U41(X1, X2)) -> U41(proper(X1), proper(X2))
1144.16/291.59	   proper(U42(X)) -> U42(proper(X))
1144.16/291.59	   proper(isNatIList(X)) -> isNatIList(proper(X))
1144.16/291.59	   proper(U51(X1, X2)) -> U51(proper(X1), proper(X2))
1144.16/291.59	   proper(U52(X)) -> U52(proper(X))
1144.16/291.59	   proper(isNatList(X)) -> isNatList(proper(X))
1144.16/291.59	   proper(U61(X1, X2, X3)) -> U61(proper(X1), proper(X2), proper(X3))
1144.16/291.59	   proper(U62(X1, X2)) -> U62(proper(X1), proper(X2))
1144.16/291.59	   proper(isNat(X)) -> isNat(proper(X))
1144.16/291.59	   proper(s(X)) -> s(proper(X))
1144.16/291.59	   proper(length(X)) -> length(proper(X))
1144.16/291.59	   proper(nil) -> ok(nil)
1144.16/291.59	   cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
1144.16/291.59	   U11(ok(X)) -> ok(U11(X))
1144.16/291.59	   U21(ok(X)) -> ok(U21(X))
1144.16/291.59	   U31(ok(X)) -> ok(U31(X))
1144.16/291.59	   U41(ok(X1), ok(X2)) -> ok(U41(X1, X2))
1144.16/291.59	   U42(ok(X)) -> ok(U42(X))
1144.16/291.59	   isNatIList(ok(X)) -> ok(isNatIList(X))
1144.16/291.59	   U51(ok(X1), ok(X2)) -> ok(U51(X1, X2))
1144.16/291.59	   U52(ok(X)) -> ok(U52(X))
1144.16/291.59	   isNatList(ok(X)) -> ok(isNatList(X))

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job log

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