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TRS Stand 20472 pair #381710418
details
property
value
status
complete
benchmark
aprove2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n003.star.cs.uiowa.edu
space
Secret_05_TRS
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.312184095383 seconds
cpu usage
0.308674549
max memory
1.374208E7
stage attributes
key
value
output-size
1834
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 div : [o * o] --> o divByZeroError : [] --> o false : [] --> o ge : [o * o] --> o if : [o * o * o] --> o ify : [o * o * o] --> o minus : [o * o] --> o s : [o] --> o true : [] --> o ge(X, 0) => true ge(0, s(X)) => false ge(s(X), s(Y)) => ge(X, Y) minus(X, 0) => X minus(s(X), s(Y)) => minus(X, Y) div(X, Y) => ify(ge(Y, s(0)), X, Y) ify(false, X, Y) => divByZeroError ify(true, X, Y) => if(ge(X, Y), X, Y) if(false, X, Y) => 0 if(true, X, Y) => s(div(minus(X, Y), 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 : [] --> vc div : [vc * vc] --> vc divByZeroError : [] --> vc false : [] --> bc ge : [vc * vc] --> bc if : [bc * vc * vc] --> vc ify : [bc * vc * vc] --> vc minus : [vc * vc] --> vc s : [vc] --> vc true : [] --> bc +++ 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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