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TRS Stand 20472 pair #381714067
details
property
value
status
complete
benchmark
emmes-nonloop-ex3_3.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n050.star.cs.uiowa.edu
space
EEG_IJCAR_12
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.630852937698 seconds
cpu usage
0.347859746
max memory
1.1833344E7
stage attributes
key
value
output-size
1700
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 double : [o] --> o f : [o * o] --> o false : [] --> o gt : [o * o] --> o plus : [o * o] --> o s : [o] --> o times : [o * o] --> o true : [] --> o f(true, X) => f(gt(X, 0), double(X)) gt(s(X), 0) => true gt(0, X) => false gt(s(X), s(Y)) => gt(X, Y) double(X) => times(s(s(0)), X) times(0, X) => 0 times(s(X), Y) => plus(times(X, Y), Y) plus(0, X) => X plus(s(X), Y) => plus(X, s(Y)) 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 : [] --> hc double : [hc] --> hc f : [ua * hc] --> x false : [] --> ua gt : [hc * hc] --> ua plus : [hc * hc] --> hc s : [hc] --> hc times : [hc * hc] --> hc true : [] --> ua +++ 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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