Integer TRS Innermost pair #487100504

details

property	value
status	complete
benchmark	eratosthenes_small.itrs
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n145.star.cs.uiowa.edu
space	Mixed_ITRS_2014

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	25.706 seconds
cpu usage	78.9384
user time	77.4048
system time	1.53354
max virtual memory	1.9548476E7
max residence set size	5000048.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.itrs
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination of the given ITRS could be proven:

(0) ITRS
(1) ITRStoIDPProof [EQUIVALENT, 0 ms]
(2) IDP
(3) UsableRulesProof [EQUIVALENT, 0 ms]
(4) IDP
(5) IDependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) IDP
        (8) UsableRulesProof [EQUIVALENT, 0 ms]
        (9) IDP
        (10) IDPNonInfProof [SOUND, 146 ms]
        (11) IDP
        (12) IDependencyGraphProof [EQUIVALENT, 0 ms]
        (13) TRUE
    (14) IDP
        (15) UsableRulesProof [EQUIVALENT, 0 ms]
        (16) IDP
        (17) IDPNonInfProof [SOUND, 223 ms]
        (18) IDP
        (19) IDependencyGraphProof [EQUIVALENT, 0 ms]
        (20) TRUE
    (21) IDP
        (22) UsableRulesProof [EQUIVALENT, 0 ms]
        (23) IDP
        (24) IDPtoQDPProof [SOUND, 43 ms]
        (25) QDP
        (26) QReductionProof [EQUIVALENT, 0 ms]
        (27) QDP
        (28) QDPOrderProof [EQUIVALENT, 42 ms]
        (29) QDP
        (30) PisEmptyProof [EQUIVALENT, 0 ms]
        (31) YES
    (32) IDP
        (33) UsableRulesProof [EQUIVALENT, 0 ms]
        (34) IDP
        (35) IDPNonInfProof [SOUND, 34 ms]
        (36) IDP
        (37) IDependencyGraphProof [EQUIVALENT, 0 ms]
        (38) TRUE


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

(0)
Obligation:
ITRS problem:

The following function symbols are pre-defined:
<<<
 & 	~ 	Bwand: (Integer, Integer) -> Integer
 >= 	~ 	Ge: (Integer, Integer) -> Boolean
 | 	~ 	Bwor: (Integer, Integer) -> Integer
 / 	~ 	Div: (Integer, Integer) -> Integer
 != 	~ 	Neq: (Integer, Integer) -> Boolean
 && 	~ 	Land: (Boolean, Boolean) -> Boolean
 ! 	~ 	Lnot: (Boolean) -> Boolean
 = 	~ 	Eq: (Integer, Integer) -> Boolean
 <= 	~ 	Le: (Integer, Integer) -> Boolean
 ^ 	~ 	Bwxor: (Integer, Integer) -> Integer
 % 	~ 	Mod: (Integer, Integer) -> Integer
 > 	~ 	Gt: (Integer, Integer) -> Boolean
 + 	~ 	Add: (Integer, Integer) -> Integer
 -1 	~ 	UnaryMinus: (Integer) -> Integer
 < 	~ 	Lt: (Integer, Integer) -> Boolean
 || 	~ 	Lor: (Boolean, Boolean) -> Boolean
 - 	~ 	Sub: (Integer, Integer) -> Integer
 ~ 	~ 	Bwnot: (Integer) -> Integer
 * 	~ 	Mul: (Integer, Integer) -> Integer
>>>

The TRS R consists of the following rules:
primes(x) -> sieve(nats(2, x))
nats(x, y) -> Cond_nats(x > y, x, y)
Cond_nats(TRUE, x, y) -> nil
nats(x, y) -> Cond_nats1(y >= x, x, y)
Cond_nats1(TRUE, x, y) -> cons(x, nats(x + 1, y))
sieve(nil) -> nil
sieve(cons(x, ys)) -> cons(x, sieve(filter(x, ys)))
filter(x, nil) -> nil
filter(x, cons(y, zs)) -> if(isdiv(x, y), x, y, zs)
if(TRUE, x, y, zs) -> filter(x, zs)
if(FALSE, x, y, zs) -> cons(y, filter(x, zs))
isdiv(x, 0) -> Cond_isdiv(x > 0, x, 0)
Cond_isdiv(TRUE, x, 0) -> TRUE
isdiv(x, y) -> Cond_isdiv1(x > y && y > 0, x, y)
Cond_isdiv1(TRUE, x, y) -> FALSE
isdiv(x, y) -> Cond_isdiv2(y >= x && x > 0, x, y)
Cond_isdiv2(TRUE, x, y) -> isdiv(x, y - x)
The set Q consists of the following terms:
primes(x0)
nats(x0, x1)
Cond_nats(TRUE, x0, x1)
Cond_nats1(TRUE, x0, x1)

popout

output may be truncated. 'popout' for the full output.

job log

popout

actions all output return to Integer TRS Innermost