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TRS Stand 20472 pair #381710569
details
property
value
status
complete
benchmark
tower_sizeChange.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n022.star.cs.uiowa.edu
space
AProVE_06
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.520669937134 seconds
cpu usage
0.470464905
max memory
1.3287424E7
stage attributes
key
value
output-size
1708
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 a : [] --> o b : [] --> o double : [o] --> o exp : [o] --> o f : [o * o * o] --> o half : [o] --> o s : [o] --> o tower : [o] --> o tower(X) => f(a, X, s(0)) f(a, 0, X) => X f(a, s(X), Y) => f(b, Y, s(X)) f(b, X, Y) => f(a, half(Y), exp(X)) exp(0) => s(0) exp(s(X)) => double(exp(X)) double(0) => 0 double(s(X)) => s(s(double(X))) half(0) => double(0) half(s(0)) => half(0) half(s(s(X))) => s(half(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 : [] --> vc a : [] --> ma b : [] --> ma double : [vc] --> vc exp : [vc] --> vc f : [ma * vc * vc] --> vc half : [vc] --> vc s : [vc] --> vc tower : [vc] --> vc +++ 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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