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TRS Stand 20472 pair #381712933
details
property
value
status
complete
benchmark
15.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n047.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
1.46871519089 seconds
cpu usage
1.46481318
max memory
2.7947008E7
stage attributes
key
value
output-size
1926
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 add : [o * o] --> o cond1 : [o * o * o] --> o cond2 : [o * o * o] --> o cond3 : [o * o * o] --> o false : [] --> o gr : [o * o] --> o p : [o] --> o s : [o] --> o true : [] --> o cond1(true, X, Y) => cond2(gr(X, 0), X, Y) cond2(true, X, Y) => cond1(gr(add(X, Y), 0), p(X), Y) cond2(false, X, Y) => cond3(gr(Y, 0), X, Y) cond3(true, X, Y) => cond1(gr(add(X, Y), 0), X, p(Y)) cond3(false, X, Y) => cond1(gr(add(X, Y), 0), X, Y) gr(0, X) => false gr(s(X), 0) => true gr(s(X), s(Y)) => gr(X, Y) add(0, X) => X add(s(X), Y) => s(add(X, Y)) p(0) => 0 p(s(X)) => 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 : [] --> xd add : [xd * xd] --> xd cond1 : [bd * xd * xd] --> gc cond2 : [bd * xd * xd] --> gc cond3 : [bd * xd * xd] --> gc false : [] --> bd gr : [xd * xd] --> bd p : [xd] --> xd s : [xd] --> xd true : [] --> bd +++ 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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