MAYBE
Input TRS:
      1: minus(x,0()) -> x
      2: minus(s(x),s(y)) -> minus(x,y)
      3: quot(0(),s(y)) -> 0()
      4: quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
      5: plus(0(),y) -> y
      6: plus(s(x),y) -> s(plus(x,y))
      7: plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
      8: plus(plus(x,s(0())),plus(y,s(s(z)))) -> plus(plus(y,s(s(z))),plus(x,s(0())))
      9: rand(x) ->= x
      10: rand(x) ->= rand(s(x))
Number of strict rules: 8
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #minus(s(x),s(y)) -> #minus(x,y)
     #2: #plus(s(x),y) -> #plus(x,y)
     #3: #plus(minus(x,s(0())),minus(y,s(s(z)))) -> #plus(minus(y,s(s(z))),minus(x,s(0())))
     #4: #plus(plus(x,s(0())),plus(y,s(s(z)))) -> #plus(plus(y,s(s(z))),plus(x,s(0())))
     #5: #quot(s(x),s(y)) -> #quot(minus(x,y),s(y))
     #6: #quot(s(x),s(y)) -> #minus(x,y)
Number of SCCs: 3, DPs: 5
  SCC { #1 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  failed.