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TRS Stand 20472 pair #381709724
details
property
value
status
complete
benchmark
cade01.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n030.star.cs.uiowa.edu
space
GTSSK07
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.174272060394 seconds
cpu usage
0.161614236
max memory
7266304.0
stage attributes
key
value
output-size
1533
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] --> o false : [] --> o gt : [o * o] --> o minus : [o * o] --> o s : [o] --> o true : [] --> o minus(X, Y) => cond(gt(X, Y), X, Y) cond(false, X, Y) => 0 cond(true, X, Y) => s(minus(X, s(Y))) gt(0, X) => false gt(s(X), 0) => true gt(s(X), s(Y)) => gt(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 : [] --> fb cond : [jb * fb * fb] --> fb false : [] --> jb gt : [fb * fb] --> jb minus : [fb * fb] --> fb s : [fb] --> fb true : [] --> jb +++ 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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