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TRS Contextsensitive pair #487092539
details
property
value
status
complete
benchmark
Ex18_Luc06.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n151.star.cs.uiowa.edu
space
CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.30677 seconds
cpu usage
2.81443
user time
2.67548
system time
0.138951
max virtual memory
1.8341532E7
max residence set size
199832.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given CSR could be proven: (0) CSR (1) CSRRRRProof [EQUIVALENT, 66 ms] (2) CSR (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: f(f(a)) -> f(g(f(a))) The replacement map contains the following entries: f: {1} a: empty set g: empty set ---------------------------------------- (1) CSRRRRProof (EQUIVALENT) The following CSR is given: Context-sensitive rewrite system: The TRS R consists of the following rules: f(f(a)) -> f(g(f(a))) The replacement map contains the following entries: f: {1} a: empty set g: empty set Used ordering: Polynomial interpretation [POLO]: POL(a) = 1 POL(f(x_1)) = 1 + x_1 POL(g(x_1)) = 1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: f(f(a)) -> f(g(f(a))) ---------------------------------------- (2) Obligation: Context-sensitive rewrite system: R is empty. ---------------------------------------- (3) RisEmptyProof (EQUIVALENT) The CSR R is empty. Hence, termination is trivially proven. ---------------------------------------- (4) YES
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