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TRS Stand 20472 pair #381713171
details
property
value
status
complete
benchmark
#4.30.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n071.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.268090009689 seconds
cpu usage
0.264601756
max memory
1.1739136E7
stage attributes
key
value
output-size
1692
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 false : [] --> o if!6220quot : [o * o * o] --> o le : [o * o] --> o minus : [o * o] --> o quot : [o * o] --> o s : [o] --> o true : [] --> o minus(X, 0) => X minus(s(X), s(Y)) => minus(X, Y) le(0, X) => true le(s(X), 0) => false le(s(X), s(Y)) => le(X, Y) quot(X, s(Y)) => if!6220quot(le(s(Y), X), X, s(Y)) if!6220quot(true, X, Y) => s(quot(minus(X, Y), Y)) if!6220quot(false, X, Y) => 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 : [] --> bc false : [] --> hb if!6220quot : [hb * bc * bc] --> bc le : [bc * bc] --> hb minus : [bc * bc] --> bc quot : [bc * bc] --> bc s : [bc] --> bc true : [] --> hb +++ 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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