details

property	value
status	complete
benchmark	pical.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n143.star.cs.uiowa.edu
space	Hamana_17

run statistics

property	value
solver	Wanda 2.2a
configuration	default
runtime (wallclock)	0.0685301 seconds
cpu usage	0.068553
user time	0.057188
system time	0.011365
max virtual memory	113188.0
max residence set size	3304.0

stage attributes

key	value
starexec-result	YES

output

YES We consider the system theBenchmark. Alphabet: NIL : [] --> A in : [] --> N -> (N -> A) -> A new : [] --> (N -> A) -> A out : [] --> N -> N -> A -> A sum : [] --> A -> A -> A tau : [] --> A -> A Rules: sum NIL x => x new (/\x.y) => y new (/\x.sum (f x) (g x)) => sum (new (/\y.f y)) (new (/\z.g z)) new (/\x.out x y (f x)) => NIL new (/\x.out y z (f x)) => out y z (new (/\u.f u)) new (/\x.in y (/\z.f x z)) => in y (/\u.new (/\v.f v u)) new (/\x.tau (f x)) => tau (new (/\y.f y)) new (/\x.in x (/\y.f x y)) => NIL Using the transformations described in [Kop11], this system can be brought in a form without leading free variables in the left-hand side, and where the left-hand side of a variable is always a functional term or application headed by a functional term. We now transform the resulting AFS into an AFSM by replacing all free variables by meta-variables (with arity 0). This leads to the following AFSM: Alphabet: NIL : [] --> A in : [N * N -> A] --> A new : [N -> A] --> A out : [N * N * A] --> A sum : [A * A] --> A tau : [A] --> A ~AP1 : [N -> A * N] --> A ~AP2 : [N -> N -> A * N] --> N -> A Rules: sum(NIL, X) => X new(/\x.X) => X new(/\x.sum(~AP1(F, x), ~AP1(G, x))) => sum(new(/\y.~AP1(F, y)), new(/\z.~AP1(G, z))) new(/\x.out(x, X, ~AP1(F, x))) => NIL new(/\x.out(X, Y, ~AP1(F, x))) => out(X, Y, new(/\y.~AP1(F, y))) new(/\x.in(X, /\y.~AP1(~AP2(F, x), y))) => in(X, /\z.new(/\u.~AP1(~AP2(F, u), z))) new(/\x.tau(~AP1(F, x))) => tau(new(/\y.~AP1(F, y))) new(/\x.in(x, /\y.~AP1(~AP2(F, x), y))) => NIL ~AP1(F, X) => F X ~AP2(F, X) => F X Symbol ~AP2 is an encoding for application that is only used in innocuous ways. We can simplify the program (without losing non-termination) by removing it. This gives: Alphabet: NIL : [] --> A in : [N * N -> A] --> A new : [N -> A] --> A out : [N * N * A] --> A sum : [A * A] --> A tau : [A] --> A ~AP1 : [N -> A * N] --> A Rules: sum(NIL, X) => X new(/\x.X) => X new(/\x.sum(~AP1(F, x), ~AP1(G, x))) => sum(new(/\y.~AP1(F, y)), new(/\z.~AP1(G, z))) new(/\x.out(x, X, ~AP1(F, x))) => NIL new(/\x.out(X, Y, ~AP1(F, x))) => out(X, Y, new(/\y.~AP1(F, y))) new(/\x.in(X, /\y.~AP1(F(x), y))) => in(X, /\z.new(/\u.~AP1(F(u), z))) new(/\x.tau(~AP1(F, x))) => tau(new(/\y.~AP1(F, y))) new(/\x.in(x, /\y.~AP1(F(x), y))) => NIL ~AP1(F, X) => F X We use rule removal, following [Kop12, Theorem 2.23]. This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): sum(NIL, X) >? X new(/\x.X) >? X new(/\x.sum(~AP1(F, x), ~AP1(G, x))) >? sum(new(/\y.~AP1(F, y)), new(/\z.~AP1(G, z))) new(/\x.out(x, X, ~AP1(F, x))) >? NIL new(/\x.out(X, Y, ~AP1(F, x))) >? out(X, Y, new(/\y.~AP1(F, y))) new(/\x.in(X, /\y.~AP1(F(x), y))) >? in(X, /\z.new(/\u.~AP1(F(u), z))) new(/\x.tau(~AP1(F, x))) >? tau(new(/\y.~AP1(F, y))) new(/\x.in(x, /\y.~AP1(F(x), y))) >? NIL ~AP1(F, X) >? F X We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: NIL = 0 in = \y0G1.3 + y0 + 2G1(0) new = \G0.2 + 3G0(0) out = \y0y1y2.3 + y0 + y1 + 2y2 sum = \y0y1.3 + y0 + y1 tau = \y0.3 + y0 ~AP1 = \G0y1.3 + y1 + G0(y1) popout

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

job log

popout

actions

all output return to Higher Order Rewriting Union Beta