TRS Equational pair #516978332

details

property	value
status	complete
benchmark	PEANO-NAT_nokinds.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n095.star.cs.uiowa.edu
space	Mixed_C

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	13.7041649818 seconds
cpu usage	19.810574887
max memory	1.269792768E9

stage attributes

key	value
output-size	83841
starexec-result	MAYBE

output

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


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


MAYBE
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


Termination of the given ETRS could not be shown:

(0) ETRS
(1) EquationalDependencyPairsProof [EQUIVALENT, 0 ms]
(2) EDP
(3) EDependencyGraphProof [EQUIVALENT, 3 ms]
(4) AND
    (5) EDP
        (6) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (7) EDP
        (8) EUsableRulesReductionPairsProof [EQUIVALENT, 122 ms]
        (9) EDP
        (10) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (11) TRUE
    (12) EDP
        (13) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (14) EDP
        (15) EUsableRulesReductionPairsProof [EQUIVALENT, 58 ms]
        (16) EDP
        (17) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (18) TRUE
    (19) EDP
        (20) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (21) EDP
        (22) EUsableRulesReductionPairsProof [EQUIVALENT, 45 ms]
        (23) EDP
        (24) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (25) TRUE
    (26) EDP
        (27) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (28) EDP
        (29) EUsableRulesReductionPairsProof [EQUIVALENT, 34 ms]
        (30) EDP
        (31) PisEmptyProof [EQUIVALENT, 0 ms]
        (32) YES
    (33) EDP
        (34) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (35) EDP
        (36) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (37) EDP
        (38) PisEmptyProof [EQUIVALENT, 0 ms]
        (39) YES
    (40) EDP
        (41) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (42) EDP
        (43) EUsableRulesProof [EQUIVALENT, 6 ms]
        (44) EDP
    (45) EDP


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

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

   1 -> s_(0)
   2 -> s_(s_(0))
   3 -> s_(s_(s_(0)))
   4 -> s_(s_(s_(s_(0))))
   5 -> s_(s_(s_(s_(s_(0)))))
   6 -> s_(s_(s_(s_(s_(s_(0))))))
   7 -> s_(s_(s_(s_(s_(s_(s_(0)))))))
   U101(tt, M, N) -> d(N, M)
   U11(tt) -> 0
   U111(tt) -> 0
   U121(tt, M', N') -> U122(equal(_>_(N', M'), true), M', N')
   U122(tt, M', N') -> gcd(d(N', M'), M')
   U131(tt, N') -> N'
   U141(tt, N) -> N
   U151(tt) -> s_(0)
   U161(tt, M', N) -> U162(equal(_>_(M', N), true))
   U162(tt) -> 0
   U171(tt, M', N) -> U172(equal(_>_(N, M'), true), M', N)
   U172(tt, M', N) -> s_(quot(d(N, M'), M'))
   U21(tt, M, N) -> s_(_+_(N, _+_(M, _*_(N, M))))
   U31(tt, N) -> N
   U41(tt, M, N) -> s_(s_(_+_(N, M)))
   U51(tt, M, N) -> _>_(M, N)
   U61(tt) -> false
   U71(tt) -> true
   U81(tt, M, N) -> _>_(N, M)
   U91(tt, N) -> N
   _*_(N, 0) -> U11(isNat(N))
   _*_(s_(N), s_(M)) -> U21(and(isNat(M), isNat(N)), M, N)
   _+_(N, 0) -> U31(isNat(N), N)
   _+_(s_(N), s_(M)) -> U41(and(isNat(M), isNat(N)), M, N)
   _<_(N, M) -> U51(and(isNat(M), isNat(N)), M, N)

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actions all output return to TRS Equational