TRS Equational pair #487092755

details

property	value
status	complete
benchmark	AC54.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n145.star.cs.uiowa.edu
space	AProVE_AC_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.80954 seconds
cpu usage	7.31154
user time	7.0518
system time	0.259735
max virtual memory	1.841096E7
max residence set size	446744.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 0 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) EUsableRulesReductionPairsProof [EQUIVALENT, 9 ms]
        (14) EDP
        (15) ERuleRemovalProof [EQUIVALENT, 0 ms]
        (16) EDP
        (17) EDPPoloProof [EQUIVALENT, 8 ms]
        (18) EDP
        (19) PisEmptyProof [EQUIVALENT, 0 ms]
        (20) YES
    (21) EDP
        (22) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (23) EDP
        (24) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (25) EDP
        (26) PisEmptyProof [EQUIVALENT, 0 ms]
        (27) YES
    (28) EDP
        (29) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (30) EDP
        (31) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (32) EDP
        (33) ERuleRemovalProof [EQUIVALENT, 17 ms]
        (34) EDP
        (35) ERuleRemovalProof [EQUIVALENT, 0 ms]
        (36) EDP
        (37) EUsableRulesReductionPairsProof [EQUIVALENT, 10 ms]
        (38) EDP
        (39) EDPProblemToQDPProblemProof [EQUIVALENT, 0 ms]
        (40) QDP
        (41) UsableRulesProof [EQUIVALENT, 0 ms]
        (42) QDP
        (43) MRRProof [EQUIVALENT, 7 ms]
        (44) QDP
        (45) DependencyGraphProof [EQUIVALENT, 0 ms]
        (46) TRUE
    (47) EDP
        (48) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (49) EDP
        (50) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (51) EDP
        (52) PisEmptyProof [EQUIVALENT, 0 ms]
        (53) YES
    (54) EDP
        (55) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (56) EDP
        (57) EDPPoloProof [EQUIVALENT, 0 ms]
        (58) EDP
        (59) PisEmptyProof [EQUIVALENT, 0 ms]
        (60) YES


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

(0)
Obligation:
Equational rewrite system:
The TRS R consists of the following rules:

   minus(x, 0) -> x
   minus(s(x), s(y)) -> minus(x, y)
   minus(minus(x, y), z) -> minus(x, plus(y, z))
   quot(0, s(y)) -> 0
   quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
   plus(0, y) -> y
   plus(s(x), y) -> s(plus(x, y))
   app(nil, k) -> k
   app(l, nil) -> l
   app(cons(x, l), k) -> cons(x, app(l, k))
   sum(cons(x, nil)) -> cons(x, nil)
   sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l))
   sum(app(l, cons(x, cons(y, k)))) -> sum(app(l, sum(cons(x, cons(y, k)))))

The set E consists of the following equations:

   plus(x, y) == plus(y, x)
   plus(plus(x, y), z) == plus(x, plus(y, z))


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(1) EquationalDependencyPairsProof (EQUIVALENT)

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