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TRS Stand 20472 pair #381713176
details
property
value
status
complete
benchmark
Ex2_Luc03b.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n069.star.cs.uiowa.edu
space
Strategy_removed_CSR_05
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.581707954407 seconds
cpu usage
0.139387285
max memory
6385664.0
stage attributes
key
value
output-size
1581
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 add : [o * o] --> o cons : [o * o] --> o from : [o] --> o fst : [o * o] --> o len : [o] --> o nil : [] --> o s : [o] --> o fst(0, X) => nil fst(s(X), cons(Y, Z)) => cons(Y, fst(X, Z)) from(X) => cons(X, from(s(X))) add(0, X) => X add(s(X), Y) => s(add(X, Y)) len(nil) => 0 len(cons(X, Y)) => s(len(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 : [] --> pb add : [pb * pb] --> pb cons : [pb * lb] --> lb from : [pb] --> lb fst : [pb * lb] --> lb len : [lb] --> pb nil : [] --> lb s : [pb] --> pb +++ 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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