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TRS Stand 20472 pair #381711854
details
property
value
status
complete
benchmark
otto03.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
AProVE_07
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.282576084137 seconds
cpu usage
0.180045322
max memory
8306688.0
stage attributes
key
value
output-size
1652
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 fac : [o] --> o false : [] --> o help : [o * o] --> o if : [o * o * o] --> o lt : [o * o] --> o s : [o] --> o times : [o * o] --> o true : [] --> o lt(0, s(X)) => true lt(X, 0) => false lt(s(X), s(Y)) => lt(X, Y) fac(X) => help(X, 0) help(X, Y) => if(lt(Y, X), X, Y) if(true, X, Y) => times(s(Y), help(X, s(Y))) if(false, X, Y) => s(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 : [] --> ub fac : [ub] --> ub false : [] --> xa help : [ub * ub] --> ub if : [xa * ub * ub] --> ub lt : [ub * ub] --> xa s : [ub] --> ub times : [ub * ub] --> ub true : [] --> xa +++ 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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