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)))

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)))
  TDG 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)))
   graph:
    gcd#(s(x),s(y)) -> gcd#(-(s(max(x,y)),s(min(x,y))),s(min(x,y))) ->
    gcd#(s(x),s(y)) -> gcd#(-(s(max(x,y)),s(min(x,y))),s(min(x,y)))
    gcd#(s(x),s(y)) -> gcd#(-(s(max(x,y)),s(min(x,y))),s(min(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))) ->
    gcd#(s(x),s(y)) -> max#(x,y)
    gcd#(s(x),s(y)) -> gcd#(-(s(max(x,y)),s(min(x,y))),s(min(x,y))) ->
    gcd#(s(x),s(y)) -> min#(x,y)
    gcd#(s(x),s(y)) -> -#(s(max(x,y)),s(min(x,y))) ->
    -#(s(x),s(y)) -> -#(x,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)
    -#(s(x),s(y)) -> -#(x,y) -> -#(s(x),s(y)) -> -#(x,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: 4
    #rules: 4
    #arcs: 10/49
    DPs:
     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)))
    Open
    
    DPs:
     -#(s(x),s(y)) -> -#(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)))
    KBO Processor:
     argument filtering:
      pi(0) = []
      pi(min) = [0,1]
      pi(s) = [0]
      pi(max) = [0,1]
      pi(-) = [0]
      pi(gcd) = []
      pi(-#) = 0
     weight function:
      w0 = 1
      w(-#) = w(gcd) = w(s) = w(0) = 1
      w(-) = w(max) = w(min) = 0
     precedence:
      -# ~ gcd ~ - ~ max ~ s ~ min ~ 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))
       -(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)))
     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))
     -(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)))
    KBO Processor:
     argument filtering:
      pi(0) = []
      pi(min) = [0,1]
      pi(s) = [0]
      pi(max) = [0,1]
      pi(-) = [0]
      pi(gcd) = []
      pi(max#) = 0
     weight function:
      w0 = 1
      w(max#) = w(gcd) = w(s) = w(0) = 1
      w(-) = w(max) = w(min) = 0
     precedence:
      max# ~ gcd ~ - ~ max ~ s ~ min ~ 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))
       -(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)))
     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))
     -(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)))
    KBO Processor:
     argument filtering:
      pi(0) = []
      pi(min) = [0,1]
      pi(s) = [0]
      pi(max) = [0,1]
      pi(-) = [0]
      pi(gcd) = []
      pi(min#) = 0
     weight function:
      w0 = 1
      w(min#) = w(gcd) = w(s) = w(0) = 1
      w(-) = w(max) = w(min) = 0
     precedence:
      min# ~ gcd ~ - ~ max ~ s ~ min ~ 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))
       -(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)))
     Qed