MAYBE

Problem:
 min(x,0()) -> 0()
 min(0(),y) -> 0()
 min(s(x),s(y)) -> s(min(x,y))
 max(x,0()) -> x
 max(0(),y) -> y
 max(s(x),s(y)) -> s(max(x,y))
 -(x,0()) -> x
 -(s(x),s(y)) -> -(x,y)
 gcd(s(x),s(y)) -> gcd(-(s(max(x,y)),s(min(x,y))),s(min(x,y)))
 gcd(s(x),0()) -> s(x)
 gcd(0(),s(y)) -> s(y)

Proof:
 DP Processor:
  DPs:
   min#(s(x),s(y)) -> min#(x,y)
   max#(s(x),s(y)) -> max#(x,y)
   -#(s(x),s(y)) -> -#(x,y)
   gcd#(s(x),s(y)) -> min#(x,y)
   gcd#(s(x),s(y)) -> max#(x,y)
   gcd#(s(x),s(y)) -> -#(s(max(x,y)),s(min(x,y)))
   gcd#(s(x),s(y)) -> gcd#(-(s(max(x,y)),s(min(x,y))),s(min(x,y)))
  TRS:
   min(x,0()) -> 0()
   min(0(),y) -> 0()
   min(s(x),s(y)) -> s(min(x,y))
   max(x,0()) -> x
   max(0(),y) -> y
   max(s(x),s(y)) -> s(max(x,y))
   -(x,0()) -> x
   -(s(x),s(y)) -> -(x,y)
   gcd(s(x),s(y)) -> gcd(-(s(max(x,y)),s(min(x,y))),s(min(x,y)))
   gcd(s(x),0()) -> s(x)
   gcd(0(),s(y)) -> s(y)
  Usable Rule Processor:
   DPs:
    min#(s(x),s(y)) -> min#(x,y)
    max#(s(x),s(y)) -> max#(x,y)
    -#(s(x),s(y)) -> -#(x,y)
    gcd#(s(x),s(y)) -> min#(x,y)
    gcd#(s(x),s(y)) -> max#(x,y)
    gcd#(s(x),s(y)) -> -#(s(max(x,y)),s(min(x,y)))
    gcd#(s(x),s(y)) -> gcd#(-(s(max(x,y)),s(min(x,y))),s(min(x,y)))
   TRS:
    min(x,0()) -> 0()
    min(0(),y) -> 0()
    min(s(x),s(y)) -> s(min(x,y))
    max(x,0()) -> x
    max(0(),y) -> y
    max(s(x),s(y)) -> s(max(x,y))
    -(s(x),s(y)) -> -(x,y)
    -(x,0()) -> x
   Open