TRS Equational pair #487092818

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	n143.star.cs.uiowa.edu
space	Mixed_AC

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	8.81712 seconds
cpu usage	17.9144
user time	17.235
system time	0.679435
max virtual memory	1.8286836E7
max residence set size	1127284.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 147 ms]
(2) EDP
(3) EDependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) EDP
        (6) ESharpUsableEquationsProof [EQUIVALENT, 5 ms]
        (7) EDP
        (8) EUsableRulesReductionPairsProof [EQUIVALENT, 30 ms]
        (9) EDP
        (10) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (11) TRUE
    (12) EDP
        (13) ESharpUsableEquationsProof [EQUIVALENT, 12 ms]
        (14) EDP
        (15) EDPPoloProof [EQUIVALENT, 93 ms]
        (16) EDP
        (17) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (18) EDP
        (19) EDPPoloProof [EQUIVALENT, 81 ms]
        (20) EDP
        (21) EDPPoloProof [EQUIVALENT, 84 ms]
        (22) EDP
        (23) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (24) TRUE
    (25) EDP
        (26) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (27) EDP
        (28) EUsableRulesReductionPairsProof [EQUIVALENT, 13 ms]
        (29) EDP
        (30) PisEmptyProof [EQUIVALENT, 0 ms]
        (31) YES
    (32) EDP
        (33) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (34) EDP
        (35) EDPPoloProof [EQUIVALENT, 263 ms]
        (36) EDP
        (37) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (38) EDP
        (39) EDPPoloProof [EQUIVALENT, 240 ms]
        (40) EDP
        (41) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (42) EDP
        (43) EDPPoloProof [EQUIVALENT, 78 ms]
        (44) EDP
        (45) PisEmptyProof [EQUIVALENT, 0 ms]
        (46) YES
    (47) EDP
        (48) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (49) EDP
        (50) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (51) EDP
        (52) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (53) 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))
   U52(tt) -> tt
   U61(tt, V2) -> U62(isBin(V2))
   U62(tt) -> tt
   U71(tt) -> tt

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job log

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actions all output return to TRS Equational