MAYBE
Time: 0.144798
TRS:
 {            p s x -> x,
              p 0() -> s s 0(),
            p p s x -> p x,
       le(s x, s y) -> le(x, y),
       le(s x, 0()) -> false(),
         le(0(), y) -> true(),
       le(p s x, x) -> le(x, x),
   if(true(), x, y) -> 0(),
  if(false(), x, y) -> s minus(p x, y),
        minus(x, y) -> if(le(x, y), x, y)}
 DP:
  DP:
   {          p# p s x -> p# x,
         le#(s x, s y) -> le#(x, y),
         le#(p s x, x) -> le#(x, x),
    if#(false(), x, y) -> p# x,
    if#(false(), x, y) -> minus#(p x, y),
          minus#(x, y) -> le#(x, y),
          minus#(x, y) -> if#(le(x, y), x, y)}
  TRS:
  {            p s x -> x,
               p 0() -> s s 0(),
             p p s x -> p x,
        le(s x, s y) -> le(x, y),
        le(s x, 0()) -> false(),
          le(0(), y) -> true(),
        le(p s x, x) -> le(x, x),
    if(true(), x, y) -> 0(),
   if(false(), x, y) -> s minus(p x, y),
         minus(x, y) -> if(le(x, y), x, y)}
  UR:
   {       p s x -> x,
           p 0() -> s s 0(),
         p p s x -> p x,
    le(s x, s y) -> le(x, y),
    le(s x, 0()) -> false(),
      le(0(), y) -> true(),
    le(p s x, x) -> le(x, x),
         a(z, w) -> z,
         a(z, w) -> w}
   EDG:
    {(le#(p s x, x) -> le#(x, x), le#(p s x, x) -> le#(x, x))
     (le#(p s x, x) -> le#(x, x), le#(s x, s y) -> le#(x, y))
     (p# p s x -> p# x, p# p s x -> p# x)
     (le#(s x, s y) -> le#(x, y), le#(p s x, x) -> le#(x, x))
     (le#(s x, s y) -> le#(x, y), le#(s x, s y) -> le#(x, y))
     (minus#(x, y) -> le#(x, y), le#(s x, s y) -> le#(x, y))
     (minus#(x, y) -> le#(x, y), le#(p s x, x) -> le#(x, x))
     (if#(false(), x, y) -> p# x, p# p s x -> p# x)
     (minus#(x, y) -> if#(le(x, y), x, y), if#(false(), x, y) -> p# x)
     (minus#(x, y) -> if#(le(x, y), x, y), if#(false(), x, y) -> minus#(p x, y))
     (if#(false(), x, y) -> minus#(p x, y), minus#(x, y) -> le#(x, y))
     (if#(false(), x, y) -> minus#(p x, y), minus#(x, y) -> if#(le(x, y), x, y))}
    STATUS:
     arrows: 0.755102
     SCCS (3):
      Scc:
       {if#(false(), x, y) -> minus#(p x, y),
              minus#(x, y) -> if#(le(x, y), x, y)}
      Scc:
       {p# p s x -> p# x}
      Scc:
       {le#(s x, s y) -> le#(x, y),
        le#(p s x, x) -> le#(x, x)}
      
      SCC (2):
       Strict:
        {if#(false(), x, y) -> minus#(p x, y),
               minus#(x, y) -> if#(le(x, y), x, y)}
       Weak:
       {            p s x -> x,
                    p 0() -> s s 0(),
                  p p s x -> p x,
             le(s x, s y) -> le(x, y),
             le(s x, 0()) -> false(),
               le(0(), y) -> true(),
             le(p s x, x) -> le(x, x),
         if(true(), x, y) -> 0(),
        if(false(), x, y) -> s minus(p x, y),
              minus(x, y) -> if(le(x, y), x, y)}
       Fail
      
      SCC (1):
       Strict:
        {p# p s x -> p# x}
       Weak:
       {            p s x -> x,
                    p 0() -> s s 0(),
                  p p s x -> p x,
             le(s x, s y) -> le(x, y),
             le(s x, 0()) -> false(),
               le(0(), y) -> true(),
             le(p s x, x) -> le(x, x),
         if(true(), x, y) -> 0(),
        if(false(), x, y) -> s minus(p x, y),
              minus(x, y) -> if(le(x, y), x, y)}
       POLY:
        Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
        Interpretation:
         [if](x0, x1, x2) = x0 + x1,
         
         [le](x0, x1) = x0 + 1,
         
         [minus](x0, x1) = x0 + 1,
         
         [s](x0) = x0 + 1,
         
         [p](x0) = x0 + 1,
         
         [0] = 1,
         
         [true] = 0,
         
         [false] = 1,
         
         [p#](x0) = x0
        Strict:
         p# p s x -> p# x
         2 + 1x >= 0 + 1x
        Weak:
         minus(x, y) -> if(le(x, y), x, y)
         1 + 1x + 0y >= 1 + 2x + 0y
         if(false(), x, y) -> s minus(p x, y)
         1 + 1x + 0y >= 3 + 1x + 0y
         if(true(), x, y) -> 0()
         0 + 1x + 0y >= 1
         le(p s x, x) -> le(x, x)
         3 + 1x >= 1 + 1x
         le(0(), y) -> true()
         2 + 0y >= 0
         le(s x, 0()) -> false()
         2 + 1x >= 1
         le(s x, s y) -> le(x, y)
         2 + 1x + 0y >= 1 + 1x + 0y
         p p s x -> p x
         3 + 1x >= 1 + 1x
         p 0() -> s s 0()
         2 >= 3
         p s x -> x
         2 + 1x >= 1x
       Qed
     
     SCC (2):
      Strict:
       {le#(s x, s y) -> le#(x, y),
        le#(p s x, x) -> le#(x, x)}
      Weak:
      {            p s x -> x,
                   p 0() -> s s 0(),
                 p p s x -> p x,
            le(s x, s y) -> le(x, y),
            le(s x, 0()) -> false(),
              le(0(), y) -> true(),
            le(p s x, x) -> le(x, x),
        if(true(), x, y) -> 0(),
       if(false(), x, y) -> s minus(p x, y),
             minus(x, y) -> if(le(x, y), x, y)}
      POLY:
       Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
       Interpretation:
        [if](x0, x1, x2) = 0,
        
        [le](x0, x1) = x0 + 1,
        
        [minus](x0, x1) = 0,
        
        [s](x0) = x0 + 1,
        
        [p](x0) = 0,
        
        [0] = 1,
        
        [true] = 0,
        
        [false] = 0,
        
        [le#](x0, x1) = x0
       Strict:
        le#(p s x, x) -> le#(x, x)
        0 + 1x >= 0 + 1x
        le#(s x, s y) -> le#(x, y)
        1 + 0x + 1y >= 0 + 0x + 1y
       Weak:
        minus(x, y) -> if(le(x, y), x, y)
        0 + 0x + 0y >= 0 + 0x + 0y
        if(false(), x, y) -> s minus(p x, y)
        0 + 0x + 0y >= 1 + 0x + 0y
        if(true(), x, y) -> 0()
        0 + 0x + 0y >= 1
        le(p s x, x) -> le(x, x)
        1 + 0x >= 1 + 1x
        le(0(), y) -> true()
        2 + 0y >= 0
        le(s x, 0()) -> false()
        2 + 1x >= 0
        le(s x, s y) -> le(x, y)
        2 + 1x + 0y >= 1 + 1x + 0y
        p p s x -> p x
        0 + 0x >= 0 + 0x
        p 0() -> s s 0()
        0 >= 3
        p s x -> x
        0 + 0x >= 1x
      SCCS (1):
       Scc:
        {le#(p s x, x) -> le#(x, x)}
       
       SCC (1):
        Strict:
         {le#(p s x, x) -> le#(x, x)}
        Weak:
        {            p s x -> x,
                     p 0() -> s s 0(),
                   p p s x -> p x,
              le(s x, s y) -> le(x, y),
              le(s x, 0()) -> false(),
                le(0(), y) -> true(),
              le(p s x, x) -> le(x, x),
          if(true(), x, y) -> 0(),
         if(false(), x, y) -> s minus(p x, y),
               minus(x, y) -> if(le(x, y), x, y)}
        POLY:
         Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
         Interpretation:
          [if](x0, x1, x2) = 0,
          
          [le](x0, x1) = x0 + 1,
          
          [minus](x0, x1) = 0,
          
          [s](x0) = x0 + 1,
          
          [p](x0) = x0,
          
          [0] = 1,
          
          [true] = 0,
          
          [false] = 0,
          
          [le#](x0, x1) = x0 + x1
         Strict:
          le#(p s x, x) -> le#(x, x)
          1 + 2x >= 0 + 2x
         Weak:
          minus(x, y) -> if(le(x, y), x, y)
          0 + 0x + 0y >= 0 + 0x + 0y
          if(false(), x, y) -> s minus(p x, y)
          0 + 0x + 0y >= 1 + 0x + 0y
          if(true(), x, y) -> 0()
          0 + 0x + 0y >= 1
          le(p s x, x) -> le(x, x)
          2 + 1x >= 1 + 1x
          le(0(), y) -> true()
          2 + 0y >= 0
          le(s x, 0()) -> false()
          2 + 1x >= 0
          le(s x, s y) -> le(x, y)
          2 + 1x + 0y >= 1 + 1x + 0y
          p p s x -> p x
          1 + 1x >= 0 + 1x
          p 0() -> s s 0()
          1 >= 3
          p s x -> x
          1 + 1x >= 1x
        Qed