YES

Problem:
 min(X,0()) -> X
 min(s(X),s(Y)) -> min(X,Y)
 quot(0(),s(Y)) -> 0()
 quot(s(X),s(Y)) -> s(quot(min(X,Y),s(Y)))
 log(s(0())) -> 0()
 log(s(s(X))) -> s(log(s(quot(X,s(s(0()))))))

Proof:
 DP Processor:
  DPs:
   min#(s(X),s(Y)) -> min#(X,Y)
   quot#(s(X),s(Y)) -> min#(X,Y)
   quot#(s(X),s(Y)) -> quot#(min(X,Y),s(Y))
   log#(s(s(X))) -> quot#(X,s(s(0())))
   log#(s(s(X))) -> log#(s(quot(X,s(s(0())))))
  TRS:
   min(X,0()) -> X
   min(s(X),s(Y)) -> min(X,Y)
   quot(0(),s(Y)) -> 0()
   quot(s(X),s(Y)) -> s(quot(min(X,Y),s(Y)))
   log(s(0())) -> 0()
   log(s(s(X))) -> s(log(s(quot(X,s(s(0()))))))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [log#](x0) = 2x0,
    
    [quot#](x0, x1) = 5x0 + x1,
    
    [min#](x0, x1) = x1,
    
    [log](x0) = 6x0 + 5,
    
    [quot](x0, x1) = x0,
    
    [s](x0) = 2x0 + 1,
    
    [min](x0, x1) = x0,
    
    [0] = 0
   orientation:
    min#(s(X),s(Y)) = 2Y + 1 >= Y = min#(X,Y)
    
    quot#(s(X),s(Y)) = 10X + 2Y + 6 >= Y = min#(X,Y)
    
    quot#(s(X),s(Y)) = 10X + 2Y + 6 >= 5X + 2Y + 1 = quot#(min(X,Y),s(Y))
    
    log#(s(s(X))) = 8X + 6 >= 5X + 3 = quot#(X,s(s(0())))
    
    log#(s(s(X))) = 8X + 6 >= 4X + 2 = log#(s(quot(X,s(s(0())))))
    
    min(X,0()) = X >= X = X
    
    min(s(X),s(Y)) = 2X + 1 >= X = min(X,Y)
    
    quot(0(),s(Y)) = 0 >= 0 = 0()
    
    quot(s(X),s(Y)) = 2X + 1 >= 2X + 1 = s(quot(min(X,Y),s(Y)))
    
    log(s(0())) = 11 >= 0 = 0()
    
    log(s(s(X))) = 24X + 23 >= 24X + 23 = s(log(s(quot(X,s(s(0()))))))
   problem:
    DPs:
     
    TRS:
     min(X,0()) -> X
     min(s(X),s(Y)) -> min(X,Y)
     quot(0(),s(Y)) -> 0()
     quot(s(X),s(Y)) -> s(quot(min(X,Y),s(Y)))
     log(s(0())) -> 0()
     log(s(s(X))) -> s(log(s(quot(X,s(s(0()))))))
   Qed