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TRS Stand 20472 pair #381711402
details
property
value
status
complete
benchmark
#4.30b.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n025.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
4.1240530014 seconds
cpu usage
3.24505006
max memory
1.3049856E7
stage attributes
key
value
output-size
1728
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 false : [] --> o if!6220mod : [o * o * o] --> o le : [o * o] --> o minus : [o * o] --> o mod : [o * o] --> o s : [o] --> o true : [] --> o le(0, X) => true le(s(X), 0) => false le(s(X), s(Y)) => le(X, Y) minus(X, 0) => X minus(s(X), s(Y)) => minus(X, Y) mod(0, X) => 0 mod(s(X), 0) => 0 mod(s(X), s(Y)) => if!6220mod(le(Y, X), s(X), s(Y)) if!6220mod(true, X, Y) => mod(minus(X, Y), Y) if!6220mod(false, s(X), s(Y)) => s(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 : [] --> sc false : [] --> ub if!6220mod : [ub * sc * sc] --> sc le : [sc * sc] --> ub minus : [sc * sc] --> sc mod : [sc * sc] --> sc s : [sc] --> sc true : [] --> ub +++ 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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