*** 1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        gcd(x,0()) -> x
        gcd(0(),y) -> y
        gcd(s(x),s(y)) -> if(<(x,y),gcd(s(x),-(y,x)),gcd(-(x,y),s(y)))
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {gcd/2} / {-/2,0/0, c_1(x)
        gcd#(0(),y) -> c_2(y)
        gcd#(s(x),s(y)) -> c_3(x,y,gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y)))
      Weak DPs
        
      
      and mark the set of starting terms.
*** 1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        gcd#(x,0()) -> c_1(x)
        gcd#(0(),y) -> c_2(y)
        gcd#(s(x),s(y)) -> c_3(x,y,gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y)))
      Strict TRS Rules:
        gcd(x,0()) -> x
        gcd(0(),y) -> y
        gcd(s(x),s(y)) -> if(<(x,y),gcd(s(x),-(y,x)),gcd(-(x,y),s(y)))
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {gcd/2,gcd#/2} / {-/2,0/0, c_1(x)
        gcd#(0(),y) -> c_2(y)
        gcd#(s(x),s(y)) -> c_3(x,y,gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y)))
*** 1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        gcd#(x,0()) -> c_1(x)
        gcd#(0(),y) -> c_2(y)
        gcd#(s(x),s(y)) -> c_3(x,y,gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y)))
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {gcd/2,gcd#/2} / {-/2,0/0, c_1(x)
           -->_1 gcd#(s(x),s(y)) -> c_3(x,y,gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y))):3
           -->_1 gcd#(0(),y) -> c_2(y):2
           -->_1 gcd#(x,0()) -> c_1(x):1
        
        2:S:gcd#(0(),y) -> c_2(y)
           -->_1 gcd#(s(x),s(y)) -> c_3(x,y,gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y))):3
           -->_1 gcd#(0(),y) -> c_2(y):2
           -->_1 gcd#(x,0()) -> c_1(x):1
        
        3:S:gcd#(s(x),s(y)) -> c_3(x,y,gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y)))
           -->_2 gcd#(s(x),s(y)) -> c_3(x,y,gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y))):3
           -->_1 gcd#(s(x),s(y)) -> c_3(x,y,gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y))):3
           -->_2 gcd#(0(),y) -> c_2(y):2
           -->_1 gcd#(0(),y) -> c_2(y):2
           -->_2 gcd#(x,0()) -> c_1(x):1
           -->_1 gcd#(x,0()) -> c_1(x):1
        
      Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
        gcd#(s(x),s(y)) -> c_3(x,y)
*** 1.1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        gcd#(x,0()) -> c_1(x)
        gcd#(0(),y) -> c_2(y)
        gcd#(s(x),s(y)) -> c_3(x,y)
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {gcd/2,gcd#/2} / {-/2,0/0, [8] x + [0] 
                      = c_1(x)      
      
          gcd#(0(),y) = [8] y + [11]
                      > [1] y + [1] 
                      = c_2(y)      
      
      gcd#(s(x),s(y)) = [19]        
                      > [6]         
                      = c_3(x,y)    
      
      
      Following rules are (at-least) weakly oriented:
      
*** 1.1.1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        gcd#(x,0()) -> c_1(x)
        gcd#(0(),y) -> c_2(y)
        gcd#(s(x),s(y)) -> c_3(x,y)
      Weak TRS Rules:
        
      Signature:
        {gcd/2,gcd#/2} / {-/2,0/0,