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TRS Stand 20472 pair #381711387
details
property
value
status
complete
benchmark
mod.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n090.star.cs.uiowa.edu
space
AProVE_09_Inductive
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.394272089005 seconds
cpu usage
0.390570243
max memory
1.78176E7
stage attributes
key
value
output-size
1904
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 false : [] --> o gt : [o * o] --> o if : [o * o * o] --> o if1 : [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), Y) => if(gt(s(X), Y), X, Y) if(true, X, Y) => s(minus(X, Y)) if(false, X, Y) => 0 mod(X, 0) => 0 mod(X, s(Y)) => if1(lt(X, s(Y)), X, s(Y)) if1(true, X, Y) => X if1(false, X, Y) => mod(minus(X, Y), Y) gt(0, X) => false gt(s(X), 0) => true gt(s(X), s(Y)) => gt(X, Y) 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 : [] --> wd false : [] --> ae gt : [wd * wd] --> ae if : [ae * wd * wd] --> wd if1 : [ae * wd * wd] --> wd lt : [wd * wd] --> ae minus : [wd * wd] --> wd mod : [wd * wd] --> wd s : [wd] --> wd true : [] --> ae +++ 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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