details

property	value
status	complete
benchmark	maxsort.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n016.star.cs.uiowa.edu
space	AProVE_09_Inductive

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.738086938858 seconds
cpu usage	0.727485994
max memory	3.8322176E7

stage attributes

key	value
output-size	2239
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 del : [o * o] --> o eq : [o * o] --> o false : [] --> o ge : [o * o] --> o if1 : [o * o * o * o] --> o if2 : [o * o * o * o] --> o max : [o] --> o nil : [] --> o s : [o] --> o sort : [o] --> o true : [] --> o max(nil) => 0 max(cons(X, nil)) => X max(cons(X, cons(Y, Z))) => if1(ge(X, Y), X, Y, Z) if1(true, X, Y, Z) => max(cons(X, Z)) if1(false, X, Y, Z) => max(cons(Y, Z)) del(X, nil) => nil del(X, cons(Y, Z)) => if2(eq(X, Y), X, Y, Z) if2(true, X, Y, Z) => Z if2(false, X, Y, Z) => cons(Y, del(X, Z)) eq(0, 0) => true eq(0, s(X)) => false eq(s(X), 0) => false eq(s(X), s(Y)) => eq(X, Y) sort(nil) => nil sort(cons(X, Y)) => cons(max(cons(X, Y)), sort(del(max(cons(X, Y)), cons(X, Y)))) ge(X, 0) => true ge(0, s(X)) => false ge(s(X), s(Y)) => ge(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 : [] --> vf cons : [vf * ff] --> ff del : [vf * ff] --> ff eq : [vf * vf] --> zf false : [] --> zf ge : [vf * vf] --> zf if1 : [zf * vf * vf * ff] --> vf if2 : [zf * vf * vf * ff] --> ff max : [ff] --> vf nil : [] --> ff s : [vf] --> vf sort : [ff] --> ff true : [] --> zf +++ 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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