Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308230

details

property	value
status	complete
benchmark	MYNAT_complete_noand_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n170.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	13.8641 seconds
cpu usage	50.4929
user time	48.4236
system time	2.06929
max virtual memory	1.9221268E7
max residence set size	4018676.0

stage attributes

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

output

50.15/13.78	WORST_CASE(Omega(n^1), O(n^1))
50.15/13.80	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
50.15/13.80	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
50.15/13.80	
50.15/13.80	
50.15/13.80	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
50.15/13.80	
50.15/13.80	(0) CpxTRS
50.15/13.80	(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 5 ms]
50.15/13.80	(2) CpxTRS
50.15/13.80	    (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
50.15/13.80	    (4) CpxTRS
50.15/13.80	    (5) CpxTrsToCdtProof [UPPER BOUND(ID), 6 ms]
50.15/13.80	    (6) CdtProblem
50.15/13.80	    (7) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
50.15/13.80	    (8) CdtProblem
50.15/13.80	    (9) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
50.15/13.80	    (10) CdtProblem
50.15/13.80	    (11) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
50.15/13.80	    (12) CdtProblem
50.15/13.80	    (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 270 ms]
50.15/13.80	    (14) CdtProblem
50.15/13.80	    (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 69 ms]
50.15/13.80	    (16) CdtProblem
50.15/13.80	    (17) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms]
50.15/13.80	    (18) BOUNDS(1, 1)
50.15/13.80	(19) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
50.15/13.80	(20) TRS for Loop Detection
50.15/13.80	    (21) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
50.15/13.80	    (22) BEST
50.15/13.80	        (23) proven lower bound
50.15/13.80	            (24) LowerBoundPropagationProof [FINISHED, 0 ms]
50.15/13.80	            (25) BOUNDS(n^1, INF)
50.15/13.80	        (26) TRS for Loop Detection
50.15/13.80	
50.15/13.80	
50.15/13.80	----------------------------------------
50.15/13.80	
50.15/13.80	(0)
50.15/13.80	Obligation:
50.15/13.80	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
50.15/13.80	
50.15/13.80	
50.15/13.80	The TRS R consists of the following rules:
50.15/13.80	
50.15/13.80	   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
50.15/13.80	   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
50.15/13.80	   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
50.15/13.80	   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
50.15/13.80	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
50.15/13.80	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
50.15/13.80	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
50.15/13.80	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
50.15/13.80	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
50.15/13.80	   active(U16(tt)) -> mark(tt)
50.15/13.80	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
50.15/13.80	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
50.15/13.80	   active(U23(tt)) -> mark(tt)
50.15/13.80	   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
50.15/13.80	   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
50.15/13.80	   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
50.15/13.80	   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
50.15/13.80	   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
50.15/13.80	   active(U36(tt)) -> mark(tt)
50.15/13.80	   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
50.15/13.80	   active(U42(tt)) -> mark(tt)
50.15/13.80	   active(U51(tt)) -> mark(tt)
50.15/13.80	   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
50.15/13.80	   active(U62(tt)) -> mark(tt)
50.15/13.80	   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
50.15/13.80	   active(U72(tt, N)) -> mark(N)
50.15/13.80	   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
50.15/13.80	   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
50.15/13.80	   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
50.15/13.80	   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
50.15/13.80	   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
50.15/13.80	   active(U92(tt)) -> mark(0)
50.15/13.80	   active(isNat(0)) -> mark(tt)
50.15/13.80	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
50.15/13.80	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
50.15/13.80	   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
50.15/13.80	   active(isNatKind(0)) -> mark(tt)
50.15/13.80	   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
50.15/13.80	   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
50.15/13.80	   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
50.15/13.80	   active(plus(N, 0)) -> mark(U71(isNat(N), N))
50.15/13.80	   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
50.15/13.80	   active(x(N, 0)) -> mark(U91(isNat(N), N))
50.15/13.80	   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
50.15/13.80	   active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3)
50.15/13.80	   active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3)
50.15/13.80	   active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3)
50.15/13.80	   active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3)
50.15/13.80	   active(plus(X1, X2)) -> plus(active(X1), X2)
50.15/13.80	   active(plus(X1, X2)) -> plus(X1, active(X2))
50.15/13.80	   active(x(X1, X2)) -> x(active(X1), X2)
50.15/13.80	   active(x(X1, X2)) -> x(X1, active(X2))
50.15/13.80	   active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3)
50.15/13.80	   active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3)
50.15/13.80	   active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3)

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job log

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