TRS Equational pair #516978161

details

property	value
status	complete
benchmark	BAG_nokinds-noand.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n056.star.cs.uiowa.edu
space	Mixed_AC

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	6.36914610863 seconds
cpu usage	18.537973971
max memory	1.129660416E9

stage attributes

key	value
output-size	110353
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


Termination of the given ETRS could be proven:

(0) ETRS
(1) EquationalDependencyPairsProof [EQUIVALENT, 166 ms]
(2) EDP
(3) EDependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) EDP
        (6) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (7) EDP
        (8) EUsableRulesReductionPairsProof [EQUIVALENT, 31 ms]
        (9) EDP
        (10) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (11) TRUE
    (12) EDP
        (13) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (14) EDP
        (15) EDPPoloProof [EQUIVALENT, 131 ms]
        (16) EDP
        (17) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (18) EDP
        (19) EDPPoloProof [EQUIVALENT, 46 ms]
        (20) EDP
        (21) PisEmptyProof [EQUIVALENT, 0 ms]
        (22) YES
    (23) EDP
        (24) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (25) EDP
        (26) EUsableRulesReductionPairsProof [EQUIVALENT, 19 ms]
        (27) EDP
        (28) PisEmptyProof [EQUIVALENT, 0 ms]
        (29) YES
    (30) EDP
        (31) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (32) EDP
        (33) EDPPoloProof [EQUIVALENT, 406 ms]
        (34) EDP
        (35) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (36) EDP
        (37) EDPPoloProof [EQUIVALENT, 229 ms]
        (38) EDP
        (39) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (40) EDP
        (41) EDPPoloProof [EQUIVALENT, 92 ms]
        (42) EDP
        (43) PisEmptyProof [EQUIVALENT, 0 ms]
        (44) YES
    (45) EDP
        (46) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (47) EDP
        (48) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (49) EDP
        (50) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (51) 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, X, Y) -> U102(isBin(Y), X, Y)
   U102(tt, X, Y) -> 0(mult(X, Y))
   U11(tt) -> tt
   U111(tt, X, Y) -> U112(isBin(Y), X, Y)
   U112(tt, X, Y) -> plus(0(mult(X, Y)), Y)
   U121(tt, X) -> X
   U131(tt, X, Y) -> U132(isBin(Y), X, Y)
   U132(tt, X, Y) -> 0(plus(X, Y))
   U141(tt, X, Y) -> U142(isBin(Y), X, Y)
   U142(tt, X, Y) -> 1(plus(X, Y))
   U151(tt, X, Y) -> U152(isBin(Y), X, Y)
   U152(tt, X, Y) -> 0(plus(plus(X, Y), 1(z)))
   U161(tt, X) -> X
   U171(tt, A, B) -> U172(isBag(B), A, B)
   U172(tt, A, B) -> mult(prod(A), prod(B))
   U181(tt, X) -> X
   U191(tt, A, B) -> U192(isBag(B), A, B)
   U192(tt, A, B) -> plus(sum(A), sum(B))
   U21(tt, V2) -> U22(isBag(V2))
   U22(tt) -> tt
   U31(tt) -> tt
   U41(tt) -> tt
   U51(tt, V2) -> U52(isBin(V2))

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actions all output return to TRS Equational