details

property	value
status	complete
benchmark	h04.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n145.star.cs.uiowa.edu
space	Hamana_Kikuchi_18

run statistics

property	value
solver	Wanda 2.2a
configuration	default
runtime (wallclock)	60.5844 seconds
cpu usage	60.5613
user time	54.2707
system time	6.29056
max virtual memory	4108840.0
max residence set size	4006596.0

stage attributes

key	value
starexec-result	MAYBE

output

MAYBE We consider the system theBenchmark. Alphabet: 0 : [] --> N even : [] --> N -> N -> B false : [] --> B g : [] --> N -> B h : [] --> N -> (N -> B) -> N -> B not : [] --> B -> B rec : [] --> (N -> (N -> B) -> N -> B) -> B -> N -> B s : [] --> N -> N true : [] --> B Rules: rec f (i 0) => i rec f (i (s x)) => f x (rec f (i x)) g x => true h x f y => not (f y) not true => false not false => true even x y => rec h (g 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 even : [N] --> N -> B false : [] --> B g : [] --> N -> B h : [] --> N -> (N -> B) -> N -> B not : [B] --> B 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 rec(F, ~AP1(G, s(X))) => F X rec(F, ~AP1(G, X)) g X => true h X F Y => not(~AP1(F, Y)) not(true) => false not(false) => true even(X) Y => ~AP1(rec(h, g X), Y) rec(F, even(X) 0) => even(X) rec(F, g 0) => g rec(F, h X G 0) => h X G rec(F, even(X) s(Y)) => F Y rec(F, even(X) Y) rec(F, g s(X)) => F X rec(F, g X) rec(F, h X G s(Y)) => F Y rec(F, h X G Y) ~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

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job log

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actions

all output return to Higher Order Rewriting Union Beta