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TRS Stand 20472 pair #381710409
details
property
value
status
complete
benchmark
3.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n078.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.182518005371 seconds
cpu usage
0.172608491
max memory
7757824.0
stage attributes
key
value
output-size
1527
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 add : [o * o] --> o cond : [o * o * o] --> o false : [] --> o gr : [o * o] --> o s : [o] --> o true : [] --> o cond(true, X, Y) => cond(gr(X, Y), X, add(X, Y)) gr(0, X) => false gr(s(X), 0) => true gr(s(X), s(Y)) => gr(X, Y) add(0, X) => X add(s(X), Y) => s(add(X, Y)) 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 : [] --> ib add : [ib * ib] --> ib cond : [ua * ib * ib] --> x false : [] --> ua gr : [ib * ib] --> ua s : [ib] --> ib true : [] --> ua +++ 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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