Higher_Order_Rewriting_Union_Beta 2019-03-28 22.10 pair #432270591

details

property	value
status	complete
benchmark	Applicative_05__Hamming.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n109.star.cs.uiowa.edu
space	Uncurried_Applicative_11

run statistics

property	value
solver	Wanda 2.1c
configuration	default
runtime (wallclock)	0.0143811 seconds
cpu usage	0.014295
user time	0.010962
system time	0.003333
max virtual memory	113176.0
max residence set size	1620.0

stage attributes

key	value
starexec-result	NO

output

0.00/0.01	NO
0.00/0.01	We consider the system theBenchmark.
0.00/0.01	
0.00/0.01	  Alphabet:
0.00/0.01	
0.00/0.01	    0 : [] --> b 
0.00/0.01	    cons : [b * c] --> c 
0.00/0.01	    eq : [b * b] --> a 
0.00/0.01	    false : [] --> a 
0.00/0.01	    hamming : [] --> c 
0.00/0.01	    if : [a * c * c] --> c 
0.00/0.01	    list1 : [] --> c 
0.00/0.01	    list2 : [] --> c 
0.00/0.01	    list3 : [] --> c 
0.00/0.01	    lt : [b * b] --> a 
0.00/0.01	    map : [b -> b * c] --> c 
0.00/0.01	    merge : [c * c] --> c 
0.00/0.01	    mult : [b] --> b -> b 
0.00/0.01	    nil : [] --> c 
0.00/0.01	    plus : [b * b] --> b 
0.00/0.01	    s : [b] --> b 
0.00/0.01	    true : [] --> a 
0.00/0.01	
0.00/0.01	  Rules:
0.00/0.01	
0.00/0.01	    if(true, x, y) => x 
0.00/0.01	    if(false, x, y) => y 
0.00/0.01	    lt(s(x), s(y)) => lt(x, y) 
0.00/0.01	    lt(0, s(x)) => true 
0.00/0.01	    lt(x, 0) => false 
0.00/0.01	    eq(x, x) => true 
0.00/0.01	    eq(s(x), 0) => false 
0.00/0.01	    eq(0, s(x)) => false 
0.00/0.01	    merge(x, nil) => x 
0.00/0.01	    merge(nil, x) => x 
0.00/0.01	    merge(cons(x, y), cons(z, u)) => if(lt(x, z), cons(x, merge(y, cons(z, u))), if(eq(x, z), cons(x, merge(y, u)), cons(z, merge(cons(x, y), u)))) 
0.00/0.01	    map(f, nil) => nil 
0.00/0.01	    map(f, cons(x, y)) => cons(f x, map(f, y)) 
0.00/0.01	    mult(0) x => 0 
0.00/0.01	    mult(s(x)) y => plus(y, mult(x) y) 
0.00/0.01	    plus(0, x) => 0 
0.00/0.01	    plus(s(x), y) => s(plus(x, y)) 
0.00/0.01	    list1 => map(mult(s(s(0))), hamming) 
0.00/0.01	    list2 => map(mult(s(s(s(0)))), hamming) 
0.00/0.01	    list3 => map(mult(s(s(s(s(s(0)))))), hamming) 
0.00/0.01	    hamming => cons(s(0), merge(list1, merge(list2, list3))) 
0.00/0.01	
0.00/0.01	This AFS is converted to an AFSM simply by replacing all free variables by meta-variables (with arity 0).
0.00/0.01	
0.00/0.01	It is easy to see that this system is non-terminating:
0.00/0.01	
0.00/0.01	  list1 
0.00/0.01	    => map(mult(s(s(0))), hamming) 
0.00/0.01	    => map(mult(s(s(0))), cons(s(0), merge(list1, merge(list2, list3)))) 
0.00/0.01	    |> list1 
0.00/0.01	
0.00/0.01	That is, a term s reduces to a term t which has a subterm that is an instance of the original term.
0.00/0.01	
0.00/0.01	EOF

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