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Integer_TRS_Innermost 2019-03-21 04.53 pair #429994944
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
n048.star.cs.uiowa.edu
space
Mixed_ITRS_2014
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
25.7919 seconds
cpu usage
79.8836
user time
78.2853
system time
1.59827
max virtual memory
1.955428E7
max residence set size
5028080.0
stage attributes
key
value
starexec-result
YES
output
79.46/25.66 YES 79.46/25.69 proof of /export/starexec/sandbox/benchmark/theBenchmark.itrs 79.46/25.69 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 79.46/25.69 79.46/25.69 79.46/25.69 Termination of the given ITRS could be proven: 79.46/25.69 79.46/25.69 (0) ITRS 79.46/25.69 (1) ITRStoIDPProof [EQUIVALENT, 0 ms] 79.46/25.69 (2) IDP 79.46/25.69 (3) UsableRulesProof [EQUIVALENT, 0 ms] 79.46/25.69 (4) IDP 79.46/25.69 (5) IDependencyGraphProof [EQUIVALENT, 0 ms] 79.46/25.69 (6) AND 79.46/25.69 (7) IDP 79.46/25.69 (8) UsableRulesProof [EQUIVALENT, 0 ms] 79.46/25.69 (9) IDP 79.46/25.69 (10) IDPNonInfProof [SOUND, 188 ms] 79.46/25.69 (11) IDP 79.46/25.69 (12) IDependencyGraphProof [EQUIVALENT, 0 ms] 79.46/25.69 (13) TRUE 79.46/25.69 (14) IDP 79.46/25.69 (15) UsableRulesProof [EQUIVALENT, 0 ms] 79.46/25.69 (16) IDP 79.46/25.69 (17) IDPNonInfProof [SOUND, 247 ms] 79.46/25.69 (18) IDP 79.46/25.69 (19) IDependencyGraphProof [EQUIVALENT, 0 ms] 79.46/25.69 (20) TRUE 79.46/25.69 (21) IDP 79.46/25.69 (22) UsableRulesProof [EQUIVALENT, 0 ms] 79.46/25.69 (23) IDP 79.46/25.69 (24) IDPtoQDPProof [SOUND, 4 ms] 79.46/25.69 (25) QDP 79.46/25.69 (26) QReductionProof [EQUIVALENT, 0 ms] 79.46/25.69 (27) QDP 79.46/25.69 (28) QDPOrderProof [EQUIVALENT, 25 ms] 79.46/25.69 (29) QDP 79.46/25.69 (30) PisEmptyProof [EQUIVALENT, 0 ms] 79.46/25.69 (31) YES 79.46/25.69 (32) IDP 79.46/25.69 (33) UsableRulesProof [EQUIVALENT, 0 ms] 79.46/25.69 (34) IDP 79.46/25.69 (35) IDPNonInfProof [SOUND, 47 ms] 79.46/25.69 (36) IDP 79.46/25.69 (37) IDependencyGraphProof [EQUIVALENT, 0 ms] 79.46/25.69 (38) TRUE 79.46/25.69 79.46/25.69 79.46/25.69 ---------------------------------------- 79.46/25.69 79.46/25.69 (0) 79.46/25.69 Obligation: 79.46/25.69 ITRS problem: 79.46/25.69 79.46/25.69 The following function symbols are pre-defined: 79.46/25.69 <<< 79.46/25.69 & ~ Bwand: (Integer, Integer) -> Integer 79.46/25.69 >= ~ Ge: (Integer, Integer) -> Boolean 79.46/25.69 | ~ Bwor: (Integer, Integer) -> Integer 79.46/25.69 / ~ Div: (Integer, Integer) -> Integer 79.46/25.69 != ~ Neq: (Integer, Integer) -> Boolean 79.46/25.69 && ~ Land: (Boolean, Boolean) -> Boolean 79.46/25.69 ! ~ Lnot: (Boolean) -> Boolean 79.46/25.69 = ~ Eq: (Integer, Integer) -> Boolean 79.46/25.69 <= ~ Le: (Integer, Integer) -> Boolean 79.46/25.69 ^ ~ Bwxor: (Integer, Integer) -> Integer 79.46/25.69 % ~ Mod: (Integer, Integer) -> Integer 79.46/25.69 > ~ Gt: (Integer, Integer) -> Boolean 79.46/25.69 + ~ Add: (Integer, Integer) -> Integer 79.46/25.69 -1 ~ UnaryMinus: (Integer) -> Integer 79.46/25.69 < ~ Lt: (Integer, Integer) -> Boolean 79.46/25.69 || ~ Lor: (Boolean, Boolean) -> Boolean 79.46/25.69 - ~ Sub: (Integer, Integer) -> Integer 79.46/25.69 ~ ~ Bwnot: (Integer) -> Integer 79.46/25.69 * ~ Mul: (Integer, Integer) -> Integer 79.46/25.69 >>> 79.46/25.69 79.46/25.69 The TRS R consists of the following rules: 79.46/25.69 primes(x) -> sieve(nats(2, x)) 79.46/25.69 nats(x, y) -> Cond_nats(x > y, x, y) 79.46/25.69 Cond_nats(TRUE, x, y) -> nil 79.46/25.69 nats(x, y) -> Cond_nats1(y >= x, x, y) 79.46/25.69 Cond_nats1(TRUE, x, y) -> cons(x, nats(x + 1, y)) 79.46/25.69 sieve(nil) -> nil 79.46/25.69 sieve(cons(x, ys)) -> cons(x, sieve(filter(x, ys))) 79.46/25.69 filter(x, nil) -> nil 79.46/25.69 filter(x, cons(y, zs)) -> if(isdiv(x, y), x, y, zs) 79.46/25.69 if(TRUE, x, y, zs) -> filter(x, zs) 79.46/25.69 if(FALSE, x, y, zs) -> cons(y, filter(x, zs)) 79.46/25.69 isdiv(x, 0) -> Cond_isdiv(x > 0, x, 0) 79.46/25.69 Cond_isdiv(TRUE, x, 0) -> TRUE 79.46/25.69 isdiv(x, y) -> Cond_isdiv1(x > y && y > 0, x, y) 79.46/25.69 Cond_isdiv1(TRUE, x, y) -> FALSE 79.46/25.69 isdiv(x, y) -> Cond_isdiv2(y >= x && x > 0, x, y) 79.46/25.69 Cond_isdiv2(TRUE, x, y) -> isdiv(x, y - x) 79.46/25.69 The set Q consists of the following terms: 79.46/25.69 primes(x0) 79.46/25.69 nats(x0, x1) 79.46/25.69 Cond_nats(TRUE, x0, x1) 79.46/25.69 Cond_nats1(TRUE, x0, x1)
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