TRS Equational pair #487092803

details

property	value
status	complete
benchmark	BAG_nokinds.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n140.star.cs.uiowa.edu
space	Mixed_AC

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	6.13044 seconds
cpu usage	17.2944
user time	16.6303
system time	0.66407
max virtual memory	1.8285664E7
max residence set size	1451496.0

stage attributes

key	value
starexec-result	YES

output

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 129 ms]
(2) EDP
(3) EDependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) EDP
        (6) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (7) EDP
        (8) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (9) EDP
        (10) PisEmptyProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) EDP
        (13) ESharpUsableEquationsProof [EQUIVALENT, 13 ms]
        (14) EDP
        (15) EDPPoloProof [EQUIVALENT, 89 ms]
        (16) EDP
        (17) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (18) EDP
        (19) EDPPoloProof [EQUIVALENT, 9 ms]
        (20) EDP
        (21) PisEmptyProof [EQUIVALENT, 0 ms]
        (22) YES
    (23) EDP
        (24) ESharpUsableEquationsProof [EQUIVALENT, 6 ms]
        (25) EDP
        (26) EDPPoloProof [EQUIVALENT, 772 ms]
        (27) EDP
        (28) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (29) EDP
        (30) EDPPoloProof [EQUIVALENT, 751 ms]
        (31) EDP
        (32) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (33) EDP
        (34) EDPPoloProof [EQUIVALENT, 60 ms]
        (35) EDP
        (36) PisEmptyProof [EQUIVALENT, 0 ms]
        (37) YES
    (38) EDP
        (39) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (40) EDP
        (41) EUsableRulesReductionPairsProof [EQUIVALENT, 7 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) -> X
   U11(tt) -> z
   U111(tt, A, B) -> plus(sum(A), sum(B))
   U21(tt, X, Y) -> 0(mult(X, Y))
   U31(tt, X, Y) -> plus(0(mult(X, Y)), Y)
   U41(tt, X) -> X
   U51(tt, X, Y) -> 0(plus(X, Y))
   U61(tt, X, Y) -> 1(plus(X, Y))
   U71(tt, X, Y) -> 0(plus(plus(X, Y), 1(z)))
   U81(tt, X) -> X
   U91(tt, A, B) -> mult(prod(A), prod(B))
   and(tt, X) -> X
   isBag(empty) -> tt
   isBag(singl(V1)) -> isBin(V1)
   isBag(union(V1, V2)) -> and(isBag(V1), isBag(V2))
   isBin(z) -> tt
   isBin(0(V1)) -> isBin(V1)
   isBin(1(V1)) -> isBin(V1)
   isBin(mult(V1, V2)) -> and(isBin(V1), isBin(V2))
   isBin(plus(V1, V2)) -> and(isBin(V1), isBin(V2))
   isBin(prod(V1)) -> isBag(V1)
   isBin(sum(V1)) -> isBag(V1)
   mult(z, X) -> U11(isBin(X))
   mult(0(X), Y) -> U21(and(isBin(X), isBin(Y)), X, Y)
   mult(1(X), Y) -> U31(and(isBin(X), isBin(Y)), X, Y)
   plus(z, X) -> U41(isBin(X), X)
   plus(0(X), 0(Y)) -> U51(and(isBin(X), isBin(Y)), X, Y)
   plus(0(X), 1(Y)) -> U61(and(isBin(X), isBin(Y)), X, Y)
   plus(1(X), 1(Y)) -> U71(and(isBin(X), isBin(Y)), X, Y)

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actions all output return to TRS Equational