Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Higher_Order_Rewriting_Union_Beta 2019-03-28 22.10 pair #432270697
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
n007.star.cs.uiowa.edu
space
Uncurried_Applicative_11
run statistics
property
value
solver
Wanda 2.1c
configuration
default
runtime (wallclock)
1.25706 seconds
cpu usage
1.25765
user time
1.16261
system time
0.095034
max virtual memory
146324.0
max residence set size
30612.0
stage attributes
key
value
starexec-result
YES
output
1.06/1.12 YES 1.22/1.25 We consider the system theBenchmark. 1.22/1.25 1.22/1.25 Alphabet: 1.22/1.25 1.22/1.25 and : [a * a] --> a 1.22/1.25 cons : [c * d] --> d 1.22/1.25 false : [] --> b 1.22/1.25 filter : [c -> b * d] --> d 1.22/1.25 filter2 : [b * c -> b * c * d] --> d 1.22/1.25 map : [c -> c * d] --> d 1.22/1.25 nil : [] --> d 1.22/1.25 not : [a] --> a 1.22/1.25 or : [a * a] --> a 1.22/1.25 true : [] --> b 1.22/1.25 1.22/1.25 Rules: 1.22/1.25 1.22/1.25 not(not(x)) => x 1.22/1.25 not(or(x, y)) => and(not(x), not(y)) 1.22/1.25 not(and(x, y)) => or(not(x), not(y)) 1.22/1.25 and(x, or(y, z)) => or(and(x, y), and(x, z)) 1.22/1.25 and(or(x, y), z) => or(and(z, x), and(z, y)) 1.22/1.25 map(f, nil) => nil 1.22/1.25 map(f, cons(x, y)) => cons(f x, map(f, y)) 1.22/1.25 filter(f, nil) => nil 1.22/1.25 filter(f, cons(x, y)) => filter2(f x, f, x, y) 1.22/1.25 filter2(true, f, x, y) => cons(x, filter(f, y)) 1.22/1.25 filter2(false, f, x, y) => filter(f, y) 1.22/1.25 1.22/1.25 This AFS is converted to an AFSM simply by replacing all free variables by meta-variables (with arity 0). 1.22/1.25 1.22/1.25 We use rule removal, following [Kop12, Theorem 2.23]. 1.22/1.25 1.22/1.25 This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): 1.22/1.25 1.22/1.25 not(not(X)) >? X 1.22/1.25 not(or(X, Y)) >? and(not(X), not(Y)) 1.22/1.25 not(and(X, Y)) >? or(not(X), not(Y)) 1.22/1.25 and(X, or(Y, Z)) >? or(and(X, Y), and(X, Z)) 1.22/1.25 and(or(X, Y), Z) >? or(and(Z, X), and(Z, Y)) 1.22/1.25 map(F, nil) >? nil 1.22/1.25 map(F, cons(X, Y)) >? cons(F X, map(F, Y)) 1.22/1.25 filter(F, nil) >? nil 1.22/1.25 filter(F, cons(X, Y)) >? filter2(F X, F, X, Y) 1.22/1.25 filter2(true, F, X, Y) >? cons(X, filter(F, Y)) 1.22/1.25 filter2(false, F, X, Y) >? filter(F, Y) 1.22/1.25 1.22/1.25 We use a recursive path ordering as defined in [Kop12, Chapter 5]. 1.22/1.25 1.22/1.25 Argument functions: 1.22/1.25 1.22/1.25 [[filter(x_1, x_2)]] = filter(x_2, x_1) 1.22/1.25 [[filter2(x_1, x_2, x_3, x_4)]] = filter2(x_4, x_2, x_1, x_3) 1.22/1.25 [[nil]] = _|_ 1.22/1.25 1.22/1.25 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 1.22/1.25 1.22/1.25 Taking the argument function into account, and fixing the greater / greater equal choices, the constraints can be denoted as follows: 1.22/1.25 1.22/1.25 not(not(X)) >= X 1.22/1.25 not(or(X, Y)) > and(not(X), not(Y)) 1.22/1.25 not(and(X, Y)) >= or(not(X), not(Y)) 1.22/1.25 and(X, or(Y, Z)) >= or(and(X, Y), and(X, Z)) 1.22/1.25 and(or(X, Y), Z) >= or(and(Z, X), and(Z, Y)) 1.22/1.25 map(F, _|_) >= _|_ 1.22/1.25 map(F, cons(X, Y)) >= cons(@_{o -> o}(F, X), map(F, Y)) 1.22/1.25 filter(F, _|_) >= _|_ 1.22/1.25 filter(F, cons(X, Y)) >= filter2(@_{o -> o}(F, X), F, X, Y) 1.22/1.25 filter2(true, F, X, Y) >= cons(X, filter(F, Y)) 1.22/1.25 filter2(false, F, X, Y) >= filter(F, Y) 1.22/1.25 1.22/1.25 With these choices, we have: 1.22/1.25 1.22/1.25 1] not(not(X)) >= X because [2], by (Star) 1.22/1.25 2] not*(not(X)) >= X because [3], by (Select) 1.22/1.25 3] not(X) >= X because [4], by (Star) 1.22/1.25 4] not*(X) >= X because [5], by (Select) 1.22/1.25 5] X >= X by (Meta) 1.22/1.25 1.22/1.25 6] not(or(X, Y)) > and(not(X), not(Y)) because [7], by definition 1.22/1.25 7] not*(or(X, Y)) >= and(not(X), not(Y)) because not > and, [8] and [12], by (Copy) 1.22/1.25 8] not*(or(X, Y)) >= not(X) because not in Mul and [9], by (Stat) 1.22/1.25 9] or(X, Y) > X because [10], by definition 1.22/1.25 10] or*(X, Y) >= X because [11], by (Select) 1.22/1.25 11] X >= X by (Meta) 1.22/1.25 12] not*(or(X, Y)) >= not(Y) because not in Mul and [13], by (Stat) 1.22/1.25 13] or(X, Y) > Y because [14], by definition 1.22/1.25 14] or*(X, Y) >= Y because [15], by (Select) 1.22/1.25 15] Y >= Y by (Meta) 1.22/1.25 1.22/1.25 16] not(and(X, Y)) >= or(not(X), not(Y)) because [17], by (Star) 1.22/1.25 17] not*(and(X, Y)) >= or(not(X), not(Y)) because not > or, [18] and [22], by (Copy) 1.22/1.25 18] not*(and(X, Y)) >= not(X) because not in Mul and [19], by (Stat) 1.22/1.25 19] and(X, Y) > X because [20], by definition 1.22/1.25 20] and*(X, Y) >= X because [21], by (Select) 1.22/1.25 21] X >= X by (Meta) 1.22/1.25 22] not*(and(X, Y)) >= not(Y) because not in Mul and [23], by (Stat) 1.22/1.25 23] and(X, Y) > Y because [24], by definition 1.22/1.25 24] and*(X, Y) >= Y because [25], by (Select)
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Higher_Order_Rewriting_Union_Beta 2019-03-28 22.10