TRS Standard pair #487068858

details

property	value
status	complete
benchmark	Liveness6.4.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n192.star.cs.uiowa.edu
space	AProVE_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	28.1189 seconds
cpu usage	72.3412
user time	70.2559
system time	2.08529
max virtual memory	3.7409776E7
max residence set size	4433396.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) QTRSRRRProof [EQUIVALENT, 64 ms]
(2) QTRS
(3) QTRSRRRProof [EQUIVALENT, 26 ms]
(4) QTRS
(5) DependencyPairsProof [EQUIVALENT, 0 ms]
(6) QDP
(7) DependencyGraphProof [EQUIVALENT, 0 ms]
(8) AND
    (9) QDP
        (10) UsableRulesProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QDP
        (15) UsableRulesProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (18) YES
    (19) QDP
        (20) UsableRulesProof [EQUIVALENT, 0 ms]
        (21) QDP
        (22) TransformationProof [EQUIVALENT, 0 ms]
        (23) QDP
        (24) TransformationProof [EQUIVALENT, 0 ms]
        (25) QDP
        (26) TransformationProof [EQUIVALENT, 0 ms]
        (27) QDP
        (28) DependencyGraphProof [EQUIVALENT, 0 ms]
        (29) QDP
        (30) TransformationProof [EQUIVALENT, 0 ms]
        (31) QDP
        (32) DependencyGraphProof [EQUIVALENT, 0 ms]
        (33) QDP
        (34) TransformationProof [EQUIVALENT, 0 ms]
        (35) QDP
        (36) TransformationProof [EQUIVALENT, 0 ms]
        (37) QDP
        (38) QDPOrderProof [EQUIVALENT, 34 ms]
        (39) QDP
        (40) QDPOrderProof [EQUIVALENT, 88 ms]
        (41) QDP
        (42) SemLabProof [SOUND, 1607 ms]
        (43) QDP
        (44) DependencyGraphProof [EQUIVALENT, 0 ms]
        (45) AND
            (46) QDP
                (47) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
                (48) QDP
                (49) MRRProof [EQUIVALENT, 0 ms]
                (50) QDP
                (51) PisEmptyProof [EQUIVALENT, 0 ms]
                (52) YES
            (53) QDP
                (54) MRRProof [EQUIVALENT, 4 ms]
                (55) QDP
                (56) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
                (57) QDP
                (58) MRRProof [EQUIVALENT, 0 ms]
                (59) QDP
                (60) DependencyGraphProof [EQUIVALENT, 0 ms]
                (61) QDP
                (62) MRRProof [EQUIVALENT, 0 ms]
                (63) QDP
                (64) DependencyGraphProof [EQUIVALENT, 0 ms]
                (65) TRUE
            (66) QDP
                (67) MRRProof [EQUIVALENT, 0 ms]
                (68) QDP
                (69) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
                (70) QDP
                (71) MRRProof [EQUIVALENT, 0 ms]
                (72) QDP
                (73) DependencyGraphProof [EQUIVALENT, 0 ms]
                (74) TRUE


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

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

   top1(free(x), y) -> top2(check(new(x)), y)
   top1(free(x), y) -> top2(new(x), check(y))
   top1(free(x), y) -> top2(check(x), new(y))
   top1(free(x), y) -> top2(x, check(new(y)))
   top2(x, free(y)) -> top1(check(new(x)), y)
   top2(x, free(y)) -> top1(new(x), check(y))
   top2(x, free(y)) -> top1(check(x), new(y))
   top2(x, free(y)) -> top1(x, check(new(y)))
   new(free(x)) -> free(new(x))

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