Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308226

details

property	value
status	complete
benchmark	LengthOfFiniteLists_complete_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n149.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	295.532 seconds
cpu usage	1159.01
user time	1143.62
system time	15.3904
max virtual memory	5.7401704E7
max residence set size	1.5083788E7

stage attributes

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

output

1143.39/291.61	WORST_CASE(Omega(n^1), ?)
1158.63/295.45	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
1158.63/295.45	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
1158.63/295.45	
1158.63/295.45	
1158.63/295.45	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1158.63/295.45	
1158.63/295.45	(0) CpxTRS
1158.63/295.45	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
1158.63/295.45	(2) TRS for Loop Detection
1158.63/295.45	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
1158.63/295.45	(4) BEST
1158.63/295.45	    (5) proven lower bound
1158.63/295.45	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
1158.63/295.45	        (7) BOUNDS(n^1, INF)
1158.63/295.45	    (8) TRS for Loop Detection
1158.63/295.45	
1158.63/295.45	
1158.63/295.45	----------------------------------------
1158.63/295.45	
1158.63/295.45	(0)
1158.63/295.45	Obligation:
1158.63/295.45	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1158.63/295.45	
1158.63/295.45	
1158.63/295.45	The TRS R consists of the following rules:
1158.63/295.45	
1158.63/295.45	   active(zeros) -> mark(cons(0, zeros))
1158.63/295.45	   active(U11(tt, V1)) -> mark(U12(isNatList(V1)))
1158.63/295.45	   active(U12(tt)) -> mark(tt)
1158.63/295.45	   active(U21(tt, V1)) -> mark(U22(isNat(V1)))
1158.63/295.45	   active(U22(tt)) -> mark(tt)
1158.63/295.45	   active(U31(tt, V)) -> mark(U32(isNatList(V)))
1158.63/295.45	   active(U32(tt)) -> mark(tt)
1158.63/295.45	   active(U41(tt, V1, V2)) -> mark(U42(isNat(V1), V2))
1158.63/295.45	   active(U42(tt, V2)) -> mark(U43(isNatIList(V2)))
1158.63/295.45	   active(U43(tt)) -> mark(tt)
1158.63/295.45	   active(U51(tt, V1, V2)) -> mark(U52(isNat(V1), V2))
1158.63/295.45	   active(U52(tt, V2)) -> mark(U53(isNatList(V2)))
1158.63/295.45	   active(U53(tt)) -> mark(tt)
1158.63/295.45	   active(U61(tt, L)) -> mark(s(length(L)))
1158.63/295.45	   active(and(tt, X)) -> mark(X)
1158.63/295.45	   active(isNat(0)) -> mark(tt)
1158.63/295.45	   active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1), V1))
1158.63/295.45	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
1158.63/295.45	   active(isNatIList(V)) -> mark(U31(isNatIListKind(V), V))
1158.63/295.45	   active(isNatIList(zeros)) -> mark(tt)
1158.63/295.45	   active(isNatIList(cons(V1, V2))) -> mark(U41(and(isNatKind(V1), isNatIListKind(V2)), V1, V2))
1158.63/295.45	   active(isNatIListKind(nil)) -> mark(tt)
1158.63/295.45	   active(isNatIListKind(zeros)) -> mark(tt)
1158.63/295.45	   active(isNatIListKind(cons(V1, V2))) -> mark(and(isNatKind(V1), isNatIListKind(V2)))
1158.63/295.45	   active(isNatKind(0)) -> mark(tt)
1158.63/295.45	   active(isNatKind(length(V1))) -> mark(isNatIListKind(V1))
1158.63/295.45	   active(isNatKind(s(V1))) -> mark(isNatKind(V1))
1158.63/295.45	   active(isNatList(nil)) -> mark(tt)
1158.63/295.45	   active(isNatList(cons(V1, V2))) -> mark(U51(and(isNatKind(V1), isNatIListKind(V2)), V1, V2))
1158.63/295.45	   active(length(nil)) -> mark(0)
1158.63/295.45	   active(length(cons(N, L))) -> mark(U61(and(and(isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L))
1158.63/295.45	   active(cons(X1, X2)) -> cons(active(X1), X2)
1158.63/295.45	   active(U11(X1, X2)) -> U11(active(X1), X2)
1158.63/295.45	   active(U12(X)) -> U12(active(X))
1158.63/295.45	   active(U21(X1, X2)) -> U21(active(X1), X2)
1158.63/295.45	   active(U22(X)) -> U22(active(X))
1158.63/295.45	   active(U31(X1, X2)) -> U31(active(X1), X2)
1158.63/295.45	   active(U32(X)) -> U32(active(X))
1158.63/295.45	   active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3)
1158.63/295.45	   active(U42(X1, X2)) -> U42(active(X1), X2)
1158.63/295.45	   active(U43(X)) -> U43(active(X))
1158.63/295.45	   active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3)
1158.63/295.45	   active(U52(X1, X2)) -> U52(active(X1), X2)
1158.63/295.45	   active(U53(X)) -> U53(active(X))
1158.63/295.45	   active(U61(X1, X2)) -> U61(active(X1), X2)
1158.63/295.45	   active(s(X)) -> s(active(X))
1158.63/295.45	   active(length(X)) -> length(active(X))
1158.63/295.45	   active(and(X1, X2)) -> and(active(X1), X2)
1158.63/295.45	   cons(mark(X1), X2) -> mark(cons(X1, X2))
1158.63/295.45	   U11(mark(X1), X2) -> mark(U11(X1, X2))
1158.63/295.45	   U12(mark(X)) -> mark(U12(X))
1158.63/295.45	   U21(mark(X1), X2) -> mark(U21(X1, X2))
1158.63/295.45	   U22(mark(X)) -> mark(U22(X))
1158.63/295.45	   U31(mark(X1), X2) -> mark(U31(X1, X2))
1158.63/295.45	   U32(mark(X)) -> mark(U32(X))
1158.63/295.45	   U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3))
1158.63/295.45	   U42(mark(X1), X2) -> mark(U42(X1, X2))
1158.63/295.45	   U43(mark(X)) -> mark(U43(X))
1158.63/295.45	   U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3))
1158.63/295.45	   U52(mark(X1), X2) -> mark(U52(X1, X2))
1158.63/295.45	   U53(mark(X)) -> mark(U53(X))
1158.63/295.45	   U61(mark(X1), X2) -> mark(U61(X1, X2))
1158.63/295.45	   s(mark(X)) -> mark(s(X))
1158.63/295.45	   length(mark(X)) -> mark(length(X))
1158.63/295.45	   and(mark(X1), X2) -> mark(and(X1, X2))
1158.63/295.45	   proper(zeros) -> ok(zeros)
1158.63/295.45	   proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
1158.63/295.45	   proper(0) -> ok(0)
1158.63/295.45	   proper(U11(X1, X2)) -> U11(proper(X1), proper(X2))
1158.63/295.45	   proper(tt) -> ok(tt)
1158.63/295.45	   proper(U12(X)) -> U12(proper(X))
1158.63/295.45	   proper(isNatList(X)) -> isNatList(proper(X))
1158.63/295.45	   proper(U21(X1, X2)) -> U21(proper(X1), proper(X2))

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job log

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