details

property	value
status	complete
benchmark	thiemann05.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n091.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.445791959763 seconds
cpu usage	0.443188048
max memory	2.0393984E7

stage attributes

key	value
output-size	2029
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. concat : [o * o] --> o cons : [o * o] --> o false : [] --> o if1 : [o * o * o * o] --> o if2 : [o * o * o] --> o isLeaf : [o] --> o leaf : [] --> o left : [o] --> o less!6220leaves : [o * o] --> o right : [o] --> o true : [] --> o isLeaf(leaf) => true isLeaf(cons(X, Y)) => false left(cons(X, Y)) => X right(cons(X, Y)) => Y concat(leaf, X) => X concat(cons(X, Y), Z) => cons(X, concat(Y, Z)) less!6220leaves(X, Y) => if1(isLeaf(X), isLeaf(Y), X, Y) if1(X, true, Y, Z) => false if1(X, false, Y, Z) => if2(X, Y, Z) if2(true, X, Y) => true if2(false, X, Y) => less!6220leaves(concat(left(X), right(X)), concat(left(Y), right(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: concat : [hd * hd] --> hd cons : [hd * hd] --> hd false : [] --> id if1 : [id * id * hd * hd] --> id if2 : [id * hd * hd] --> id isLeaf : [hd] --> id leaf : [] --> hd left : [hd] --> hd less!6220leaves : [hd * hd] --> id right : [hd] --> hd true : [] --> id +++ 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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