TRS Equat 89423 pair #381732698

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	n033.star.cs.uiowa.edu
space	Mixed_AC

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	7.54628109932 seconds
cpu usage	19.772150422
max memory	1.874497536E9

stage attributes

key	value
output-size	109153
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given ETRS could be proven:

(0) ETRS
(1) EquationalDependencyPairsProof [EQUIVALENT, 144 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, 33 ms]
        (14) EDP
        (15) EDPPoloProof [EQUIVALENT, 82 ms]
        (16) EDP
        (17) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (18) EDP
        (19) EDPPoloProof [EQUIVALENT, 31 ms]
        (20) EDP
        (21) PisEmptyProof [EQUIVALENT, 0 ms]
        (22) YES
    (23) EDP
        (24) ESharpUsableEquationsProof [EQUIVALENT, 17 ms]
        (25) EDP
        (26) EDPPoloProof [EQUIVALENT, 757 ms]
        (27) EDP
        (28) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (29) EDP
        (30) EDPPoloProof [EQUIVALENT, 801 ms]
        (31) EDP
        (32) EDPPoloProof [EQUIVALENT, 536 ms]
        (33) EDP
        (34) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (35) EDP
        (36) EDPPoloProof [EQUIVALENT, 56 ms]
        (37) EDP
        (38) EDPPoloProof [EQUIVALENT, 65 ms]
        (39) EDP
        (40) PisEmptyProof [EQUIVALENT, 0 ms]
        (41) YES
    (42) EDP
        (43) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (44) EDP
        (45) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (46) EDP
        (47) PisEmptyProof [EQUIVALENT, 0 ms]
        (48) YES
    (49) EDP
        (50) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (51) EDP
        (52) EUsableRulesReductionPairsProof [EQUIVALENT, 3 ms]
        (53) EDP
        (54) EDependencyGraphProof [EQUIVALENT, 0 ms]
        (55) 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))

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actions all output return to TRS Equat 89423