details

property	value
status	complete
benchmark	Applicative_05__Ex9Maps.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n146.star.cs.uiowa.edu
space	Uncurried_Applicative_11

run statistics

property	value
solver	Wanda 2.2a
configuration	default
runtime (wallclock)	17.3934 seconds
cpu usage	17.3863
user time	17.0202
system time	0.366086
max virtual memory	539364.0
max residence set size	198752.0

stage attributes

key	value
starexec-result	YES

output

YES We consider the system theBenchmark. Alphabet: cons : [d * e] --> e g : [] --> b map!fac62201 : [d -> d * e] --> e map!fac62202 : [d -> a -> d * a * e] --> e map!fac62203 : [b -> d -> c -> d * b * c * e] --> e Rules: map!fac62201(f, cons(x, y)) => cons(f x, map!fac62201(f, y)) map!fac62202(f, x, cons(y, z)) => cons(f y x, map!fac62202(f, x, z)) map!fac62203(f, g, x, cons(y, z)) => cons(f g y x, map!fac62203(f, g, x, z)) 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]): map!fac62201(F, cons(X, Y)) >? cons(F X, map!fac62201(F, Y)) map!fac62202(F, X, cons(Y, Z)) >? cons(F Y X, map!fac62202(F, X, Z)) map!fac62203(F, g, X, cons(Y, Z)) >? cons(F g Y X, map!fac62203(F, g, X, Z)) We use a recursive path ordering as defined in [Kop12, Chapter 5]. Argument functions: [[g]] = _|_ We choose Lex = {} and Mul = {@_{o -> o -> o -> o}, @_{o -> o -> o}, @_{o -> o}, cons, map!fac62201, map!fac62202, map!fac62203}, and the following precedence: map!fac62201 > map!fac62203 > @_{o -> o -> o} = map!fac62202 > @_{o -> o} > cons > @_{o -> o -> o -> o} Taking the argument function into account, and fixing the greater / greater equal choices, the constraints can be denoted as follows: map!fac62201(F, cons(X, Y)) > cons(@_{o -> o}(F, X), map!fac62201(F, Y)) map!fac62202(F, X, cons(Y, Z)) >= cons(@_{o -> o}(@_{o -> o -> o}(F, Y), X), map!fac62202(F, X, Z)) map!fac62203(F, _|_, X, cons(Y, Z)) >= cons(@_{o -> o}(@_{o -> o -> o}(@_{o -> o -> o -> o}(F, _|_), Y), X), map!fac62203(F, _|_, X, Z)) With these choices, we have: 1] map!fac62201(F, cons(X, Y)) > cons(@_{o -> o}(F, X), map!fac62201(F, Y)) because [2], by definition 2] map!fac62201*(F, cons(X, Y)) >= cons(@_{o -> o}(F, X), map!fac62201(F, Y)) because map!fac62201 > cons, [3] and [10], by (Copy) 3] map!fac62201*(F, cons(X, Y)) >= @_{o -> o}(F, X) because map!fac62201 > @_{o -> o}, [4] and [6], by (Copy) 4] map!fac62201*(F, cons(X, Y)) >= F because [5], by (Select) 5] F >= F by (Meta) 6] map!fac62201*(F, cons(X, Y)) >= 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] map!fac62201*(F, cons(X, Y)) >= map!fac62201(F, Y) because map!fac62201 in Mul, [11] and [12], by (Stat) 11] F >= F by (Meta) 12] cons(X, Y) > Y because [13], by definition 13] cons*(X, Y) >= Y because [14], by (Select) 14] Y >= Y by (Meta) 15] map!fac62202(F, X, cons(Y, Z)) >= cons(@_{o -> o}(@_{o -> o -> o}(F, Y), X), map!fac62202(F, X, Z)) because [16], by (Star) 16] map!fac62202*(F, X, cons(Y, Z)) >= cons(@_{o -> o}(@_{o -> o -> o}(F, Y), X), map!fac62202(F, X, Z)) because map!fac62202 > cons, [17] and [25], by (Copy) 17] map!fac62202*(F, X, cons(Y, Z)) >= @_{o -> o}(@_{o -> o -> o}(F, Y), X) because map!fac62202 > @_{o -> o}, [18] and [23], by (Copy) 18] map!fac62202*(F, X, cons(Y, Z)) >= @_{o -> o -> o}(F, Y) because map!fac62202 = @_{o -> o -> o}, map!fac62202 in Mul, [19] and [20], by (Stat) 19] F >= F by (Meta) 20] cons(Y, Z) > Y because [21], by definition 21] cons*(Y, Z) >= Y because [22], by (Select) 22] Y >= Y by (Meta) 23] map!fac62202*(F, X, cons(Y, Z)) >= X because [24], by (Select) 24] X >= X by (Meta) 25] map!fac62202*(F, X, cons(Y, Z)) >= map!fac62202(F, X, Z) because map!fac62202 in Mul, [19], [26] and [27], by (Stat) 26] X >= X by (Meta) 27] cons(Y, Z) > Z because [28], by definition 28] cons*(Y, Z) >= Z because [29], by (Select) 29] Z >= Z by (Meta) 30] map!fac62203(F, _|_, X, cons(Y, Z)) >= cons(@_{o -> o}(@_{o -> o -> o}(@_{o -> o -> o -> o}(F, _|_), Y), X), map!fac62203(F, _|_, X, Z)) because [31], by (Star) 31] map!fac62203*(F, _|_, X, cons(Y, Z)) >= cons(@_{o -> o}(@_{o -> o -> o}(@_{o -> o -> o -> o}(F, _|_), Y), X), map!fac62203(F, _|_, X, Z)) because map!fac62203 > cons, [32] and [44], by (Copy) 32] map!fac62203*(F, _|_, X, cons(Y, Z)) >= @_{o -> o}(@_{o -> o -> o}(@_{o -> o -> o -> o}(F, _|_), Y), X) because map!fac62203 > @_{o -> o}, [33] and [42], by (Copy) 33] map!fac62203*(F, _|_, X, cons(Y, Z)) >= @_{o -> o -> o}(@_{o -> o -> o -> o}(F, _|_), Y) because map!fac62203 > @_{o -> o -> o}, [34] and [38], by (Copy) 34] map!fac62203*(F, _|_, X, cons(Y, Z)) >= @_{o -> o -> o -> o}(F, _|_) because map!fac62203 > @_{o -> o -> o -> o}, [35] and [37], by (Copy) 35] map!fac62203*(F, _|_, X, cons(Y, Z)) >= F because [36], by (Select) 36] F >= F by (Meta) 37] map!fac62203*(F, _|_, X, cons(Y, Z)) >= _|_ by (Bot) 38] map!fac62203*(F, _|_, X, cons(Y, Z)) >= Y because [39], by (Select) 39] cons(Y, Z) >= Y because [40], by (Star) 40] cons*(Y, Z) >= Y because [41], by (Select) 41] Y >= Y by (Meta) 42] map!fac62203*(F, _|_, X, cons(Y, Z)) >= X because [43], by (Select) 43] X >= X by (Meta) 44] map!fac62203*(F, _|_, X, cons(Y, Z)) >= map!fac62203(F, _|_, X, Z) because map!fac62203 in Mul, [45], [46], [47] and [48], by (Stat) 45] F >= F by (Meta) 46] _|_ >= _|_ by (Bot) 47] X >= X by (Meta) 48] cons(Y, Z) > Z because [49], by definition 49] cons*(Y, Z) >= Z because [50], by (Select) 50] Z >= Z by (Meta) We can thus remove the following rules: map!fac62201(F, cons(X, Y)) => cons(F X, map!fac62201(F, Y)) popout

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

job log

popout

actions

all output return to Higher Order Rewriting Union Beta