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TRS Stand 20472 pair #381710228
details
property
value
status
complete
benchmark
isList.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n069.star.cs.uiowa.edu
space
AProVE_10
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.0955679416656 seconds
cpu usage
0.080907775
max memory
3289088.0
stage attributes
key
value
output-size
1374
starexec-result
MAYBE
output
/export/starexec/sandbox/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- MAYBE We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. Cons : [o * o] --> o f : [o * o] --> o isList : [o] --> o nil : [] --> o tt : [] --> o xs : [] --> o f(tt, X) => f(isList(X), X) isList(Cons(X, xs)) => isList(xs) isList(nil) => tt As the system is orthogonal, it is terminating if it is innermost terminating by [Gra95]. Then, by [FuhGieParSchSwi11], it suffices to prove (innermost) termination of the typed system, with sort annotations chosen to respect the rules, as follows: Cons : [z * z] --> z f : [aa * z] --> n isList : [z] --> aa nil : [] --> z tt : [] --> aa xs : [] --> z +++ Citations +++ [FuhGieParSchSwi11] C. Fuhs, J. Giesl, M. Parting, P. Schneider-Kamp, and S. Swiderski. Proving Termination by Dependency Pairs and Inductive Theorem Proving. In volume 47(2) of Journal of Automated Reasoning. 133--160, 2011. [Gra95] B. Gramlich. Abstract Relations Between Restricted Termination and Confluence Properties of Rewrite Systems. In volume 24(1-2) of Fundamentae Informaticae. 3--23, 1995.
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