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TRS Stand 20472 pair #381714464
details
property
value
status
complete
benchmark
otto09.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n190.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.647513151169 seconds
cpu usage
0.64411963
max memory
1.8845696E7
stage attributes
key
value
output-size
1768
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 false : [] --> o help : [o * o * o] --> o if : [o * o * o * o] --> o lt : [o * o] --> o plus : [o * o] --> o quot : [o * o] --> o s : [o] --> o true : [] --> o lt(X, 0) => false lt(0, s(X)) => true lt(s(X), s(Y)) => lt(X, Y) plus(X, 0) => X plus(X, s(Y)) => s(plus(X, Y)) quot(X, s(Y)) => help(X, s(Y), 0) help(X, s(Y), Z) => if(lt(Z, X), X, s(Y), Z) if(true, X, s(Y), Z) => s(help(X, s(Y), plus(Z, s(Y)))) if(false, X, s(Y), Z) => 0 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 : [] --> wc false : [] --> ub help : [wc * wc * wc] --> wc if : [ub * wc * wc * wc] --> wc lt : [wc * wc] --> ub plus : [wc * wc] --> wc quot : [wc * wc] --> wc s : [wc] --> wc true : [] --> ub +++ 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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