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TRS Stand 20472 pair #381714584
details
property
value
status
complete
benchmark
thiemann08.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n048.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.269431114197 seconds
cpu usage
0.215237229
max memory
1.1399168E7
stage attributes
key
value
output-size
1962
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. cons : [o * o] --> o empty : [o] --> o false : [] --> o head : [o] --> o if : [o * o * o] --> o last : [o * o] --> o nil : [] --> o rev : [o] --> o rev1 : [o * o] --> o rev2 : [o * o] --> o tail : [o] --> o true : [] --> o empty(nil) => true empty(cons(X, Y)) => false head(cons(X, Y)) => X tail(nil) => nil tail(cons(X, Y)) => Y rev(nil) => nil rev(cons(X, Y)) => cons(rev1(X, Y), rev2(X, Y)) last(X, Y) => if(empty(Y), X, Y) if(true, X, Y) => X if(false, X, Y) => last(head(Y), tail(Y)) rev2(X, nil) => nil rev2(X, cons(Y, Z)) => rev(cons(X, rev2(Y, Z))) 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: cons : [wc * fd] --> fd empty : [fd] --> ub false : [] --> ub head : [fd] --> wc if : [ub * wc * fd] --> wc last : [wc * fd] --> wc nil : [] --> fd rev : [fd] --> fd rev1 : [wc * fd] --> wc rev2 : [wc * fd] --> fd tail : [fd] --> fd 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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