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Integer_TRS_Innermost 2019-03-21 04.53 pair #429994930
details
property
value
status
complete
benchmark
19.itrs
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n130.star.cs.uiowa.edu
space
Mixed_ITRS_2014
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.91879 seconds
cpu usage
7.66761
user time
7.19252
system time
0.475099
max virtual memory
4.1372592E7
max residence set size
516000.0
stage attributes
key
value
starexec-result
YES
output
6.98/2.70 YES 7.57/2.87 proof of /export/starexec/sandbox/benchmark/theBenchmark.itrs 7.57/2.87 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 7.57/2.87 7.57/2.87 7.57/2.87 Termination of the given ITRS could be proven: 7.57/2.87 7.57/2.87 (0) ITRS 7.57/2.87 (1) ITRStoIDPProof [EQUIVALENT, 0 ms] 7.57/2.87 (2) IDP 7.57/2.87 (3) UsableRulesProof [EQUIVALENT, 0 ms] 7.57/2.87 (4) IDP 7.57/2.87 (5) IDPNonInfProof [SOUND, 413 ms] 7.57/2.87 (6) IDP 7.57/2.87 (7) IDependencyGraphProof [EQUIVALENT, 0 ms] 7.57/2.87 (8) IDP 7.57/2.87 (9) IDPNonInfProof [SOUND, 168 ms] 7.57/2.87 (10) IDP 7.57/2.87 (11) IDependencyGraphProof [EQUIVALENT, 0 ms] 7.57/2.87 (12) TRUE 7.57/2.87 7.57/2.87 7.57/2.87 ---------------------------------------- 7.57/2.87 7.57/2.87 (0) 7.57/2.87 Obligation: 7.57/2.87 ITRS problem: 7.57/2.87 7.57/2.87 The following function symbols are pre-defined: 7.57/2.87 <<< 7.57/2.87 & ~ Bwand: (Integer, Integer) -> Integer 7.57/2.87 >= ~ Ge: (Integer, Integer) -> Boolean 7.57/2.87 | ~ Bwor: (Integer, Integer) -> Integer 7.57/2.87 / ~ Div: (Integer, Integer) -> Integer 7.57/2.87 != ~ Neq: (Integer, Integer) -> Boolean 7.57/2.87 && ~ Land: (Boolean, Boolean) -> Boolean 7.57/2.87 ! ~ Lnot: (Boolean) -> Boolean 7.57/2.87 = ~ Eq: (Integer, Integer) -> Boolean 7.57/2.87 <= ~ Le: (Integer, Integer) -> Boolean 7.57/2.87 ^ ~ Bwxor: (Integer, Integer) -> Integer 7.57/2.88 % ~ Mod: (Integer, Integer) -> Integer 7.57/2.88 > ~ Gt: (Integer, Integer) -> Boolean 7.57/2.88 + ~ Add: (Integer, Integer) -> Integer 7.57/2.88 -1 ~ UnaryMinus: (Integer) -> Integer 7.57/2.88 < ~ Lt: (Integer, Integer) -> Boolean 7.57/2.88 || ~ Lor: (Boolean, Boolean) -> Boolean 7.57/2.88 - ~ Sub: (Integer, Integer) -> Integer 7.57/2.88 ~ ~ Bwnot: (Integer) -> Integer 7.57/2.88 * ~ Mul: (Integer, Integer) -> Integer 7.57/2.88 >>> 7.57/2.88 7.57/2.88 The TRS R consists of the following rules: 7.57/2.88 eval(x, y, z) -> Cond_eval(x > z, x, y, z) 7.57/2.88 Cond_eval(TRUE, x, y, z) -> eval(x - 1, y, z) 7.57/2.88 eval(x, y, z) -> Cond_eval1(y > z && x > z, x, y, z) 7.57/2.88 Cond_eval1(TRUE, x, y, z) -> eval(x - 1, y, z) 7.57/2.88 eval(x, y, z) -> Cond_eval2(x > z && z >= x && y > z, x, y, z) 7.57/2.88 Cond_eval2(TRUE, x, y, z) -> eval(x, y - 1, z) 7.57/2.88 eval(x, y, z) -> Cond_eval3(y > z && z >= x, x, y, z) 7.57/2.88 Cond_eval3(TRUE, x, y, z) -> eval(x, y - 1, z) 7.57/2.88 eval(x, y, z) -> Cond_eval4(x > z && z >= x && z >= y, x, y, z) 7.57/2.88 Cond_eval4(TRUE, x, y, z) -> eval(x, y, z) 7.57/2.88 eval(x, y, z) -> Cond_eval5(y > z && z >= x && z >= y, x, y, z) 7.57/2.88 Cond_eval5(TRUE, x, y, z) -> eval(x, y, z) 7.57/2.88 The set Q consists of the following terms: 7.57/2.88 eval(x0, x1, x2) 7.57/2.88 Cond_eval(TRUE, x0, x1, x2) 7.57/2.88 Cond_eval1(TRUE, x0, x1, x2) 7.57/2.88 Cond_eval2(TRUE, x0, x1, x2) 7.57/2.88 Cond_eval3(TRUE, x0, x1, x2) 7.57/2.88 Cond_eval4(TRUE, x0, x1, x2) 7.57/2.88 Cond_eval5(TRUE, x0, x1, x2) 7.57/2.88 7.57/2.88 ---------------------------------------- 7.57/2.88 7.57/2.88 (1) ITRStoIDPProof (EQUIVALENT) 7.57/2.88 Added dependency pairs 7.57/2.88 ---------------------------------------- 7.57/2.88 7.57/2.88 (2) 7.57/2.88 Obligation: 7.57/2.88 IDP problem: 7.57/2.88 The following function symbols are pre-defined: 7.57/2.88 <<< 7.57/2.88 & ~ Bwand: (Integer, Integer) -> Integer 7.57/2.88 >= ~ Ge: (Integer, Integer) -> Boolean 7.57/2.88 | ~ Bwor: (Integer, Integer) -> Integer 7.57/2.88 / ~ Div: (Integer, Integer) -> Integer 7.57/2.88 != ~ Neq: (Integer, Integer) -> Boolean 7.57/2.88 && ~ Land: (Boolean, Boolean) -> Boolean 7.57/2.88 ! ~ Lnot: (Boolean) -> Boolean 7.57/2.88 = ~ Eq: (Integer, Integer) -> Boolean 7.57/2.88 <= ~ Le: (Integer, Integer) -> Boolean 7.57/2.88 ^ ~ Bwxor: (Integer, Integer) -> Integer 7.57/2.88 % ~ Mod: (Integer, Integer) -> Integer 7.57/2.88 > ~ Gt: (Integer, Integer) -> Boolean 7.57/2.88 + ~ Add: (Integer, Integer) -> Integer 7.57/2.88 -1 ~ UnaryMinus: (Integer) -> Integer 7.57/2.88 < ~ Lt: (Integer, Integer) -> Boolean 7.57/2.88 || ~ Lor: (Boolean, Boolean) -> Boolean
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