Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Higher Order Rewriting Union Beta pair #487094013
details
property
value
status
complete
benchmark
Applicative_first_order_05__18.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n138.star.cs.uiowa.edu
space
Uncurried_Applicative_11
run statistics
property
value
solver
Wanda 2.2a
configuration
default
runtime (wallclock)
0.331098 seconds
cpu usage
0.331235
user time
0.305367
system time
0.025868
max virtual memory
113188.0
max residence set size
9352.0
stage attributes
key
value
starexec-result
YES
output
YES We consider the system theBenchmark. Alphabet: !facplus : [b * b] --> b !factimes : [a * b] --> b cons : [d * e] --> e false : [] --> c filter : [d -> c * e] --> e filter2 : [c * d -> c * d * e] --> e map : [d -> d * e] --> e nil : [] --> e true : [] --> c Rules: !factimes(x, !facplus(y, z)) => !facplus(!factimes(x, y), !factimes(x, z)) 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]): !factimes(X, !facplus(Y, Z)) >? !facplus(!factimes(X, Y), !factimes(X, Z)) 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: [[filter2(x_1, x_2, x_3, x_4)]] = filter2(x_2, x_4, x_1, x_3) [[nil]] = _|_ We choose Lex = {@_{o -> o}, filter, filter2} and Mul = {!facplus, !factimes, cons, false, map, true}, and the following precedence: map > false > @_{o -> o} = filter = filter2 > !factimes > !facplus > cons > true Taking the argument function into account, and fixing the greater / greater equal choices, the constraints can be denoted as follows: !factimes(X, !facplus(Y, Z)) > !facplus(!factimes(X, Y), !factimes(X, Z)) 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] !factimes(X, !facplus(Y, Z)) > !facplus(!factimes(X, Y), !factimes(X, Z)) because [2], by definition 2] !factimes*(X, !facplus(Y, Z)) >= !facplus(!factimes(X, Y), !factimes(X, Z)) because !factimes > !facplus, [3] and [8], by (Copy) 3] !factimes*(X, !facplus(Y, Z)) >= !factimes(X, Y) because !factimes in Mul, [4] and [5], by (Stat) 4] X >= X by (Meta) 5] !facplus(Y, Z) > Y because [6], by definition 6] !facplus*(Y, Z) >= Y because [7], by (Select) 7] Y >= Y by (Meta) 8] !factimes*(X, !facplus(Y, Z)) >= !factimes(X, Z) because !factimes in Mul, [4] and [9], by (Stat) 9] !facplus(Y, Z) > Z because [10], by definition 10] !facplus*(Y, Z) >= Z because [11], by (Select) 11] Z >= Z by (Meta) 12] map(F, _|_) >= _|_ by (Bot) 13] map(F, cons(X, Y)) >= cons(@_{o -> o}(F, X), map(F, Y)) because [14], by (Star) 14] map*(F, cons(X, Y)) >= cons(@_{o -> o}(F, X), map(F, Y)) because map > cons, [15] and [22], by (Copy) 15] map*(F, cons(X, Y)) >= @_{o -> o}(F, X) because map > @_{o -> o}, [16] and [18], by (Copy) 16] map*(F, cons(X, Y)) >= F because [17], by (Select) 17] F >= F by (Meta) 18] map*(F, cons(X, Y)) >= X because [19], by (Select) 19] cons(X, Y) >= X because [20], by (Star) 20] cons*(X, Y) >= X because [21], by (Select) 21] X >= X by (Meta) 22] map*(F, cons(X, Y)) >= map(F, Y) because map in Mul, [23] and [24], by (Stat) 23] F >= F by (Meta) 24] cons(X, Y) > Y because [25], by definition 25] cons*(X, Y) >= Y because [26], by (Select) 26] Y >= Y by (Meta) 27] filter(F, _|_) >= _|_ by (Bot) 28] filter(F, cons(X, Y)) >= filter2(@_{o -> o}(F, X), F, X, Y) because [29], by (Star) 29] filter*(F, cons(X, Y)) >= filter2(@_{o -> o}(F, X), F, X, Y) because filter = filter2, [30], [31], [34], [38], [39] and [41], by (Stat) 30] F >= F by (Meta) 31] cons(X, Y) > Y because [32], by definition 32] cons*(X, Y) >= Y because [33], by (Select) 33] Y >= Y by (Meta) 34] filter*(F, cons(X, Y)) >= @_{o -> o}(F, X) because filter = @_{o -> o}, [30], [35], [38] and [39], by (Stat) 35] cons(X, Y) > X because [36], by definition 36] cons*(X, Y) >= X because [37], 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