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))
 minus(x,0()) -> x
 minus(s(x),s(y)) -> s(minus(x,any(y)))
 gcd(s(x),s(y)) -> gcd(minus(max(x,y),min(x,y)),s(min(x,y)))
 any(s(x)) -> s(s(any(x)))
 any(x) -> x

Proof:
 DP Processor:
  DPs:
   min#(s(x),s(y)) -> min#(x,y)
   max#(s(x),s(y)) -> max#(x,y)
   minus#(s(x),s(y)) -> any#(y)
   minus#(s(x),s(y)) -> minus#(x,any(y))
   gcd#(s(x),s(y)) -> min#(x,y)
   gcd#(s(x),s(y)) -> max#(x,y)
   gcd#(s(x),s(y)) -> minus#(max(x,y),min(x,y))
   gcd#(s(x),s(y)) -> gcd#(minus(max(x,y),min(x,y)),s(min(x,y)))
   any#(s(x)) -> any#(x)
  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))
   minus(x,0()) -> x
   minus(s(x),s(y)) -> s(minus(x,any(y)))
   gcd(s(x),s(y)) -> gcd(minus(max(x,y),min(x,y)),s(min(x,y)))
   any(s(x)) -> s(s(any(x)))
   any(x) -> x
  TDG Processor:
   DPs:
    min#(s(x),s(y)) -> min#(x,y)
    max#(s(x),s(y)) -> max#(x,y)
    minus#(s(x),s(y)) -> any#(y)
    minus#(s(x),s(y)) -> minus#(x,any(y))
    gcd#(s(x),s(y)) -> min#(x,y)
    gcd#(s(x),s(y)) -> max#(x,y)
    gcd#(s(x),s(y)) -> minus#(max(x,y),min(x,y))
    gcd#(s(x),s(y)) -> gcd#(minus(max(x,y),min(x,y)),s(min(x,y)))
    any#(s(x)) -> any#(x)
   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))
    minus(x,0()) -> x
    minus(s(x),s(y)) -> s(minus(x,any(y)))
    gcd(s(x),s(y)) -> gcd(minus(max(x,y),min(x,y)),s(min(x,y)))
    any(s(x)) -> s(s(any(x)))
    any(x) -> x
   graph:
    gcd#(s(x),s(y)) -> gcd#(minus(max(x,y),min(x,y)),s(min(x,y))) ->
    gcd#(s(x),s(y)) -> gcd#(minus(max(x,y),min(x,y)),s(min(x,y)))
    gcd#(s(x),s(y)) -> gcd#(minus(max(x,y),min(x,y)),s(min(x,y))) ->
    gcd#(s(x),s(y)) -> minus#(max(x,y),min(x,y))
    gcd#(s(x),s(y)) -> gcd#(minus(max(x,y),min(x,y)),s(min(x,y))) ->
    gcd#(s(x),s(y)) -> max#(x,y)
    gcd#(s(x),s(y)) -> gcd#(minus(max(x,y),min(x,y)),s(min(x,y))) ->
    gcd#(s(x),s(y)) -> min#(x,y)
    gcd#(s(x),s(y)) -> minus#(max(x,y),min(x,y)) ->
    minus#(s(x),s(y)) -> minus#(x,any(y))
    gcd#(s(x),s(y)) -> minus#(max(x,y),min(x,y)) ->
    minus#(s(x),s(y)) -> any#(y)
    gcd#(s(x),s(y)) -> max#(x,y) -> max#(s(x),s(y)) -> max#(x,y)
    gcd#(s(x),s(y)) -> min#(x,y) -> min#(s(x),s(y)) -> min#(x,y)
    any#(s(x)) -> any#(x) -> any#(s(x)) -> any#(x)
    minus#(s(x),s(y)) -> any#(y) -> any#(s(x)) -> any#(x)
    minus#(s(x),s(y)) -> minus#(x,any(y)) ->
    minus#(s(x),s(y)) -> minus#(x,any(y))
    minus#(s(x),s(y)) -> minus#(x,any(y)) ->
    minus#(s(x),s(y)) -> any#(y)
    max#(s(x),s(y)) -> max#(x,y) -> max#(s(x),s(y)) -> max#(x,y)
    min#(s(x),s(y)) -> min#(x,y) -> min#(s(x),s(y)) -> min#(x,y)
   SCC Processor:
    #sccs: 5
    #rules: 5
    #arcs: 14/81
    DPs:
     gcd#(s(x),s(y)) -> gcd#(minus(max(x,y),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))
     minus(x,0()) -> x
     minus(s(x),s(y)) -> s(minus(x,any(y)))
     gcd(s(x),s(y)) -> gcd(minus(max(x,y),min(x,y)),s(min(x,y)))
     any(s(x)) -> s(s(any(x)))
     any(x) -> x
    Open
    
    DPs:
     minus#(s(x),s(y)) -> minus#(x,any(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))
     minus(x,0()) -> x
     minus(s(x),s(y)) -> s(minus(x,any(y)))
     gcd(s(x),s(y)) -> gcd(minus(max(x,y),min(x,y)),s(min(x,y)))
     any(s(x)) -> s(s(any(x)))
     any(x) -> x
    Subterm Criterion Processor:
     simple projection:
      pi(minus#) = 0
     problem:
      DPs:
       
      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))
       minus(x,0()) -> x
       minus(s(x),s(y)) -> s(minus(x,any(y)))
       gcd(s(x),s(y)) -> gcd(minus(max(x,y),min(x,y)),s(min(x,y)))
       any(s(x)) -> s(s(any(x)))
       any(x) -> x
     Qed
    
    DPs:
     any#(s(x)) -> any#(x)
    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))
     minus(x,0()) -> x
     minus(s(x),s(y)) -> s(minus(x,any(y)))
     gcd(s(x),s(y)) -> gcd(minus(max(x,y),min(x,y)),s(min(x,y)))
     any(s(x)) -> s(s(any(x)))
     any(x) -> x
    Subterm Criterion Processor:
     simple projection:
      pi(any#) = 0
     problem:
      DPs:
       
      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))
       minus(x,0()) -> x
       minus(s(x),s(y)) -> s(minus(x,any(y)))
       gcd(s(x),s(y)) -> gcd(minus(max(x,y),min(x,y)),s(min(x,y)))
       any(s(x)) -> s(s(any(x)))
       any(x) -> x
     Qed
    
    DPs:
     max#(s(x),s(y)) -> max#(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))
     minus(x,0()) -> x
     minus(s(x),s(y)) -> s(minus(x,any(y)))
     gcd(s(x),s(y)) -> gcd(minus(max(x,y),min(x,y)),s(min(x,y)))
     any(s(x)) -> s(s(any(x)))
     any(x) -> x
    Subterm Criterion Processor:
     simple projection:
      pi(max#) = 1
     problem:
      DPs:
       
      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))
       minus(x,0()) -> x
       minus(s(x),s(y)) -> s(minus(x,any(y)))
       gcd(s(x),s(y)) -> gcd(minus(max(x,y),min(x,y)),s(min(x,y)))
       any(s(x)) -> s(s(any(x)))
       any(x) -> x
     Qed
    
    DPs:
     min#(s(x),s(y)) -> 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))
     minus(x,0()) -> x
     minus(s(x),s(y)) -> s(minus(x,any(y)))
     gcd(s(x),s(y)) -> gcd(minus(max(x,y),min(x,y)),s(min(x,y)))
     any(s(x)) -> s(s(any(x)))
     any(x) -> x
    Subterm Criterion Processor:
     simple projection:
      pi(min#) = 1
     problem:
      DPs:
       
      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))
       minus(x,0()) -> x
       minus(s(x),s(y)) -> s(minus(x,any(y)))
       gcd(s(x),s(y)) -> gcd(minus(max(x,y),min(x,y)),s(min(x,y)))
       any(s(x)) -> s(s(any(x)))
       any(x) -> x
     Qed