Input TRS:
    1: f(x,y) -> g1(x,x,y)
    2: f(x,y) -> g1(y,x,x)
    3: f(x,y) -> g2(x,y,y)
    4: f(x,y) -> g2(y,y,x)
    5: g1(x,x,y) -> h(x,y)
    6: g1(y,x,x) -> h(x,y)
    7: g2(x,y,y) -> h(x,y)
    8: g2(y,y,x) -> h(x,y)
    9: h(x,x) -> x
Number of strict rules: 9
Direct Order(PosReal,>,Poly) ... removes: 4 8 1 3 5 7 9 6 2
     h(x1,x2)	weight: (/ 1 4) + x1 + x2
    g1(x1,x2,x3)	weight: (/ 1 2) + x1 + x2 + x3
    g2(x1,x2,x3)	weight: (/ 1 2) + x1 + x2 + x3
     f(x1,x2)	weight: (/ 3 4) + 2 * x1 + 2 * x2
Number of strict rules: 0
YES