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TRS Stand 20472 pair #381712381
details
property
value
status
complete
benchmark
otto05.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n069.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.275941848755 seconds
cpu usage
0.272511541
max memory
1.2283904E7
stage attributes
key
value
output-size
1926
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 1 : [] --> o false : [] --> o half : [o] --> o help : [o * o] --> o ifa : [o * o] --> o ifb : [o * o * o] --> o logZeroError : [] --> o logarithm : [o] --> o lt : [o * o] --> o s : [o] --> o true : [] --> o lt(0, s(X)) => true lt(X, 0) => false lt(s(X), s(Y)) => lt(X, Y) logarithm(X) => ifa(lt(0, X), X) ifa(true, X) => help(X, 1) ifa(false, X) => logZeroError help(X, Y) => ifb(lt(Y, X), X, Y) ifb(true, X, Y) => help(half(X), s(Y)) ifb(false, X, Y) => Y half(0) => 0 half(s(0)) => 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 : [] --> dd 1 : [] --> dd false : [] --> sb half : [dd] --> dd help : [dd * dd] --> dd ifa : [sb * dd] --> dd ifb : [sb * dd * dd] --> dd logZeroError : [] --> dd logarithm : [dd] --> dd lt : [dd * dd] --> sb s : [dd] --> dd true : [] --> sb +++ 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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