Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308222

details

property	value
status	complete
benchmark	PEANO_complete_noand_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n093.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	10.1826 seconds
cpu usage	35.229
user time	33.2757
system time	1.95332
max virtual memory	5.6417816E7
max residence set size	4154008.0

stage attributes

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

output

34.79/10.06	WORST_CASE(Omega(n^1), O(n^1))
34.79/10.08	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
34.79/10.08	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
34.79/10.08	
34.79/10.08	
34.79/10.08	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
34.79/10.08	
34.79/10.08	(0) CpxTRS
34.79/10.08	(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms]
34.79/10.08	(2) CpxTRS
34.79/10.08	    (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
34.79/10.08	    (4) CpxTRS
34.79/10.08	    (5) CpxTrsMatchBoundsTAProof [FINISHED, 568 ms]
34.79/10.08	    (6) BOUNDS(1, n^1)
34.79/10.08	(7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
34.79/10.08	(8) CpxTRS
34.79/10.08	    (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
34.79/10.08	    (10) typed CpxTrs
34.79/10.08	    (11) OrderProof [LOWER BOUND(ID), 9 ms]
34.79/10.08	    (12) typed CpxTrs
34.79/10.08	    (13) RewriteLemmaProof [LOWER BOUND(ID), 496 ms]
34.79/10.08	    (14) BEST
34.79/10.08	        (15) proven lower bound
34.79/10.08	            (16) LowerBoundPropagationProof [FINISHED, 0 ms]
34.79/10.08	            (17) BOUNDS(n^1, INF)
34.79/10.08	        (18) typed CpxTrs
34.79/10.08	            (19) RewriteLemmaProof [LOWER BOUND(ID), 142 ms]
34.79/10.08	            (20) typed CpxTrs
34.79/10.08	            (21) RewriteLemmaProof [LOWER BOUND(ID), 161 ms]
34.79/10.08	            (22) typed CpxTrs
34.79/10.08	            (23) RewriteLemmaProof [LOWER BOUND(ID), 67 ms]
34.79/10.08	            (24) typed CpxTrs
34.79/10.08	            (25) RewriteLemmaProof [LOWER BOUND(ID), 95 ms]
34.79/10.08	            (26) typed CpxTrs
34.79/10.08	            (27) RewriteLemmaProof [LOWER BOUND(ID), 146 ms]
34.79/10.08	            (28) typed CpxTrs
34.79/10.08	            (29) RewriteLemmaProof [LOWER BOUND(ID), 65 ms]
34.79/10.08	            (30) typed CpxTrs
34.79/10.08	            (31) RewriteLemmaProof [LOWER BOUND(ID), 109 ms]
34.79/10.08	            (32) typed CpxTrs
34.79/10.08	            (33) RewriteLemmaProof [LOWER BOUND(ID), 114 ms]
34.79/10.08	            (34) typed CpxTrs
34.79/10.08	            (35) RewriteLemmaProof [LOWER BOUND(ID), 196 ms]
34.79/10.08	            (36) typed CpxTrs
34.79/10.08	            (37) RewriteLemmaProof [LOWER BOUND(ID), 195 ms]
34.79/10.08	            (38) typed CpxTrs
34.79/10.08	            (39) RewriteLemmaProof [LOWER BOUND(ID), 111 ms]
34.79/10.08	            (40) typed CpxTrs
34.79/10.08	            (41) RewriteLemmaProof [LOWER BOUND(ID), 76 ms]
34.79/10.08	            (42) typed CpxTrs
34.79/10.08	            (43) RewriteLemmaProof [LOWER BOUND(ID), 119 ms]
34.79/10.08	            (44) typed CpxTrs
34.79/10.08	            (45) RewriteLemmaProof [LOWER BOUND(ID), 165 ms]
34.79/10.08	            (46) typed CpxTrs
34.79/10.08	            (47) RewriteLemmaProof [LOWER BOUND(ID), 64 ms]
34.79/10.08	            (48) typed CpxTrs
34.79/10.08	            (49) RewriteLemmaProof [LOWER BOUND(ID), 87 ms]
34.79/10.08	            (50) typed CpxTrs
34.79/10.08	            (51) RewriteLemmaProof [LOWER BOUND(ID), 15 ms]
34.79/10.08	            (52) typed CpxTrs
34.79/10.08	            (53) RewriteLemmaProof [LOWER BOUND(ID), 130 ms]
34.79/10.08	            (54) typed CpxTrs
34.79/10.08	            (55) RewriteLemmaProof [LOWER BOUND(ID), 153 ms]
34.79/10.08	            (56) typed CpxTrs
34.79/10.08	
34.79/10.08	
34.79/10.08	----------------------------------------
34.79/10.08	
34.79/10.08	(0)
34.79/10.08	Obligation:
34.79/10.08	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
34.79/10.08	
34.79/10.08	
34.79/10.08	The TRS R consists of the following rules:
34.79/10.08	
34.79/10.08	   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
34.79/10.08	   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
34.79/10.08	   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
34.79/10.08	   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
34.79/10.08	   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
34.79/10.08	   active(U16(tt)) -> mark(tt)
34.79/10.08	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
34.79/10.08	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
34.79/10.08	   active(U23(tt)) -> mark(tt)
34.79/10.08	   active(U31(tt, V2)) -> mark(U32(isNatKind(V2)))
34.79/10.08	   active(U32(tt)) -> mark(tt)
34.79/10.08	   active(U41(tt)) -> mark(tt)
34.79/10.08	   active(U51(tt, N)) -> mark(U52(isNatKind(N), N))
34.79/10.08	   active(U52(tt, N)) -> mark(N)
34.79/10.08	   active(U61(tt, M, N)) -> mark(U62(isNatKind(M), M, N))
34.79/10.08	   active(U62(tt, M, N)) -> mark(U63(isNat(N), M, N))
34.79/10.08	   active(U63(tt, M, N)) -> mark(U64(isNatKind(N), M, N))
34.79/10.08	   active(U64(tt, M, N)) -> mark(s(plus(N, M)))
34.79/10.08	   active(isNat(0)) -> mark(tt)
34.79/10.08	   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
34.79/10.08	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
34.79/10.08	   active(isNatKind(0)) -> mark(tt)
34.79/10.08	   active(isNatKind(plus(V1, V2))) -> mark(U31(isNatKind(V1), V2))
34.79/10.08	   active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1)))
34.79/10.08	   active(plus(N, 0)) -> mark(U51(isNat(N), N))

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