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TRS Stand 20472 pair #381710915
details
property
value
status
complete
benchmark
aprove3.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n098.star.cs.uiowa.edu
space
Secret_05_TRS
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
1.72402000427 seconds
cpu usage
1.714397809
max memory
3.6970496E7
stage attributes
key
value
output-size
1906
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. 0 : [] --> o false : [] --> o function : [o * o * o * o] --> o if : [] --> o iszero : [] --> o p : [] --> o plus : [] --> o s : [o] --> o third : [] --> o true : [] --> o function(iszero, 0, X, Y) => true function(iszero, s(X), Y, Z) => false function(p, 0, X, Y) => 0 function(p, s(0), X, Y) => 0 function(p, s(s(X)), Y, Z) => s(function(p, s(X), X, X)) function(plus, X, Y, Z) => function(if, function(iszero, Y, Y, Y), Y, Z) function(if, true, X, Y) => Y function(if, false, X, Y) => function(plus, function(third, X, Y, Y), function(p, X, X, Y), s(Y)) function(third, X, Y, Z) => Z 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 : [] --> ld false : [] --> ld function : [sc * ld * ld * ld] --> ld if : [] --> sc iszero : [] --> sc p : [] --> sc plus : [] --> sc s : [ld] --> ld third : [] --> sc true : [] --> ld +++ 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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