TRS_Innermost 2019-03-28 22.12 pair #432271100

details

property	value
status	complete
benchmark	OvConsOS_complete_noand_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n062.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.91012 seconds
cpu usage	11.8499
user time	11.3727
system time	0.477276
max virtual memory	1.8679512E7
max residence set size	1060000.0

stage attributes

key	value
starexec-result	YES

output

11.49/3.81	YES
11.68/3.83	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
11.68/3.83	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
11.68/3.83	
11.68/3.83	
11.68/3.83	Termination w.r.t. Q of the given QTRS could be proven:
11.68/3.83	
11.68/3.83	(0) QTRS
11.68/3.83	(1) QTRSToCSRProof [SOUND, 0 ms]
11.68/3.83	(2) CSR
11.68/3.83	(3) CSRRRRProof [EQUIVALENT, 161 ms]
11.68/3.83	(4) CSR
11.68/3.83	(5) CSRRRRProof [EQUIVALENT, 37 ms]
11.68/3.83	(6) CSR
11.68/3.83	(7) CSRRRRProof [EQUIVALENT, 48 ms]
11.68/3.83	(8) CSR
11.68/3.83	(9) CSDependencyPairsProof [EQUIVALENT, 95 ms]
11.68/3.83	(10) QCSDP
11.68/3.83	(11) QCSDependencyGraphProof [EQUIVALENT, 1 ms]
11.68/3.83	(12) AND
11.68/3.83	    (13) QCSDP
11.68/3.83	        (14) QCSUsableRulesProof [EQUIVALENT, 6 ms]
11.68/3.83	        (15) QCSDP
11.68/3.83	        (16) QCSDPMuMonotonicPoloProof [EQUIVALENT, 11 ms]
11.68/3.83	        (17) QCSDP
11.68/3.83	        (18) PIsEmptyProof [EQUIVALENT, 0 ms]
11.68/3.83	        (19) YES
11.68/3.83	    (20) QCSDP
11.68/3.83	        (21) QCSUsableRulesProof [EQUIVALENT, 21 ms]
11.68/3.83	        (22) QCSDP
11.68/3.83	        (23) QCSDPMuMonotonicPoloProof [EQUIVALENT, 78 ms]
11.68/3.83	        (24) QCSDP
11.68/3.83	        (25) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
11.68/3.83	        (26) QCSDP
11.68/3.83	        (27) QCSDPSubtermProof [EQUIVALENT, 0 ms]
11.68/3.83	        (28) QCSDP
11.68/3.83	        (29) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
11.68/3.83	        (30) TRUE
11.68/3.83	    (31) QCSDP
11.68/3.83	        (32) QCSDPSubtermProof [EQUIVALENT, 9 ms]
11.68/3.83	        (33) QCSDP
11.68/3.83	        (34) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
11.68/3.83	        (35) TRUE
11.68/3.83	    (36) QCSDP
11.68/3.83	        (37) QCSDPReductionPairProof [EQUIVALENT, 87 ms]
11.68/3.83	        (38) QCSDP
11.68/3.83	        (39) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
11.68/3.83	        (40) TRUE
11.68/3.83	
11.68/3.83	
11.68/3.83	----------------------------------------
11.68/3.83	
11.68/3.83	(0)
11.68/3.83	Obligation:
11.68/3.83	Q restricted rewrite system:
11.68/3.83	The TRS R consists of the following rules:
11.68/3.83	
11.68/3.83	   active(zeros) -> mark(cons(0, zeros))
11.68/3.83	   active(U101(tt, V1, V2)) -> mark(U102(isNatKind(V1), V1, V2))
11.68/3.83	   active(U102(tt, V1, V2)) -> mark(U103(isNatIListKind(V2), V1, V2))
11.68/3.83	   active(U103(tt, V1, V2)) -> mark(U104(isNatIListKind(V2), V1, V2))
11.68/3.83	   active(U104(tt, V1, V2)) -> mark(U105(isNat(V1), V2))
11.68/3.83	   active(U105(tt, V2)) -> mark(U106(isNatIList(V2)))
11.68/3.83	   active(U106(tt)) -> mark(tt)
11.68/3.83	   active(U11(tt, V1)) -> mark(U12(isNatIListKind(V1), V1))
11.68/3.83	   active(U111(tt, L, N)) -> mark(U112(isNatIListKind(L), L, N))
11.68/3.83	   active(U112(tt, L, N)) -> mark(U113(isNat(N), L, N))
11.68/3.83	   active(U113(tt, L, N)) -> mark(U114(isNatKind(N), L))
11.68/3.83	   active(U114(tt, L)) -> mark(s(length(L)))
11.68/3.83	   active(U12(tt, V1)) -> mark(U13(isNatList(V1)))
11.68/3.83	   active(U121(tt, IL)) -> mark(U122(isNatIListKind(IL)))
11.68/3.83	   active(U122(tt)) -> mark(nil)
11.68/3.83	   active(U13(tt)) -> mark(tt)
11.68/3.83	   active(U131(tt, IL, M, N)) -> mark(U132(isNatIListKind(IL), IL, M, N))
11.68/3.83	   active(U132(tt, IL, M, N)) -> mark(U133(isNat(M), IL, M, N))
11.68/3.83	   active(U133(tt, IL, M, N)) -> mark(U134(isNatKind(M), IL, M, N))
11.68/3.83	   active(U134(tt, IL, M, N)) -> mark(U135(isNat(N), IL, M, N))
11.68/3.83	   active(U135(tt, IL, M, N)) -> mark(U136(isNatKind(N), IL, M, N))
11.68/3.83	   active(U136(tt, IL, M, N)) -> mark(cons(N, take(M, IL)))
11.68/3.83	   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
11.68/3.83	   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
11.68/3.83	   active(U23(tt)) -> mark(tt)
11.68/3.83	   active(U31(tt, V)) -> mark(U32(isNatIListKind(V), V))
11.68/3.83	   active(U32(tt, V)) -> mark(U33(isNatList(V)))
11.68/3.83	   active(U33(tt)) -> mark(tt)
11.68/3.83	   active(U41(tt, V1, V2)) -> mark(U42(isNatKind(V1), V1, V2))
11.68/3.83	   active(U42(tt, V1, V2)) -> mark(U43(isNatIListKind(V2), V1, V2))
11.68/3.83	   active(U43(tt, V1, V2)) -> mark(U44(isNatIListKind(V2), V1, V2))
11.68/3.83	   active(U44(tt, V1, V2)) -> mark(U45(isNat(V1), V2))
11.68/3.83	   active(U45(tt, V2)) -> mark(U46(isNatIList(V2)))
11.68/3.83	   active(U46(tt)) -> mark(tt)
11.68/3.83	   active(U51(tt, V2)) -> mark(U52(isNatIListKind(V2)))
11.68/3.83	   active(U52(tt)) -> mark(tt)
11.68/3.83	   active(U61(tt, V2)) -> mark(U62(isNatIListKind(V2)))
11.68/3.83	   active(U62(tt)) -> mark(tt)
11.68/3.83	   active(U71(tt)) -> mark(tt)
11.68/3.83	   active(U81(tt)) -> mark(tt)
11.68/3.83	   active(U91(tt, V1, V2)) -> mark(U92(isNatKind(V1), V1, V2))
11.68/3.83	   active(U92(tt, V1, V2)) -> mark(U93(isNatIListKind(V2), V1, V2))
11.68/3.83	   active(U93(tt, V1, V2)) -> mark(U94(isNatIListKind(V2), V1, V2))

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actions all output return to TRS_Innermost 2019-03-28 22.12