TRS Inner 89993 pair #381734079

details

property	value
status	complete
benchmark	LengthOfFiniteLists_complete_noand_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n190.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	7.32390117645 seconds
cpu usage	23.051724787
max memory	2.7913216E9

stage attributes

key	value
output-size	146824
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 137 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 8 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) QReductionProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QDP
        (13) UsableRulesProof [EQUIVALENT, 0 ms]
        (14) QDP
        (15) QReductionProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (18) YES
    (19) QDP
        (20) UsableRulesProof [EQUIVALENT, 0 ms]
        (21) QDP
        (22) QReductionProof [EQUIVALENT, 0 ms]
        (23) QDP
        (24) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (25) YES
    (26) QDP
        (27) QDPOrderProof [EQUIVALENT, 439 ms]
        (28) QDP
        (29) QDPOrderProof [EQUIVALENT, 399 ms]
        (30) QDP
        (31) DependencyGraphProof [EQUIVALENT, 0 ms]
        (32) AND
            (33) QDP
                (34) QDPOrderProof [EQUIVALENT, 302 ms]
                (35) QDP
                (36) DependencyGraphProof [EQUIVALENT, 0 ms]
                (37) TRUE
            (38) QDP
                (39) UsableRulesProof [EQUIVALENT, 0 ms]
                (40) QDP
                (41) QReductionProof [EQUIVALENT, 0 ms]
                (42) QDP
                (43) QDPSizeChangeProof [EQUIVALENT, 0 ms]
                (44) YES


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

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

   a__zeros -> cons(0, zeros)
   a__U11(tt, V1) -> a__U12(a__isNatIListKind(V1), V1)
   a__U12(tt, V1) -> a__U13(a__isNatList(V1))
   a__U13(tt) -> tt
   a__U21(tt, V1) -> a__U22(a__isNatKind(V1), V1)
   a__U22(tt, V1) -> a__U23(a__isNat(V1))
   a__U23(tt) -> tt
   a__U31(tt, V) -> a__U32(a__isNatIListKind(V), V)
   a__U32(tt, V) -> a__U33(a__isNatList(V))
   a__U33(tt) -> tt
   a__U41(tt, V1, V2) -> a__U42(a__isNatKind(V1), V1, V2)
   a__U42(tt, V1, V2) -> a__U43(a__isNatIListKind(V2), V1, V2)
   a__U43(tt, V1, V2) -> a__U44(a__isNatIListKind(V2), V1, V2)
   a__U44(tt, V1, V2) -> a__U45(a__isNat(V1), V2)
   a__U45(tt, V2) -> a__U46(a__isNatIList(V2))
   a__U46(tt) -> tt
   a__U51(tt, V2) -> a__U52(a__isNatIListKind(V2))
   a__U52(tt) -> tt
   a__U61(tt) -> tt
   a__U71(tt) -> tt
   a__U81(tt, V1, V2) -> a__U82(a__isNatKind(V1), V1, V2)
   a__U82(tt, V1, V2) -> a__U83(a__isNatIListKind(V2), V1, V2)
   a__U83(tt, V1, V2) -> a__U84(a__isNatIListKind(V2), V1, V2)
   a__U84(tt, V1, V2) -> a__U85(a__isNat(V1), V2)
   a__U85(tt, V2) -> a__U86(a__isNatList(V2))
   a__U86(tt) -> tt
   a__U91(tt, L, N) -> a__U92(a__isNatIListKind(L), L, N)
   a__U92(tt, L, N) -> a__U93(a__isNat(N), L, N)
   a__U93(tt, L, N) -> a__U94(a__isNatKind(N), L)
   a__U94(tt, L) -> s(a__length(mark(L)))
   a__isNat(0) -> tt
   a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1), V1)
   a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1)

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