details

property	value
status	complete
benchmark	challenge_fab.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n003.star.cs.uiowa.edu
space	AProVE_10

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.348520994186 seconds
cpu usage	0.343361461
max memory	1.1894784E7

stage attributes

key	value
output-size	1788
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 and : [o * o] --> o cons : [o * o] --> o from : [o] --> o fromCond : [o * o] --> o is!6220nat : [o] --> o is!6220natlist : [o] --> o nil : [] --> o s : [o] --> o tt : [] --> o and(tt, tt) => tt is!6220nat(0) => tt is!6220nat(s(X)) => is!6220nat(X) is!6220natlist(nil) => tt is!6220natlist(cons(X, Y)) => and(is!6220nat(X), is!6220natlist(Y)) from(X) => fromCond(is!6220natlist(X), X) fromCond(tt, cons(X, Y)) => from(cons(s(X), cons(X, 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 : [] --> nb and : [za * za] --> za cons : [nb * nb] --> nb from : [nb] --> ob fromCond : [za * nb] --> ob is!6220nat : [nb] --> za is!6220natlist : [nb] --> za nil : [] --> nb s : [nb] --> nb tt : [] --> za +++ 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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