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Integer TRS Innermost pair #487528889
details
property
value
status
complete
benchmark
18.itrs
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n141.star.cs.uiowa.edu
space
Mixed_ITRS_2014
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.84436511993 seconds
cpu usage
7.296794345
max memory
4.34225152E8
stage attributes
key
value
output-size
105708
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.itrs /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given ITRS could be proven: (0) ITRS (1) ITRStoIDPProof [EQUIVALENT, 0 ms] (2) IDP (3) UsableRulesProof [EQUIVALENT, 0 ms] (4) IDP (5) IDPNonInfProof [SOUND, 342 ms] (6) AND (7) IDP (8) IDependencyGraphProof [EQUIVALENT, 0 ms] (9) IDP (10) IDPNonInfProof [SOUND, 115 ms] (11) IDP (12) IDependencyGraphProof [EQUIVALENT, 0 ms] (13) IDP (14) IDPNonInfProof [SOUND, 45 ms] (15) IDP (16) IDependencyGraphProof [EQUIVALENT, 0 ms] (17) TRUE (18) IDP (19) IDependencyGraphProof [EQUIVALENT, 0 ms] (20) 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: eval(x, y) -> Cond_eval(x > 0, x, y) Cond_eval(TRUE, x, y) -> eval(x - 1, y) eval(x, y) -> Cond_eval1(y > 0 && x > 0, x, y) Cond_eval1(TRUE, x, y) -> eval(x - 1, y) eval(x, y) -> Cond_eval2(x > 0 && 0 >= x && y > 0, x, y) Cond_eval2(TRUE, x, y) -> eval(x, y - 1) eval(x, y) -> Cond_eval3(y > 0 && 0 >= x, x, y) Cond_eval3(TRUE, x, y) -> eval(x, y - 1) eval(x, y) -> Cond_eval4(x > 0 && 0 >= x && 0 >= y, x, y) Cond_eval4(TRUE, x, y) -> eval(x, y) eval(x, y) -> Cond_eval5(y > 0 && 0 >= x && 0 >= y, x, y) Cond_eval5(TRUE, x, y) -> eval(x, y) The set Q consists of the following terms: eval(x0, x1) Cond_eval(TRUE, x0, x1) Cond_eval1(TRUE, x0, x1) Cond_eval2(TRUE, x0, x1) Cond_eval3(TRUE, x0, x1) Cond_eval4(TRUE, x0, x1) Cond_eval5(TRUE, x0, x1) ---------------------------------------- (1) ITRStoIDPProof (EQUIVALENT) Added dependency pairs ---------------------------------------- (2) Obligation: IDP problem: The following function symbols are pre-defined: <<< & ~ Bwand: (Integer, Integer) -> Integer >= ~ Ge: (Integer, Integer) -> Boolean
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