TRS Standard pair #615299592

details

property	value
status	complete
benchmark	OvConsOS_nosorts-noand_FR.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n051.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE23
configuration	standard
runtime (wallclock)	5.15316009521 seconds
cpu usage	15.626143114
max memory	9.45065984E8

stage attributes

key	value
output-size	26950
starexec-result	"NO"

output

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


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


NO
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished


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

(0) QTRS
(1) QTRSRRRProof [EQUIVALENT, 136 ms]
(2) QTRS
(3) QTRSRRRProof [EQUIVALENT, 42 ms]
(4) QTRS
(5) DependencyPairsProof [EQUIVALENT, 19 ms]
(6) QDP
(7) DependencyGraphProof [EQUIVALENT, 0 ms]
(8) AND
    (9) QDP
        (10) UsableRulesProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) UsableRulesReductionPairsProof [EQUIVALENT, 41 ms]
        (13) QDP
        (14) DependencyGraphProof [EQUIVALENT, 0 ms]
        (15) QDP
        (16) UsableRulesProof [EQUIVALENT, 0 ms]
        (17) QDP
        (18) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (19) YES
    (20) QDP
        (21) UsableRulesProof [EQUIVALENT, 0 ms]
        (22) QDP
        (23) UsableRulesReductionPairsProof [EQUIVALENT, 24 ms]
        (24) QDP
        (25) UsableRulesProof [EQUIVALENT, 0 ms]
        (26) QDP
        (27) TransformationProof [EQUIVALENT, 0 ms]
        (28) QDP
        (29) TransformationProof [EQUIVALENT, 0 ms]
        (30) QDP
        (31) DependencyGraphProof [EQUIVALENT, 0 ms]
        (32) QDP
        (33) MRRProof [EQUIVALENT, 10 ms]
        (34) QDP
        (35) NonTerminationLoopProof [COMPLETE, 17 ms]
        (36) NO


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

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

   zeros -> cons(0, n__zeros)
   U11(tt, L) -> U12(tt, activate(L))
   U12(tt, L) -> s(length(activate(L)))
   U21(tt, IL, M, N) -> U22(tt, activate(IL), activate(M), activate(N))
   U22(tt, IL, M, N) -> U23(tt, activate(IL), activate(M), activate(N))
   U23(tt, IL, M, N) -> cons(activate(N), n__take(activate(M), activate(IL)))
   length(nil) -> 0
   length(cons(N, L)) -> U11(tt, activate(L))
   take(0, IL) -> nil
   take(s(M), cons(N, IL)) -> U21(tt, activate(IL), M, N)
   zeros -> n__zeros
   take(X1, X2) -> n__take(X1, X2)
   activate(n__zeros) -> zeros
   activate(n__take(X1, X2)) -> take(activate(X1), activate(X2))
   activate(X) -> X

Q is empty.

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

(1) QTRSRRRProof (EQUIVALENT)
Used ordering:
Polynomial interpretation [POLO]:

   POL(0) = 0
   POL(U11(x_1, x_2)) = 1 + 2*x_1 + x_2
   POL(U12(x_1, x_2)) = 1 + 2*x_1 + x_2
   POL(U21(x_1, x_2, x_3, x_4)) = x_1 + 2*x_2 + 2*x_3 + 2*x_4
   POL(U22(x_1, x_2, x_3, x_4)) = 2*x_1 + 2*x_2 + 2*x_3 + 2*x_4
   POL(U23(x_1, x_2, x_3, x_4)) = x_1 + 2*x_2 + 2*x_3 + 2*x_4
   POL(activate(x_1)) = x_1
   POL(cons(x_1, x_2)) = 2*x_1 + x_2
   POL(length(x_1)) = 1 + x_1
   POL(n__take(x_1, x_2)) = 2*x_1 + 2*x_2
   POL(n__zeros) = 0
   POL(nil) = 0
   POL(s(x_1)) = x_1
   POL(take(x_1, x_2)) = 2*x_1 + 2*x_2
   POL(tt) = 0
   POL(zeros) = 0
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

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