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TRS Stand 20472 pair #381712387
details
property
value
status
complete
benchmark
6.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n040.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.141857147217 seconds
cpu usage
0.124330659
max memory
4595712.0
stage attributes
key
value
output-size
1453
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. 0 : [] --> o cond : [o * o] --> o false : [] --> o odd : [o] --> o p : [o] --> o s : [o] --> o true : [] --> o cond(true, X) => cond(odd(X), p(X)) odd(0) => false odd(s(0)) => true odd(s(s(X))) => odd(X) p(0) => 0 p(s(X)) => X 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 : [] --> ta cond : [la * ta] --> s false : [] --> la odd : [ta] --> la p : [ta] --> ta s : [ta] --> ta true : [] --> la +++ 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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