TRS Equational pair #487523247

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	n147.star.cs.uiowa.edu
space	Mixed_AC

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	48.5558588505 seconds
cpu usage	63.875615186
max memory	4.325289984E9

stage attributes

key	value
output-size	234283
starexec-result	YES

output

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


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


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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination of the given ETRS could be proven:

(0) ETRS
(1) EquationalDependencyPairsProof [EQUIVALENT, 154 ms]
(2) EDP
(3) EDependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) EDP
        (6) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (7) EDP
        (8) EUsableRulesReductionPairsProof [EQUIVALENT, 35 ms]
        (9) EDP
        (10) PisEmptyProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) EDP
        (13) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (14) EDP
        (15) EUsableRulesReductionPairsProof [EQUIVALENT, 140 ms]
        (16) EDP
        (17) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (18) TRUE
    (19) EDP
        (20) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (21) EDP
        (22) EDPPoloProof [EQUIVALENT, 567 ms]
        (23) EDP
        (24) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (25) EDP
        (26) EDPPoloProof [EQUIVALENT, 363 ms]
        (27) EDP
        (28) EDPPoloProof [EQUIVALENT, 348 ms]
        (29) EDP
        (30) PisEmptyProof [EQUIVALENT, 0 ms]
        (31) YES
    (32) EDP
        (33) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (34) EDP
        (35) EDPPoloProof [EQUIVALENT, 15.7 s]
        (36) EDP
        (37) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (38) EDP
        (39) EDPPoloProof [EQUIVALENT, 14.6 s]
        (40) EDP
        (41) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (42) EDP
        (43) EDPPoloProof [EQUIVALENT, 397 ms]
        (44) EDP
        (45) PisEmptyProof [EQUIVALENT, 0 ms]
        (46) YES
    (47) EDP
        (48) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (49) EDP
        (50) EUsableRulesReductionPairsProof [EQUIVALENT, 64 ms]
        (51) EDP
        (52) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (53) TRUE
    (54) EDP
        (55) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (56) EDP
        (57) EUsableRulesReductionPairsProof [EQUIVALENT, 25 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

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actions all output return to TRS Equational