details

property	value
status	complete
benchmark	AotoYamada_05__013.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n144.star.cs.uiowa.edu
space	Uncurried_Applicative_11

run statistics

property	value
solver	Wanda 2.2a
configuration	default
runtime (wallclock)	0.121612 seconds
cpu usage	0.116939
user time	0.097605
system time	0.019334
max virtual memory	113188.0
max residence set size	3272.0

stage attributes

key	value
starexec-result	YES

output

YES We consider the system theBenchmark. Alphabet: append : [c * c] --> c cons : [b * c] --> c flatwith : [a -> b * b] --> c flatwithsub : [a -> b * c] --> c leaf : [a] --> b nil : [] --> c node : [c] --> b Rules: append(nil, x) => x append(cons(x, y), z) => cons(x, append(y, z)) flatwith(f, leaf(x)) => cons(f x, nil) flatwith(f, node(x)) => flatwithsub(f, x) flatwithsub(f, nil) => nil flatwithsub(f, cons(x, y)) => append(flatwith(f, x), flatwithsub(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]): append(nil, X) >? X append(cons(X, Y), Z) >? cons(X, append(Y, Z)) flatwith(F, leaf(X)) >? cons(F X, nil) flatwith(F, node(X)) >? flatwithsub(F, X) flatwithsub(F, nil) >? nil flatwithsub(F, cons(X, Y)) >? append(flatwith(F, X), flatwithsub(F, Y)) We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: append = \y0y1.y0 + y1 cons = \y0y1.1 + y0 + y1 flatwith = \G0y1.y1 + G0(y1) + 2y1G0(y1) flatwithsub = \G0y1.y1 + G0(0) + G0(y1) + 2y1G0(y1) leaf = \y0.3 + 3y0 nil = 2 node = \y0.3 + 3y0 Using this interpretation, the requirements translate to: [[append(nil, _x0)]] = 2 + x0 > x0 = [[_x0]] [[append(cons(_x0, _x1), _x2)]] = 1 + x0 + x1 + x2 >= 1 + x0 + x1 + x2 = [[cons(_x0, append(_x1, _x2))]] [[flatwith(_F0, leaf(_x1))]] = 3 + 3x1 + 6x1F0(3 + 3x1) + 7F0(3 + 3x1) >= 3 + x1 + F0(x1) = [[cons(_F0 _x1, nil)]] [[flatwith(_F0, node(_x1))]] = 3 + 3x1 + 6x1F0(3 + 3x1) + 7F0(3 + 3x1) > x1 + F0(0) + F0(x1) + 2x1F0(x1) = [[flatwithsub(_F0, _x1)]] [[flatwithsub(_F0, nil)]] = 2 + F0(0) + 5F0(2) >= 2 = [[nil]] [[flatwithsub(_F0, cons(_x1, _x2))]] = 1 + x1 + x2 + F0(0) + 2x1F0(1 + x1 + x2) + 2x2F0(1 + x1 + x2) + 3F0(1 + x1 + x2) > x1 + x2 + F0(0) + F0(x1) + F0(x2) + 2x1F0(x1) + 2x2F0(x2) = [[append(flatwith(_F0, _x1), flatwithsub(_F0, _x2))]] We can thus remove the following rules: append(nil, X) => X flatwith(F, node(X)) => flatwithsub(F, X) flatwithsub(F, cons(X, Y)) => append(flatwith(F, X), flatwithsub(F, Y)) We use rule removal, following [Kop12, Theorem 2.23]. This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): append(cons(X, Y), Z) >? cons(X, append(Y, Z)) flatwith(F, leaf(X)) >? cons(F X, nil) flatwithsub(F, nil) >? nil We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: append = \y0y1.y1 + 3y0 cons = \y0y1.y0 + y1 flatwith = \G0y1.3 + 3y1 + G0(0) + y1G0(y1) flatwithsub = \G0y1.3 + 3y1 + G0(0) leaf = \y0.3 + 3y0 nil = 0 Using this interpretation, the requirements translate to: [[append(cons(_x0, _x1), _x2)]] = x2 + 3x0 + 3x1 >= x0 + x2 + 3x1 = [[cons(_x0, append(_x1, _x2))]] [[flatwith(_F0, leaf(_x1))]] = 12 + 9x1 + F0(0) + 3x1F0(3 + 3x1) + 3F0(3 + 3x1) > x1 + F0(x1) = [[cons(_F0 _x1, nil)]] [[flatwithsub(_F0, nil)]] = 3 + F0(0) > 0 = [[nil]] We can thus remove the following rules: flatwith(F, leaf(X)) => cons(F X, nil) flatwithsub(F, nil) => nil We use rule removal, following [Kop12, Theorem 2.23]. This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): append(cons(X, Y), Z) >? cons(X, append(Y, Z)) We orient these requirements with a polynomial interpretation in the natural numbers. popout

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

job log

popout

actions

all output return to Higher Order Rewriting Union Beta