MAYBE
Time: 1.681655
TRS:
 {           g h2(x, y, h1(z, u)) -> h2(s x, y, h1(z, u)),
                   f(x, h1(y, z)) -> h2(0(), x, h1(y, z)),
                    f(j(x, y), y) -> g f(x, k y),
                       k h1(x, y) -> h1(s x, y),
                            k h x -> h1(0(), x),
  h2(x, j(y, h1(z, u)), h1(z, u)) -> h2(s x, y, h1(s z, u)),
                      i f(x, h y) -> y,
           i h2(s x, y, h1(x, z)) -> z}
 DP:
  DP:
   {           g# h2(x, y, h1(z, u)) -> h2#(s x, y, h1(z, u)),
                     f#(x, h1(y, z)) -> h2#(0(), x, h1(y, z)),
                      f#(j(x, y), y) -> g# f(x, k y),
                      f#(j(x, y), y) -> f#(x, k y),
                      f#(j(x, y), y) -> k# y,
    h2#(x, j(y, h1(z, u)), h1(z, u)) -> h2#(s x, y, h1(s z, u))}
  TRS:
  {           g h2(x, y, h1(z, u)) -> h2(s x, y, h1(z, u)),
                    f(x, h1(y, z)) -> h2(0(), x, h1(y, z)),
                     f(j(x, y), y) -> g f(x, k y),
                        k h1(x, y) -> h1(s x, y),
                             k h x -> h1(0(), x),
   h2(x, j(y, h1(z, u)), h1(z, u)) -> h2(s x, y, h1(s z, u)),
                       i f(x, h y) -> y,
            i h2(s x, y, h1(x, z)) -> z}
  UR:
   {           g h2(x, y, h1(z, u)) -> h2(s x, y, h1(z, u)),
                     f(x, h1(y, z)) -> h2(0(), x, h1(y, z)),
                      f(j(x, y), y) -> g f(x, k y),
                         k h1(x, y) -> h1(s x, y),
                              k h x -> h1(0(), x),
    h2(x, j(y, h1(z, u)), h1(z, u)) -> h2(s x, y, h1(s z, u))}
   EDG:
    {(g# h2(x, y, h1(z, u)) -> h2#(s x, y, h1(z, u)), h2#(x, j(y, h1(z, u)), h1(z, u)) -> h2#(s x, y, h1(s z, u)))
     (h2#(x, j(y, h1(z, u)), h1(z, u)) -> h2#(s x, y, h1(s z, u)), h2#(x, j(y, h1(z, u)), h1(z, u)) -> h2#(s x, y, h1(s z, u)))
     (f#(j(x, y), y) -> g# f(x, k y), g# h2(x, y, h1(z, u)) -> h2#(s x, y, h1(z, u)))
     (f#(j(x, y), y) -> f#(x, k y), f#(x, h1(y, z)) -> h2#(0(), x, h1(y, z)))
     (f#(j(x, y), y) -> f#(x, k y), f#(j(x, y), y) -> g# f(x, k y))
     (f#(j(x, y), y) -> f#(x, k y), f#(j(x, y), y) -> f#(x, k y))
     (f#(j(x, y), y) -> f#(x, k y), f#(j(x, y), y) -> k# y)
     (f#(x, h1(y, z)) -> h2#(0(), x, h1(y, z)), h2#(x, j(y, h1(z, u)), h1(z, u)) -> h2#(s x, y, h1(s z, u)))}
    STATUS:
     arrows: 0.777778
     SCCS (2):
      Scc:
       {f#(j(x, y), y) -> f#(x, k y)}
      Scc:
       {h2#(x, j(y, h1(z, u)), h1(z, u)) -> h2#(s x, y, h1(s z, u))}
      
      SCC (1):
       Strict:
        {f#(j(x, y), y) -> f#(x, k y)}
       Weak:
       {           g h2(x, y, h1(z, u)) -> h2(s x, y, h1(z, u)),
                         f(x, h1(y, z)) -> h2(0(), x, h1(y, z)),
                          f(j(x, y), y) -> g f(x, k y),
                             k h1(x, y) -> h1(s x, y),
                                  k h x -> h1(0(), x),
        h2(x, j(y, h1(z, u)), h1(z, u)) -> h2(s x, y, h1(s z, u)),
                            i f(x, h y) -> y,
                 i h2(s x, y, h1(x, z)) -> z}
       Open
      
      
      
      SCC (1):
       Strict:
        {h2#(x, j(y, h1(z, u)), h1(z, u)) -> h2#(s x, y, h1(s z, u))}
       Weak:
       {           g h2(x, y, h1(z, u)) -> h2(s x, y, h1(z, u)),
                         f(x, h1(y, z)) -> h2(0(), x, h1(y, z)),
                          f(j(x, y), y) -> g f(x, k y),
                             k h1(x, y) -> h1(s x, y),
                                  k h x -> h1(0(), x),
        h2(x, j(y, h1(z, u)), h1(z, u)) -> h2(s x, y, h1(s z, u)),
                            i f(x, h y) -> y,
                 i h2(s x, y, h1(x, z)) -> z}
       Open