TRS Equat 89423 pair #381732691

details

property	value
status	complete
benchmark	PEANO-NAT_nosorts.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n098.star.cs.uiowa.edu
space	Mixed_C

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	5.68003821373 seconds
cpu usage	10.984159137
max memory	1.607671808E9

stage attributes

key	value
output-size	36030
starexec-result	MAYBE

output

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


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


MAYBE
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given ETRS could not be shown:

(0) ETRS
(1) EquationalDependencyPairsProof [EQUIVALENT, 0 ms]
(2) EDP
(3) EDependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) EDP
        (6) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (7) EDP
        (8) EUsableRulesReductionPairsProof [EQUIVALENT, 63 ms]
        (9) EDP
        (10) PisEmptyProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) EDP
        (13) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (14) EDP
        (15) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (16) EDP
        (17) PisEmptyProof [EQUIVALENT, 0 ms]
        (18) YES
    (19) EDP
        (20) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (21) EDP
        (22) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (23) EDP
        (24) PisEmptyProof [EQUIVALENT, 0 ms]
        (25) YES
    (26) EDP
        (27) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (28) EDP
        (29) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (30) EDP
        (31) PisEmptyProof [EQUIVALENT, 0 ms]
        (32) YES
    (33) EDP
        (34) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (35) EDP
        (36) EUsableRulesProof [EQUIVALENT, 5 ms]
        (37) EDP
    (38) 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)))))))
   U11(tt, M', N') -> U12(equal(_>_(N', M'), true), M', N')
   U12(tt, M', N') -> gcd(d(N', M'), M')
   U21(tt, M', N) -> U22(equal(_>_(M', N), true))
   U22(tt) -> 0
   U31(tt, M', N) -> U32(equal(_>_(N, M'), true), M', N)
   U32(tt, M', N) -> s_(quot(d(N, M'), M'))
   _*_(N, 0) -> 0
   _*_(s_(N), s_(M)) -> s_(_+_(N, _+_(M, _*_(N, M))))
   _+_(N, 0) -> N
   _+_(s_(N), s_(M)) -> s_(s_(_+_(N, M)))
   _<_(N, M) -> _>_(M, N)
   _>_(0, M) -> false
   _>_(N', 0) -> true
   _>_(s_(N), s_(M)) -> _>_(N, M)
   and(tt, X) -> X
   d(0, N) -> N
   d(s_(N), s_(M)) -> d(N, M)
   equal(X, X) -> tt
   gcd(0, N) -> 0
   gcd(N', M') -> U11(tt, M', N')
   gcd(N', N') -> N'
   p_(s_(N)) -> N
   quot(M', M') -> s_(0)
   quot(N, M') -> U21(tt, M', N)
   quot(N, M') -> U31(tt, M', N)

The set E consists of the following equations:

   _*_(x, y) == _*_(y, x)
   _+_(x, y) == _+_(y, x)
   d(x, y) == d(y, x)
   gcd(x, y) == gcd(y, x)

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actions all output return to TRS Equat 89423