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TRS Stand 20472 pair #381710073
details
property
value
status
complete
benchmark
division.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n098.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.391565084457 seconds
cpu usage
0.388279826
max memory
1.675264E7
stage attributes
key
value
output-size
1855
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] --> o division : [o * o] --> o false : [] --> o if : [o * o * o * o] --> o inc : [o] --> o lt : [o * o] --> o minus : [o * o] --> o s : [o] --> o true : [] --> o division(X, Y) => div(X, Y, 0) div(X, Y, Z) => if(lt(X, Y), X, Y, inc(Z)) if(true, X, Y, Z) => Z if(false, X, s(Y), Z) => div(minus(X, s(Y)), s(Y), Z) minus(X, 0) => X minus(s(X), s(Y)) => minus(X, Y) lt(X, 0) => false lt(0, s(X)) => true lt(s(X), s(Y)) => lt(X, Y) inc(0) => s(0) inc(s(X)) => s(inc(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 : [] --> hd div : [hd * hd * hd] --> hd division : [hd * hd] --> hd false : [] --> vc if : [vc * hd * hd * hd] --> hd inc : [hd] --> hd lt : [hd * hd] --> vc minus : [hd * hd] --> hd s : [hd] --> hd true : [] --> vc +++ 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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