details

property	value
status	complete
benchmark	kop12thesis_ex2.11.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	Kop_13

run statistics

property	value
solver	Wanda 2.2a
configuration	default
runtime (wallclock)	0.349735 seconds
cpu usage	0.350263
user time	0.312466
system time	0.037797
max virtual memory	113188.0
max residence set size	11656.0

stage attributes

key	value
starexec-result	YES

output

YES We consider the system theBenchmark. Alphabet: cons : [nat * list] --> list emap : [nat -> nat * list] --> list nil : [] --> list twice : [nat -> nat] --> nat -> nat Rules: emap(f, nil) => nil emap(f, cons(x, y)) => cons(f x, emap(/\z.twice(f) z, y)) twice(f) x => f (f 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]): emap(F, nil) >? nil emap(F, cons(X, Y)) >? cons(F X, emap(/\x.twice(F, x), Y)) twice(F, X) >? F (F X) We use a recursive path ordering as defined in [Kop12, Chapter 5]. Argument functions: [[emap(x_1, x_2)]] = emap(x_2, x_1) [[nil]] = _|_ We choose Lex = {emap} and Mul = {@_{o -> o}, cons, twice}, and the following precedence: emap > cons > twice > @_{o -> o} Taking the argument function into account, and fixing the greater / greater equal choices, the constraints can be denoted as follows: emap(F, _|_) > _|_ emap(F, cons(X, Y)) >= cons(@_{o -> o}(F, X), emap(/\x.twice(F, x), Y)) twice(F, X) >= @_{o -> o}(F, @_{o -> o}(F, X)) With these choices, we have: 1] emap(F, _|_) > _|_ because [2], by definition 2] emap*(F, _|_) >= _|_ by (Bot) 3] emap(F, cons(X, Y)) >= cons(@_{o -> o}(F, X), emap(/\x.twice(F, x), Y)) because [4], by (Star) 4] emap*(F, cons(X, Y)) >= cons(@_{o -> o}(F, X), emap(/\x.twice(F, x), Y)) because emap > cons, [5] and [12], by (Copy) 5] emap*(F, cons(X, Y)) >= @_{o -> o}(F, X) because emap > @_{o -> o}, [6] and [8], by (Copy) 6] emap*(F, cons(X, Y)) >= F because [7], by (Select) 7] F >= F by (Meta) 8] emap*(F, cons(X, Y)) >= X because [9], by (Select) 9] cons(X, Y) >= X because [10], by (Star) 10] cons*(X, Y) >= X because [11], by (Select) 11] X >= X by (Meta) 12] emap*(F, cons(X, Y)) >= emap(/\x.twice(F, x), Y) because [13], [16] and [21], by (Stat) 13] cons(X, Y) > Y because [14], by definition 14] cons*(X, Y) >= Y because [15], by (Select) 15] Y >= Y by (Meta) 16] emap*(F, cons(X, Y)) >= /\y.twice(F, y) because [17], by (F-Abs) 17] emap*(F, cons(X, Y), x) >= twice(F, x) because emap > twice, [18] and [19], by (Copy) 18] emap*(F, cons(X, Y), x) >= F because [7], by (Select) 19] emap*(F, cons(X, Y), x) >= x because [20], by (Select) 20] x >= x by (Var) 21] emap*(F, cons(X, Y)) >= Y because [22], by (Select) 22] cons(X, Y) >= Y because [14], by (Star) 23] twice(F, X) >= @_{o -> o}(F, @_{o -> o}(F, X)) because [24], by (Star) 24] twice*(F, X) >= @_{o -> o}(F, @_{o -> o}(F, X)) because twice > @_{o -> o}, [25] and [27], by (Copy) 25] twice*(F, X) >= F because [26], by (Select) 26] F >= F by (Meta) 27] twice*(F, X) >= @_{o -> o}(F, X) because twice > @_{o -> o}, [25] and [28], by (Copy) 28] twice*(F, X) >= X because [29], by (Select) 29] X >= X by (Meta) We can thus remove the following rules: emap(F, nil) => nil We use rule removal, following [Kop12, Theorem 2.23]. This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): emap(F, cons(X, Y)) >? cons(F X, emap(/\x.twice(F, x), Y)) twice(F, X) >? F (F X) We use a recursive path ordering as defined in [Kop12, Chapter 5]. Argument functions: [[emap(x_1, x_2)]] = emap(x_2, x_1) We choose Lex = {emap} and Mul = {@_{o -> o}, cons, twice}, and the following precedence: emap > cons > twice > @_{o -> o} Taking the argument function into account, and fixing the greater / greater equal choices, the constraints can be denoted as follows: emap(F, cons(X, Y)) >= cons(@_{o -> o}(F, X), emap(/\x.twice(F, x), Y)) twice(F, X) > @_{o -> o}(F, @_{o -> o}(F, X)) With these choices, we have: popout

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

job log

popout

actions

all output return to Higher Order Rewriting Union Beta