MAYBE

Problem:
 plus(0(),Y) -> Y
 plus(s(X),Y) -> s(plus(X,Y))
 min(X,0()) -> X
 min(s(X),s(Y)) -> min(X,Y)
 min(min(X,Y),Z()) -> min(X,plus(Y,Z()))
 quot(0(),s(Y)) -> 0()
 quot(s(X),s(Y)) -> s(quot(min(X,Y),s(Y)))

Proof:
 DP Processor:
  DPs:
   plus#(s(X),Y) -> plus#(X,Y)
   min#(s(X),s(Y)) -> min#(X,Y)
   min#(min(X,Y),Z()) -> plus#(Y,Z())
   min#(min(X,Y),Z()) -> min#(X,plus(Y,Z()))
   quot#(s(X),s(Y)) -> min#(X,Y)
   quot#(s(X),s(Y)) -> quot#(min(X,Y),s(Y))
  TRS:
   plus(0(),Y) -> Y
   plus(s(X),Y) -> s(plus(X,Y))
   min(X,0()) -> X
   min(s(X),s(Y)) -> min(X,Y)
   min(min(X,Y),Z()) -> min(X,plus(Y,Z()))
   quot(0(),s(Y)) -> 0()
   quot(s(X),s(Y)) -> s(quot(min(X,Y),s(Y)))
  Open