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TRS Standard pair #487071308
details
property
value
status
complete
benchmark
Ex16_Luc06_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n180.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.63006 seconds
cpu usage
3.531
user time
3.34088
system time
0.190123
max virtual memory
1.8474676E7
max residence set size
238156.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 46 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5) AAECC Innermost [EQUIVALENT, 0 ms] (6) QTRS (7) DependencyPairsProof [EQUIVALENT, 0 ms] (8) QDP (9) DependencyGraphProof [EQUIVALENT, 0 ms] (10) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(X, X) -> f(a, n__b) b -> a b -> n__b activate(n__b) -> b activate(X) -> X Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(a) = 0 POL(activate(x_1)) = 2 + x_1 POL(b) = 2 POL(f(x_1, x_2)) = x_1 + x_2 POL(n__b) = 0 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: b -> a b -> n__b activate(X) -> X ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(X, X) -> f(a, n__b) activate(n__b) -> b Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(a) = 0 POL(activate(x_1)) = 1 + x_1 POL(b) = 0 POL(f(x_1, x_2)) = x_1 + x_2 POL(n__b) = 0 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: activate(n__b) -> b ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(X, X) -> f(a, n__b) Q is empty. ---------------------------------------- (5) AAECC Innermost (EQUIVALENT) We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is none
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