details

property	value
status	complete
benchmark	h62.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n137.star.cs.uiowa.edu
space	Hamana_Kikuchi_18

run statistics

property	value
solver	Wanda 2.2a
configuration	default
runtime (wallclock)	10.472 seconds
cpu usage	10.4654
user time	10.2706
system time	0.194808
max virtual memory	441660.0
max residence set size	112792.0

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 xap : [list -> nat -> list * list] --> nat -> list yap : [nat -> list * nat] --> list Rules: app(nil, x) => x app(cons(x, y), z) => cons(x, app(y, z)) foldl(/\x./\y.yap(xap(f, x), y), z, nil) => z foldl(/\x./\y.yap(xap(f, x), y), z, cons(u, v)) => foldl(/\w./\x'.yap(xap(f, w), x'), yap(xap(f, z), u), v) iconsc x y => cons(y, x) reverse(x) => foldl(/\y./\z.yap(xap(iconsc, y), z), nil, x) reverse1(x) => foldl(/\y./\z.app(cons(z, nil), y), nil, x) xap(f, x) => f x yap(f, x) => f x This AFS is converted to an AFSM simply by replacing all free variables by meta-variables (with arity 0). Symbol xap is an encoding for application that is only used in innocuous ways. We can simplify the program (without losing non-termination) by removing it. 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 yap : [nat -> list * nat] --> list Rules: app(nil, X) => X app(cons(X, Y), Z) => cons(X, app(Y, Z)) foldl(/\x./\y.yap(F(x), y), X, nil) => X foldl(/\x./\y.yap(F(x), y), X, cons(Y, Z)) => foldl(/\z./\u.yap(F(z), u), yap(F(X), Y), Z) iconsc(X) Y => cons(Y, X) reverse(X) => foldl(/\x./\y.yap(iconsc(x), y), nil, X) reverse1(X) => foldl(/\x./\y.app(cons(y, nil), x), nil, X) yap(F, X) => F 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.yap(F(x), y), X, nil) >? X foldl(/\x./\y.yap(F(x), y), X, cons(Y, Z)) >? foldl(/\z./\u.yap(F(z), u), yap(F(X), Y), Z) iconsc(X) Y >? cons(Y, X) reverse(X) >? foldl(/\x./\y.yap(iconsc(x), y), nil, X) reverse1(X) >? foldl(/\x./\y.app(cons(y, nil), x), nil, X) yap(F, X) >? F 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 = {@_{o -> o}, app, cons, iconsc, reverse, reverse1, yap}, and the following precedence: reverse > iconsc > reverse1 > app > foldl > yap > @_{o -> o} > cons 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.yap(F(x), y), X, _|_) >= X foldl(/\x./\y.yap(F(x), y), X, cons(Y, Z)) >= foldl(/\x./\y.yap(F(x), y), yap(F(X), Y), Z) @_{o -> o}(iconsc(X), Y) >= cons(Y, X) reverse(X) >= foldl(/\x./\y.yap(iconsc(x), y), _|_, X) reverse1(X) >= foldl(/\x./\y.app(cons(y, _|_), x), _|_, X) yap(F, X) > @_{o -> o}(F, X) With these choices, we have: 1] app(_|_, X) >= X because [2], by (Star) 2] app*(_|_, X) >= X because [3], by (Select) 3] X >= X by (Meta) 4] app(cons(X, Y), Z) >= cons(X, app(Y, Z)) because [5], by (Star) 5] app*(cons(X, Y), Z) >= cons(X, app(Y, Z)) because app > cons, [6] and [10], by (Copy) 6] app*(cons(X, Y), Z) >= X because [7], by (Select) 7] cons(X, Y) >= X because [8], by (Star) 8] cons*(X, Y) >= X because [9], by (Select) 9] X >= X by (Meta) 10] app*(cons(X, Y), Z) >= app(Y, Z) because app in Mul, [11] and [14], by (Stat) 11] cons(X, Y) > Y because [12], by definition popout

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actions

all output return to Higher Order Rewriting Union Beta