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TRS Stand 20472 pair #381711703
details
property
value
status
complete
benchmark
ex2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n033.star.cs.uiowa.edu
space
AProVE_10
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.182307004929 seconds
cpu usage
0.169631586
max memory
6332416.0
stage attributes
key
value
output-size
1356
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 f : [o * o] --> o g : [o * o] --> o h : [o] --> o s : [o] --> o tt : [] --> o g(tt, X) => g(h(f(X, X)), s(X)) h(f(0, X)) => tt f(s(X), Y) => f(X, s(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 : [] --> ia f : [ia * ia] --> ja g : [z * ia] --> s h : [ja] --> z s : [ia] --> ia tt : [] --> z +++ 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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