YES

Problem 1:

(VAR vu95NonEmpty x)
(RULES
a -> b
f(x) -> x | x ->* b
)

Problem 1:

Well-founded Relation Processor:
-> Rules:
 a -> b
 f(x) -> x | x ->* b
->AGES Output:

Model Results

System:
mod InTheory is
sort S .
sort Bool .


op _->*_ : S S -> Bool [m = 2] .
op _->_ : S S -> Bool [m = 2] .
op a :  -> S .
op f : S -> S .
op b :  -> S .
op fSNonEmpty :  -> S .
op sqsupset : S S -> Bool [wellfounded m = 1] .

endm


Property:
x ->R* x
x ->R y /\ y ->R* z => x ->R* z
x1 ->R y1 => f(x1) ->R f(y1)
a ->R b
x ->R* b => f(x) ->R x
x ->R y => sqsupset(x,y)

Results:


Domains:
S: |N U {-1}

Function Interpretations:
|[a]| = 0
|[b]| = - 1
|[f(x_1_1:S)]| = 4 + 3.x_1_1:S
|[fSNonEmpty]| = 1

Predicate Interpretations:
 x_1_1:S ->* x_2_1:S <=> ((1 + x_2_1:S >= 0) /\ (1 + x_1_1:S >= x_2_1:S))
 x_1_1:S -> x_2_1:S <=> (x_1_1:S >= 1 + x_2_1:S)
sqsupset(x_1_1:S,x_2_1:S) <=> (x_1_1:S >= 1 + x_2_1:S)

The problem is finite.
0.35user 0.12system 0:00.75elapsed 63%CPU (0avgtext+0avgdata 19920maxresident)k
26064inputs+56outputs (117major+6336minor)pagefaults 0swaps