MAYBE
(ignored inputs)COMMENT doi:10.4230/LIPIcs.RTA.2013.319 [115] Example 4.1 submitted by: Aart Middeldorp
Rewrite Rules:
   [ +(a,?x) -> a,
     +(b,g(a)) -> a,
     +(0,?x) -> ?x,
     +(?x,+(?y,?z)) -> +(+(?x,?y),?z),
     +(+(?x,?y),?z) -> +(?x,+(?y,?z)),
     +(?x,?y) -> +(?y,?x) ]
Apply Direct Methods...
Inner CPs:
   [ +(?x_2,a) = +(+(?x_2,a),?x),
     +(?x_2,a) = +(+(?x_2,b),g(a)),
     +(?x_2,?x_1) = +(+(?x_2,0),?x_1),
     +(?x_2,+(?x_3,+(?y_3,?z_3))) = +(+(?x_2,+(?x_3,?y_3)),?z_3),
     +(?x_2,+(?y_4,?x_4)) = +(+(?x_2,?x_4),?y_4),
     +(a,?z_3) = +(a,+(?x,?z_3)),
     +(a,?z_3) = +(b,+(g(a),?z_3)),
     +(?x_1,?z_3) = +(0,+(?x_1,?z_3)),
     +(+(+(?x_2,?y_2),?z_2),?z_3) = +(?x_2,+(+(?y_2,?z_2),?z_3)),
     +(+(?y_4,?x_4),?z_3) = +(?x_4,+(?y_4,?z_3)),
     +(?x_1,+(+(?x,?y),?z)) = +(+(?x_1,?x),+(?y,?z)),
     +(+(?x,+(?y,?z)),?z_1) = +(+(?x,?y),+(?z,?z_1)) ]
Outer CPs:
   [ a = +(+(a,?y_2),?z_2),
     a = +(?x,a),
     a = +(g(a),b),
     +(?y_2,?z_2) = +(+(0,?y_2),?z_2),
     ?x_1 = +(?x_1,0),
     +(+(+(?x_3,?y_3),?y_2),?z_2) = +(?x_3,+(?y_3,+(?y_2,?z_2))),
     +(+(?x_2,?y_2),?z_2) = +(+(?y_2,?z_2),?x_2),
     +(?x_3,+(?y_3,?z_3)) = +(?z_3,+(?x_3,?y_3)) ]
Linear
(inner) Parallel CPs: (not computed)
unknown Toyama (Parallel CPs)
Direct Methods: Can't judge

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