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TRS Stand 20472 pair #381710064
details
property
value
status
complete
benchmark
cade14.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n070.star.cs.uiowa.edu
space
GTSSK07
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.406618833542 seconds
cpu usage
0.398674978
max memory
1.3996032E7
stage attributes
key
value
output-size
1853
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 cond1 : [o * o * o] --> o cond2 : [o * o * o] --> o diff : [o * o] --> o equal : [o * o] --> o false : [] --> o gt : [o * o] --> o s : [o] --> o true : [] --> o diff(X, Y) => cond1(equal(X, Y), X, Y) cond1(true, X, Y) => 0 cond1(false, X, Y) => cond2(gt(X, Y), X, Y) cond2(true, X, Y) => s(diff(X, s(Y))) cond2(false, X, Y) => s(diff(s(X), Y)) gt(0, X) => false gt(s(X), 0) => true gt(s(X), s(Y)) => gt(X, Y) equal(0, 0) => true equal(s(X), 0) => false equal(0, s(X)) => false equal(s(X), s(Y)) => equal(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 : [] --> id cond1 : [md * id * id] --> id cond2 : [md * id * id] --> id diff : [id * id] --> id equal : [id * id] --> md false : [] --> md gt : [id * id] --> md s : [id] --> id true : [] --> md +++ 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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