TRS Contextsensitive pair #487092519

details

property	value
status	complete
benchmark	Ex4_DLMMU04.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n138.star.cs.uiowa.edu
space	CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.19219 seconds
cpu usage	6.21923
user time	5.94242
system time	0.27681
max virtual memory	1.8607004E7
max residence set size	482172.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination of the given CSR could be proven:

(0) CSR
(1) CSRRRRProof [EQUIVALENT, 60 ms]
(2) CSR
(3) CSRRRRProof [EQUIVALENT, 0 ms]
(4) CSR
(5) CSDependencyPairsProof [EQUIVALENT, 25 ms]
(6) QCSDP
(7) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
(8) AND
    (9) QCSDP
        (10) QCSUsableRulesProof [EQUIVALENT, 0 ms]
        (11) QCSDP
        (12) QCSDPMuMonotonicPoloProof [EQUIVALENT, 9 ms]
        (13) QCSDP
        (14) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (15) AND
            (16) QCSDP
                (17) QCSDPMuMonotonicPoloProof [EQUIVALENT, 0 ms]
                (18) QCSDP
                (19) PIsEmptyProof [EQUIVALENT, 0 ms]
                (20) YES
            (21) QCSDP
                (22) QCSDPMuMonotonicPoloProof [EQUIVALENT, 0 ms]
                (23) QCSDP
                (24) PIsEmptyProof [EQUIVALENT, 0 ms]
                (25) YES
    (26) QCSDP
        (27) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (28) QCSDP
        (29) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (30) TRUE
    (31) QCSDP
        (32) QCSDPReductionPairProof [EQUIVALENT, 68 ms]
        (33) QCSDP
        (34) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (35) TRUE


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

(0)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   and(tt, T) -> T
   isNatIList(IL) -> isNatList(IL)
   isNat(0) -> tt
   isNat(s(N)) -> isNat(N)
   isNat(length(L)) -> isNatList(L)
   isNatIList(zeros) -> tt
   isNatIList(cons(N, IL)) -> and(isNat(N), isNatIList(IL))
   isNatList(nil) -> tt
   isNatList(cons(N, L)) -> and(isNat(N), isNatList(L))
   isNatList(take(N, IL)) -> and(isNat(N), isNatIList(IL))
   zeros -> cons(0, zeros)
   take(0, IL) -> uTake1(isNatIList(IL))
   uTake1(tt) -> nil
   take(s(M), cons(N, IL)) -> uTake2(and(isNat(M), and(isNat(N), isNatIList(IL))), M, N, IL)
   uTake2(tt, M, N, IL) -> cons(N, take(M, IL))
   length(cons(N, L)) -> uLength(and(isNat(N), isNatList(L)), L)
   uLength(tt, L) -> s(length(L))

The replacement map contains the following entries:

and: {1, 2}
tt: empty set
isNatIList: empty set
isNatList: empty set
isNat: empty set
0: empty set
s: {1}
length: {1}
zeros: empty set
cons: {1}
nil: empty set
take: {1, 2}
uTake1: {1}
uTake2: {1}
uLength: {1}

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

(1) CSRRRRProof (EQUIVALENT)
The following CSR is given: Context-sensitive rewrite system:
The TRS R consists of the following rules:

   and(tt, T) -> T
   isNatIList(IL) -> isNatList(IL)
   isNat(0) -> tt
   isNat(s(N)) -> isNat(N)
   isNat(length(L)) -> isNatList(L)
   isNatIList(zeros) -> tt

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actions all output return to TRS Contextsensitive