details

property	value
status	complete
benchmark	Applicative_first_order_05__#3.16.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n054.star.cs.uiowa.edu
space	Uncurried_Applicative_11

run statistics

property	value
solver	Wanda
configuration	HigherOrder
runtime (wallclock)	0.271568059921 seconds
cpu usage	0.267877957
max memory	1.2136448E7

stage attributes

key	value
output-size	11750
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_HigherOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. Alphabet: 0 : [] --> 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 plus : [a * a] --> a s : [a] --> a times : [a * a] --> a true : [] --> b Rules: times(x, 0) => 0 times(x, s(y)) => plus(times(x, y), x) plus(x, 0) => x plus(0, x) => x plus(x, s(y)) => s(plus(x, y)) plus(s(x), y) => s(plus(x, 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]): times(X, 0) >? 0 times(X, s(Y)) >? plus(times(X, Y), X) plus(X, 0) >? X plus(0, X) >? X plus(X, s(Y)) >? s(plus(X, Y)) plus(s(X), Y) >? s(plus(X, 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) about to try horpo We use a recursive path ordering as defined in [Kop12, Chapter 5]. Argument functions: [[0]] = _|_ [[filter2(x_1, x_2, x_3, x_4)]] = filter2(x_2, x_4, x_1, x_3) [[nil]] = _|_ We choose Lex = {filter, filter2} and Mul = {@_{o -> o}, cons, false, map, plus, s, times, true}, and the following precedence: false > filter = filter2 > map > @_{o -> o} > cons > times > plus > s > true Taking the argument function into account, and fixing the greater / greater equal choices, the constraints can be denoted as follows: times(X, _|_) >= _|_ times(X, s(Y)) >= plus(times(X, Y), X) plus(X, _|_) > X plus(_|_, X) >= X plus(X, s(Y)) > s(plus(X, Y)) plus(s(X), Y) >= s(plus(X, 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] times(X, _|_) >= _|_ by (Bot) 2] times(X, s(Y)) >= plus(times(X, Y), X) because [3], by (Star) 3] times*(X, s(Y)) >= plus(times(X, Y), X) because times > plus, [4] and [9], by (Copy) 4] times*(X, s(Y)) >= times(X, Y) because times in Mul, [5] and [6], by (Stat) 5] X >= X by (Meta) 6] s(Y) > Y because [7], by definition 7] s*(Y) >= Y because [8], by (Select) 8] Y >= Y by (Meta) 9] times*(X, s(Y)) >= X because [5], by (Select) 10] plus(X, _|_) > X because [11], by definition 11] plus*(X, _|_) >= X because [12], by (Select) 12] X >= X by (Meta) popout

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

job log

popout

actions

all output return to HRS union beta 16688