% With abs as a definition: abs ::= dup 0 < [] [neg] branch

?- joy(`[abs] ii <=`, [int(A), int(C)], [bool(B)]).

% Eight solutions:

B = false,
A in 0..sup,
A#=<C+ -1,
A+1#=_67378,
C in 1..sup,
C+1#=_67426,
_67426 in 1..sup,
_67378 in 1..sup ;


B = true,
A in 0..sup,
A#>=C,
A+1#=_67204,
C in 0..sup,
C+1#=_67252,
_67252 in 1..sup,
_67204 in 1..sup ;


B = false,
A in inf.. -1,
_67892+A#=0,
A+1#=_67912,
_67892 in 1..sup,
_67892#=<C+ -1,
C in 2..sup,
C+1#=_68008,
_68008 in 1..sup,
_67912 in inf..0 ;


B = true,
A in inf.. -1,
_67724+A#=0,
A+1#=_67744,
_67724 in 1..sup,
_67724#>=C,
C in 0..sup,
C+1#=_67834,
_67834 in 1..sup,
_67744 in inf..0 ;


B = false,
A in 0..sup,
A#=<_67850+ -1,
A+1#=_67870,
_67850 in 1..sup,
_67850+C#=0,
C in inf.. -1,
C+1#=_67966,
_67966 in inf..0,
_67870 in 1..sup ;


B = true,
A in 1..sup,
A#>=_67762,
A+1#=_67780,
_67762 in 1..sup,
_67762+C#=0,
C in inf.. -1,
C+1#=_67876,
_67876 in inf..0,
_67780 in 1..sup ;


B = false,
A in inf.. -1,
_68746+A#=0,
A+1#=_68766,
_68746 in 1..sup,
_68746#=<_68818+ -1,
_68818 in 2..sup,
_68818+C#=0,
C in inf.. -2,
C+1#=_68910,
_68910 in inf..0,
_68766 in inf..0 ;


B = true,
A in inf.. -1,
_68258+A#=0,
A+1#=_68278,
_68258 in 1..sup,
_68258#>=_68326,
_68326 in 1..sup,
_68326+C#=0,
C in inf.. -1,
C+1#=_68416,
_68416 in inf..0,
_68278 in inf..0 ;


false.


% If we add a function rule for it using CLP(FD)...:

    func(abs, [int(A)|S], [int(B)|S]) :- B #= abs(A).

?- joy(`[abs] ii <=`, [int(A), int(C)], [bool(B)]).

% We get eighteen solutions!  Egad.

B = false,
_7784#=abs(A),
_7784 in 0..sup,
_7784#=<_7836+ -1,
_7836 in 1..sup,
_7836#=abs(C),
C in inf.. -1\/1..sup ;


B = true,
_6512#=abs(A),
_6512 in 0..sup,
_6512#>=_6560,
_6560 in 0..sup,
_6560#=abs(C) ;


B = false,
A in 0..sup,
A#=<_8820+ -1,
A+1#=_8840,
_8820 in 1..sup,
_8820#=abs(C),
C in inf.. -1\/1..sup,
_8840 in 1..sup ;


B = true,
A in 0..sup,
A#>=_7544,
A+1#=_7562,
_7544 in 0..sup,
_7544#=abs(C),
_7562 in 1..sup ;


B = false,
A in inf.. -1,
_9354+A#=0,
A+1#=_9374,
_9354 in 1..sup,
_9354#=<_9426+ -1,
_9426 in 2..sup,
_9426#=abs(C),
C in inf.. -2\/2..sup,
_9374 in inf..0 ;


B = true,
A in inf.. -1,
_8082+A#=0,
A+1#=_8102,
_8082 in 1..sup,
_8082#>=_8150,
_8150 in 0..sup,
_8150#=abs(C),
_8102 in inf..0 ;


B = false,
_7686#=abs(A),
_7686 in 0..sup,
_7686#=<C+ -1,
C in 1..sup,
C+1#=_7782,
_7782 in 1..sup ;


B = true,
_7518#=abs(A),
_7518 in 0..sup,
_7518#>=C,
C in 0..sup,
C+1#=_7608,
_7608 in 1..sup ;


B = false,
A in 0..sup,
A#=<C+ -1,
A+1#=_8742,
C in 1..sup,
C+1#=_8790,
_8790 in 1..sup,
_8742 in 1..sup ;


B = true,
A in 0..sup,
A#>=C,
A+1#=_8568,
C in 0..sup,
C+1#=_8616,
_8616 in 1..sup,
_8568 in 1..sup ;


B = false,
A in inf.. -1,
_9256+A#=0,
A+1#=_9276,
_9256 in 1..sup,
_9256#=<C+ -1,
C in 2..sup,
C+1#=_9372,
_9372 in 1..sup,
_9276 in inf..0 ;


B = true,
A in inf.. -1,
_9088+A#=0,
A+1#=_9108,
_9088 in 1..sup,
_9088#>=C,
C in 0..sup,
C+1#=_9198,
_9198 in 1..sup,
_9108 in inf..0 ;


B = false,
_8178#=abs(A),
_8178 in 0..sup,
_8178#=<_8230+ -1,
_8230 in 1..sup,
_8230+C#=0,
C in inf.. -1,
C+1#=_8322,
_8322 in inf..0 ;


B = true,
A in inf.. -1\/1..sup,
_9272#=abs(A),
_9272 in 1..sup,
_9272#>=_9320,
_9320 in 1..sup,
_9320+C#=0,
C in inf.. -1,
C+1#=_9410,
_9410 in inf..0 ;


B = false,
A in 0..sup,
A#=<_9214+ -1,
A+1#=_9234,
_9214 in 1..sup,
_9214+C#=0,
C in inf.. -1,
C+1#=_9330,
_9330 in inf..0,
_9234 in 1..sup ;


B = true,
A in 1..sup,
A#>=_9126,
A+1#=_9144,
_9126 in 1..sup,
_9126+C#=0,
C in inf.. -1,
C+1#=_9240,
_9240 in inf..0,
_9144 in 1..sup ;


B = false,
A in inf.. -1,
_10110+A#=0,
A+1#=_10130,
_10110 in 1..sup,
_10110#=<_10182+ -1,
_10182 in 2..sup,
_10182+C#=0,
C in inf.. -2,
C+1#=_10274,
_10274 in inf..0,
_10130 in inf..0 ;


B = true,
A in inf.. -1,
_9622+A#=0,
A+1#=_9642,
_9622 in 1..sup,
_9622#>=_9690,
_9690 in 1..sup,
_9690+C#=0,
C in inf.. -1,
C+1#=_9780,
_9780 in inf..0,
_9642 in inf..0 ;


false.