details

property	value
status	complete
benchmark	h05.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n142.star.cs.uiowa.edu
space	Hamana_Kikuchi_18

run statistics

property	value
solver	Wanda 2.2a
configuration	default
runtime (wallclock)	129.53 seconds
cpu usage	129.488
user time	116.028
system time	13.4595
max virtual memory	8817496.0
max residence set size	8559328.0

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 rec f (i (s x)) => f x (rec f (i x)) 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 rec(F, ~AP1(G, s(X))) => F X rec(F, ~AP1(G, X)) 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) rec(F, g s(X)) => F X rec(F, g X) rec(F, g2 s(X)) => F X rec(F, g2 X) rec(F, geq(X) s(Y)) => F Y rec(F, geq(X) Y) rec(F, h X G s(Y)) => F Y rec(F, h X G Y) rec(F, h2 X G s(Y)) => F Y rec(F, h2 X G Y) rec(F, iszero(X) s(Y)) => F Y rec(F, iszero(X) 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

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

job log

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actions

all output return to Higher Order Rewriting Union Beta