TRS Inner 89993 pair #381734139

details

property	value
status	complete
benchmark	Ex4_DLMMU04_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n081.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	16.225386858 seconds
cpu usage	60.516351496
max memory	3.125194752E9

stage attributes

key	value
output-size	108849
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


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

(0) QTRS
(1) DependencyPairsProof [EQUIVALENT, 94 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) QDP
(5) QDPOrderProof [EQUIVALENT, 217 ms]
(6) QDP
(7) DependencyGraphProof [EQUIVALENT, 0 ms]
(8) AND
    (9) QDP
        (10) QDPQMonotonicMRRProof [EQUIVALENT, 53 ms]
        (11) QDP
        (12) QDPQMonotonicMRRProof [EQUIVALENT, 38 ms]
        (13) QDP
        (14) QDPOrderProof [EQUIVALENT, 213 ms]
        (15) QDP
        (16) DependencyGraphProof [EQUIVALENT, 0 ms]
        (17) TRUE
    (18) QDP
        (19) QDPOrderProof [EQUIVALENT, 93 ms]
        (20) QDP
        (21) QDPOrderProof [EQUIVALENT, 0 ms]
        (22) QDP
        (23) QDPOrderProof [EQUIVALENT, 64 ms]
        (24) QDP
        (25) QDPOrderProof [EQUIVALENT, 82 ms]
        (26) QDP
        (27) DependencyGraphProof [EQUIVALENT, 0 ms]
        (28) AND
            (29) QDP
                (30) UsableRulesProof [EQUIVALENT, 1 ms]
                (31) QDP
                (32) QReductionProof [EQUIVALENT, 0 ms]
                (33) QDP
                (34) QDPSizeChangeProof [EQUIVALENT, 0 ms]
                (35) YES
            (36) QDP
                (37) QDPOrderProof [EQUIVALENT, 91 ms]
                (38) QDP
                (39) QDPQMonotonicMRRProof [EQUIVALENT, 86 ms]
                (40) QDP
                (41) QDPQMonotonicMRRProof [EQUIVALENT, 66 ms]
                (42) QDP
                (43) QDPOrderProof [EQUIVALENT, 218 ms]
                (44) QDP
                (45) QDPQMonotonicMRRProof [EQUIVALENT, 127 ms]
                (46) QDP
                (47) DependencyGraphProof [EQUIVALENT, 0 ms]
                (48) QDP
                (49) UsableRulesProof [EQUIVALENT, 0 ms]
                (50) QDP
                (51) QReductionProof [EQUIVALENT, 0 ms]
                (52) QDP
                (53) QDPSizeChangeProof [EQUIVALENT, 0 ms]
                (54) YES


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

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

   a__and(tt, T) -> mark(T)
   a__isNatIList(IL) -> a__isNatList(IL)
   a__isNat(0) -> tt
   a__isNat(s(N)) -> a__isNat(N)
   a__isNat(length(L)) -> a__isNatList(L)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(N, IL)) -> a__and(a__isNat(N), a__isNatIList(IL))
   a__isNatList(nil) -> tt
   a__isNatList(cons(N, L)) -> a__and(a__isNat(N), a__isNatList(L))
   a__isNatList(take(N, IL)) -> a__and(a__isNat(N), a__isNatIList(IL))
   a__zeros -> cons(0, zeros)
   a__take(0, IL) -> a__uTake1(a__isNatIList(IL))
   a__uTake1(tt) -> nil
   a__take(s(M), cons(N, IL)) -> a__uTake2(a__and(a__isNat(M), a__and(a__isNat(N), a__isNatIList(IL))), M, N, IL)
   a__uTake2(tt, M, N, IL) -> cons(mark(N), take(M, IL))
   a__length(cons(N, L)) -> a__uLength(a__and(a__isNat(N), a__isNatList(L)), L)
   a__uLength(tt, L) -> s(a__length(mark(L)))
   mark(and(X1, X2)) -> a__and(mark(X1), mark(X2))
   mark(isNatIList(X)) -> a__isNatIList(X)
   mark(isNatList(X)) -> a__isNatList(X)
   mark(isNat(X)) -> a__isNat(X)
   mark(length(X)) -> a__length(mark(X))
   mark(zeros) -> a__zeros

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