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TRS Stand 20472 pair #381711558
details
property
value
status
complete
benchmark
enger-nonloop-toOne.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n074.star.cs.uiowa.edu
space
EEG_IJCAR_12
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
1.3589758873 seconds
cpu usage
0.657867011
max memory
1.1419648E7
stage attributes
key
value
output-size
1433
starexec-result
MAYBE
output
/export/starexec/sandbox2/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- MAYBE We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. 0 : [] --> o eq : [o * o] --> o f : [o * o] --> o s : [o] --> o toOne : [o] --> o tt : [] --> o f(tt, X) => f(eq(toOne(X), s(0)), s(X)) eq(s(X), s(Y)) => eq(X, Y) eq(0, 0) => tt toOne(s(s(X))) => toOne(s(X)) toOne(s(0)) => s(0) 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: 0 : [] --> za eq : [za * za] --> ka f : [ka * za] --> w s : [za] --> za toOne : [za] --> za tt : [] --> ka +++ 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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