details

property	value
status	complete
benchmark	Ex7_BLR02.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)	0.16937994957 seconds
cpu usage	0.137786315
max memory	6361088.0

stage attributes

key	value
output-size	1649
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 2nd : [o] --> o cons : [o * o] --> o from : [o] --> o head : [o] --> o nil : [] --> o s : [o] --> o sel : [o * o] --> o take : [o * o] --> o from(X) => cons(X, from(s(X))) head(cons(X, Y)) => X 2nd(cons(X, Y)) => head(Y) take(0, X) => nil take(s(X), cons(Y, Z)) => cons(Y, take(X, Z)) sel(0, cons(X, Y)) => X sel(s(X), cons(Y, Z)) => sel(X, 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: 0 : [] --> ub 2nd : [qb] --> ub cons : [ub * qb] --> qb from : [ub] --> qb head : [qb] --> ub nil : [] --> qb s : [ub] --> ub sel : [ub * qb] --> ub take : [ub * qb] --> qb +++ 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. popout

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