MAYBE
(ignored inputs)COMMENT [16] Example 3 submitted by: Takahito Aoto , Junichi Yoshida , and Yoshihito Toyama
Rewrite Rules:
   [ if(true,?x,?y) -> ?x,
     if(false,?x,?y) -> ?y,
     -(s(?x),s(?y)) -> -(?x,?y),
     -(?x,0) -> ?x,
     -(0,?x) -> 0,
     <(s(?x),s(?y)) -> <(?x,?y),
     <(0,s(?x)) -> true,
     <(?x,0) -> false,
     mod(0,?y) -> 0,
     mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))),
     mod(?x,0) -> ?x,
     gcd(?x,?y) -> gcd(?y,mod(?x,?y)),
     gcd(?x,0) -> ?x,
     gcd(0,?x) -> ?x ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [ 0 = 0,
     0 = if(<(0,s(?y_9)),0,mod(-(0,s(?y_9)),s(?y_9))),
     0 = 0,
     gcd(0,mod(?x_11,0)) = ?x_11,
     gcd(?y_11,mod(0,?y_11)) = ?y_11,
     0 = 0 ]
Left-Linear, not Right-Linear
(inner) Parallel CPs: (not computed)
unknown Toyama (Parallel CPs)
Direct Methods: Can't judge

Combined result: Can't judge
62.trs: Failure(unknown CR)
(0 msec.)