Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308183

details

property	value
status	complete
benchmark	OvConsOS_complete_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n051.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	295.104 seconds
cpu usage	1160.26
user time	1143.24
system time	17.02
max virtual memory	5.720884E7
max residence set size	1.5121268E7

stage attributes

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

output

1146.49/291.58	WORST_CASE(Omega(n^1), ?)
1160.01/295.03	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
1160.01/295.03	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
1160.01/295.03	
1160.01/295.03	
1160.01/295.03	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1160.01/295.03	
1160.01/295.03	(0) CpxTRS
1160.01/295.03	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
1160.01/295.03	(2) TRS for Loop Detection
1160.01/295.03	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
1160.01/295.03	(4) BEST
1160.01/295.03	    (5) proven lower bound
1160.01/295.03	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
1160.01/295.03	        (7) BOUNDS(n^1, INF)
1160.01/295.03	    (8) TRS for Loop Detection
1160.01/295.03	
1160.01/295.03	
1160.01/295.03	----------------------------------------
1160.01/295.03	
1160.01/295.03	(0)
1160.01/295.03	Obligation:
1160.01/295.03	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1160.01/295.03	
1160.01/295.03	
1160.01/295.03	The TRS R consists of the following rules:
1160.01/295.03	
1160.01/295.03	   active(zeros) -> mark(cons(0, zeros))
1160.01/295.03	   active(U11(tt, V1)) -> mark(U12(isNatList(V1)))
1160.01/295.03	   active(U12(tt)) -> mark(tt)
1160.01/295.03	   active(U21(tt, V1)) -> mark(U22(isNat(V1)))
1160.01/295.03	   active(U22(tt)) -> mark(tt)
1160.01/295.03	   active(U31(tt, V)) -> mark(U32(isNatList(V)))
1160.01/295.03	   active(U32(tt)) -> mark(tt)
1160.01/295.03	   active(U41(tt, V1, V2)) -> mark(U42(isNat(V1), V2))
1160.01/295.03	   active(U42(tt, V2)) -> mark(U43(isNatIList(V2)))
1160.01/295.03	   active(U43(tt)) -> mark(tt)
1160.01/295.03	   active(U51(tt, V1, V2)) -> mark(U52(isNat(V1), V2))
1160.01/295.03	   active(U52(tt, V2)) -> mark(U53(isNatList(V2)))
1160.01/295.03	   active(U53(tt)) -> mark(tt)
1160.01/295.03	   active(U61(tt, V1, V2)) -> mark(U62(isNat(V1), V2))
1160.01/295.03	   active(U62(tt, V2)) -> mark(U63(isNatIList(V2)))
1160.01/295.03	   active(U63(tt)) -> mark(tt)
1160.01/295.03	   active(U71(tt, L)) -> mark(s(length(L)))
1160.01/295.03	   active(U81(tt)) -> mark(nil)
1160.01/295.03	   active(U91(tt, IL, M, N)) -> mark(cons(N, take(M, IL)))
1160.01/295.03	   active(and(tt, X)) -> mark(X)
1160.01/295.03	   active(isNat(0)) -> mark(tt)
1160.01/295.03	   active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1), V1))
1160.01/295.03	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
1160.01/295.03	   active(isNatIList(V)) -> mark(U31(isNatIListKind(V), V))
1160.01/295.03	   active(isNatIList(zeros)) -> mark(tt)
1160.01/295.03	   active(isNatIList(cons(V1, V2))) -> mark(U41(and(isNatKind(V1), isNatIListKind(V2)), V1, V2))
1160.01/295.03	   active(isNatIListKind(nil)) -> mark(tt)
1160.01/295.03	   active(isNatIListKind(zeros)) -> mark(tt)
1160.01/295.03	   active(isNatIListKind(cons(V1, V2))) -> mark(and(isNatKind(V1), isNatIListKind(V2)))
1160.01/295.03	   active(isNatIListKind(take(V1, V2))) -> mark(and(isNatKind(V1), isNatIListKind(V2)))
1160.01/295.03	   active(isNatKind(0)) -> mark(tt)
1160.01/295.03	   active(isNatKind(length(V1))) -> mark(isNatIListKind(V1))
1160.01/295.03	   active(isNatKind(s(V1))) -> mark(isNatKind(V1))
1160.01/295.03	   active(isNatList(nil)) -> mark(tt)
1160.01/295.03	   active(isNatList(cons(V1, V2))) -> mark(U51(and(isNatKind(V1), isNatIListKind(V2)), V1, V2))
1160.01/295.03	   active(isNatList(take(V1, V2))) -> mark(U61(and(isNatKind(V1), isNatIListKind(V2)), V1, V2))
1160.01/295.03	   active(length(nil)) -> mark(0)
1160.01/295.03	   active(length(cons(N, L))) -> mark(U71(and(and(isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L))
1160.01/295.03	   active(take(0, IL)) -> mark(U81(and(isNatIList(IL), isNatIListKind(IL))))
1160.01/295.03	   active(take(s(M), cons(N, IL))) -> mark(U91(and(and(isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), IL, M, N))
1160.01/295.03	   active(cons(X1, X2)) -> cons(active(X1), X2)
1160.01/295.03	   active(U11(X1, X2)) -> U11(active(X1), X2)
1160.01/295.03	   active(U12(X)) -> U12(active(X))
1160.01/295.03	   active(U21(X1, X2)) -> U21(active(X1), X2)
1160.01/295.03	   active(U22(X)) -> U22(active(X))
1160.01/295.03	   active(U31(X1, X2)) -> U31(active(X1), X2)
1160.01/295.03	   active(U32(X)) -> U32(active(X))
1160.01/295.03	   active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3)
1160.01/295.03	   active(U42(X1, X2)) -> U42(active(X1), X2)
1160.01/295.03	   active(U43(X)) -> U43(active(X))
1160.01/295.03	   active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3)
1160.01/295.03	   active(U52(X1, X2)) -> U52(active(X1), X2)
1160.01/295.03	   active(U53(X)) -> U53(active(X))
1160.01/295.03	   active(U61(X1, X2, X3)) -> U61(active(X1), X2, X3)
1160.01/295.03	   active(U62(X1, X2)) -> U62(active(X1), X2)
1160.01/295.03	   active(U63(X)) -> U63(active(X))
1160.01/295.03	   active(U71(X1, X2)) -> U71(active(X1), X2)
1160.01/295.03	   active(s(X)) -> s(active(X))
1160.01/295.03	   active(length(X)) -> length(active(X))
1160.01/295.03	   active(U81(X)) -> U81(active(X))
1160.01/295.03	   active(U91(X1, X2, X3, X4)) -> U91(active(X1), X2, X3, X4)
1160.01/295.03	   active(take(X1, X2)) -> take(active(X1), X2)
1160.01/295.03	   active(take(X1, X2)) -> take(X1, active(X2))
1160.01/295.03	   active(and(X1, X2)) -> and(active(X1), X2)
1160.01/295.03	   cons(mark(X1), X2) -> mark(cons(X1, X2))
1160.01/295.03	   U11(mark(X1), X2) -> mark(U11(X1, X2))
1160.01/295.03	   U12(mark(X)) -> mark(U12(X))
1160.01/295.03	   U21(mark(X1), X2) -> mark(U21(X1, X2))
1160.01/295.03	   U22(mark(X)) -> mark(U22(X))
1160.01/295.03	   U31(mark(X1), X2) -> mark(U31(X1, X2))
1160.01/295.03	   U32(mark(X)) -> mark(U32(X))
1160.01/295.03	   U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3))
1160.01/295.03	   U42(mark(X1), X2) -> mark(U42(X1, X2))

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