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TRS Stand 20472 pair #381712735
details
property
value
status
complete
benchmark
append-wrong.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n051.star.cs.uiowa.edu
space
CiME_04
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.168215990067 seconds
cpu usage
0.164802118
max memory
7999488.0
stage attributes
key
value
output-size
1731
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. append : [o * o] --> o cons : [o * o] --> o false : [] --> o hd : [o] --> o ifappend : [o * o * o] --> o is!6220empty : [o] --> o nil : [] --> o tl : [o] --> o true : [] --> o is!6220empty(nil) => true is!6220empty(cons(X, Y)) => false hd(cons(X, Y)) => X tl(cons(X, Y)) => cons(X, Y) append(X, Y) => ifappend(X, Y, is!6220empty(X)) ifappend(X, Y, true) => Y ifappend(X, Y, false) => cons(hd(X), append(tl(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: append : [rb * rb] --> rb cons : [mb * rb] --> rb false : [] --> ya hd : [rb] --> mb ifappend : [rb * rb * ya] --> rb is!6220empty : [rb] --> ya nil : [] --> rb tl : [rb] --> rb true : [] --> ya +++ 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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