TRS Equational pair #487092809

details

property	value
status	complete
benchmark	BAG_complete-noand.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n146.star.cs.uiowa.edu
space	Mixed_AC

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	42.2281 seconds
cpu usage	61.6973
user time	60.0185
system time	1.6788
max virtual memory	1.8395252E7
max residence set size	3917984.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination of the given ETRS could be proven:

(0) ETRS
(1) EquationalDependencyPairsProof [EQUIVALENT, 135 ms]
(2) EDP
(3) EDependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) EDP
        (6) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (7) EDP
        (8) EUsableRulesReductionPairsProof [EQUIVALENT, 8 ms]
        (9) EDP
        (10) PisEmptyProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) EDP
        (13) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (14) EDP
        (15) EUsableRulesReductionPairsProof [EQUIVALENT, 112 ms]
        (16) EDP
        (17) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (18) TRUE
    (19) EDP
        (20) ESharpUsableEquationsProof [EQUIVALENT, 19 ms]
        (21) EDP
        (22) EDPPoloProof [EQUIVALENT, 588 ms]
        (23) EDP
        (24) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (25) EDP
        (26) EDPPoloProof [EQUIVALENT, 332 ms]
        (27) EDP
        (28) EDPPoloProof [EQUIVALENT, 378 ms]
        (29) EDP
        (30) PisEmptyProof [EQUIVALENT, 0 ms]
        (31) YES
    (32) EDP
        (33) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (34) EDP
        (35) EDPPoloProof [EQUIVALENT, 16.2 s]
        (36) EDP
        (37) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (38) EDP
        (39) EDPPoloProof [EQUIVALENT, 14.9 s]
        (40) EDP
        (41) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (42) EDP
        (43) EDPPoloProof [EQUIVALENT, 455 ms]
        (44) EDP
        (45) PisEmptyProof [EQUIVALENT, 0 ms]
        (46) YES
    (47) EDP
        (48) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (49) EDP
        (50) EUsableRulesReductionPairsProof [EQUIVALENT, 12 ms]
        (51) EDP
        (52) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (53) TRUE
    (54) EDP
        (55) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (56) EDP
        (57) EUsableRulesReductionPairsProof [EQUIVALENT, 18 ms]
        (58) EDP
        (59) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (60) TRUE


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

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

   union(X, empty) -> X
   union(empty, X) -> X
   0(z) -> z
   U101(tt, V1) -> U102(isBagKind(V1), V1)
   U102(tt, V1) -> U103(isBag(V1))
   U103(tt) -> tt
   U11(tt, V1) -> U12(isBinKind(V1), V1)
   U111(tt) -> tt
   U12(tt, V1) -> U13(isBin(V1))
   U121(tt) -> tt
   U13(tt) -> tt
   U131(tt, V2) -> U132(isBinKind(V2))
   U132(tt) -> tt
   U141(tt, V2) -> U142(isBinKind(V2))
   U142(tt) -> tt
   U151(tt) -> tt
   U161(tt) -> tt
   U171(tt, X) -> U172(isBinKind(X))
   U172(tt) -> z
   U181(tt, X, Y) -> U182(isBinKind(X), X, Y)
   U182(tt, X, Y) -> U183(isBin(Y), X, Y)
   U183(tt, X, Y) -> U184(isBinKind(Y), X, Y)
   U184(tt, X, Y) -> 0(mult(X, Y))

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actions all output return to TRS Equational