details

property	value
status	complete
benchmark	zerolist.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n101.star.cs.uiowa.edu
space	AProVE_09_Inductive

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.33206820488 seconds
cpu usage	0.324630175
max memory	1.2673024E7

stage attributes

key	value
output-size	1678
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 cons : [o * o] --> o nil : [] --> o s : [o] --> o sub : [o * o] --> o zero : [o] --> o zero2 : [o * o] --> o sub(0, 0) => 0 sub(s(X), 0) => s(X) sub(0, s(X)) => 0 sub(s(X), s(Y)) => sub(X, Y) zero(nil) => zero2(0, nil) zero(cons(X, Y)) => zero2(sub(X, X), cons(X, Y)) zero2(0, nil) => nil zero2(0, cons(X, Y)) => cons(sub(X, X), zero(Y)) zero2(s(X), nil) => zero(nil) zero2(s(X), cons(Y, Z)) => zero(cons(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: 0 : [] --> mc cons : [mc * uc] --> uc nil : [] --> uc s : [mc] --> mc sub : [mc * mc] --> mc zero : [uc] --> uc zero2 : [mc * uc] --> uc +++ 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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