TRS_Innermost 2019-03-28 22.12 pair #432271026

details

property	value
status	complete
benchmark	PEANO_complete_iGM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n165.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.59164 seconds
cpu usage	6.3501
user time	6.11014
system time	0.239957
max virtual memory	1.8408888E7
max residence set size	382008.0

stage attributes

key	value
starexec-result	YES

output

6.17/2.55	YES
6.17/2.55	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
6.17/2.55	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.17/2.55	
6.17/2.55	
6.17/2.55	Termination w.r.t. Q of the given QTRS could be proven:
6.17/2.55	
6.17/2.55	(0) QTRS
6.17/2.55	(1) QTRSRRRProof [EQUIVALENT, 511 ms]
6.17/2.55	(2) QTRS
6.17/2.55	(3) QTRSRRRProof [EQUIVALENT, 54 ms]
6.17/2.55	(4) QTRS
6.17/2.55	(5) QTRSRRRProof [EQUIVALENT, 2 ms]
6.17/2.55	(6) QTRS
6.17/2.55	(7) RisEmptyProof [EQUIVALENT, 0 ms]
6.17/2.55	(8) YES
6.17/2.55	
6.17/2.55	
6.17/2.55	----------------------------------------
6.17/2.55	
6.17/2.55	(0)
6.17/2.55	Obligation:
6.17/2.55	Q restricted rewrite system:
6.17/2.55	The TRS R consists of the following rules:
6.17/2.55	
6.17/2.55	   active(U11(tt, V1, V2)) -> mark(U12(isNat(V1), V2))
6.17/2.55	   active(U12(tt, V2)) -> mark(U13(isNat(V2)))
6.17/2.55	   active(U13(tt)) -> mark(tt)
6.17/2.55	   active(U21(tt, V1)) -> mark(U22(isNat(V1)))
6.17/2.55	   active(U22(tt)) -> mark(tt)
6.17/2.55	   active(U31(tt, N)) -> mark(N)
6.17/2.55	   active(U41(tt, M, N)) -> mark(s(plus(N, M)))
6.17/2.55	   active(and(tt, X)) -> mark(X)
6.17/2.55	   active(isNat(0)) -> mark(tt)
6.17/2.55	   active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2))
6.17/2.55	   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
6.17/2.55	   active(isNatKind(0)) -> mark(tt)
6.17/2.55	   active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2)))
6.17/2.55	   active(isNatKind(s(V1))) -> mark(isNatKind(V1))
6.17/2.55	   active(plus(N, 0)) -> mark(U31(and(isNat(N), isNatKind(N)), N))
6.17/2.55	   active(plus(N, s(M))) -> mark(U41(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
6.17/2.55	   mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3))
6.17/2.55	   mark(tt) -> active(tt)
6.17/2.55	   mark(U12(X1, X2)) -> active(U12(mark(X1), X2))
6.17/2.55	   mark(isNat(X)) -> active(isNat(X))
6.17/2.55	   mark(U13(X)) -> active(U13(mark(X)))
6.17/2.55	   mark(U21(X1, X2)) -> active(U21(mark(X1), X2))
6.17/2.55	   mark(U22(X)) -> active(U22(mark(X)))
6.17/2.55	   mark(U31(X1, X2)) -> active(U31(mark(X1), X2))
6.17/2.55	   mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3))
6.17/2.55	   mark(s(X)) -> active(s(mark(X)))
6.17/2.55	   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2)))
6.17/2.55	   mark(and(X1, X2)) -> active(and(mark(X1), X2))
6.17/2.55	   mark(0) -> active(0)
6.17/2.55	   mark(isNatKind(X)) -> active(isNatKind(X))
6.17/2.55	   U11(mark(X1), X2, X3) -> U11(X1, X2, X3)
6.17/2.55	   U11(X1, mark(X2), X3) -> U11(X1, X2, X3)
6.17/2.55	   U11(X1, X2, mark(X3)) -> U11(X1, X2, X3)
6.17/2.55	   U11(active(X1), X2, X3) -> U11(X1, X2, X3)
6.17/2.55	   U11(X1, active(X2), X3) -> U11(X1, X2, X3)
6.17/2.55	   U11(X1, X2, active(X3)) -> U11(X1, X2, X3)
6.17/2.55	   U12(mark(X1), X2) -> U12(X1, X2)
6.17/2.55	   U12(X1, mark(X2)) -> U12(X1, X2)
6.17/2.55	   U12(active(X1), X2) -> U12(X1, X2)
6.17/2.55	   U12(X1, active(X2)) -> U12(X1, X2)
6.17/2.55	   isNat(mark(X)) -> isNat(X)
6.17/2.55	   isNat(active(X)) -> isNat(X)
6.17/2.55	   U13(mark(X)) -> U13(X)
6.17/2.55	   U13(active(X)) -> U13(X)
6.17/2.55	   U21(mark(X1), X2) -> U21(X1, X2)
6.17/2.55	   U21(X1, mark(X2)) -> U21(X1, X2)
6.17/2.55	   U21(active(X1), X2) -> U21(X1, X2)
6.17/2.55	   U21(X1, active(X2)) -> U21(X1, X2)
6.17/2.55	   U22(mark(X)) -> U22(X)
6.17/2.55	   U22(active(X)) -> U22(X)
6.17/2.55	   U31(mark(X1), X2) -> U31(X1, X2)
6.17/2.55	   U31(X1, mark(X2)) -> U31(X1, X2)
6.17/2.55	   U31(active(X1), X2) -> U31(X1, X2)
6.17/2.55	   U31(X1, active(X2)) -> U31(X1, X2)
6.17/2.55	   U41(mark(X1), X2, X3) -> U41(X1, X2, X3)
6.17/2.55	   U41(X1, mark(X2), X3) -> U41(X1, X2, X3)
6.17/2.55	   U41(X1, X2, mark(X3)) -> U41(X1, X2, X3)
6.17/2.55	   U41(active(X1), X2, X3) -> U41(X1, X2, X3)
6.17/2.55	   U41(X1, active(X2), X3) -> U41(X1, X2, X3)
6.17/2.56	   U41(X1, X2, active(X3)) -> U41(X1, X2, X3)
6.17/2.56	   s(mark(X)) -> s(X)
6.17/2.56	   s(active(X)) -> s(X)
6.17/2.56	   plus(mark(X1), X2) -> plus(X1, X2)
6.17/2.56	   plus(X1, mark(X2)) -> plus(X1, X2)
6.17/2.56	   plus(active(X1), X2) -> plus(X1, X2)
6.17/2.56	   plus(X1, active(X2)) -> plus(X1, X2)
6.17/2.56	   and(mark(X1), X2) -> and(X1, X2)
6.17/2.56	   and(X1, mark(X2)) -> and(X1, X2)
6.17/2.56	   and(active(X1), X2) -> and(X1, X2)
6.17/2.56	   and(X1, active(X2)) -> and(X1, X2)
6.17/2.56	   isNatKind(mark(X)) -> isNatKind(X)
6.17/2.56	   isNatKind(active(X)) -> isNatKind(X)
6.17/2.56	
6.17/2.56	The set Q consists of the following terms:
6.17/2.56

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