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TRS Stand 20472 pair #381713378
details
property
value
status
complete
benchmark
Ex9_BLR02.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n093.star.cs.uiowa.edu
space
Strategy_removed_CSR_05
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.271733999252 seconds
cpu usage
0.249641155
max memory
1.333248E7
stage attributes
key
value
output-size
1647
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 cons : [o * o] --> o filter : [o * o * o] --> o nats : [o] --> o s : [o] --> o sieve : [o] --> o zprimes : [] --> o filter(cons(X, Y), 0, Z) => cons(0, filter(Y, Z, Z)) filter(cons(X, Y), s(Z), U) => cons(X, filter(Y, Z, U)) sieve(cons(0, X)) => cons(0, sieve(X)) sieve(cons(s(X), Y)) => cons(s(X), sieve(filter(Y, X, X))) nats(X) => cons(X, nats(s(X))) zprimes => sieve(nats(s(s(0)))) 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 : [] --> ac cons : [ac * cc] --> cc filter : [cc * ac * ac] --> cc nats : [ac] --> cc s : [ac] --> ac sieve : [cc] --> cc zprimes : [] --> cc +++ 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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