YES
Time: 0.034718
TRS:
 {  half 0() -> 0(),
  half s s x -> s half x,
   log s 0() -> 0(),
   log s s x -> s log s half x}
 DP:
  DP:
   {half# s s x -> half# x,
     log# s s x -> half# x,
     log# s s x -> log# s half x}
  TRS:
  {  half 0() -> 0(),
   half s s x -> s half x,
    log s 0() -> 0(),
    log s s x -> s log s half x}
  UR:
   {  half 0() -> 0(),
    half s s x -> s half x}
   EDG:
    {(half# s s x -> half# x, half# s s x -> half# x)
     (log# s s x -> half# x, half# s s x -> half# x)
     (log# s s x -> log# s half x, log# s s x -> half# x)
     (log# s s x -> log# s half x, log# s s x -> log# s half x)}
    STATUS:
     arrows: 0.555556
     SCCS (2):
      Scc:
       {log# s s x -> log# s half x}
      Scc:
       {half# s s x -> half# x}
      
      SCC (1):
       Strict:
        {log# s s x -> log# s half x}
       Weak:
       {  half 0() -> 0(),
        half s s x -> s half x,
         log s 0() -> 0(),
         log s s x -> s log s half x}
       POLY:
        Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
        Interpretation:
         [half](x0) = x0,
         
         [s](x0) = x0 + 1,
         
         [log](x0) = 0,
         
         [0] = 1,
         
         [log#](x0) = x0
        Strict:
         log# s s x -> log# s half x
         2 + 1x >= 1 + 1x
        Weak:
         log s s x -> s log s half x
         0 + 0x >= 1 + 0x
         log s 0() -> 0()
         0 >= 1
         half s s x -> s half x
         2 + 1x >= 1 + 1x
         half 0() -> 0()
         1 >= 1
       Qed
     
     SCC (1):
      Strict:
       {half# s s x -> half# x}
      Weak:
      {  half 0() -> 0(),
       half s s x -> s half x,
        log s 0() -> 0(),
        log s s x -> s log s half x}
      POLY:
       Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
       Interpretation:
        [half](x0) = x0 + 1,
        
        [s](x0) = x0 + 1,
        
        [log](x0) = x0,
        
        [0] = 1,
        
        [half#](x0) = x0
       Strict:
        half# s s x -> half# x
        2 + 1x >= 0 + 1x
       Weak:
        log s s x -> s log s half x
        2 + 1x >= 3 + 1x
        log s 0() -> 0()
        2 >= 1
        half s s x -> s half x
        3 + 1x >= 2 + 1x
        half 0() -> 0()
        2 >= 1
      Qed