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TRS Stand 20472 pair #381711249
details
property
value
status
complete
benchmark
ex05.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n021.star.cs.uiowa.edu
space
Zantema_15
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
12.5331549644 seconds
cpu usage
12.522118397
max memory
1.2570624E7
stage attributes
key
value
output-size
1476
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 double : [o] --> o f : [o * o * o * o] --> o isNat : [o] --> o s : [o] --> o true : [] --> o f(true, true, X, s(Y)) => f(isNat(X), isNat(Y), s(X), double(s(Y))) isNat(0) => true isNat(s(X)) => isNat(X) double(0) => 0 double(s(X)) => s(s(double(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 : [] --> ya double : [ya] --> ya f : [ma * ma * ya * ya] --> ba isNat : [ya] --> ma s : [ya] --> ya true : [] --> ma +++ 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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