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TRS Stand 20472 pair #381711856
details
property
value
status
complete
benchmark
gcdhard.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n046.star.cs.uiowa.edu
space
AProVE_09_Inductive
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.948804855347 seconds
cpu usage
0.942738317
max memory
2.6574848E7
stage attributes
key
value
output-size
1835
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 gcd : [o * o] --> o if : [o * o * o] --> o lt : [o * o] --> o minus : [o * o] --> o mod : [o * o] --> o s : [o] --> o true : [] --> o minus(0, X) => 0 minus(s(X), 0) => s(X) minus(s(X), s(Y)) => minus(X, Y) mod(X, 0) => 0 mod(X, s(Y)) => if(lt(X, s(Y)), X, s(Y)) if(true, X, Y) => X if(false, X, Y) => mod(minus(X, Y), Y) gcd(X, 0) => X gcd(0, s(X)) => s(X) gcd(s(X), s(Y)) => gcd(mod(s(X), s(Y)), mod(s(Y), s(X))) lt(X, 0) => false lt(0, s(X)) => true lt(s(X), s(Y)) => lt(X, 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 : [] --> sd false : [] --> wd gcd : [sd * sd] --> sd if : [wd * sd * sd] --> sd lt : [sd * sd] --> wd minus : [sd * sd] --> sd mod : [sd * sd] --> sd s : [sd] --> sd true : [] --> wd +++ 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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