TRS Standard pair #487071418

details

property	value
status	complete
benchmark	MYNAT_complete_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n181.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.81247 seconds
cpu usage	11.7688
user time	11.2224
system time	0.546361
max virtual memory	1.9072404E7
max residence set size	1132932.0

stage attributes

key	value
starexec-result	YES

output

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 [EQUIVALENT, 0 ms]
(2) CSR
(3) CSDependencyPairsProof [EQUIVALENT, 0 ms]
(4) QCSDP
(5) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) QCSDP
        (8) QCSDPReductionPairProof [EQUIVALENT, 71 ms]
        (9) QCSDP
        (10) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (11) AND
            (12) QCSDP
                (13) QCSDPReductionPairProof [EQUIVALENT, 297 ms]
                (14) QCSDP
                (15) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
                (16) TRUE
            (17) QCSDP
                (18) QCSDPReductionPairProof [EQUIVALENT, 357 ms]
                (19) QCSDP
                (20) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
                (21) TRUE
    (22) QCSDP
        (23) QCSDPSubtermProof [EQUIVALENT, 1 ms]
        (24) QCSDP
        (25) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (26) TRUE
    (27) QCSDP
        (28) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (29) QCSDP
        (30) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (31) TRUE


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

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

   active(U11(tt, V1, V2)) -> mark(U12(isNat(V1), V2))
   active(U12(tt, V2)) -> mark(U13(isNat(V2)))
   active(U13(tt)) -> mark(tt)
   active(U21(tt, V1)) -> mark(U22(isNat(V1)))
   active(U22(tt)) -> mark(tt)
   active(U31(tt, V1, V2)) -> mark(U32(isNat(V1), V2))
   active(U32(tt, V2)) -> mark(U33(isNat(V2)))
   active(U33(tt)) -> mark(tt)
   active(U41(tt, N)) -> mark(N)
   active(U51(tt, M, N)) -> mark(s(plus(N, M)))
   active(U61(tt)) -> mark(0)
   active(U71(tt, M, N)) -> mark(plus(x(N, M), N))
   active(and(tt, X)) -> mark(X)
   active(isNat(0)) -> mark(tt)
   active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2))
   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
   active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2))
   active(isNatKind(0)) -> mark(tt)
   active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2)))
   active(isNatKind(s(V1))) -> mark(isNatKind(V1))
   active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2)))
   active(plus(N, 0)) -> mark(U41(and(isNat(N), isNatKind(N)), N))
   active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
   active(x(N, 0)) -> mark(U61(and(isNat(N), isNatKind(N))))
   active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
   active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3)
   active(U12(X1, X2)) -> U12(active(X1), X2)
   active(U13(X)) -> U13(active(X))
   active(U21(X1, X2)) -> U21(active(X1), X2)
   active(U22(X)) -> U22(active(X))
   active(U31(X1, X2, X3)) -> U31(active(X1), X2, X3)
   active(U32(X1, X2)) -> U32(active(X1), X2)
   active(U33(X)) -> U33(active(X))
   active(U41(X1, X2)) -> U41(active(X1), X2)
   active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3)
   active(s(X)) -> s(active(X))
   active(plus(X1, X2)) -> plus(active(X1), X2)
   active(plus(X1, X2)) -> plus(X1, active(X2))
   active(U61(X)) -> U61(active(X))
   active(U71(X1, X2, X3)) -> U71(active(X1), X2, X3)
   active(x(X1, X2)) -> x(active(X1), X2)
   active(x(X1, X2)) -> x(X1, active(X2))
   active(and(X1, X2)) -> and(active(X1), X2)
   U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3))
   U12(mark(X1), X2) -> mark(U12(X1, X2))
   U13(mark(X)) -> mark(U13(X))
   U21(mark(X1), X2) -> mark(U21(X1, X2))
   U22(mark(X)) -> mark(U22(X))
   U31(mark(X1), X2, X3) -> mark(U31(X1, X2, X3))
   U32(mark(X1), X2) -> mark(U32(X1, X2))
   U33(mark(X)) -> mark(U33(X))
   U41(mark(X1), X2) -> mark(U41(X1, X2))

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