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TRS Contextsensitive pair #487092511
details
property
value
status
complete
benchmark
Ex4_4_Luc96b.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n143.star.cs.uiowa.edu
space
CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.36134 seconds
cpu usage
2.71993
user time
2.58112
system time
0.138811
max virtual memory
1.8275312E7
max residence set size
199580.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given CSR could be proven: (0) CSR (1) CSRRRRProof [EQUIVALENT, 0 ms] (2) CSR (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES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(g(X), Y) -> f(X, f(g(X), Y)) The replacement map contains the following entries: f: {1} g: {1} ---------------------------------------- (1) CSRRRRProof (EQUIVALENT) The following CSR is given: Context-sensitive rewrite system: The TRS R consists of the following rules: f(g(X), Y) -> f(X, f(g(X), Y)) The replacement map contains the following entries: f: {1} g: {1} Used ordering: Polynomial interpretation [POLO]: POL(f(x_1, x_2)) = x_1 POL(g(x_1)) = 1 + x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: f(g(X), Y) -> f(X, f(g(X), Y)) ---------------------------------------- (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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