YES
(ignored inputs)COMMENT from the collection of \cite{AT2012}
Rewrite Rules:
   [ +(+(?x,?y),?z) -> +(?x,+(?y,?z)),
     +(?x,?y) -> +(?y,?x),
     *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)),
     *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)) ]
Apply Direct Methods...
Inner CPs:
   [ +(+(?y_1,?x_1),?z) = +(?x_1,+(?y_1,?z)),
     *(+(?x,+(?y,?z)),?z_2) = +(*(+(?x,?y),?z_2),*(?z,?z_2)),
     *(+(?y_1,?x_1),?z_2) = +(*(?x_1,?z_2),*(?y_1,?z_2)),
     *(?x_3,+(?x,+(?y,?z))) = +(*(?x_3,+(?x,?y)),*(?x_3,?z)),
     *(?x_3,+(?y_1,?x_1)) = +(*(?x_3,?x_1),*(?x_3,?y_1)),
     +(+(?x,+(?y,?z)),?z_1) = +(+(?x,?y),+(?z,?z_1)) ]
Outer CPs:
   [ +(?x,+(?y,?z)) = +(?z,+(?x,?y)),
     +(*(?x_2,+(?y_3,?z_3)),*(?y_2,+(?y_3,?z_3))) = +(*(+(?x_2,?y_2),?y_3),*(+(?x_2,?y_2),?z_3)) ]
not Overlay, check Termination...
unknown/not Terminating
unknown Knuth & Bendix
Left-Linear, not Right-Linear
unknown Development Closed
unknown Weakly-Non-Overlapping & Non-Collapsing & Shallow
unknown Upside-Parallel-Closed/Outside-Closed
(inner) Parallel CPs: (not computed)
unknown Toyama (Parallel CPs)
Simultaneous CPs:
   [ +(?z,+(?x_1,+(?y_1,?y))) = +(+(?x_1,?y_1),+(?y,?z)),
     +(?z,+(?y,?x)) = +(?x,+(?y,?z)),
     +(?z,+(?x,?y)) = +(?x,+(?y,?z)),
     +(+(?x_1,+(?y_1,?y)),?z) = +(+(?x_1,?y_1),+(?y,?z)),
     +(+(?y,?x),?z) = +(?x,+(?y,?z)),
     +(+(?x_2,+(?y_2,?y)),+(?z,?z_1)) = +(+(+(?x_2,?y_2),+(?y,?z)),?z_1),
     +(+(?y,?x),+(?z,?z_1)) = +(+(?x,+(?y,?z)),?z_1),
     +(*(+(?x_4,+(?y_4,?y)),?z_3),*(?z,?z_3)) = *(+(+(?x_4,?y_4),+(?y,?z)),?z_3),
     +(*(+(?y,?x),?z_3),*(?z,?z_3)) = *(+(?x,+(?y,?z)),?z_3),
     +(*(?x_4,+(?x_5,+(?y_5,?y))),*(?x_4,?z)) = *(?x_4,+(+(?x_5,?y_5),+(?y,?z))),
     +(*(?x_4,+(?y,?x)),*(?x_4,?z)) = *(?x_4,+(?x,+(?y,?z))),
     +(+(?x,?y),+(?z,?z_1)) = +(+(?x,+(?y,?z)),?z_1),
     +(*(+(?x,?y),?z_3),*(?z,?z_3)) = *(+(?x,+(?y,?z)),?z_3),
     +(*(?x_4,+(?x,?y)),*(?x_4,?z)) = *(?x_4,+(?x,+(?y,?z))),
     +(?x_1,+(?y_1,?y)) = +(?y,+(?x_1,?y_1)),
     +(?x,+(?y,?z_2)) = +(+(?y,?x),?z_2),
     +(*(?x,?z_3),*(?y,?z_3)) = *(+(?y,?x),?z_3),
     +(*(?x_4,?x),*(?x_4,?y)) = *(?x_4,+(?y,?x)),
     +(*(+(?x_5,+(?y_5,?y)),?y_3),*(+(?x_5,+(?y_5,?y)),?z_3)) = +(*(+(?x_5,?y_5),+(?y_3,?z_3)),*(?y,+(?y_3,?z_3))),
     +(*(+(?y,?x),?y_3),*(+(?y,?x),?z_3)) = +(*(?x,+(?y_3,?z_3)),*(?y,+(?y_3,?z_3))),
     +(*(+(?x,?y),?y_3),*(+(?x,?y),?z_3)) = +(*(?x,+(?y_3,?z_3)),*(?y,+(?y_3,?z_3))),
     *(+(?x_2,+(?y_2,?y)),?z) = +(*(+(?x_2,?y_2),?z),*(?y,?z)),
     *(+(?y,?x),?z) = +(*(?x,?z),*(?y,?z)),
     +(*(?x_3,+(?x_5,+(?y_5,?z))),*(?y_3,+(?x_5,+(?y_5,?z)))) = +(*(+(?x_3,?y_3),+(?x_5,?y_5)),*(+(?x_3,?y_3),?z)),
     +(*(?x_3,+(?z,?y)),*(?y_3,+(?z,?y))) = +(*(+(?x_3,?y_3),?y),*(+(?x_3,?y_3),?z)),
     +(*(?x_3,+(?y,?z)),*(?y_3,+(?y,?z))) = +(*(+(?x_3,?y_3),?y),*(+(?x_3,?y_3),?z)),
     *(?x,+(?x_2,+(?y_2,?z))) = +(*(?x,+(?x_2,?y_2)),*(?x,?z)),
     *(?x,+(?z,?y)) = +(*(?x,?y),*(?x,?z)) ]
unknown Okui (Simultaneous CPs)
unknown Strongly Depth-Preserving & Root-E-Closed/Non-E-Overlapping
unknown Strongly Weight-Preserving & Root-E-Closed/Non-E-Overlapping
check Locally Decreasing Diagrams by Rule Labelling...
Critical Pair <+(+(?y_1,?x_1),?z), +(?x_1,+(?y_1,?z))> by Rules <1, 0> preceded by [(+,1)]
 joinable by a reduction of rules <[([(+,1)],1),([],0)], []>
 joinable by a reduction of rules <[([],0),([(+,2)],1)], [([],1),([],0)]>
Critical Pair <*(+(?x,+(?y,?z)),?z_2), +(*(+(?x,?y),?z_2),*(?z,?z_2))> by Rules <0, 2> preceded by [(*,1)]
 joinable by a reduction of rules <[([],2),([(+,2)],2)], [([(+,1)],2),([],0)]>
Critical Pair <*(+(?y_1,?x_1),?z_2), +(*(?x_1,?z_2),*(?y_1,?z_2))> by Rules <1, 2> preceded by [(*,1)]
 joinable by a reduction of rules <[([],2)], [([],1)]>
Critical Pair <*(?x_3,+(?x,+(?y,?z))), +(*(?x_3,+(?x,?y)),*(?x_3,?z))> by Rules <0, 3> preceded by [(*,2)]
 joinable by a reduction of rules <[([],3),([(+,2)],3)], [([(+,1)],3),([],0)]>
Critical Pair <*(?x_3,+(?y_1,?x_1)), +(*(?x_3,?x_1),*(?x_3,?y_1))> by Rules <1, 3> preceded by [(*,2)]
 joinable by a reduction of rules <[([],3)], [([],1)]>
Critical Pair <+(+(?x,+(?y,?z)),?z_1), +(+(?x,?y),+(?z,?z_1))> by Rules <0, 0> preceded by [(+,1)]
 joinable by a reduction of rules <[([],0),([(+,2)],0)], [([],0)]>
Critical Pair <+(?y_1,+(?x,?y)), +(?x,+(?y,?y_1))> by Rules <1, 0> preceded by []
 joinable by a reduction of rules <[([],1),([],0)], []>
Critical Pair <+(*(+(?x_2,?y_2),?y_3),*(+(?x_2,?y_2),?z_3)), +(*(?x_2,+(?y_3,?z_3)),*(?y_2,+(?y_3,?z_3)))> by Rules <3, 2> preceded by []
 joinable by a reduction of rules <[([(+,2)],2),([(+,1)],2),([],0),([(+,2)],1),([(+,2)],0)], [([(+,2),(*,2)],1),([(+,2)],3),([(+,1)],3),([],0)]>
 joinable by a reduction of rules <[([(+,2)],2),([(+,1)],2),([],0),([(+,2)],1),([(+,2)],0)], [([(+,2),(*,2)],1),([(+,1)],3),([(+,2)],3),([],0)]>
 joinable by a reduction of rules <[([(+,2)],2),([(+,1)],2),([],0),([(+,2)],1),([(+,2)],0)], [([(+,2),(*,2)],1),([(+,1)],3),([],0),([(+,2),(+,2)],3)]>
 joinable by a reduction of rules <[([(+,2)],2),([(+,1)],2),([],0),([(+,2)],1),([(+,2)],0)], [([(+,2)],3),([(+,2)],1),([(+,1)],3),([],0)]>
 joinable by a reduction of rules <[([(+,2)],2),([(+,1)],2),([],0),([(+,2)],1),([(+,2)],0)], [([(+,2)],3),([(+,1)],3),([(+,2)],1),([],0)]>
 joinable by a reduction of rules <[([(+,2)],2),([(+,1)],2),([],0),([(+,2)],1),([(+,2)],0)], [([(+,2)],3),([(+,1)],3),([],0),([(+,2),(+,2)],1)]>
 joinable by a reduction of rules <[([(+,2)],2),([(+,1)],2),([],0),([(+,2)],1),([(+,2)],0)], [([(+,1)],3),([(+,2),(*,2)],1),([(+,2)],3),([],0)]>
 joinable by a reduction of rules <[([(+,2)],2),([(+,1)],2),([],0),([(+,2)],1),([(+,2)],0)], [([(+,1)],3),([(+,2),(*,2)],1),([],0),([(+,2),(+,2)],3)]>
 joinable by a reduction of rules <[([(+,2)],2),([(+,1)],2),([],0),([(+,2)],1),([(+,2)],0)], [([(+,1)],3),([(+,2)],3),([(+,2)],1),([],0)]>
 joinable by a reduction of rules <[([(+,2)],2),([(+,1)],2),([],0),([(+,2)],1),([(+,2)],0)], [([(+,1)],3),([(+,2)],3),([],0),([(+,2),(+,2)],1)]>
 joinable by a reduction of rules <[([(+,2)],2),([(+,1)],2),([],0),([(+,2)],1),([(+,2)],0)], [([(+,1)],3),([],0),([(+,2),(+,2),(*,2)],1),([(+,2),(+,2)],3)]>
 joinable by a reduction of rules <[([(+,2)],2),([(+,1)],2),([],0),([(+,2)],1),([(+,2)],0)], [([(+,1)],3),([],0),([(+,2),(+,2)],3),([(+,2),(+,2)],1)]>
 joinable by a reduction of rules <[([(+,1)],2),([(+,2)],2),([],0),([(+,2)],1),([(+,2)],0)], [([(+,2),(*,2)],1),([(+,2)],3),([(+,1)],3),([],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([(+,2)],2),([],0),([(+,2)],1),([(+,2)],0)], [([(+,2),(*,2)],1),([(+,1)],3),([(+,2)],3),([],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([(+,2)],2),([],0),([(+,2)],1),([(+,2)],0)], [([(+,2),(*,2)],1),([(+,1)],3),([],0),([(+,2),(+,2)],3)]>
 joinable by a reduction of rules <[([(+,1)],2),([(+,2)],2),([],0),([(+,2)],1),([(+,2)],0)], [([(+,2)],3),([(+,2)],1),([(+,1)],3),([],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([(+,2)],2),([],0),([(+,2)],1),([(+,2)],0)], [([(+,2)],3),([(+,1)],3),([(+,2)],1),([],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([(+,2)],2),([],0),([(+,2)],1),([(+,2)],0)], [([(+,2)],3),([(+,1)],3),([],0),([(+,2),(+,2)],1)]>
 joinable by a reduction of rules <[([(+,1)],2),([(+,2)],2),([],0),([(+,2)],1),([(+,2)],0)], [([(+,1)],3),([(+,2),(*,2)],1),([(+,2)],3),([],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([(+,2)],2),([],0),([(+,2)],1),([(+,2)],0)], [([(+,1)],3),([(+,2),(*,2)],1),([],0),([(+,2),(+,2)],3)]>
 joinable by a reduction of rules <[([(+,1)],2),([(+,2)],2),([],0),([(+,2)],1),([(+,2)],0)], [([(+,1)],3),([(+,2)],3),([(+,2)],1),([],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([(+,2)],2),([],0),([(+,2)],1),([(+,2)],0)], [([(+,1)],3),([(+,2)],3),([],0),([(+,2),(+,2)],1)]>
 joinable by a reduction of rules <[([(+,1)],2),([(+,2)],2),([],0),([(+,2)],1),([(+,2)],0)], [([(+,1)],3),([],0),([(+,2),(+,2),(*,2)],1),([(+,2),(+,2)],3)]>
 joinable by a reduction of rules <[([(+,1)],2),([(+,2)],2),([],0),([(+,2)],1),([(+,2)],0)], [([(+,1)],3),([],0),([(+,2),(+,2)],3),([(+,2),(+,2)],1)]>
 joinable by a reduction of rules <[([(+,1)],2),([],0),([(+,2),(+,2)],2),([(+,2)],1),([(+,2)],0)], [([(+,2),(*,2)],1),([(+,2)],3),([(+,1)],3),([],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([],0),([(+,2),(+,2)],2),([(+,2)],1),([(+,2)],0)], [([(+,2),(*,2)],1),([(+,1)],3),([(+,2)],3),([],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([],0),([(+,2),(+,2)],2),([(+,2)],1),([(+,2)],0)], [([(+,2),(*,2)],1),([(+,1)],3),([],0),([(+,2),(+,2)],3)]>
 joinable by a reduction of rules <[([(+,1)],2),([],0),([(+,2),(+,2)],2),([(+,2)],1),([(+,2)],0)], [([(+,2)],3),([(+,2)],1),([(+,1)],3),([],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([],0),([(+,2),(+,2)],2),([(+,2)],1),([(+,2)],0)], [([(+,2)],3),([(+,1)],3),([(+,2)],1),([],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([],0),([(+,2),(+,2)],2),([(+,2)],1),([(+,2)],0)], [([(+,2)],3),([(+,1)],3),([],0),([(+,2),(+,2)],1)]>
 joinable by a reduction of rules <[([(+,1)],2),([],0),([(+,2),(+,2)],2),([(+,2)],1),([(+,2)],0)], [([(+,1)],3),([(+,2),(*,2)],1),([(+,2)],3),([],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([],0),([(+,2),(+,2)],2),([(+,2)],1),([(+,2)],0)], [([(+,1)],3),([(+,2),(*,2)],1),([],0),([(+,2),(+,2)],3)]>
 joinable by a reduction of rules <[([(+,1)],2),([],0),([(+,2),(+,2)],2),([(+,2)],1),([(+,2)],0)], [([(+,1)],3),([(+,2)],3),([(+,2)],1),([],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([],0),([(+,2),(+,2)],2),([(+,2)],1),([(+,2)],0)], [([(+,1)],3),([(+,2)],3),([],0),([(+,2),(+,2)],1)]>
 joinable by a reduction of rules <[([(+,1)],2),([],0),([(+,2),(+,2)],2),([(+,2)],1),([(+,2)],0)], [([(+,1)],3),([],0),([(+,2),(+,2),(*,2)],1),([(+,2),(+,2)],3)]>
 joinable by a reduction of rules <[([(+,1)],2),([],0),([(+,2),(+,2)],2),([(+,2)],1),([(+,2)],0)], [([(+,1)],3),([],0),([(+,2),(+,2)],3),([(+,2),(+,2)],1)]>
 joinable by a reduction of rules <[([(+,1)],2),([],0),([(+,2)],1),([(+,2),(+,1)],2),([(+,2)],0)], [([(+,2),(*,2)],1),([(+,2)],3),([(+,1)],3),([],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([],0),([(+,2)],1),([(+,2),(+,1)],2),([(+,2)],0)], [([(+,2),(*,2)],1),([(+,1)],3),([(+,2)],3),([],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([],0),([(+,2)],1),([(+,2),(+,1)],2),([(+,2)],0)], [([(+,2),(*,2)],1),([(+,1)],3),([],0),([(+,2),(+,2)],3)]>
 joinable by a reduction of rules <[([(+,1)],2),([],0),([(+,2)],1),([(+,2),(+,1)],2),([(+,2)],0)], [([(+,2)],3),([(+,2)],1),([(+,1)],3),([],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([],0),([(+,2)],1),([(+,2),(+,1)],2),([(+,2)],0)], [([(+,2)],3),([(+,1)],3),([(+,2)],1),([],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([],0),([(+,2)],1),([(+,2),(+,1)],2),([(+,2)],0)], [([(+,2)],3),([(+,1)],3),([],0),([(+,2),(+,2)],1)]>
 joinable by a reduction of rules <[([(+,1)],2),([],0),([(+,2)],1),([(+,2),(+,1)],2),([(+,2)],0)], [([(+,1)],3),([(+,2),(*,2)],1),([(+,2)],3),([],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([],0),([(+,2)],1),([(+,2),(+,1)],2),([(+,2)],0)], [([(+,1)],3),([(+,2),(*,2)],1),([],0),([(+,2),(+,2)],3)]>
 joinable by a reduction of rules <[([(+,1)],2),([],0),([(+,2)],1),([(+,2),(+,1)],2),([(+,2)],0)], [([(+,1)],3),([(+,2)],3),([(+,2)],1),([],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([],0),([(+,2)],1),([(+,2),(+,1)],2),([(+,2)],0)], [([(+,1)],3),([(+,2)],3),([],0),([(+,2),(+,2)],1)]>
 joinable by a reduction of rules <[([(+,1)],2),([],0),([(+,2)],1),([(+,2),(+,1)],2),([(+,2)],0)], [([(+,1)],3),([],0),([(+,2),(+,2),(*,2)],1),([(+,2),(+,2)],3)]>
 joinable by a reduction of rules <[([(+,1)],2),([],0),([(+,2)],1),([(+,2),(+,1)],2),([(+,2)],0)], [([(+,1)],3),([],0),([(+,2),(+,2)],3),([(+,2),(+,2)],1)]>
 joinable by a reduction of rules <[([(+,2),(*,1)],1),([(+,2)],2),([(+,1)],2),([],0)], [([(+,2)],3),([(+,1)],3),([],0),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,2),(*,1)],1),([(+,2)],2),([(+,1)],2),([],0)], [([(+,1)],3),([(+,2)],3),([],0),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,2),(*,1)],1),([(+,2)],2),([(+,1)],2),([],0)], [([(+,1)],3),([],0),([(+,2),(+,2)],3),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,2),(*,1)],1),([(+,2)],2),([(+,1)],2),([],0)], [([(+,1)],3),([],0),([(+,2)],1),([(+,2),(+,1)],3),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,2),(*,1)],1),([(+,1)],2),([(+,2)],2),([],0)], [([(+,2)],3),([(+,1)],3),([],0),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,2),(*,1)],1),([(+,1)],2),([(+,2)],2),([],0)], [([(+,1)],3),([(+,2)],3),([],0),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,2),(*,1)],1),([(+,1)],2),([(+,2)],2),([],0)], [([(+,1)],3),([],0),([(+,2),(+,2)],3),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,2),(*,1)],1),([(+,1)],2),([(+,2)],2),([],0)], [([(+,1)],3),([],0),([(+,2)],1),([(+,2),(+,1)],3),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,2),(*,1)],1),([(+,1)],2),([],0),([(+,2),(+,2)],2)], [([(+,2)],3),([(+,1)],3),([],0),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,2),(*,1)],1),([(+,1)],2),([],0),([(+,2),(+,2)],2)], [([(+,1)],3),([(+,2)],3),([],0),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,2),(*,1)],1),([(+,1)],2),([],0),([(+,2),(+,2)],2)], [([(+,1)],3),([],0),([(+,2),(+,2)],3),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,2),(*,1)],1),([(+,1)],2),([],0),([(+,2),(+,2)],2)], [([(+,1)],3),([],0),([(+,2)],1),([(+,2),(+,1)],3),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,2)],2),([(+,2)],1),([(+,1)],2),([],0)], [([(+,2)],3),([(+,1)],3),([],0),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,2)],2),([(+,2)],1),([(+,1)],2),([],0)], [([(+,1)],3),([(+,2)],3),([],0),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,2)],2),([(+,2)],1),([(+,1)],2),([],0)], [([(+,1)],3),([],0),([(+,2),(+,2)],3),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,2)],2),([(+,2)],1),([(+,1)],2),([],0)], [([(+,1)],3),([],0),([(+,2)],1),([(+,2),(+,1)],3),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,2)],2),([(+,1)],2),([(+,2)],1),([],0)], [([(+,2)],3),([(+,1)],3),([],0),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,2)],2),([(+,1)],2),([(+,2)],1),([],0)], [([(+,1)],3),([(+,2)],3),([],0),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,2)],2),([(+,1)],2),([(+,2)],1),([],0)], [([(+,1)],3),([],0),([(+,2),(+,2)],3),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,2)],2),([(+,1)],2),([(+,2)],1),([],0)], [([(+,1)],3),([],0),([(+,2)],1),([(+,2),(+,1)],3),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,2)],2),([(+,1)],2),([],0),([(+,2),(+,2)],1)], [([(+,2)],3),([(+,1)],3),([],0),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,2)],2),([(+,1)],2),([],0),([(+,2),(+,2)],1)], [([(+,1)],3),([(+,2)],3),([],0),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,2)],2),([(+,1)],2),([],0),([(+,2),(+,2)],1)], [([(+,1)],3),([],0),([(+,2),(+,2)],3),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,2)],2),([(+,1)],2),([],0),([(+,2),(+,2)],1)], [([(+,1)],3),([],0),([(+,2)],1),([(+,2),(+,1)],3),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([(+,2),(*,1)],1),([(+,2)],2),([],0)], [([(+,2)],3),([(+,1)],3),([],0),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([(+,2),(*,1)],1),([(+,2)],2),([],0)], [([(+,1)],3),([(+,2)],3),([],0),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([(+,2),(*,1)],1),([(+,2)],2),([],0)], [([(+,1)],3),([],0),([(+,2),(+,2)],3),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([(+,2),(*,1)],1),([(+,2)],2),([],0)], [([(+,1)],3),([],0),([(+,2)],1),([(+,2),(+,1)],3),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([(+,2),(*,1)],1),([],0),([(+,2),(+,2)],2)], [([(+,2)],3),([(+,1)],3),([],0),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([(+,2),(*,1)],1),([],0),([(+,2),(+,2)],2)], [([(+,1)],3),([(+,2)],3),([],0),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([(+,2),(*,1)],1),([],0),([(+,2),(+,2)],2)], [([(+,1)],3),([],0),([(+,2),(+,2)],3),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([(+,2),(*,1)],1),([],0),([(+,2),(+,2)],2)], [([(+,1)],3),([],0),([(+,2)],1),([(+,2),(+,1)],3),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([(+,2)],2),([(+,2)],1),([],0)], [([(+,2)],3),([(+,1)],3),([],0),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([(+,2)],2),([(+,2)],1),([],0)], [([(+,1)],3),([(+,2)],3),([],0),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([(+,2)],2),([(+,2)],1),([],0)], [([(+,1)],3),([],0),([(+,2),(+,2)],3),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([(+,2)],2),([(+,2)],1),([],0)], [([(+,1)],3),([],0),([(+,2)],1),([(+,2),(+,1)],3),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([(+,2)],2),([],0),([(+,2),(+,2)],1)], [([(+,2)],3),([(+,1)],3),([],0),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([(+,2)],2),([],0),([(+,2),(+,2)],1)], [([(+,1)],3),([(+,2)],3),([],0),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([(+,2)],2),([],0),([(+,2),(+,2)],1)], [([(+,1)],3),([],0),([(+,2),(+,2)],3),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([(+,2)],2),([],0),([(+,2),(+,2)],1)], [([(+,1)],3),([],0),([(+,2)],1),([(+,2),(+,1)],3),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([],0),([(+,2),(+,2),(*,1)],1),([(+,2),(+,2)],2)], [([(+,2)],3),([(+,1)],3),([],0),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([],0),([(+,2),(+,2),(*,1)],1),([(+,2),(+,2)],2)], [([(+,1)],3),([(+,2)],3),([],0),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([],0),([(+,2),(+,2),(*,1)],1),([(+,2),(+,2)],2)], [([(+,1)],3),([],0),([(+,2),(+,2)],3),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([],0),([(+,2),(+,2),(*,1)],1),([(+,2),(+,2)],2)], [([(+,1)],3),([],0),([(+,2)],1),([(+,2),(+,1)],3),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([],0),([(+,2),(+,2)],2),([(+,2),(+,2)],1)], [([(+,2)],3),([(+,1)],3),([],0),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([],0),([(+,2),(+,2)],2),([(+,2),(+,2)],1)], [([(+,1)],3),([(+,2)],3),([],0),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([],0),([(+,2),(+,2)],2),([(+,2),(+,2)],1)], [([(+,1)],3),([],0),([(+,2),(+,2)],3),([(+,2)],1),([(+,2)],0)]>
 joinable by a reduction of rules <[([(+,1)],2),([],0),([(+,2),(+,2)],2),([(+,2),(+,2)],1)], [([(+,1)],3),([],0),([(+,2)],1),([(+,2),(+,1)],3),([(+,2)],0)]>
unknown Diagram Decreasing
   [ +(+(?x,?y),?z) -> +(?x,+(?y,?z)),
     +(?x_1,?y_1) -> +(?y_1,?x_1),
     *(+(?x_2,?y_2),?z_2) -> +(*(?x_2,?z_2),*(?y_2,?z_2)),
     *(?x_3,+(?y_3,?z_3)) -> +(*(?x_3,?y_3),*(?x_3,?z_3)) ]
Sort Assignment:
 * : 13*13=>13
 + : 13*13=>13
non-linear variables: {?z_2,?x_3}
non-linear types: {13}
types leq non-linear types: {13}
rules applicable to terms of non-linear types:
   [ +(+(?x,?y),?z) -> +(?x,+(?y,?z)),
     +(?x_1,?y_1) -> +(?y_1,?x_1),
     *(+(?x_2,?y_2),?z_2) -> +(*(?x_2,?z_2),*(?y_2,?z_2)),
     *(?x_3,+(?y_3,?z_3)) -> +(*(?x_3,?y_3),*(?x_3,?z_3)) ]
NLR:
0: {}
1: {}
2: {0,1,2,3}
3: {0,1,2,3}
unknown innermost-termination for terms of non-linear types
unknown Quasi-Linear & Linearized-Decreasing
   [ +(+(?x,?y),?z) -> +(?x,+(?y,?z)),
     +(?x_1,?y_1) -> +(?y_1,?x_1),
     *(+(?x_2,?y_2),?z_2) -> +(*(?x_2,?z_2),*(?y_2,?z_2)),
     *(?x_3,+(?y_3,?z_3)) -> +(*(?x_3,?y_3),*(?x_3,?z_3)) ]
Sort Assignment:
 * : 13*13=>13
 + : 13*13=>13
non-linear variables: {?z_2,?x_3}
non-linear types: {13}
types leq non-linear types: {13}
rules applicable to terms of non-linear types:
   [ +(+(?x,?y),?z) -> +(?x,+(?y,?z)),
     +(?x_1,?y_1) -> +(?y_1,?x_1),
     *(+(?x_2,?y_2),?z_2) -> +(*(?x_2,?z_2),*(?y_2,?z_2)),
     *(?x_3,+(?y_3,?z_3)) -> +(*(?x_3,?y_3),*(?x_3,?z_3)) ]
unknown innermost-termination for terms of non-linear types
unknown Strongly Quasi-Linear & Hierarchically Decreasing
check Non-Confluence...
obtain 14 rules by 3 steps unfolding
strenghten +(?x_5,?y_5) and +(?y_5,?x_5)
strenghten +(?x,+(?y,?x_6)) and +(?x_6,+(?x,?y))
strenghten +(?x,+(?y,?x_7)) and +(+(?x,?y),?x_7)
strenghten +(?x_1,+(?x_12,?y_1)) and +(?x_12,+(?y_1,?x_1))
strenghten +(?x_1,+(?y_1,?x_14)) and +(?x_14,+(?y_1,?x_1))
strenghten +(?x_1,+(?y_1,?z)) and +(+(?y_1,?x_1),?z)
strenghten +(?x_4,+(?x_12,?y_4)) and +(?x_12,+(?x_4,?y_4))
strenghten +(?x_8,+(?x_1,?y_1)) and +(?x_8,+(?y_1,?x_1))
strenghten +(+(?x_9,?y_9),?x_8) and +(?x_8,+(?x_9,?y_9))
strenghten +(+(?x_11,?y_11),?x_10) and +(?x_10,+(?y_11,?x_11))
strenghten +(+(?x_13,?y_13),?x_12) and +(?x_13,+(?x_12,?y_13))
strenghten +(+(?x_15,?y_15),?x_14) and +(?x_15,+(?y_15,?x_14))
strenghten +(+(?x_17,?y_17),?x_16) and +(?y_17,+(?x_16,?x_17))
strenghten +(+(?x_19,?y_19),?x_18) and +(?y_19,+(?x_19,?x_18))
strenghten +(*(?x_1,?z_2),*(?y_1,?z_2)) and *(+(?y_1,?x_1),?z_2)
strenghten +(*(?x_3,?x_1),*(?x_3,?y_1)) and *(?x_3,+(?y_1,?x_1))
strenghten +(*(?x_3,?x_4),*(?x_3,?y_4)) and *(?x_3,+(?x_4,?y_4))
strenghten +(*(?x_4,?z_2),*(?y_4,?z_2)) and *(+(?x_4,?y_4),?z_2)
strenghten +(?x,+(?x_2,+(?x_1,?y_1))) and +(?x_2,+(?x_1,+(?x,?y_1)))
strenghten +(?x,+(?y,+(?x_9,?y_9))) and +(+(?x,?y),+(?x_9,?y_9))
strenghten +(?x,+(?y,+(?x_11,?y_11))) and +(+(?x,?y),+(?y_11,?x_11))
strenghten +(?x,+(?y,+(?x_13,?y_13))) and +(?x_13,+(+(?x,?y),?y_13))
obtain 100 candidates for checking non-joinability
check by TCAP-Approximation (failure)
check by Root-Approximation (failure)
check by Ordering(rpo), check by Tree-Automata Approximation (failure)
check by Interpretation(mod2) (failure)
check by Descendants-Approximation, check by Ordering(poly) (failure)
unknown Non-Confluence
Check relative termination:
   [ *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)),
     *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)) ]
   [ +(+(?x,?y),?z) -> +(?x,+(?y,?z)),
     +(?x,?y) -> +(?y,?x) ]
Polynomial Interpretation:
  *:= (1)*x1+(2)*x1*x2+(2)*x2
  +:= (1)+(1)*x1+(1)*x2
retract *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z))
Polynomial Interpretation:
  *:= (2)*x1+(2)*x1*x2+(1)*x2
  +:= (2)+(1)*x1+(1)*x2
relatively terminating
Huet (modulo AC)
Direct Methods: CR

Final result: CR
144.trs: Success(CR)
(9843 msec.)