Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313526

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	n046.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	17.2673 seconds
cpu usage	63.887
user time	61.4045
system time	2.48249
max virtual memory	1.8812368E7
max residence set size	5296992.0

stage attributes

key	value
starexec-result	WORST_CASE(NON_POLY, ?)

output

56.10/15.28	WORST_CASE(NON_POLY, ?)
63.53/17.15	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
63.53/17.15	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
63.53/17.15	
63.53/17.15	
63.53/17.15	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
63.53/17.15	
63.53/17.15	(0) CpxTRS
63.53/17.15	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
63.53/17.15	(2) TRS for Loop Detection
63.53/17.15	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
63.53/17.15	(4) BEST
63.53/17.15	    (5) proven lower bound
63.53/17.15	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
63.53/17.15	        (7) BOUNDS(n^1, INF)
63.53/17.15	    (8) TRS for Loop Detection
63.53/17.15	        (9) DecreasingLoopProof [FINISHED, 5320 ms]
63.53/17.15	        (10) BOUNDS(EXP, INF)
63.53/17.15	
63.53/17.15	
63.53/17.15	----------------------------------------
63.53/17.15	
63.53/17.15	(0)
63.53/17.15	Obligation:
63.53/17.15	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
63.53/17.15	
63.53/17.15	
63.53/17.15	The TRS R consists of the following rules:
63.53/17.15	
63.53/17.15	   a__U101(tt, M, N) -> a__U102(a__isNatKind(M), M, N)
63.53/17.15	   a__U102(tt, M, N) -> a__U103(a__isNat(N), M, N)
63.53/17.15	   a__U103(tt, M, N) -> a__U104(a__isNatKind(N), M, N)
63.53/17.15	   a__U104(tt, M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
63.53/17.15	   a__U11(tt, V1, V2) -> a__U12(a__isNatKind(V1), V1, V2)
63.53/17.15	   a__U12(tt, V1, V2) -> a__U13(a__isNatKind(V2), V1, V2)
63.53/17.15	   a__U13(tt, V1, V2) -> a__U14(a__isNatKind(V2), V1, V2)
63.53/17.15	   a__U14(tt, V1, V2) -> a__U15(a__isNat(V1), V2)
63.53/17.15	   a__U15(tt, V2) -> a__U16(a__isNat(V2))
63.53/17.15	   a__U16(tt) -> tt
63.53/17.15	   a__U21(tt, V1) -> a__U22(a__isNatKind(V1), V1)
63.53/17.15	   a__U22(tt, V1) -> a__U23(a__isNat(V1))
63.53/17.15	   a__U23(tt) -> tt
63.53/17.15	   a__U31(tt, V1, V2) -> a__U32(a__isNatKind(V1), V1, V2)
63.53/17.15	   a__U32(tt, V1, V2) -> a__U33(a__isNatKind(V2), V1, V2)
63.53/17.15	   a__U33(tt, V1, V2) -> a__U34(a__isNatKind(V2), V1, V2)
63.53/17.15	   a__U34(tt, V1, V2) -> a__U35(a__isNat(V1), V2)
63.53/17.15	   a__U35(tt, V2) -> a__U36(a__isNat(V2))
63.53/17.15	   a__U36(tt) -> tt
63.53/17.15	   a__U41(tt, V2) -> a__U42(a__isNatKind(V2))
63.53/17.15	   a__U42(tt) -> tt
63.53/17.15	   a__U51(tt) -> tt
63.53/17.15	   a__U61(tt, V2) -> a__U62(a__isNatKind(V2))
63.53/17.15	   a__U62(tt) -> tt
63.53/17.15	   a__U71(tt, N) -> a__U72(a__isNatKind(N), N)
63.53/17.15	   a__U72(tt, N) -> mark(N)
63.53/17.15	   a__U81(tt, M, N) -> a__U82(a__isNatKind(M), M, N)
63.53/17.15	   a__U82(tt, M, N) -> a__U83(a__isNat(N), M, N)
63.53/17.15	   a__U83(tt, M, N) -> a__U84(a__isNatKind(N), M, N)
63.53/17.15	   a__U84(tt, M, N) -> s(a__plus(mark(N), mark(M)))
63.53/17.15	   a__U91(tt, N) -> a__U92(a__isNatKind(N))
63.53/17.15	   a__U92(tt) -> 0
63.53/17.15	   a__isNat(0) -> tt
63.53/17.15	   a__isNat(plus(V1, V2)) -> a__U11(a__isNatKind(V1), V1, V2)
63.53/17.15	   a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1)
63.53/17.15	   a__isNat(x(V1, V2)) -> a__U31(a__isNatKind(V1), V1, V2)
63.53/17.15	   a__isNatKind(0) -> tt
63.53/17.15	   a__isNatKind(plus(V1, V2)) -> a__U41(a__isNatKind(V1), V2)
63.53/17.15	   a__isNatKind(s(V1)) -> a__U51(a__isNatKind(V1))
63.53/17.15	   a__isNatKind(x(V1, V2)) -> a__U61(a__isNatKind(V1), V2)
63.53/17.15	   a__plus(N, 0) -> a__U71(a__isNat(N), N)
63.53/17.15	   a__plus(N, s(M)) -> a__U81(a__isNat(M), M, N)
63.53/17.15	   a__x(N, 0) -> a__U91(a__isNat(N), N)
63.53/17.15	   a__x(N, s(M)) -> a__U101(a__isNat(M), M, N)
63.53/17.15	   mark(U101(X1, X2, X3)) -> a__U101(mark(X1), X2, X3)
63.53/17.15	   mark(U102(X1, X2, X3)) -> a__U102(mark(X1), X2, X3)
63.53/17.15	   mark(isNatKind(X)) -> a__isNatKind(X)
63.53/17.15	   mark(U103(X1, X2, X3)) -> a__U103(mark(X1), X2, X3)
63.53/17.15	   mark(isNat(X)) -> a__isNat(X)
63.53/17.15	   mark(U104(X1, X2, X3)) -> a__U104(mark(X1), X2, X3)
63.53/17.15	   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
63.53/17.15	   mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
63.53/17.15	   mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
63.53/17.15	   mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
63.53/17.15	   mark(U13(X1, X2, X3)) -> a__U13(mark(X1), X2, X3)
63.53/17.15	   mark(U14(X1, X2, X3)) -> a__U14(mark(X1), X2, X3)
63.53/17.15	   mark(U15(X1, X2)) -> a__U15(mark(X1), X2)
63.53/17.15	   mark(U16(X)) -> a__U16(mark(X))
63.53/17.15	   mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
63.53/17.15	   mark(U22(X1, X2)) -> a__U22(mark(X1), X2)
63.53/17.15	   mark(U23(X)) -> a__U23(mark(X))
63.53/17.15	   mark(U31(X1, X2, X3)) -> a__U31(mark(X1), X2, X3)
63.53/17.15	   mark(U32(X1, X2, X3)) -> a__U32(mark(X1), X2, X3)
63.53/17.15	   mark(U33(X1, X2, X3)) -> a__U33(mark(X1), X2, X3)
63.53/17.15	   mark(U34(X1, X2, X3)) -> a__U34(mark(X1), X2, X3)
63.53/17.15	   mark(U35(X1, X2)) -> a__U35(mark(X1), X2)
63.53/17.15	   mark(U36(X)) -> a__U36(mark(X))
63.53/17.15	   mark(U41(X1, X2)) -> a__U41(mark(X1), X2)
63.53/17.15	   mark(U42(X)) -> a__U42(mark(X))
63.53/17.15	   mark(U51(X)) -> a__U51(mark(X))
63.53/17.15	   mark(U61(X1, X2)) -> a__U61(mark(X1), X2)

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actions all output return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40