TRS Standard pair #487069613

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	n173.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.55022 seconds
cpu usage	6.21443
user time	5.9479
system time	0.266531
max virtual memory	1.8744808E7
max residence set size	486564.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) QTRSToCSRProof [EQUIVALENT, 0 ms]
(2) CSR
(3) CSDependencyPairsProof [EQUIVALENT, 57 ms]
(4) QCSDP
(5) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) QCSDP
        (8) QCSDPSubtermProof [EQUIVALENT, 20 ms]
        (9) QCSDP
        (10) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (11) TRUE
    (12) QCSDP
        (13) QCSUsableRulesProof [EQUIVALENT, 0 ms]
        (14) QCSDP
        (15) QCSDPMuMonotonicPoloProof [EQUIVALENT, 46 ms]
        (16) QCSDP
        (17) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (18) TRUE
    (19) QCSDP
        (20) QCSDPSubtermProof [EQUIVALENT, 3 ms]
        (21) QCSDP
        (22) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (23) TRUE
    (24) QCSDP
        (25) QCSDPSubtermProof [EQUIVALENT, 7 ms]
        (26) QCSDP
        (27) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (28) TRUE


----------------------------------------

(0)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   active(U101(tt, M, N)) -> mark(U102(isNatKind(M), M, N))
   active(U102(tt, M, N)) -> mark(U103(isNat(N), M, N))
   active(U103(tt, M, N)) -> mark(U104(isNatKind(N), M, N))
   active(U104(tt, M, N)) -> mark(plus(x(N, M), N))
   active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2))
   active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2))
   active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2))
   active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2))
   active(U15(tt, V2)) -> mark(U16(isNat(V2)))
   active(U16(tt)) -> mark(tt)
   active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1))
   active(U22(tt, V1)) -> mark(U23(isNat(V1)))
   active(U23(tt)) -> mark(tt)
   active(U31(tt, V1, V2)) -> mark(U32(isNatKind(V1), V1, V2))
   active(U32(tt, V1, V2)) -> mark(U33(isNatKind(V2), V1, V2))
   active(U33(tt, V1, V2)) -> mark(U34(isNatKind(V2), V1, V2))
   active(U34(tt, V1, V2)) -> mark(U35(isNat(V1), V2))
   active(U35(tt, V2)) -> mark(U36(isNat(V2)))
   active(U36(tt)) -> mark(tt)
   active(U41(tt, V2)) -> mark(U42(isNatKind(V2)))
   active(U42(tt)) -> mark(tt)
   active(U51(tt)) -> mark(tt)
   active(U61(tt, V2)) -> mark(U62(isNatKind(V2)))
   active(U62(tt)) -> mark(tt)
   active(U71(tt, N)) -> mark(U72(isNatKind(N), N))
   active(U72(tt, N)) -> mark(N)
   active(U81(tt, M, N)) -> mark(U82(isNatKind(M), M, N))
   active(U82(tt, M, N)) -> mark(U83(isNat(N), M, N))
   active(U83(tt, M, N)) -> mark(U84(isNatKind(N), M, N))
   active(U84(tt, M, N)) -> mark(s(plus(N, M)))
   active(U91(tt, N)) -> mark(U92(isNatKind(N)))
   active(U92(tt)) -> mark(0)
   active(isNat(0)) -> mark(tt)
   active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2))
   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
   active(isNat(x(V1, V2))) -> mark(U31(isNatKind(V1), V1, V2))
   active(isNatKind(0)) -> mark(tt)
   active(isNatKind(plus(V1, V2))) -> mark(U41(isNatKind(V1), V2))
   active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
   active(isNatKind(x(V1, V2))) -> mark(U61(isNatKind(V1), V2))
   active(plus(N, 0)) -> mark(U71(isNat(N), N))
   active(plus(N, s(M))) -> mark(U81(isNat(M), M, N))
   active(x(N, 0)) -> mark(U91(isNat(N), N))
   active(x(N, s(M))) -> mark(U101(isNat(M), M, N))
   active(U101(X1, X2, X3)) -> U101(active(X1), X2, X3)
   active(U102(X1, X2, X3)) -> U102(active(X1), X2, X3)
   active(U103(X1, X2, X3)) -> U103(active(X1), X2, X3)
   active(U104(X1, X2, X3)) -> U104(active(X1), X2, X3)
   active(plus(X1, X2)) -> plus(active(X1), X2)
   active(plus(X1, X2)) -> plus(X1, active(X2))
   active(x(X1, X2)) -> x(active(X1), X2)
   active(x(X1, X2)) -> x(X1, active(X2))
   active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3)
   active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3)
   active(U13(X1, X2, X3)) -> U13(active(X1), X2, X3)

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