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))
    Usable Rule Processor:
     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()
     Arctic Interpretation Processor:
      dimension: 1
      usable rules:
       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()
      interpretation:
       [if#](x0, x1, x2) = x0 + 1x1 + x2 + 0,
       
       [gcd#](x0, x1) = 1x0 + x1 + 2,
       
       [true] = 2,
       
       [false] = 7,
       
       [le](x0, x1) = x0 + 2x1 + 0,
       
       [0] = 5,
       
       [pred](x0) = x0 + 0,
       
       [minus](x0, x1) = x0 + 1,
       
       [s](x0) = 2x0
      orientation:
       if#(true(),s(X),s(Y)) = 3X + 2Y + 2 >= 1X + 2Y + 2 = gcd#(minus(X,Y),s(Y))
       
       gcd#(s(X),s(Y)) = 3X + 2Y + 2 >= 3X + 2Y + 0 = if#(le(Y,X),s(X),s(Y))
       
       if#(false(),s(X),s(Y)) = 3X + 2Y + 7 >= 2X + 1Y + 2 = gcd#(minus(Y,X),s(X))
       
       minus(X,s(Y)) = X + 1 >= X + 1 = pred(minus(X,Y))
       
       minus(X,0()) = X + 1 >= X = X
       
       pred(s(X)) = 2X + 0 >= X = X
       
       le(s(X),s(Y)) = 2X + 4Y + 0 >= X + 2Y + 0 = le(X,Y)
       
       le(s(X),0()) = 2X + 7 >= 7 = false()
       
       le(0(),Y) = 2Y + 5 >= 2 = true()
      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()
      Restore Modifier:
       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))
       Usable Rule Processor:
        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()
        Arctic Interpretation Processor:
         dimension: 1
         usable rules:
          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()
         interpretation:
          [if#](x0, x1, x2) = x0 + 3x1 + 0,
          
          [gcd#](x0, x1) = 4x0 + 0,
          
          [true] = 1,
          
          [false] = 1,
          
          [le](x0, x1) = 4x1 + 1,
          
          [0] = 0,
          
          [pred](x0) = x0 + 0,
          
          [minus](x0, x1) = 1x0 + 0,
          
          [s](x0) = 2x0 + 1
         orientation:
          if#(true(),s(X),s(Y)) = 5X + 4 >= 5X + 4 = gcd#(minus(X,Y),s(Y))
          
          gcd#(s(X),s(Y)) = 6X + 5 >= 5X + 4 = if#(le(Y,X),s(X),s(Y))
          
          minus(X,s(Y)) = 1X + 0 >= 1X + 0 = pred(minus(X,Y))
          
          minus(X,0()) = 1X + 0 >= X = X
          
          pred(s(X)) = 2X + 1 >= X = X
          
          le(s(X),s(Y)) = 6Y + 5 >= 4Y + 1 = le(X,Y)
          
          le(s(X),0()) = 4 >= 1 = false()
          
          le(0(),Y) = 4Y + 1 >= 1 = true()
         problem:
          DPs:
           if#(true(),s(X),s(Y)) -> gcd#(minus(X,Y),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()
         Restore Modifier:
          DPs:
           if#(true(),s(X),s(Y)) -> gcd#(minus(X,Y),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