TRS Standard pair #615300110

details

property	value
status	complete
benchmark	LISTUTILITIES_nosorts-noand_FR.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n164.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE23
configuration	standard
runtime (wallclock)	2.36785006523 seconds
cpu usage	6.392994299
max memory	3.40979712E8

stage attributes

key	value
output-size	15323
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# AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished


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

(0) QTRS
(1) DependencyPairsProof [EQUIVALENT, 16 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (9) YES
    (10) QDP
        (11) QDPOrderProof [EQUIVALENT, 52 ms]
        (12) QDP
        (13) DependencyGraphProof [EQUIVALENT, 0 ms]
        (14) TRUE


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

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

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

Q is empty.

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

(1) DependencyPairsProof (EQUIVALENT)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
----------------------------------------

(2)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   U11^1(tt, N, XS) -> U12^1(tt, activate(N), activate(XS))
   U11^1(tt, N, XS) -> ACTIVATE(N)
   U11^1(tt, N, XS) -> ACTIVATE(XS)
   U12^1(tt, N, XS) -> SND(splitAt(activate(N), activate(XS)))
   U12^1(tt, N, XS) -> SPLITAT(activate(N), activate(XS))
   U12^1(tt, N, XS) -> ACTIVATE(N)
   U12^1(tt, N, XS) -> ACTIVATE(XS)
   U21^1(tt, X) -> U22^1(tt, activate(X))
   U21^1(tt, X) -> ACTIVATE(X)
   U22^1(tt, X) -> ACTIVATE(X)
   U31^1(tt, N) -> U32^1(tt, activate(N))
   U31^1(tt, N) -> ACTIVATE(N)
   U32^1(tt, N) -> ACTIVATE(N)
   U41^1(tt, N, XS) -> U42^1(tt, activate(N), activate(XS))
   U41^1(tt, N, XS) -> ACTIVATE(N)
   U41^1(tt, N, XS) -> ACTIVATE(XS)

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