details

property	value
status	complete
benchmark	Applicative_first_order_05__12.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n150.star.cs.uiowa.edu
space	Uncurried_Applicative_11

run statistics

property	value
solver	Wanda 2.2a
configuration	default
runtime (wallclock)	1.385 seconds
cpu usage	1.36928
user time	1.25374
system time	0.115544
max virtual memory	146348.0
max residence set size	30488.0

stage attributes

key	value
starexec-result	YES

output

YES We consider the system theBenchmark. Alphabet: and : [a * a] --> a cons : [c * d] --> d false : [] --> b filter : [c -> b * d] --> d filter2 : [b * c -> b * c * d] --> d map : [c -> c * d] --> d nil : [] --> d not : [a] --> a or : [a * a] --> a true : [] --> b Rules: not(not(x)) => x not(or(x, y)) => and(not(x), not(y)) not(and(x, y)) => or(not(x), not(y)) and(x, or(y, z)) => or(and(x, y), and(x, z)) and(or(x, y), z) => or(and(z, x), and(z, y)) map(f, nil) => nil map(f, cons(x, y)) => cons(f x, map(f, y)) filter(f, nil) => nil filter(f, cons(x, y)) => filter2(f x, f, x, y) filter2(true, f, x, y) => cons(x, filter(f, y)) filter2(false, f, x, y) => filter(f, y) 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]): not(not(X)) >? X not(or(X, Y)) >? and(not(X), not(Y)) not(and(X, Y)) >? or(not(X), not(Y)) and(X, or(Y, Z)) >? or(and(X, Y), and(X, Z)) and(or(X, Y), Z) >? or(and(Z, X), and(Z, Y)) map(F, nil) >? nil map(F, cons(X, Y)) >? cons(F X, map(F, Y)) filter(F, nil) >? nil filter(F, cons(X, Y)) >? filter2(F X, F, X, Y) filter2(true, F, X, Y) >? cons(X, filter(F, Y)) filter2(false, F, X, Y) >? filter(F, Y) We use a recursive path ordering as defined in [Kop12, Chapter 5]. Argument functions: [[filter(x_1, x_2)]] = filter(x_2, x_1) [[filter2(x_1, x_2, x_3, x_4)]] = filter2(x_4, x_2, x_1, x_3) [[nil]] = _|_ We choose Lex = {filter, filter2} and Mul = {@_{o -> o}, and, cons, false, map, not, or, true}, and the following precedence: false > filter = filter2 > not > and > or > map > @_{o -> o} > cons > true Taking the argument function into account, and fixing the greater / greater equal choices, the constraints can be denoted as follows: not(not(X)) >= X not(or(X, Y)) > and(not(X), not(Y)) not(and(X, Y)) >= or(not(X), not(Y)) and(X, or(Y, Z)) >= or(and(X, Y), and(X, Z)) and(or(X, Y), Z) >= or(and(Z, X), and(Z, Y)) map(F, _|_) >= _|_ map(F, cons(X, Y)) >= cons(@_{o -> o}(F, X), map(F, Y)) filter(F, _|_) >= _|_ filter(F, cons(X, Y)) >= filter2(@_{o -> o}(F, X), F, X, Y) filter2(true, F, X, Y) >= cons(X, filter(F, Y)) filter2(false, F, X, Y) >= filter(F, Y) With these choices, we have: 1] not(not(X)) >= X because [2], by (Star) 2] not*(not(X)) >= X because [3], by (Select) 3] not(X) >= X because [4], by (Star) 4] not*(X) >= X because [5], by (Select) 5] X >= X by (Meta) 6] not(or(X, Y)) > and(not(X), not(Y)) because [7], by definition 7] not*(or(X, Y)) >= and(not(X), not(Y)) because not > and, [8] and [12], by (Copy) 8] not*(or(X, Y)) >= not(X) because not in Mul and [9], by (Stat) 9] or(X, Y) > X because [10], by definition 10] or*(X, Y) >= X because [11], by (Select) 11] X >= X by (Meta) 12] not*(or(X, Y)) >= not(Y) because not in Mul and [13], by (Stat) 13] or(X, Y) > Y because [14], by definition 14] or*(X, Y) >= Y because [15], by (Select) 15] Y >= Y by (Meta) 16] not(and(X, Y)) >= or(not(X), not(Y)) because [17], by (Star) 17] not*(and(X, Y)) >= or(not(X), not(Y)) because not > or, [18] and [22], by (Copy) 18] not*(and(X, Y)) >= not(X) because not in Mul and [19], by (Stat) 19] and(X, Y) > X because [20], by definition 20] and*(X, Y) >= X because [21], by (Select) 21] X >= X by (Meta) 22] not*(and(X, Y)) >= not(Y) because not in Mul and [23], by (Stat) 23] and(X, Y) > Y because [24], by definition 24] and*(X, Y) >= Y because [25], by (Select) popout

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actions

all output return to Higher Order Rewriting Union Beta