TRS Standard pair #487072263

details

property	value
status	complete
benchmark	aprove04.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n191.star.cs.uiowa.edu
space	Secret_07_TRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.83399 seconds
cpu usage	11.3537
user time	10.8848
system time	0.468948
max virtual memory	3.737894E7
max residence set size	736368.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) AAECC Innermost [EQUIVALENT, 0 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 7 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) TransformationProof [EQUIVALENT, 0 ms]
        (34) QDP
        (35) DependencyGraphProof [EQUIVALENT, 0 ms]
        (36) QDP
        (37) UsableRulesProof [EQUIVALENT, 0 ms]
        (38) QDP
        (39) QReductionProof [EQUIVALENT, 0 ms]
        (40) QDP
        (41) TransformationProof [EQUIVALENT, 0 ms]
        (42) QDP
        (43) UsableRulesProof [EQUIVALENT, 0 ms]
        (44) QDP
        (45) TransformationProof [EQUIVALENT, 0 ms]
        (46) QDP
        (47) UsableRulesProof [EQUIVALENT, 0 ms]
        (48) QDP
        (49) QReductionProof [EQUIVALENT, 0 ms]
        (50) QDP
        (51) TransformationProof [EQUIVALENT, 0 ms]
        (52) QDP
        (53) TransformationProof [EQUIVALENT, 0 ms]
        (54) QDP
        (55) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (56) YES
    (57) QDP
        (58) UsableRulesProof [EQUIVALENT, 0 ms]
        (59) QDP
        (60) QReductionProof [EQUIVALENT, 0 ms]
        (61) QDP
        (62) NonInfProof [EQUIVALENT, 46 ms]
        (63) QDP
        (64) DependencyGraphProof [EQUIVALENT, 0 ms]
        (65) TRUE


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

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

   lcm(x, y) -> lcmIter(x, y, 0, times(x, y))
   lcmIter(x, y, z, u) -> if(or(ge(0, x), ge(z, u)), x, y, z, u)
   if(true, x, y, z, u) -> z
   if(false, x, y, z, u) -> if2(divisible(z, y), x, y, z, u)
   if2(true, x, y, z, u) -> z
   if2(false, x, y, z, u) -> lcmIter(x, y, plus(x, z), u)
   plus(0, y) -> y
   plus(s(x), y) -> s(plus(x, y))
   times(x, y) -> ifTimes(ge(0, x), x, y)
   ifTimes(true, x, y) -> 0
   ifTimes(false, x, y) -> plus(y, times(y, p(x)))
   p(s(x)) -> x
   p(0) -> s(s(0))
   ge(x, 0) -> true
   ge(0, s(y)) -> false
   ge(s(x), s(y)) -> ge(x, y)
   or(true, y) -> true
   or(false, y) -> y

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