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TRS Stand 20472 pair #381711075
details
property
value
status
complete
benchmark
tpa07.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n021.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
4.52888417244 seconds
cpu usage
4.52383112
max memory
7.4919936E7
stage attributes
key
value
output-size
1586
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. !minus : [o * o] --> o !plus : [o * o] --> o !times : [o * o] --> o 0 : [] --> o f : [o * o] --> o s : [o] --> o !minus(X, 0) => X !minus(s(X), s(Y)) => !minus(X, Y) !plus(0, X) => X !plus(s(X), Y) => s(!plus(X, Y)) !times(X, 0) => 0 !times(X, s(Y)) => !plus(X, !times(X, Y)) f(s(X), Y) => f(!minus(!times(s(X), s(Y)), s(!times(s(X), Y))), !times(Y, 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: !minus : [xb * xb] --> xb !plus : [xb * xb] --> xb !times : [xb * xb] --> xb 0 : [] --> xb f : [xb * xb] --> yb s : [xb] --> xb +++ 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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