YES

Problem 1:

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

Problem 1:

Well-founded Relation Processor:
-> Rules:
 a -> c
 a -> d
 f(x) -> x | x ->* c
->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 c :  -> S .
op d :  -> 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 c
a ->R d
x ->R* c => f(x) ->R x
x ->R y => sqsupset(x,y)

Results:


Domains:
S: -|N \ {0}

Function Interpretations:
|[a]| = - 2
|[c]| = - 1
|[d]| = - 1
|[f(x_1_1:S)]| = - 3 + 2.x_1_1:S
|[fSNonEmpty]| = - 1

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

The problem is finite.
0.38user 0.06system 0:00.73elapsed 61%CPU (0avgtext+0avgdata 21916maxresident)k
26072inputs+64outputs (117major+6865minor)pagefaults 0swaps