TRS Standard pair #516963400

details

property	value
status	complete
benchmark	LISTUTILITIES_nosorts_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	AProVE21
configuration	standard
runtime (wallclock)	2.55990099907 seconds
cpu usage	7.14797356
max memory	4.95558656E8

stage attributes

key	value
output-size	35871
starexec-result	YES

output

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


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


YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


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

(0) QTRS
(1) QTRSToCSRProof [EQUIVALENT, 0 ms]
(2) CSR
(3) CSRInnermostProof [EQUIVALENT, 0 ms]
(4) CSR
(5) CSDependencyPairsProof [EQUIVALENT, 10 ms]
(6) QCSDP
(7) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
(8) AND
    (9) QCSDP
        (10) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (11) QCSDP
        (12) PIsEmptyProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QCSDP
        (15) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (16) QCSDP
        (17) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (18) TRUE


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

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

   active(U11(tt, N, XS)) -> mark(U12(tt, N, XS))
   active(U12(tt, N, XS)) -> mark(snd(splitAt(N, XS)))
   active(U21(tt, X)) -> mark(U22(tt, X))
   active(U22(tt, X)) -> mark(X)
   active(U31(tt, N)) -> mark(U32(tt, N))
   active(U32(tt, N)) -> mark(N)
   active(U41(tt, N, XS)) -> mark(U42(tt, N, XS))
   active(U42(tt, N, XS)) -> mark(head(afterNth(N, XS)))
   active(U51(tt, Y)) -> mark(U52(tt, Y))
   active(U52(tt, Y)) -> mark(Y)
   active(U61(tt, N, X, XS)) -> mark(U62(tt, N, X, XS))
   active(U62(tt, N, X, XS)) -> mark(U63(tt, N, X, XS))
   active(U63(tt, N, X, XS)) -> mark(U64(splitAt(N, XS), X))
   active(U64(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS))
   active(U71(tt, XS)) -> mark(U72(tt, XS))
   active(U72(tt, XS)) -> mark(XS)
   active(U81(tt, N, XS)) -> mark(U82(tt, N, XS))
   active(U82(tt, N, XS)) -> mark(fst(splitAt(N, XS)))
   active(afterNth(N, XS)) -> mark(U11(tt, N, XS))
   active(fst(pair(X, Y))) -> mark(U21(tt, X))
   active(head(cons(N, XS))) -> mark(U31(tt, N))
   active(natsFrom(N)) -> mark(cons(N, natsFrom(s(N))))
   active(sel(N, XS)) -> mark(U41(tt, N, XS))
   active(snd(pair(X, Y))) -> mark(U51(tt, Y))
   active(splitAt(0, XS)) -> mark(pair(nil, XS))
   active(splitAt(s(N), cons(X, XS))) -> mark(U61(tt, N, X, XS))
   active(tail(cons(N, XS))) -> mark(U71(tt, XS))
   active(take(N, XS)) -> mark(U81(tt, N, XS))
   active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3)
   active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3)
   active(snd(X)) -> snd(active(X))
   active(splitAt(X1, X2)) -> splitAt(active(X1), X2)
   active(splitAt(X1, X2)) -> splitAt(X1, active(X2))
   active(U21(X1, X2)) -> U21(active(X1), X2)
   active(U22(X1, X2)) -> U22(active(X1), X2)
   active(U31(X1, X2)) -> U31(active(X1), X2)
   active(U32(X1, X2)) -> U32(active(X1), X2)
   active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3)
   active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3)
   active(head(X)) -> head(active(X))
   active(afterNth(X1, X2)) -> afterNth(active(X1), X2)
   active(afterNth(X1, X2)) -> afterNth(X1, active(X2))
   active(U51(X1, X2)) -> U51(active(X1), X2)
   active(U52(X1, X2)) -> U52(active(X1), X2)
   active(U61(X1, X2, X3, X4)) -> U61(active(X1), X2, X3, X4)
   active(U62(X1, X2, X3, X4)) -> U62(active(X1), X2, X3, X4)
   active(U63(X1, X2, X3, X4)) -> U63(active(X1), X2, X3, X4)
   active(U64(X1, X2)) -> U64(active(X1), X2)
   active(pair(X1, X2)) -> pair(active(X1), X2)
   active(pair(X1, X2)) -> pair(X1, active(X2))
   active(cons(X1, X2)) -> cons(active(X1), X2)
   active(U71(X1, X2)) -> U71(active(X1), X2)
   active(U72(X1, X2)) -> U72(active(X1), X2)
   active(U81(X1, X2, X3)) -> U81(active(X1), X2, X3)
   active(U82(X1, X2, X3)) -> U82(active(X1), X2, X3)
   active(fst(X)) -> fst(active(X))
   active(natsFrom(X)) -> natsFrom(active(X))
   active(s(X)) -> s(active(X))
   active(sel(X1, X2)) -> sel(active(X1), X2)

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