Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Higher_Order_Rewriting_Union_Beta 2019-03-28 22.10 pair #432270605
details
property
value
status
complete
benchmark
Applicative_05__TreeHeight.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n139.star.cs.uiowa.edu
space
Uncurried_Applicative_11
run statistics
property
value
solver
Wanda 2.1c
configuration
default
runtime (wallclock)
0.092753 seconds
cpu usage
0.092784
user time
0.081588
system time
0.011196
max virtual memory
113176.0
max residence set size
3244.0
stage attributes
key
value
starexec-result
YES
output
0.00/0.08 YES 0.00/0.09 We consider the system theBenchmark. 0.00/0.09 0.00/0.09 Alphabet: 0.00/0.09 0.00/0.09 0 : [] --> d 0.00/0.09 cons : [d * c] --> c 0.00/0.09 false : [] --> a 0.00/0.09 height : [] --> d -> d 0.00/0.09 if : [a * d] --> d 0.00/0.09 le : [d * d] --> a 0.00/0.09 map : [d -> d * c] --> c 0.00/0.09 maxlist : [d * c] --> d 0.00/0.09 nil : [] --> c 0.00/0.09 node : [b * c] --> d 0.00/0.09 s : [d] --> d 0.00/0.09 true : [] --> a 0.00/0.09 0.00/0.09 Rules: 0.00/0.09 0.00/0.09 map(f, nil) => nil 0.00/0.09 map(f, cons(x, y)) => cons(f x, map(f, y)) 0.00/0.09 le(0, x) => true 0.00/0.09 le(s(x), 0) => false 0.00/0.09 le(s(x), s(y)) => le(x, y) 0.00/0.09 maxlist(x, cons(y, z)) => if(le(x, y), maxlist(y, z)) 0.00/0.09 maxlist(x, nil) => x 0.00/0.09 height node(x, y) => s(maxlist(0, map(height, y))) 0.00/0.09 0.00/0.09 This AFS is converted to an AFSM simply by replacing all free variables by meta-variables (with arity 0). 0.00/0.09 0.00/0.09 We use rule removal, following [Kop12, Theorem 2.23]. 0.00/0.09 0.00/0.09 This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): 0.00/0.09 0.00/0.09 map(F, nil) >? nil 0.00/0.09 map(F, cons(X, Y)) >? cons(F X, map(F, Y)) 0.00/0.09 le(0, X) >? true 0.00/0.09 le(s(X), 0) >? false 0.00/0.09 le(s(X), s(Y)) >? le(X, Y) 0.00/0.09 maxlist(X, cons(Y, Z)) >? if(le(X, Y), maxlist(Y, Z)) 0.00/0.09 maxlist(X, nil) >? X 0.00/0.09 height node(X, Y) >? s(maxlist(0, map(height, Y))) 0.00/0.09 0.00/0.09 We orient these requirements with a polynomial interpretation in the natural numbers. 0.00/0.09 0.00/0.09 The following interpretation satisfies the requirements: 0.00/0.09 0.00/0.09 0 = 0 0.00/0.09 cons = \y0y1.2 + 2y0 + 2y1 0.00/0.09 false = 0 0.00/0.09 height = \y0.0 0.00/0.09 if = \y0y1.y0 + y1 0.00/0.09 le = \y0y1.1 + y0 + y1 0.00/0.09 map = \G0y1.2y1 + G0(0) + 2y1G0(y1) 0.00/0.09 maxlist = \y0y1.1 + y0 + y1 0.00/0.09 nil = 0 0.00/0.09 node = \y0y1.3 + y0 + 3y1 0.00/0.09 s = \y0.y0 0.00/0.09 true = 0 0.00/0.09 0.00/0.09 Using this interpretation, the requirements translate to: 0.00/0.09 0.00/0.09 [[map(_F0, nil)]] = F0(0) >= 0 = [[nil]] 0.00/0.09 [[map(_F0, cons(_x1, _x2))]] = 4 + 4x1 + 4x2 + F0(0) + 4x1F0(2 + 2x1 + 2x2) + 4x2F0(2 + 2x1 + 2x2) + 4F0(2 + 2x1 + 2x2) > 2 + 2x1 + 4x2 + 2F0(0) + 2F0(x1) + 4x2F0(x2) = [[cons(_F0 _x1, map(_F0, _x2))]] 0.00/0.09 [[le(0, _x0)]] = 1 + x0 > 0 = [[true]] 0.00/0.09 [[le(s(_x0), 0)]] = 1 + x0 > 0 = [[false]] 0.00/0.09 [[le(s(_x0), s(_x1))]] = 1 + x0 + x1 >= 1 + x0 + x1 = [[le(_x0, _x1)]] 0.00/0.09 [[maxlist(_x0, cons(_x1, _x2))]] = 3 + x0 + 2x1 + 2x2 > 2 + x0 + x2 + 2x1 = [[if(le(_x0, _x1), maxlist(_x1, _x2))]] 0.00/0.09 [[maxlist(_x0, nil)]] = 1 + x0 > x0 = [[_x0]] 0.00/0.09 [[height node(_x0, _x1)]] = 3 + x0 + 3x1 > 1 + 2x1 = [[s(maxlist(0, map(height, _x1)))]] 0.00/0.09 0.00/0.09 We can thus remove the following rules: 0.00/0.09 0.00/0.09 map(F, cons(X, Y)) => cons(F X, map(F, Y)) 0.00/0.09 le(0, X) => true 0.00/0.09 le(s(X), 0) => false 0.00/0.09 maxlist(X, cons(Y, Z)) => if(le(X, Y), maxlist(Y, Z)) 0.00/0.09 maxlist(X, nil) => X 0.00/0.09 height node(X, Y) => s(maxlist(0, map(height, Y))) 0.00/0.09 0.00/0.09 We use rule removal, following [Kop12, Theorem 2.23]. 0.00/0.09 0.00/0.09 This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): 0.00/0.09 0.00/0.09 map(F, nil) >? nil 0.00/0.09 le(s(X), s(Y)) >? le(X, Y) 0.00/0.09 0.00/0.09 We orient these requirements with a polynomial interpretation in the natural numbers. 0.00/0.09 0.00/0.09 The following interpretation satisfies the requirements: 0.00/0.09 0.00/0.09 le = \y0y1.y0 + y1 0.00/0.09 map = \G0y1.3 + 3y1 + G0(0) 0.00/0.09 nil = 0 0.00/0.09 s = \y0.3 + 3y0 0.00/0.09 0.00/0.09 Using this interpretation, the requirements translate to: 0.00/0.09 0.00/0.09 [[map(_F0, nil)]] = 3 + F0(0) > 0 = [[nil]]
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