TRS Innermost pair #487524343

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	n084.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.39991307259 seconds
cpu usage	6.365585761
max memory	5.2074496E8

stage attributes

key	value
output-size	65131
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 [SOUND, 0 ms]
(2) CSR
(3) CSDependencyPairsProof [EQUIVALENT, 63 ms]
(4) QCSDP
(5) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) QCSDP
        (8) QCSDPSubtermProof [EQUIVALENT, 9 ms]
        (9) QCSDP
        (10) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (11) TRUE
    (12) QCSDP
        (13) QCSUsableRulesProof [EQUIVALENT, 0 ms]
        (14) QCSDP
        (15) QCSDPMuMonotonicPoloProof [EQUIVALENT, 72 ms]
        (16) QCSDP
        (17) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (18) TRUE
    (19) QCSDP
        (20) QCSDPSubtermProof [EQUIVALENT, 5 ms]
        (21) QCSDP
        (22) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (23) TRUE
    (24) QCSDP
        (25) QCSDPSubtermProof [EQUIVALENT, 14 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)

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job log

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actions all output return to TRS Innermost