TRS Innermost pair #516979025

details

property	value
status	complete
benchmark	Ex4_DLMMU04_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n168.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	3.17906284332 seconds
cpu usage	9.445585403
max memory	6.77351424E8

stage attributes

key	value
output-size	36252
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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 [SOUND, 0 ms]
(2) CSR
(3) CSRRRRProof [EQUIVALENT, 62 ms]
(4) CSR
(5) CSRRRRProof [EQUIVALENT, 0 ms]
(6) CSR
(7) CSDependencyPairsProof [EQUIVALENT, 17 ms]
(8) QCSDP
(9) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
(10) AND
    (11) QCSDP
        (12) QCSUsableRulesProof [EQUIVALENT, 5 ms]
        (13) QCSDP
        (14) QCSDPMuMonotonicPoloProof [EQUIVALENT, 0 ms]
        (15) QCSDP
        (16) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (17) AND
            (18) QCSDP
                (19) QCSDPMuMonotonicPoloProof [EQUIVALENT, 3 ms]
                (20) QCSDP
                (21) PIsEmptyProof [EQUIVALENT, 0 ms]
                (22) YES
            (23) QCSDP
                (24) QCSDPMuMonotonicPoloProof [EQUIVALENT, 4 ms]
                (25) QCSDP
                (26) PIsEmptyProof [EQUIVALENT, 0 ms]
                (27) YES
    (28) QCSDP
        (29) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (30) QCSDP
        (31) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (32) TRUE
    (33) QCSDP
        (34) QCSDPReductionPairProof [EQUIVALENT, 110 ms]
        (35) QCSDP
        (36) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (37) TRUE


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

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

   active(and(tt, T)) -> mark(T)
   active(isNatIList(IL)) -> mark(isNatList(IL))
   active(isNat(0)) -> mark(tt)
   active(isNat(s(N))) -> mark(isNat(N))
   active(isNat(length(L))) -> mark(isNatList(L))
   active(isNatIList(zeros)) -> mark(tt)
   active(isNatIList(cons(N, IL))) -> mark(and(isNat(N), isNatIList(IL)))
   active(isNatList(nil)) -> mark(tt)
   active(isNatList(cons(N, L))) -> mark(and(isNat(N), isNatList(L)))
   active(isNatList(take(N, IL))) -> mark(and(isNat(N), isNatIList(IL)))
   active(zeros) -> mark(cons(0, zeros))
   active(take(0, IL)) -> mark(uTake1(isNatIList(IL)))
   active(uTake1(tt)) -> mark(nil)
   active(take(s(M), cons(N, IL))) -> mark(uTake2(and(isNat(M), and(isNat(N), isNatIList(IL))), M, N, IL))
   active(uTake2(tt, M, N, IL)) -> mark(cons(N, take(M, IL)))
   active(length(cons(N, L))) -> mark(uLength(and(isNat(N), isNatList(L)), L))
   active(uLength(tt, L)) -> mark(s(length(L)))
   active(and(X1, X2)) -> and(active(X1), X2)
   active(and(X1, X2)) -> and(X1, active(X2))
   active(s(X)) -> s(active(X))
   active(length(X)) -> length(active(X))
   active(cons(X1, X2)) -> cons(active(X1), X2)
   active(take(X1, X2)) -> take(active(X1), X2)
   active(take(X1, X2)) -> take(X1, active(X2))
   active(uTake1(X)) -> uTake1(active(X))
   active(uTake2(X1, X2, X3, X4)) -> uTake2(active(X1), X2, X3, X4)
   active(uLength(X1, X2)) -> uLength(active(X1), X2)
   and(mark(X1), X2) -> mark(and(X1, X2))
   and(X1, mark(X2)) -> mark(and(X1, X2))
   s(mark(X)) -> mark(s(X))
   length(mark(X)) -> mark(length(X))
   cons(mark(X1), X2) -> mark(cons(X1, X2))
   take(mark(X1), X2) -> mark(take(X1, X2))
   take(X1, mark(X2)) -> mark(take(X1, X2))
   uTake1(mark(X)) -> mark(uTake1(X))
   uTake2(mark(X1), X2, X3, X4) -> mark(uTake2(X1, X2, X3, X4))
   uLength(mark(X1), X2) -> mark(uLength(X1, X2))
   proper(and(X1, X2)) -> and(proper(X1), proper(X2))
   proper(tt) -> ok(tt)
   proper(isNatIList(X)) -> isNatIList(proper(X))

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