YES

Problem:
 minus(X,s(Y)) -> pred(minus(X,Y))
 minus(X,0()) -> X
 pred(s(X)) -> X
 le(s(X),s(Y)) -> le(X,Y)
 le(s(X),0()) -> false()
 le(0(),Y) -> true()
 gcd(0(),Y) -> 0()
 gcd(s(X),0()) -> s(X)
 gcd(s(X),s(Y)) -> if(le(Y,X),s(X),s(Y))
 if(true(),s(X),s(Y)) -> gcd(minus(X,Y),s(Y))
 if(false(),s(X),s(Y)) -> gcd(minus(Y,X),s(X))

Proof:
 DP Processor:
  DPs:
   minus#(X,s(Y)) -> minus#(X,Y)
   minus#(X,s(Y)) -> pred#(minus(X,Y))
   le#(s(X),s(Y)) -> le#(X,Y)
   gcd#(s(X),s(Y)) -> le#(Y,X)
   gcd#(s(X),s(Y)) -> if#(le(Y,X),s(X),s(Y))
   if#(true(),s(X),s(Y)) -> minus#(X,Y)
   if#(true(),s(X),s(Y)) -> gcd#(minus(X,Y),s(Y))
   if#(false(),s(X),s(Y)) -> minus#(Y,X)
   if#(false(),s(X),s(Y)) -> gcd#(minus(Y,X),s(X))
  TRS:
   minus(X,s(Y)) -> pred(minus(X,Y))
   minus(X,0()) -> X
   pred(s(X)) -> X
   le(s(X),s(Y)) -> le(X,Y)
   le(s(X),0()) -> false()
   le(0(),Y) -> true()
   gcd(0(),Y) -> 0()
   gcd(s(X),0()) -> s(X)
   gcd(s(X),s(Y)) -> if(le(Y,X),s(X),s(Y))
   if(true(),s(X),s(Y)) -> gcd(minus(X,Y),s(Y))
   if(false(),s(X),s(Y)) -> gcd(minus(Y,X),s(X))
  TDG Processor:
   DPs:
    minus#(X,s(Y)) -> minus#(X,Y)
    minus#(X,s(Y)) -> pred#(minus(X,Y))
    le#(s(X),s(Y)) -> le#(X,Y)
    gcd#(s(X),s(Y)) -> le#(Y,X)
    gcd#(s(X),s(Y)) -> if#(le(Y,X),s(X),s(Y))
    if#(true(),s(X),s(Y)) -> minus#(X,Y)
    if#(true(),s(X),s(Y)) -> gcd#(minus(X,Y),s(Y))
    if#(false(),s(X),s(Y)) -> minus#(Y,X)
    if#(false(),s(X),s(Y)) -> gcd#(minus(Y,X),s(X))
   TRS:
    minus(X,s(Y)) -> pred(minus(X,Y))
    minus(X,0()) -> X
    pred(s(X)) -> X
    le(s(X),s(Y)) -> le(X,Y)
    le(s(X),0()) -> false()
    le(0(),Y) -> true()
    gcd(0(),Y) -> 0()
    gcd(s(X),0()) -> s(X)
    gcd(s(X),s(Y)) -> if(le(Y,X),s(X),s(Y))
    if(true(),s(X),s(Y)) -> gcd(minus(X,Y),s(Y))
    if(false(),s(X),s(Y)) -> gcd(minus(Y,X),s(X))
   graph:
    if#(true(),s(X),s(Y)) -> gcd#(minus(X,Y),s(Y)) ->
    gcd#(s(X),s(Y)) -> if#(le(Y,X),s(X),s(Y))
    if#(true(),s(X),s(Y)) -> gcd#(minus(X,Y),s(Y)) ->
    gcd#(s(X),s(Y)) -> le#(Y,X)
    if#(true(),s(X),s(Y)) -> minus#(X,Y) ->
    minus#(X,s(Y)) -> pred#(minus(X,Y))
    if#(true(),s(X),s(Y)) -> minus#(X,Y) ->
    minus#(X,s(Y)) -> minus#(X,Y)
    if#(false(),s(X),s(Y)) -> gcd#(minus(Y,X),s(X)) ->
    gcd#(s(X),s(Y)) -> if#(le(Y,X),s(X),s(Y))
    if#(false(),s(X),s(Y)) -> gcd#(minus(Y,X),s(X)) ->
    gcd#(s(X),s(Y)) -> le#(Y,X)
    if#(false(),s(X),s(Y)) -> minus#(Y,X) ->
    minus#(X,s(Y)) -> pred#(minus(X,Y))
    if#(false(),s(X),s(Y)) -> minus#(Y,X) ->
    minus#(X,s(Y)) -> minus#(X,Y)
    gcd#(s(X),s(Y)) -> if#(le(Y,X),s(X),s(Y)) ->
    if#(false(),s(X),s(Y)) -> gcd#(minus(Y,X),s(X))
    gcd#(s(X),s(Y)) -> if#(le(Y,X),s(X),s(Y)) ->
    if#(false(),s(X),s(Y)) -> minus#(Y,X)
    gcd#(s(X),s(Y)) -> if#(le(Y,X),s(X),s(Y)) ->
    if#(true(),s(X),s(Y)) -> gcd#(minus(X,Y),s(Y))
    gcd#(s(X),s(Y)) -> if#(le(Y,X),s(X),s(Y)) ->
    if#(true(),s(X),s(Y)) -> minus#(X,Y)
    gcd#(s(X),s(Y)) -> le#(Y,X) -> le#(s(X),s(Y)) -> le#(X,Y)
    le#(s(X),s(Y)) -> le#(X,Y) -> le#(s(X),s(Y)) -> le#(X,Y)
    minus#(X,s(Y)) -> minus#(X,Y) ->
    minus#(X,s(Y)) -> pred#(minus(X,Y))
    minus#(X,s(Y)) -> minus#(X,Y) -> minus#(X,s(Y)) -> minus#(X,Y)
   SCC Processor:
    #sccs: 3
    #rules: 5
    #arcs: 16/81
    DPs:
     if#(true(),s(X),s(Y)) -> gcd#(minus(X,Y),s(Y))
     gcd#(s(X),s(Y)) -> if#(le(Y,X),s(X),s(Y))
     if#(false(),s(X),s(Y)) -> gcd#(minus(Y,X),s(X))
    TRS:
     minus(X,s(Y)) -> pred(minus(X,Y))
     minus(X,0()) -> X
     pred(s(X)) -> X
     le(s(X),s(Y)) -> le(X,Y)
     le(s(X),0()) -> false()
     le(0(),Y) -> true()
     gcd(0(),Y) -> 0()
     gcd(s(X),0()) -> s(X)
     gcd(s(X),s(Y)) -> if(le(Y,X),s(X),s(Y))
     if(true(),s(X),s(Y)) -> gcd(minus(X,Y),s(Y))
     if(false(),s(X),s(Y)) -> gcd(minus(Y,X),s(X))
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [if#](x0, x1, x2) = x0 + 1x1 + x2,
      
      [gcd#](x0, x1) = 1x0 + x1,
      
      [if](x0, x1, x2) = x0 + 1x1 + x2 + 4,
      
      [gcd](x0, x1) = 1x0 + x1 + 4,
      
      [true] = 0,
      
      [false] = 0,
      
      [le](x0, x1) = x0 + 2x1,
      
      [0] = 3,
      
      [pred](x0) = x0,
      
      [minus](x0, x1) = x0 + 1x1,
      
      [s](x0) = 2x0
     orientation:
      if#(true(),s(X),s(Y)) = 3X + 2Y + 0 >= 1X + 2Y = gcd#(minus(X,Y),s(Y))
      
      gcd#(s(X),s(Y)) = 3X + 2Y >= 3X + 2Y = if#(le(Y,X),s(X),s(Y))
      
      if#(false(),s(X),s(Y)) = 3X + 2Y + 0 >= 2X + 1Y = gcd#(minus(Y,X),s(X))
      
      minus(X,s(Y)) = X + 3Y >= X + 1Y = pred(minus(X,Y))
      
      minus(X,0()) = X + 4 >= X = X
      
      pred(s(X)) = 2X >= X = X
      
      le(s(X),s(Y)) = 2X + 4Y >= X + 2Y = le(X,Y)
      
      le(s(X),0()) = 2X + 5 >= 0 = false()
      
      le(0(),Y) = 2Y + 3 >= 0 = true()
      
      gcd(0(),Y) = Y + 4 >= 3 = 0()
      
      gcd(s(X),0()) = 3X + 4 >= 2X = s(X)
      
      gcd(s(X),s(Y)) = 3X + 2Y + 4 >= 3X + 2Y + 4 = if(le(Y,X),s(X),s(Y))
      
      if(true(),s(X),s(Y)) = 3X + 2Y + 4 >= 1X + 2Y + 4 = gcd(minus(X,Y),s(Y))
      
      if(false(),s(X),s(Y)) = 3X + 2Y + 4 >= 2X + 1Y + 4 = gcd(minus(Y,X),s(X))
     problem:
      DPs:
       if#(true(),s(X),s(Y)) -> gcd#(minus(X,Y),s(Y))
       gcd#(s(X),s(Y)) -> if#(le(Y,X),s(X),s(Y))
      TRS:
       minus(X,s(Y)) -> pred(minus(X,Y))
       minus(X,0()) -> X
       pred(s(X)) -> X
       le(s(X),s(Y)) -> le(X,Y)
       le(s(X),0()) -> false()
       le(0(),Y) -> true()
       gcd(0(),Y) -> 0()
       gcd(s(X),0()) -> s(X)
       gcd(s(X),s(Y)) -> if(le(Y,X),s(X),s(Y))
       if(true(),s(X),s(Y)) -> gcd(minus(X,Y),s(Y))
       if(false(),s(X),s(Y)) -> gcd(minus(Y,X),s(X))
     Arctic Interpretation Processor:
      dimension: 1
      interpretation:
       [if#](x0, x1, x2) = x0 + x1 + 0,
       
       [gcd#](x0, x1) = x0 + 0,
       
       [if](x0, x1, x2) = x0 + x1 + x2 + 0,
       
       [gcd](x0, x1) = 1x0 + x1 + 0,
       
       [true] = 0,
       
       [false] = 0,
       
       [le](x0, x1) = x1 + 0,
       
       [0] = 2,
       
       [pred](x0) = x0 + 0,
       
       [minus](x0, x1) = x0 + 0,
       
       [s](x0) = 1x0 + 1
      orientation:
       if#(true(),s(X),s(Y)) = 1X + 1 >= X + 0 = gcd#(minus(X,Y),s(Y))
       
       gcd#(s(X),s(Y)) = 1X + 1 >= 1X + 1 = if#(le(Y,X),s(X),s(Y))
       
       minus(X,s(Y)) = X + 0 >= X + 0 = pred(minus(X,Y))
       
       minus(X,0()) = X + 0 >= X = X
       
       pred(s(X)) = 1X + 1 >= X = X
       
       le(s(X),s(Y)) = 1Y + 1 >= Y + 0 = le(X,Y)
       
       le(s(X),0()) = 2 >= 0 = false()
       
       le(0(),Y) = Y + 0 >= 0 = true()
       
       gcd(0(),Y) = Y + 3 >= 2 = 0()
       
       gcd(s(X),0()) = 2X + 2 >= 1X + 1 = s(X)
       
       gcd(s(X),s(Y)) = 2X + 1Y + 2 >= 1X + 1Y + 1 = if(le(Y,X),s(X),s(Y))
       
       if(true(),s(X),s(Y)) = 1X + 1Y + 1 >= 1X + 1Y + 1 = gcd(minus(X,Y),s(Y))
       
       if(false(),s(X),s(Y)) = 1X + 1Y + 1 >= 1X + 1Y + 1 = gcd(minus(Y,X),s(X))
      problem:
       DPs:
        gcd#(s(X),s(Y)) -> if#(le(Y,X),s(X),s(Y))
       TRS:
        minus(X,s(Y)) -> pred(minus(X,Y))
        minus(X,0()) -> X
        pred(s(X)) -> X
        le(s(X),s(Y)) -> le(X,Y)
        le(s(X),0()) -> false()
        le(0(),Y) -> true()
        gcd(0(),Y) -> 0()
        gcd(s(X),0()) -> s(X)
        gcd(s(X),s(Y)) -> if(le(Y,X),s(X),s(Y))
        if(true(),s(X),s(Y)) -> gcd(minus(X,Y),s(Y))
        if(false(),s(X),s(Y)) -> gcd(minus(Y,X),s(X))
      SCC Processor:
       #sccs: 0
       #rules: 0
       #arcs: 4/1
       
    
    DPs:
     minus#(X,s(Y)) -> minus#(X,Y)
    TRS:
     minus(X,s(Y)) -> pred(minus(X,Y))
     minus(X,0()) -> X
     pred(s(X)) -> X
     le(s(X),s(Y)) -> le(X,Y)
     le(s(X),0()) -> false()
     le(0(),Y) -> true()
     gcd(0(),Y) -> 0()
     gcd(s(X),0()) -> s(X)
     gcd(s(X),s(Y)) -> if(le(Y,X),s(X),s(Y))
     if(true(),s(X),s(Y)) -> gcd(minus(X,Y),s(Y))
     if(false(),s(X),s(Y)) -> gcd(minus(Y,X),s(X))
    Subterm Criterion Processor:
     simple projection:
      pi(minus#) = 1
     problem:
      DPs:
       
      TRS:
       minus(X,s(Y)) -> pred(minus(X,Y))
       minus(X,0()) -> X
       pred(s(X)) -> X
       le(s(X),s(Y)) -> le(X,Y)
       le(s(X),0()) -> false()
       le(0(),Y) -> true()
       gcd(0(),Y) -> 0()
       gcd(s(X),0()) -> s(X)
       gcd(s(X),s(Y)) -> if(le(Y,X),s(X),s(Y))
       if(true(),s(X),s(Y)) -> gcd(minus(X,Y),s(Y))
       if(false(),s(X),s(Y)) -> gcd(minus(Y,X),s(X))
     Qed
    
    DPs:
     le#(s(X),s(Y)) -> le#(X,Y)
    TRS:
     minus(X,s(Y)) -> pred(minus(X,Y))
     minus(X,0()) -> X
     pred(s(X)) -> X
     le(s(X),s(Y)) -> le(X,Y)
     le(s(X),0()) -> false()
     le(0(),Y) -> true()
     gcd(0(),Y) -> 0()
     gcd(s(X),0()) -> s(X)
     gcd(s(X),s(Y)) -> if(le(Y,X),s(X),s(Y))
     if(true(),s(X),s(Y)) -> gcd(minus(X,Y),s(Y))
     if(false(),s(X),s(Y)) -> gcd(minus(Y,X),s(X))
    Subterm Criterion Processor:
     simple projection:
      pi(le#) = 1
     problem:
      DPs:
       
      TRS:
       minus(X,s(Y)) -> pred(minus(X,Y))
       minus(X,0()) -> X
       pred(s(X)) -> X
       le(s(X),s(Y)) -> le(X,Y)
       le(s(X),0()) -> false()
       le(0(),Y) -> true()
       gcd(0(),Y) -> 0()
       gcd(s(X),0()) -> s(X)
       gcd(s(X),s(Y)) -> if(le(Y,X),s(X),s(Y))
       if(true(),s(X),s(Y)) -> gcd(minus(X,Y),s(Y))
       if(false(),s(X),s(Y)) -> gcd(minus(Y,X),s(X))
     Qed