details

property	value
status	complete
benchmark	4.61.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n083.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.73788690567 seconds
cpu usage	0.702625034
max memory	2.4887296E7

stage attributes

key	value
output-size	1958
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. !770!870 : [o * o] --> o !dot : [o * o] --> o 0 : [] --> o bsort : [o] --> o bubble : [o] --> o butlast : [o] --> o if : [o * o * o] --> o last : [o] --> o nil : [] --> o bsort(nil) => nil bsort(!dot(X, Y)) => last(!dot(bubble(!dot(X, Y)), bsort(butlast(bubble(!dot(X, Y)))))) bubble(nil) => nil bubble(!dot(X, nil)) => !dot(X, nil) bubble(!dot(X, !dot(Y, Z))) => if(!770!870(X, Y), !dot(Y, bubble(!dot(X, Z))), !dot(X, bubble(!dot(Y, Z)))) last(nil) => 0 last(!dot(X, nil)) => X last(!dot(X, !dot(Y, Z))) => last(!dot(Y, Z)) butlast(nil) => nil butlast(!dot(X, nil)) => nil butlast(!dot(X, !dot(Y, Z))) => !dot(X, butlast(!dot(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: !770!870 : [rd * rd] --> lb !dot : [rd * rd] --> rd 0 : [] --> rd bsort : [rd] --> rd bubble : [rd] --> rd butlast : [rd] --> rd if : [lb * rd * rd] --> rd last : [rd] --> rd nil : [] --> rd +++ 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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all output return to TRS Stand 20472