Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307989

details

property	value
status	complete
benchmark	MYNAT_nokinds_noand_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n178.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	3.69816 seconds
cpu usage	10.8807
user time	10.124
system time	0.756659
max virtual memory	1.8279384E7
max residence set size	2554616.0

stage attributes

key	value
starexec-result	WORST_CASE(NON_POLY, ?)

output

10.30/3.41	WORST_CASE(NON_POLY, ?)
10.58/3.51	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
10.58/3.51	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.58/3.51	
10.58/3.51	
10.58/3.51	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
10.58/3.51	
10.58/3.51	(0) CpxTRS
10.58/3.51	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
10.58/3.51	(2) TRS for Loop Detection
10.58/3.51	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
10.58/3.51	(4) BEST
10.58/3.51	    (5) proven lower bound
10.58/3.51	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
10.58/3.51	        (7) BOUNDS(n^1, INF)
10.58/3.51	    (8) TRS for Loop Detection
10.58/3.51	        (9) DecreasingLoopProof [FINISHED, 1351 ms]
10.58/3.51	        (10) BOUNDS(EXP, INF)
10.58/3.51	
10.58/3.51	
10.58/3.51	----------------------------------------
10.58/3.51	
10.58/3.51	(0)
10.58/3.51	Obligation:
10.58/3.51	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
10.58/3.51	
10.58/3.51	
10.58/3.51	The TRS R consists of the following rules:
10.58/3.51	
10.58/3.51	   a__U11(tt, V2) -> a__U12(a__isNat(V2))
10.58/3.51	   a__U12(tt) -> tt
10.58/3.51	   a__U21(tt) -> tt
10.58/3.51	   a__U31(tt, V2) -> a__U32(a__isNat(V2))
10.58/3.51	   a__U32(tt) -> tt
10.58/3.51	   a__U41(tt, N) -> mark(N)
10.58/3.51	   a__U51(tt, M, N) -> a__U52(a__isNat(N), M, N)
10.58/3.51	   a__U52(tt, M, N) -> s(a__plus(mark(N), mark(M)))
10.58/3.51	   a__U61(tt) -> 0
10.58/3.51	   a__U71(tt, M, N) -> a__U72(a__isNat(N), M, N)
10.58/3.51	   a__U72(tt, M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
10.58/3.51	   a__isNat(0) -> tt
10.58/3.51	   a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2)
10.58/3.51	   a__isNat(s(V1)) -> a__U21(a__isNat(V1))
10.58/3.51	   a__isNat(x(V1, V2)) -> a__U31(a__isNat(V1), V2)
10.58/3.51	   a__plus(N, 0) -> a__U41(a__isNat(N), N)
10.58/3.51	   a__plus(N, s(M)) -> a__U51(a__isNat(M), M, N)
10.58/3.51	   a__x(N, 0) -> a__U61(a__isNat(N))
10.58/3.51	   a__x(N, s(M)) -> a__U71(a__isNat(M), M, N)
10.58/3.51	   mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
10.58/3.51	   mark(U12(X)) -> a__U12(mark(X))
10.58/3.51	   mark(isNat(X)) -> a__isNat(X)
10.58/3.51	   mark(U21(X)) -> a__U21(mark(X))
10.58/3.51	   mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
10.58/3.51	   mark(U32(X)) -> a__U32(mark(X))
10.58/3.51	   mark(U41(X1, X2)) -> a__U41(mark(X1), X2)
10.58/3.51	   mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
10.58/3.51	   mark(U52(X1, X2, X3)) -> a__U52(mark(X1), X2, X3)
10.58/3.51	   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
10.58/3.51	   mark(U61(X)) -> a__U61(mark(X))
10.58/3.51	   mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3)
10.58/3.51	   mark(U72(X1, X2, X3)) -> a__U72(mark(X1), X2, X3)
10.58/3.51	   mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
10.58/3.51	   mark(tt) -> tt
10.58/3.51	   mark(s(X)) -> s(mark(X))
10.58/3.51	   mark(0) -> 0
10.58/3.51	   a__U11(X1, X2) -> U11(X1, X2)
10.58/3.51	   a__U12(X) -> U12(X)
10.58/3.51	   a__isNat(X) -> isNat(X)
10.58/3.51	   a__U21(X) -> U21(X)
10.58/3.51	   a__U31(X1, X2) -> U31(X1, X2)
10.58/3.51	   a__U32(X) -> U32(X)
10.58/3.51	   a__U41(X1, X2) -> U41(X1, X2)
10.58/3.51	   a__U51(X1, X2, X3) -> U51(X1, X2, X3)
10.58/3.51	   a__U52(X1, X2, X3) -> U52(X1, X2, X3)
10.58/3.51	   a__plus(X1, X2) -> plus(X1, X2)
10.58/3.51	   a__U61(X) -> U61(X)
10.58/3.51	   a__U71(X1, X2, X3) -> U71(X1, X2, X3)
10.58/3.51	   a__U72(X1, X2, X3) -> U72(X1, X2, X3)
10.58/3.51	   a__x(X1, X2) -> x(X1, X2)
10.58/3.51	
10.58/3.51	S is empty.
10.58/3.51	Rewrite Strategy: FULL
10.58/3.51	----------------------------------------
10.58/3.51	
10.58/3.51	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
10.58/3.51	Transformed a relative TRS into a decreasing-loop problem.
10.58/3.51	----------------------------------------
10.58/3.51	
10.58/3.51	(2)
10.58/3.51	Obligation:
10.58/3.51	Analyzing the following TRS for decreasing loops:
10.58/3.51	
10.58/3.51	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
10.58/3.51	
10.58/3.51	
10.58/3.51	The TRS R consists of the following rules:
10.58/3.51	
10.58/3.51	   a__U11(tt, V2) -> a__U12(a__isNat(V2))
10.58/3.51	   a__U12(tt) -> tt
10.58/3.51	   a__U21(tt) -> tt

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