details

property	value
status	complete
benchmark	#3.42.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n051.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.153517961502 seconds
cpu usage	0.142044972
max memory	6639616.0

stage attributes

key	value
output-size	1559
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 conv : [o] --> o half : [o] --> o lastbit : [o] --> o nil : [] --> o s : [o] --> o half(0) => 0 half(s(0)) => 0 half(s(s(X))) => s(half(X)) lastbit(0) => 0 lastbit(s(0)) => s(0) lastbit(s(s(X))) => lastbit(X) conv(0) => cons(nil, 0) conv(s(X)) => cons(conv(half(s(X))), lastbit(s(X))) 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 cons : [ob * nb] --> ob conv : [nb] --> ob half : [nb] --> nb lastbit : [nb] --> nb nil : [] --> ob s : [nb] --> nb +++ 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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