Higher_Order_Rewriting_Union_Beta 2019-03-28 22.10 pair #432270687

details

property	value
status	complete
benchmark	Applicative_first_order_05__01.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n145.star.cs.uiowa.edu
space	Uncurried_Applicative_11

run statistics

property	value
solver	Wanda 2.1c
configuration	default
runtime (wallclock)	0.187718 seconds
cpu usage	0.187688
user time	0.166936
system time	0.020752
max virtual memory	113176.0
max residence set size	4672.0

stage attributes

key	value
starexec-result	YES

output

0.00/0.17	YES
0.00/0.18	We consider the system theBenchmark.
0.00/0.18	
0.00/0.18	  Alphabet:
0.00/0.18	
0.00/0.18	    !fac3220 : [a * a] --> a 
0.00/0.18	    !facdiv : [a * a] --> a 
0.00/0.18	    !facdot : [a * a] --> a 
0.00/0.18	    cons : [c * d] --> d 
0.00/0.18	    e : [] --> a 
0.00/0.18	    false : [] --> b 
0.00/0.18	    filter : [c -> b * d] --> d 
0.00/0.18	    filter2 : [b * c -> b * c * d] --> d 
0.00/0.18	    map : [c -> c * d] --> d 
0.00/0.18	    nil : [] --> d 
0.00/0.18	    true : [] --> b 
0.00/0.18	
0.00/0.18	  Rules:
0.00/0.18	
0.00/0.18	    !fac3220(x, x) => e 
0.00/0.18	    !fac3220(e, x) => x 
0.00/0.18	    !fac3220(x, !facdot(x, y)) => y 
0.00/0.18	    !fac3220(!facdiv(x, y), x) => y 
0.00/0.18	    !facdiv(x, x) => e 
0.00/0.18	    !facdiv(x, e) => x 
0.00/0.18	    !facdiv(!facdot(x, y), y) => x 
0.00/0.18	    !facdiv(x, !fac3220(y, x)) => y 
0.00/0.18	    !facdot(e, x) => x 
0.00/0.18	    !facdot(x, e) => x 
0.00/0.18	    !facdot(x, !fac3220(x, y)) => y 
0.00/0.18	    !facdot(!facdiv(x, y), y) => x 
0.00/0.18	    map(f, nil) => nil 
0.00/0.18	    map(f, cons(x, y)) => cons(f x, map(f, y)) 
0.00/0.18	    filter(f, nil) => nil 
0.00/0.18	    filter(f, cons(x, y)) => filter2(f x, f, x, y) 
0.00/0.18	    filter2(true, f, x, y) => cons(x, filter(f, y)) 
0.00/0.18	    filter2(false, f, x, y) => filter(f, y) 
0.00/0.18	
0.00/0.18	This AFS is converted to an AFSM simply by replacing all free variables by meta-variables (with arity 0).
0.00/0.18	
0.00/0.18	We use rule removal, following [Kop12, Theorem 2.23].
0.00/0.18	
0.00/0.18	This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]):
0.00/0.18	
0.00/0.18	  !fac3220(X, X) >? e 
0.00/0.18	  !fac3220(e, X) >? X 
0.00/0.18	  !fac3220(X, !facdot(X, Y)) >? Y 
0.00/0.18	  !fac3220(!facdiv(X, Y), X) >? Y 
0.00/0.18	  !facdiv(X, X) >? e 
0.00/0.18	  !facdiv(X, e) >? X 
0.00/0.18	  !facdiv(!facdot(X, Y), Y) >? X 
0.00/0.18	  !facdiv(X, !fac3220(Y, X)) >? Y 
0.00/0.18	  !facdot(e, X) >? X 
0.00/0.18	  !facdot(X, e) >? X 
0.00/0.18	  !facdot(X, !fac3220(X, Y)) >? Y 
0.00/0.18	  !facdot(!facdiv(X, Y), Y) >? X 
0.00/0.18	  map(F, nil) >? nil 
0.00/0.18	  map(F, cons(X, Y)) >? cons(F X, map(F, Y)) 
0.00/0.18	  filter(F, nil) >? nil 
0.00/0.18	  filter(F, cons(X, Y)) >? filter2(F X, F, X, Y) 
0.00/0.18	  filter2(true, F, X, Y) >? cons(X, filter(F, Y)) 
0.00/0.18	  filter2(false, F, X, Y) >? filter(F, Y) 
0.00/0.18	
0.00/0.18	We orient these requirements with a polynomial interpretation in the natural numbers.
0.00/0.18	
0.00/0.18	The following interpretation satisfies the requirements:
0.00/0.18	
0.00/0.18	  !fac3220 = \y0y1.3 + y0 + 2y1 
0.00/0.18	  !facdiv = \y0y1.3 + y0 + y1 
0.00/0.18	  !facdot = \y0y1.3 + y0 + 2y1 
0.00/0.18	  cons = \y0y1.3 + y0 + y1 
0.00/0.18	  e = 0 
0.00/0.18	  false = 3 
0.00/0.18	  filter = \G0y1.1 + 3y1 + 2G0(0) + 3y1G0(y1) 
0.00/0.18	  filter2 = \y0G1y2y3.y2 + 2y0 + 3y3 + G1(0) + G1(y2) + 3y3G1(y3) 
0.00/0.18	  map = \G0y1.3y1 + G0(y1) + 2y1G0(y1) 
0.00/0.18	  nil = 0 
0.00/0.18	  true = 3 
0.00/0.18	
0.00/0.18	Using this interpretation, the requirements translate to:
0.00/0.18	
0.00/0.18	  [[!fac3220(_x0, _x0)]] = 3 + 3x0 > 0 = [[e]] 
0.00/0.18	  [[!fac3220(e, _x0)]] = 3 + 2x0 > x0 = [[_x0]] 
0.00/0.18	  [[!fac3220(_x0, !facdot(_x0, _x1))]] = 9 + 3x0 + 4x1 > x1 = [[_x1]] 
0.00/0.18	  [[!fac3220(!facdiv(_x0, _x1), _x0)]] = 6 + x1 + 3x0 > x1 = [[_x1]] 
0.00/0.18	  [[!facdiv(_x0, _x0)]] = 3 + 2x0 > 0 = [[e]] 
0.00/0.18	  [[!facdiv(_x0, e)]] = 3 + x0 > x0 = [[_x0]] 
0.00/0.18	  [[!facdiv(!facdot(_x0, _x1), _x1)]] = 6 + x0 + 3x1 > x0 = [[_x0]] 
0.00/0.18	  [[!facdiv(_x0, !fac3220(_x1, _x0))]] = 6 + x1 + 3x0 > x1 = [[_x1]] 
0.00/0.18	  [[!facdot(e, _x0)]] = 3 + 2x0 > x0 = [[_x0]] 
0.00/0.18	  [[!facdot(_x0, e)]] = 3 + x0 > x0 = [[_x0]] 
0.00/0.18	  [[!facdot(_x0, !fac3220(_x0, _x1))]] = 9 + 3x0 + 4x1 > x1 = [[_x1]] 
0.00/0.18	  [[!facdot(!facdiv(_x0, _x1), _x1)]] = 6 + x0 + 3x1 > x0 = [[_x0]] 
0.00/0.18	  [[map(_F0, nil)]] = F0(0) >= 0 = [[nil]] 
0.00/0.18	  [[map(_F0, cons(_x1, _x2))]] = 9 + 3x1 + 3x2 + 2x1F0(3 + x1 + x2) + 2x2F0(3 + x1 + x2) + 7F0(3 + x1 + x2) > 3 + x1 + 3x2 + F0(x1) + F0(x2) + 2x2F0(x2) = [[cons(_F0 _x1, map(_F0, _x2))]] 
0.00/0.18	  [[filter(_F0, nil)]] = 1 + 2F0(0) > 0 = [[nil]] 
0.00/0.18	  [[filter(_F0, cons(_x1, _x2))]] = 10 + 3x1 + 3x2 + 2F0(0) + 3x1F0(3 + x1 + x2) + 3x2F0(3 + x1 + x2) + 9F0(3 + x1 + x2) > 3x1 + 3x2 + F0(0) + 3x2F0(x2) + 3F0(x1) = [[filter2(_F0 _x1, _F0, _x1, _x2)]] 
0.00/0.18	  [[filter2(true, _F0, _x1, _x2)]] = 6 + x1 + 3x2 + F0(0) + F0(x1) + 3x2F0(x2) > 4 + x1 + 3x2 + 2F0(0) + 3x2F0(x2) = [[cons(_x1, filter(_F0, _x2))]] 
0.00/0.18	  [[filter2(false, _F0, _x1, _x2)]] = 6 + x1 + 3x2 + F0(0) + F0(x1) + 3x2F0(x2) > 1 + 3x2 + 2F0(0) + 3x2F0(x2) = [[filter(_F0, _x2)]] 
0.00/0.18

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