Higher_Order_Rewriting_Union_Beta 2019-03-28 22.10 pair #432270539

details

property	value
status	complete
benchmark	AotoYamada_05__020.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n115.star.cs.uiowa.edu
space	Uncurried_Applicative_11

run statistics

property	value
solver	Wanda 2.1c
configuration	default
runtime (wallclock)	0.183208 seconds
cpu usage	0.169557
user time	0.144606
system time	0.024951
max virtual memory	113176.0
max residence set size	6620.0

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	    0 : [] --> a 
0.00/0.18	    comp : [b -> b * b -> b] --> b -> b 
0.00/0.18	    plus : [a * a] --> a 
0.00/0.18	    s : [a] --> a 
0.00/0.18	    times : [a * a] --> a 
0.00/0.18	    twice : [b -> b] --> b -> b 
0.00/0.18	
0.00/0.18	  Rules:
0.00/0.18	
0.00/0.18	    plus(0, x) => x 
0.00/0.18	    plus(s(x), y) => s(plus(x, y)) 
0.00/0.18	    times(0, x) => 0 
0.00/0.18	    times(s(x), y) => plus(times(x, y), y) 
0.00/0.18	    comp(f, g) x => f (g x) 
0.00/0.18	    twice(f) => comp(f, f) 
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	  plus(0, X) >? X 
0.00/0.18	  plus(s(X), Y) >? s(plus(X, Y)) 
0.00/0.18	  times(0, X) >? 0 
0.00/0.18	  times(s(X), Y) >? plus(times(X, Y), Y) 
0.00/0.18	  comp(F, G) X >? F (G X) 
0.00/0.18	  twice(F) >? comp(F, F) 
0.00/0.18	
0.00/0.18	We use a recursive path ordering as defined in [Kop12, Chapter 5].
0.00/0.18	
0.00/0.18	Argument functions:
0.00/0.18	
0.00/0.18	  [[0]] = _|_ 
0.00/0.18	
0.00/0.18	We choose Lex = {} and Mul = {@_{o -> o}, comp, plus, s, times, twice}, and the following precedence: times > plus > s > twice > comp > @_{o -> o}
0.00/0.18	
0.00/0.18	Taking the argument function into account, and fixing the greater / greater equal choices, the constraints can be denoted as follows:
0.00/0.18	
0.00/0.18	  plus(_|_, X) >= X 
0.00/0.18	  plus(s(X), Y) >= s(plus(X, Y)) 
0.00/0.18	  times(_|_, X) >= _|_ 
0.00/0.18	  times(s(X), Y) > plus(times(X, Y), Y) 
0.00/0.18	  @_{o -> o}(comp(F, G), X) > @_{o -> o}(F, @_{o -> o}(G, X)) 
0.00/0.18	  twice(F) >= comp(F, F) 
0.00/0.18	
0.00/0.18	With these choices, we have:
0.00/0.18	
0.00/0.18	  1] plus(_|_, X) >= X  because [2], by (Star) 
0.00/0.18	  2] plus*(_|_, X) >= X  because [3], by (Select) 
0.00/0.18	  3] X >= X  by (Meta) 
0.00/0.18	
0.00/0.18	  4] plus(s(X), Y) >= s(plus(X, Y))  because [5], by (Star) 
0.00/0.18	  5] plus*(s(X), Y) >= s(plus(X, Y))  because plus > s and [6], by (Copy) 
0.00/0.18	  6] plus*(s(X), Y) >= plus(X, Y)  because plus in Mul, [7] and [10], by (Stat) 
0.00/0.18	  7] s(X) > X  because [8], by definition 
0.00/0.18	  8] s*(X) >= X  because [9], by (Select) 
0.00/0.18	  9] X >= X  by (Meta) 
0.00/0.18	  10] Y >= Y  by (Meta) 
0.00/0.18	
0.00/0.18	  11] times(_|_, X) >= _|_  by (Bot) 
0.00/0.18	
0.00/0.18	  12] times(s(X), Y) > plus(times(X, Y), Y)  because [13], by definition 
0.00/0.18	  13] times*(s(X), Y) >= plus(times(X, Y), Y)  because times > plus, [14] and [19], by (Copy) 
0.00/0.18	  14] times*(s(X), Y) >= times(X, Y)  because times in Mul, [15] and [18], by (Stat) 
0.00/0.18	  15] s(X) > X  because [16], by definition 
0.00/0.18	  16] s*(X) >= X  because [17], by (Select) 
0.00/0.18	  17] X >= X  by (Meta) 
0.00/0.18	  18] Y >= Y  by (Meta) 
0.00/0.18	  19] times*(s(X), Y) >= Y  because [18], by (Select) 
0.00/0.18	
0.00/0.18	  20] @_{o -> o}(comp(F, G), X) > @_{o -> o}(F, @_{o -> o}(G, X))  because [21], by definition 
0.00/0.18	  21] @_{o -> o}*(comp(F, G), X) >= @_{o -> o}(F, @_{o -> o}(G, X))  because [22], by (Select) 
0.00/0.18	  22] comp(F, G) @_{o -> o}*(comp(F, G), X) >= @_{o -> o}(F, @_{o -> o}(G, X))  because [23] 
0.00/0.18	  23] comp*(F, G, @_{o -> o}*(comp(F, G), X)) >= @_{o -> o}(F, @_{o -> o}(G, X))  because comp > @_{o -> o}, [24] and [26], by (Copy) 
0.00/0.18	  24] comp*(F, G, @_{o -> o}*(comp(F, G), X)) >= F  because [25], by (Select) 
0.00/0.18	  25] F >= F  by (Meta) 
0.00/0.18	  26] comp*(F, G, @_{o -> o}*(comp(F, G), X)) >= @_{o -> o}(G, X)  because comp > @_{o -> o}, [27] and [29], by (Copy) 
0.00/0.18	  27] comp*(F, G, @_{o -> o}*(comp(F, G), X)) >= G  because [28], by (Select) 
0.00/0.18	  28] G >= G  by (Meta) 
0.00/0.18	  29] comp*(F, G, @_{o -> o}*(comp(F, G), X)) >= X  because [30], by (Select) 
0.00/0.18	  30] @_{o -> o}*(comp(F, G), X) >= X  because [31], by (Select) 
0.00/0.18	  31] X >= X  by (Meta) 
0.00/0.18	
0.00/0.18	  32] twice(F) >= comp(F, F)  because [33], by (Star) 
0.00/0.18	  33] twice*(F) >= comp(F, F)  because twice > comp, [34] and [34], by (Copy) 
0.00/0.18	  34] twice*(F) >= F  because [35], by (Select) 
0.00/0.18	  35] F >= F  by (Meta) 
0.00/0.18	
0.00/0.18	We can thus remove the following rules:
0.00/0.18	
0.00/0.18	  times(s(X), Y) => plus(times(X, Y), Y) 
0.00/0.18	  comp(F, G) X => F (G X) 
0.00/0.18	
0.00/0.18	We use rule removal, following [Kop12, Theorem 2.23].

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