details

property	value
status	complete
benchmark	h61.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n149.star.cs.uiowa.edu
space	Hamana_Kikuchi_18

run statistics

property	value
solver	Wanda 2.2a
configuration	default
runtime (wallclock)	0.387685 seconds
cpu usage	0.387866
user time	0.353404
system time	0.034462
max virtual memory	113188.0
max residence set size	11636.0

stage attributes

key	value
starexec-result	YES

output

YES We consider the system theBenchmark. Alphabet: app : [] --> list -> list -> list cons : [] --> nat -> list -> list foldl : [] --> (list -> nat -> list) -> list -> list -> list iconsc : [] --> list -> nat -> list nil : [] --> list reverse : [] --> list -> list reverse1 : [] --> list -> list Rules: app nil x => x app (cons x y) z => cons x (app y z) foldl (/\x./\y.f x y) z nil => z foldl (/\x./\y.f x y) z (cons u v) => foldl (/\w./\x'.f w x') (f z u) v iconsc x y => cons y x reverse x => foldl (/\y./\z.iconsc y z) nil x reverse1 x => foldl (/\y./\z.app (cons z nil) y) nil x 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: app : [list * list] --> list cons : [nat * list] --> list foldl : [list -> nat -> list * list * list] --> list iconsc : [list * nat] --> list nil : [] --> list reverse : [list] --> list reverse1 : [list] --> list ~AP1 : [list -> nat -> list * list] --> nat -> list Rules: app(nil, X) => X app(cons(X, Y), Z) => cons(X, app(Y, Z)) foldl(/\x./\y.~AP1(F, x) y, X, nil) => X foldl(/\x./\y.~AP1(F, x) y, X, cons(Y, Z)) => foldl(/\z./\u.~AP1(F, z) u, ~AP1(F, X) Y, Z) iconsc(X, Y) => cons(Y, X) reverse(X) => foldl(/\x./\y.iconsc(x, y), nil, X) reverse1(X) => foldl(/\x./\y.app(cons(y, nil), x), nil, X) foldl(/\x./\y.iconsc(x, y), X, nil) => X foldl(/\x./\y.iconsc(x, y), X, cons(Y, Z)) => foldl(/\z./\u.iconsc(z, u), iconsc(X, Y), Z) ~AP1(F, X) => F X Symbol ~AP1 is an encoding for application that is only used in innocuous ways. We can simplify the program (without losing non-termination) by removing it. Additionally, we can remove some (now-)redundant rules. This gives: Alphabet: app : [list * list] --> list cons : [nat * list] --> list foldl : [list -> nat -> list * list * list] --> list iconsc : [list * nat] --> list nil : [] --> list reverse : [list] --> list reverse1 : [list] --> list Rules: app(nil, X) => X app(cons(X, Y), Z) => cons(X, app(Y, Z)) foldl(/\x./\y.X(x, y), Y, nil) => Y foldl(/\x./\y.X(x, y), Y, cons(Z, U)) => foldl(/\z./\u.X(z, u), X(Y, Z), U) iconsc(X, Y) => cons(Y, X) reverse(X) => foldl(/\x./\y.iconsc(x, y), nil, X) reverse1(X) => foldl(/\x./\y.app(cons(y, nil), x), nil, X) We use rule removal, following [Kop12, Theorem 2.23]. This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): app(nil, X) >? X app(cons(X, Y), Z) >? cons(X, app(Y, Z)) foldl(/\x./\y.X(x, y), Y, nil) >? Y foldl(/\x./\y.X(x, y), Y, cons(Z, U)) >? foldl(/\z./\u.X(z, u), X(Y, Z), U) iconsc(X, Y) >? cons(Y, X) reverse(X) >? foldl(/\x./\y.iconsc(x, y), nil, X) reverse1(X) >? foldl(/\x./\y.app(cons(y, nil), x), nil, X) We use a recursive path ordering as defined in [Kop12, Chapter 5]. Argument functions: [[foldl(x_1, x_2, x_3)]] = foldl(x_3, x_2, x_1) [[nil]] = _|_ We choose Lex = {foldl} and Mul = {app, cons, iconsc, reverse, reverse1}, and the following precedence: reverse > iconsc > reverse1 > app > cons > foldl Taking the argument function into account, and fixing the greater / greater equal choices, the constraints can be denoted as follows: app(_|_, X) > X app(cons(X, Y), Z) >= cons(X, app(Y, Z)) foldl(/\x./\y.X(x, y), Y, _|_) > Y foldl(/\x./\y.X(x, y), Y, cons(Z, U)) > foldl(/\x./\y.X(x, y), X(Y, Z), U) popout

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job log

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actions

all output return to Higher Order Rewriting Union Beta