details

property	value
status	complete
benchmark	h08.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n139.star.cs.uiowa.edu
space	Hamana_Kikuchi_18

run statistics

property	value
solver	Wanda 2.2a
configuration	default
runtime (wallclock)	29.4233 seconds
cpu usage	29.4225
user time	26.5121
system time	2.91044
max virtual memory	2600996.0
max residence set size	2410612.0

stage attributes

key	value
starexec-result	MAYBE

output

MAYBE We consider the system theBenchmark. Alphabet: 0 : [] --> N false : [] --> B g : [] --> N -> B g2 : [] --> N -> B geq : [] --> N -> N -> B h : [] --> N -> (N -> B) -> N -> B h2 : [] --> N -> (N -> B) -> N -> B iszero : [] --> N -> N -> B pred : [] --> N -> N rec : [] --> (N -> (N -> B) -> N -> B) -> B -> N -> B s : [] --> N -> N true : [] --> B Rules: rec f (i 0) => i g x => true h x f y => false iszero x y => rec h (g x) y pred 0 => 0 pred (s x) => x g2 x => iszero x 0 h2 x f y => f (pred y) geq x y => rec h2 (g2 x) y Using the transformations described in [Kop11], this system can be brought in a form without leading free variables in the left-hand side, and where the left-hand side of a variable is always a functional term or application headed by a functional term. We now transform the resulting AFS into an AFSM by replacing all free variables by meta-variables (with arity 0). This leads to the following AFSM: Alphabet: 0 : [] --> N false : [] --> B g : [] --> N -> B g2 : [] --> N -> B geq : [N] --> N -> B h : [] --> N -> (N -> B) -> N -> B h2 : [] --> N -> (N -> B) -> N -> B iszero : [N] --> N -> B pred : [N] --> N rec : [N -> (N -> B) -> N -> B * B] --> N -> B s : [N] --> N true : [] --> B ~AP1 : [N -> B * N] --> B Rules: rec(F, ~AP1(G, 0)) => G g X => true h X F Y => false iszero(X) Y => ~AP1(rec(h, g X), Y) pred(0) => 0 pred(s(X)) => X g2 X => iszero(X) 0 h2 X F Y => ~AP1(F, pred(Y)) geq(X) Y => ~AP1(rec(h2, g2 X), Y) rec(F, g 0) => g rec(F, g2 0) => g2 rec(F, geq(X) 0) => geq(X) rec(F, h X G 0) => h X G rec(F, h2 X G 0) => h2 X G rec(F, iszero(X) 0) => iszero(X) ~AP1(F, X) => F X +++ Citations +++ [Kop11] C. Kop. Simplifying Algebraic Functional Systems. In Proceedings of CAI 2011, volume 6742 of LNCS. 201--215, Springer, 2011. popout

output may be truncated. 'popout' for the full output.

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all output return to Higher Order Rewriting Union Beta