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TRS Stand 20472 pair #381713028
details
property
value
status
complete
benchmark
ExIntrod_GM04.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
Strategy_removed_CSR_05
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.106948852539 seconds
cpu usage
0.097717346
max memory
4280320.0
stage attributes
key
value
output-size
1584
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 adx : [o] --> o cons : [o * o] --> o hd : [o] --> o incr : [o] --> o nats : [] --> o s : [o] --> o tl : [o] --> o zeros : [] --> o nats => adx(zeros) zeros => cons(0, zeros) incr(cons(X, Y)) => cons(s(X), incr(Y)) adx(cons(X, Y)) => incr(cons(X, adx(Y))) hd(cons(X, Y)) => X tl(cons(X, 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: 0 : [] --> da adx : [cb] --> cb cons : [da * cb] --> cb hd : [cb] --> da incr : [cb] --> cb nats : [] --> cb s : [da] --> da tl : [cb] --> cb zeros : [] --> cb +++ 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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