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()))))))
  TDG 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()))))))
   graph:
    log#(s(s(X))) -> log#(s(quot(X,s(s(0()))))) ->
    log#(s(s(X))) -> log#(s(quot(X,s(s(0())))))
    log#(s(s(X))) -> log#(s(quot(X,s(s(0()))))) ->
    log#(s(s(X))) -> quot#(X,s(s(0())))
    log#(s(s(X))) -> quot#(X,s(s(0()))) ->
    quot#(s(X),s(Y)) -> quot#(min(X,Y),s(Y))
    log#(s(s(X))) -> quot#(X,s(s(0()))) ->
    quot#(s(X),s(Y)) -> min#(X,Y)
    quot#(s(X),s(Y)) -> quot#(min(X,Y),s(Y)) ->
    quot#(s(X),s(Y)) -> quot#(min(X,Y),s(Y))
    quot#(s(X),s(Y)) -> quot#(min(X,Y),s(Y)) ->
    quot#(s(X),s(Y)) -> min#(X,Y)
    quot#(s(X),s(Y)) -> min#(X,Y) -> min#(s(X),s(Y)) -> min#(X,Y)
    min#(s(X),s(Y)) -> min#(X,Y) -> min#(s(X),s(Y)) -> min#(X,Y)
   SCC Processor:
    #sccs: 3
    #rules: 3
    #arcs: 8/25
    DPs:
     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()))))))
    KBO Processor:
     argument filtering:
      pi(0) = []
      pi(min) = [0]
      pi(s) = [0]
      pi(quot) = [0]
      pi(log) = [0]
      pi(log#) = 0
     weight function:
      w0 = 1
      w(log#) = w(log) = w(s) = w(0) = 1
      w(quot) = w(min) = 0
     precedence:
      log# ~ log ~ quot ~ min > 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
    
    DPs:
     quot#(s(X),s(Y)) -> quot#(min(X,Y),s(Y))
    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()))))))
    KBO Processor:
     argument filtering:
      pi(0) = []
      pi(min) = 0
      pi(s) = [0]
      pi(quot) = 0
      pi(log) = 0
      pi(quot#) = 0
     weight function:
      w0 = 1
      w(quot#) = w(s) = w(0) = 1
      w(log) = w(quot) = w(min) = 0
     precedence:
      quot# ~ log ~ quot ~ s ~ min ~ 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
    
    DPs:
     min#(s(X),s(Y)) -> min#(X,Y)
    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()))))))
    KBO Processor:
     argument filtering:
      pi(0) = []
      pi(min) = 0
      pi(s) = [0]
      pi(quot) = 0
      pi(log) = [0]
      pi(min#) = 1
     weight function:
      w0 = 1
      w(min#) = w(log) = w(quot) = w(s) = w(min) = w(0) = 1
     precedence:
      min# ~ log ~ quot ~ min ~ 0 > s
     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