TRS Standard pair #487066823

details

property	value
status	complete
benchmark	gcd.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n073.star.cs.uiowa.edu
space	AProVE_09_Inductive

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	22.3697 seconds
cpu usage	50.335
user time	48.8882
system time	1.4468
max virtual memory	1.875918E7
max residence set size	3938096.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 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) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (20) YES
    (21) QDP
        (22) UsableRulesProof [EQUIVALENT, 0 ms]
        (23) QDP
        (24) QReductionProof [EQUIVALENT, 0 ms]
        (25) QDP
        (26) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (27) YES
    (28) QDP
        (29) UsableRulesProof [EQUIVALENT, 0 ms]
        (30) QDP
        (31) QReductionProof [EQUIVALENT, 0 ms]
        (32) QDP
        (33) NonInfProof [EQUIVALENT, 66 ms]
        (34) QDP
        (35) TransformationProof [EQUIVALENT, 0 ms]
        (36) QDP
        (37) DependencyGraphProof [EQUIVALENT, 0 ms]
        (38) QDP
        (39) TransformationProof [EQUIVALENT, 0 ms]
        (40) QDP
        (41) DependencyGraphProof [EQUIVALENT, 0 ms]
        (42) QDP
        (43) TransformationProof [EQUIVALENT, 0 ms]
        (44) QDP
        (45) TransformationProof [EQUIVALENT, 0 ms]
        (46) QDP
        (47) TransformationProof [EQUIVALENT, 0 ms]
        (48) QDP
        (49) TransformationProof [EQUIVALENT, 0 ms]
        (50) QDP
        (51) Induction-Processor [SOUND, 37 ms]
        (52) AND
            (53) QDP
                (54) DependencyGraphProof [EQUIVALENT, 0 ms]
                (55) TRUE
            (56) QTRS
                (57) QTRSRRRProof [EQUIVALENT, 26 ms]
                (58) QTRS
                (59) RisEmptyProof [EQUIVALENT, 0 ms]
                (60) YES


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

   minus(s(x), y) -> if(gt(s(x), y), x, y)
   if(true, x, y) -> s(minus(x, y))
   if(false, x, y) -> 0
   gcd(x, y) -> if1(ge(x, y), x, y)
   if1(true, x, y) -> if2(gt(y, 0), x, y)
   if1(false, x, y) -> gcd(y, x)
   if2(true, x, y) -> gcd(minus(x, y), y)
   if2(false, x, y) -> x
   gt(0, y) -> false
   gt(s(x), 0) -> true
   gt(s(x), s(y)) -> gt(x, y)
   ge(x, 0) -> true
   ge(0, s(x)) -> false
   ge(s(x), s(y)) -> ge(x, y)

Q is empty.

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(1) Overlay + Local Confluence (EQUIVALENT)
The TRS is overlay and locally confluent. By [NOC] we can switch to innermost.
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