Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308349

details

property	value
status	complete
benchmark	MYNAT_complete_noand_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n035.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	10.7111 seconds
cpu usage	34.5702
user time	33.4415
system time	1.12864
max virtual memory	1.8279384E7
max residence set size	4038588.0

stage attributes

key	value
starexec-result	WORST_CASE(NON_POLY, ?)

output

34.36/10.65	WORST_CASE(NON_POLY, ?)
34.36/10.66	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
34.36/10.66	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
34.36/10.66	
34.36/10.66	
34.36/10.66	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
34.36/10.66	
34.36/10.66	(0) CpxTRS
34.36/10.66	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
34.36/10.66	(2) TRS for Loop Detection
34.36/10.66	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
34.36/10.66	(4) BEST
34.36/10.66	    (5) proven lower bound
34.36/10.66	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
34.36/10.66	        (7) BOUNDS(n^1, INF)
34.36/10.66	    (8) TRS for Loop Detection
34.36/10.66	        (9) DecreasingLoopProof [FINISHED, 7195 ms]
34.36/10.66	        (10) BOUNDS(EXP, INF)
34.36/10.66	
34.36/10.66	
34.36/10.66	----------------------------------------
34.36/10.66	
34.36/10.66	(0)
34.36/10.66	Obligation:
34.36/10.66	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
34.36/10.66	
34.36/10.66	
34.36/10.66	The TRS R consists of the following rules:
34.36/10.66	
34.36/10.66	   a__U101(tt, M, N) -> a__U102(a__isNatKind(M), M, N)
34.36/10.66	   a__U102(tt, M, N) -> a__U103(a__isNat(N), M, N)
34.36/10.66	   a__U103(tt, M, N) -> a__U104(a__isNatKind(N), M, N)
34.36/10.66	   a__U104(tt, M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
34.36/10.66	   a__U11(tt, V1, V2) -> a__U12(a__isNatKind(V1), V1, V2)
34.36/10.66	   a__U12(tt, V1, V2) -> a__U13(a__isNatKind(V2), V1, V2)
34.36/10.66	   a__U13(tt, V1, V2) -> a__U14(a__isNatKind(V2), V1, V2)
34.36/10.66	   a__U14(tt, V1, V2) -> a__U15(a__isNat(V1), V2)
34.36/10.66	   a__U15(tt, V2) -> a__U16(a__isNat(V2))
34.36/10.66	   a__U16(tt) -> tt
34.36/10.66	   a__U21(tt, V1) -> a__U22(a__isNatKind(V1), V1)
34.36/10.66	   a__U22(tt, V1) -> a__U23(a__isNat(V1))
34.36/10.66	   a__U23(tt) -> tt
34.36/10.66	   a__U31(tt, V1, V2) -> a__U32(a__isNatKind(V1), V1, V2)
34.36/10.66	   a__U32(tt, V1, V2) -> a__U33(a__isNatKind(V2), V1, V2)
34.36/10.66	   a__U33(tt, V1, V2) -> a__U34(a__isNatKind(V2), V1, V2)
34.36/10.66	   a__U34(tt, V1, V2) -> a__U35(a__isNat(V1), V2)
34.36/10.66	   a__U35(tt, V2) -> a__U36(a__isNat(V2))
34.36/10.66	   a__U36(tt) -> tt
34.36/10.66	   a__U41(tt, V2) -> a__U42(a__isNatKind(V2))
34.36/10.66	   a__U42(tt) -> tt
34.36/10.66	   a__U51(tt) -> tt
34.36/10.66	   a__U61(tt, V2) -> a__U62(a__isNatKind(V2))
34.36/10.66	   a__U62(tt) -> tt
34.36/10.66	   a__U71(tt, N) -> a__U72(a__isNatKind(N), N)
34.36/10.66	   a__U72(tt, N) -> mark(N)
34.36/10.66	   a__U81(tt, M, N) -> a__U82(a__isNatKind(M), M, N)
34.36/10.66	   a__U82(tt, M, N) -> a__U83(a__isNat(N), M, N)
34.36/10.66	   a__U83(tt, M, N) -> a__U84(a__isNatKind(N), M, N)
34.36/10.66	   a__U84(tt, M, N) -> s(a__plus(mark(N), mark(M)))
34.36/10.66	   a__U91(tt, N) -> a__U92(a__isNatKind(N))
34.36/10.66	   a__U92(tt) -> 0
34.36/10.66	   a__isNat(0) -> tt
34.36/10.66	   a__isNat(plus(V1, V2)) -> a__U11(a__isNatKind(V1), V1, V2)
34.36/10.66	   a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1)
34.36/10.66	   a__isNat(x(V1, V2)) -> a__U31(a__isNatKind(V1), V1, V2)
34.36/10.66	   a__isNatKind(0) -> tt
34.36/10.66	   a__isNatKind(plus(V1, V2)) -> a__U41(a__isNatKind(V1), V2)
34.36/10.66	   a__isNatKind(s(V1)) -> a__U51(a__isNatKind(V1))
34.36/10.66	   a__isNatKind(x(V1, V2)) -> a__U61(a__isNatKind(V1), V2)
34.36/10.66	   a__plus(N, 0) -> a__U71(a__isNat(N), N)
34.36/10.66	   a__plus(N, s(M)) -> a__U81(a__isNat(M), M, N)
34.36/10.66	   a__x(N, 0) -> a__U91(a__isNat(N), N)
34.36/10.66	   a__x(N, s(M)) -> a__U101(a__isNat(M), M, N)
34.36/10.66	   mark(U101(X1, X2, X3)) -> a__U101(mark(X1), X2, X3)
34.36/10.66	   mark(U102(X1, X2, X3)) -> a__U102(mark(X1), X2, X3)
34.36/10.66	   mark(isNatKind(X)) -> a__isNatKind(X)
34.36/10.66	   mark(U103(X1, X2, X3)) -> a__U103(mark(X1), X2, X3)
34.36/10.66	   mark(isNat(X)) -> a__isNat(X)
34.36/10.66	   mark(U104(X1, X2, X3)) -> a__U104(mark(X1), X2, X3)
34.36/10.66	   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
34.36/10.66	   mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
34.36/10.66	   mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
34.36/10.66	   mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
34.36/10.66	   mark(U13(X1, X2, X3)) -> a__U13(mark(X1), X2, X3)
34.36/10.66	   mark(U14(X1, X2, X3)) -> a__U14(mark(X1), X2, X3)
34.36/10.66	   mark(U15(X1, X2)) -> a__U15(mark(X1), X2)
34.36/10.66	   mark(U16(X)) -> a__U16(mark(X))
34.36/10.66	   mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
34.36/10.66	   mark(U22(X1, X2)) -> a__U22(mark(X1), X2)
34.36/10.66	   mark(U23(X)) -> a__U23(mark(X))
34.36/10.66	   mark(U31(X1, X2, X3)) -> a__U31(mark(X1), X2, X3)
34.36/10.66	   mark(U32(X1, X2, X3)) -> a__U32(mark(X1), X2, X3)
34.36/10.66	   mark(U33(X1, X2, X3)) -> a__U33(mark(X1), X2, X3)
34.36/10.66	   mark(U34(X1, X2, X3)) -> a__U34(mark(X1), X2, X3)
34.36/10.66	   mark(U35(X1, X2)) -> a__U35(mark(X1), X2)
34.36/10.66	   mark(U36(X)) -> a__U36(mark(X))
34.36/10.66	   mark(U41(X1, X2)) -> a__U41(mark(X1), X2)
34.36/10.66	   mark(U42(X)) -> a__U42(mark(X))
34.36/10.66	   mark(U51(X)) -> a__U51(mark(X))
34.36/10.66	   mark(U61(X1, X2)) -> a__U61(mark(X1), X2)

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