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TRS Stand 20472 pair #381710058
details
property
value
status
complete
benchmark
halfdouble.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n108.star.cs.uiowa.edu
space
AProVE_10
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.4560110569 seconds
cpu usage
0.432236006
max memory
1.11616E7
stage attributes
key
value
output-size
1522
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 eq : [o * o] --> o f : [o * o] --> o half : [o] --> o s : [o] --> o tt : [] --> o f(tt, X) => f(eq(X, half(double(X))), s(X)) eq(s(X), s(Y)) => eq(X, Y) eq(0, 0) => tt double(s(X)) => s(s(double(X))) double(0) => 0 half(s(s(X))) => s(half(X)) half(0) => 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 : [] --> lb double : [lb] --> lb eq : [lb * lb] --> na f : [na * lb] --> y half : [lb] --> lb s : [lb] --> lb tt : [] --> na +++ 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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