TRS Standard pair #487073138

details

property	value
status	complete
benchmark	thiemann13.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n175.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	7.89606 seconds
cpu usage	20.1346
user time	19.5669
system time	0.567732
max virtual memory	3.764172E7
max residence set size	1427952.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) Overlay + Local Confluence [EQUIVALENT, 0 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 0 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) QDP
        (8) UsableRulesProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) QReductionProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QDP
        (15) UsableRulesProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QReductionProof [EQUIVALENT, 0 ms]
        (18) QDP
        (19) QDPOrderProof [EQUIVALENT, 0 ms]
        (20) QDP
        (21) PisEmptyProof [EQUIVALENT, 0 ms]
        (22) YES
    (23) QDP
        (24) UsableRulesProof [EQUIVALENT, 0 ms]
        (25) QDP
        (26) QReductionProof [EQUIVALENT, 0 ms]
        (27) QDP
        (28) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (29) YES
    (30) QDP
        (31) UsableRulesProof [EQUIVALENT, 0 ms]
        (32) QDP
        (33) QReductionProof [EQUIVALENT, 0 ms]
        (34) QDP
        (35) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (36) YES
    (37) QDP
        (38) UsableRulesProof [EQUIVALENT, 0 ms]
        (39) QDP
        (40) QReductionProof [EQUIVALENT, 0 ms]
        (41) QDP
        (42) QDPQMonotonicMRRProof [EQUIVALENT, 20 ms]
        (43) QDP
        (44) QDPQMonotonicMRRProof [EQUIVALENT, 34 ms]
        (45) QDP
        (46) TransformationProof [EQUIVALENT, 0 ms]
        (47) QDP
        (48) TransformationProof [EQUIVALENT, 0 ms]
        (49) QDP
        (50) UsableRulesProof [EQUIVALENT, 0 ms]
        (51) QDP
        (52) TransformationProof [SOUND, 0 ms]
        (53) QDP
        (54) DependencyGraphProof [EQUIVALENT, 0 ms]
        (55) QDP
        (56) TransformationProof [EQUIVALENT, 0 ms]
        (57) QDP
        (58) TransformationProof [EQUIVALENT, 0 ms]
        (59) QDP
        (60) TransformationProof [EQUIVALENT, 0 ms]
        (61) QDP
        (62) UsableRulesProof [EQUIVALENT, 0 ms]
        (63) QDP
        (64) QReductionProof [EQUIVALENT, 0 ms]
        (65) QDP
        (66) TransformationProof [EQUIVALENT, 0 ms]
        (67) QDP
        (68) DependencyGraphProof [EQUIVALENT, 0 ms]
        (69) TRUE


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

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

   le(0, y) -> true
   le(s(x), 0) -> false
   le(s(x), s(y)) -> le(x, y)
   inc(0) -> 0
   inc(s(x)) -> s(inc(x))
   minus(0, y) -> 0
   minus(x, 0) -> x
   minus(s(x), s(y)) -> minus(x, y)
   quot(0, s(y)) -> 0
   quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
   log(x) -> log2(x, 0)
   log2(x, y) -> if(le(x, 0), le(x, s(0)), x, inc(y))
   if(true, b, x, y) -> log_undefined
   if(false, b, x, y) -> if2(b, x, y)

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actions all output return to TRS Standard