details

property	value
status	complete
benchmark	reverse.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	Mixed_HO_10

run statistics

property	value
solver	Wanda 2.2a
configuration	default
runtime (wallclock)	1.35624 seconds
cpu usage	0.881042
user time	0.812871
system time	0.068171
max virtual memory	131948.0
max residence set size	17272.0

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(f, x, nil) => x foldl(f, x, cons(y, z)) => foldl(f, f x y, z) iconsc => /\x./\y.cons(y, x) reverse(x) => foldl(iconsc, nil, x) reverse1(x) => foldl(/\y./\z.app(cons(z, nil), y), nil, x) This AFS is converted to an AFSM simply by replacing all free variables by meta-variables (with arity 0). 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(F, X, nil) >? X foldl(F, X, cons(Y, Z)) >? foldl(F, F X Y, Z) iconsc >? /\x./\y.cons(y, x) reverse(X) >? foldl(iconsc, 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_1, x_2) [[nil]] = _|_ We choose Lex = {foldl} and Mul = {@_{o -> o -> o}, @_{o -> o}, app, cons, iconsc, reverse, reverse1}, and the following precedence: reverse > iconsc > reverse1 > app > cons > foldl > @_{o -> o} > @_{o -> o -> o} 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(F, X, _|_) >= X foldl(F, X, cons(Y, Z)) >= foldl(F, @_{o -> o}(@_{o -> o -> o}(F, X), Y), Z) iconsc > /\x./\y.cons(y, x) reverse(X) >= foldl(iconsc, _|_, X) reverse1(X) >= foldl(/\x./\y.app(cons(y, _|_), x), _|_, 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 definition 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 12] cons*(X, Y) >= Y because [13], by (Select) 13] Y >= Y by (Meta) 14] Z >= Z by (Meta) 15] foldl(F, X, _|_) >= X because [16], by (Star) 16] foldl*(F, X, _|_) >= X because [17], by (Select) 17] X >= X by (Meta) 18] foldl(F, X, cons(Y, Z)) >= foldl(F, @_{o -> o}(@_{o -> o -> o}(F, X), Y), Z) because [19], by (Star) 19] foldl*(F, X, cons(Y, Z)) >= foldl(F, @_{o -> o}(@_{o -> o -> o}(F, X), Y), Z) because [20], [23], [25] and [33], by (Stat) 20] cons(Y, Z) > Z because [21], by definition 21] cons*(Y, Z) >= Z because [22], by (Select) 22] Z >= Z by (Meta) 23] foldl*(F, X, cons(Y, Z)) >= F because [24], by (Select) 24] F >= F by (Meta) 25] foldl*(F, X, cons(Y, Z)) >= @_{o -> o}(@_{o -> o -> o}(F, X), Y) because foldl > @_{o -> o}, [26] and [29], by (Copy) 26] foldl*(F, X, cons(Y, Z)) >= @_{o -> o -> o}(F, X) because foldl > @_{o -> o -> o}, [23] and [27], by (Copy) 27] foldl*(F, X, cons(Y, Z)) >= X because [28], by (Select) 28] X >= X by (Meta) 29] foldl*(F, X, cons(Y, Z)) >= Y because [30], by (Select) 30] cons(Y, Z) >= Y because [31], by (Star) 31] cons*(Y, Z) >= Y because [32], by (Select) 32] Y >= Y by (Meta) 33] foldl*(F, X, cons(Y, Z)) >= Z because [34], by (Select) 34] cons(Y, Z) >= Z because [21], by (Star) 35] iconsc > /\x./\y.cons(y, x) because [36], by definition 36] iconsc* >= /\y./\z.cons(z, y) because [37], by (F-Abs) 37] iconsc*(x) >= /\z.cons(z, x) because [38], by (F-Abs) 38] iconsc*(x, y) >= cons(y, x) because iconsc > cons, [39] and [41], by (Copy) popout

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