MAYBE
Time: 0.096222
TRS:
 { cond2(true(), x, y, z) -> cond2(gr(y, z), p x, p y, z),
  cond2(false(), x, y, z) -> cond1(and(eq(x, y), gr(x, z)), x, y, z),
               gr(0(), x) -> false(),
             gr(s x, 0()) -> true(),
             gr(s x, s y) -> gr(x, y),
   cond1(true(), x, y, z) -> cond2(gr(y, z), x, y, z),
                    p 0() -> 0(),
                    p s x -> x,
          and(x, false()) -> false(),
      and(true(), true()) -> true(),
          and(false(), x) -> false(),
             eq(0(), 0()) -> true(),
             eq(0(), s x) -> false(),
             eq(s x, 0()) -> false(),
             eq(s x, s y) -> eq(x, y)}
 DP:
  DP:
   { cond2#(true(), x, y, z) -> cond2#(gr(y, z), p x, p y, z),
     cond2#(true(), x, y, z) -> gr#(y, z),
     cond2#(true(), x, y, z) -> p# y,
     cond2#(true(), x, y, z) -> p# x,
    cond2#(false(), x, y, z) -> gr#(x, z),
    cond2#(false(), x, y, z) -> cond1#(and(eq(x, y), gr(x, z)), x, y, z),
    cond2#(false(), x, y, z) -> and#(eq(x, y), gr(x, z)),
    cond2#(false(), x, y, z) -> eq#(x, y),
               gr#(s x, s y) -> gr#(x, y),
     cond1#(true(), x, y, z) -> cond2#(gr(y, z), x, y, z),
     cond1#(true(), x, y, z) -> gr#(y, z),
               eq#(s x, s y) -> eq#(x, y)}
  TRS:
  { cond2(true(), x, y, z) -> cond2(gr(y, z), p x, p y, z),
   cond2(false(), x, y, z) -> cond1(and(eq(x, y), gr(x, z)), x, y, z),
                gr(0(), x) -> false(),
              gr(s x, 0()) -> true(),
              gr(s x, s y) -> gr(x, y),
    cond1(true(), x, y, z) -> cond2(gr(y, z), x, y, z),
                     p 0() -> 0(),
                     p s x -> x,
           and(x, false()) -> false(),
       and(true(), true()) -> true(),
           and(false(), x) -> false(),
              eq(0(), 0()) -> true(),
              eq(0(), s x) -> false(),
              eq(s x, 0()) -> false(),
              eq(s x, s y) -> eq(x, y)}
  UR:
   {         gr(0(), x) -> false(),
           gr(s x, 0()) -> true(),
           gr(s x, s y) -> gr(x, y),
                  p 0() -> 0(),
                  p s x -> x,
        and(x, false()) -> false(),
    and(true(), true()) -> true(),
        and(false(), x) -> false(),
           eq(0(), 0()) -> true(),
           eq(0(), s x) -> false(),
           eq(s x, 0()) -> false(),
           eq(s x, s y) -> eq(x, y),
                a(w, v) -> w,
                a(w, v) -> v}
   EDG:
    {(cond2#(true(), x, y, z) -> gr#(y, z), gr#(s x, s y) -> gr#(x, y))
     (cond2#(false(), x, y, z) -> cond1#(and(eq(x, y), gr(x, z)), x, y, z), cond1#(true(), x, y, z) -> gr#(y, z))
     (cond2#(false(), x, y, z) -> cond1#(and(eq(x, y), gr(x, z)), x, y, z), cond1#(true(), x, y, z) -> cond2#(gr(y, z), x, y, z))
     (cond1#(true(), x, y, z) -> gr#(y, z), gr#(s x, s y) -> gr#(x, y))
     (gr#(s x, s y) -> gr#(x, y), gr#(s x, s y) -> gr#(x, y))
     (eq#(s x, s y) -> eq#(x, y), eq#(s x, s y) -> eq#(x, y))
     (cond2#(false(), x, y, z) -> eq#(x, y), eq#(s x, s y) -> eq#(x, y))
     (cond1#(true(), x, y, z) -> cond2#(gr(y, z), x, y, z), cond2#(true(), x, y, z) -> cond2#(gr(y, z), p x, p y, z))
     (cond1#(true(), x, y, z) -> cond2#(gr(y, z), x, y, z), cond2#(true(), x, y, z) -> gr#(y, z))
     (cond1#(true(), x, y, z) -> cond2#(gr(y, z), x, y, z), cond2#(true(), x, y, z) -> p# y)
     (cond1#(true(), x, y, z) -> cond2#(gr(y, z), x, y, z), cond2#(true(), x, y, z) -> p# x)
     (cond1#(true(), x, y, z) -> cond2#(gr(y, z), x, y, z), cond2#(false(), x, y, z) -> gr#(x, z))
     (cond1#(true(), x, y, z) -> cond2#(gr(y, z), x, y, z), cond2#(false(), x, y, z) -> cond1#(and(eq(x, y), gr(x, z)), x, y, z))
     (cond1#(true(), x, y, z) -> cond2#(gr(y, z), x, y, z), cond2#(false(), x, y, z) -> and#(eq(x, y), gr(x, z)))
     (cond1#(true(), x, y, z) -> cond2#(gr(y, z), x, y, z), cond2#(false(), x, y, z) -> eq#(x, y))
     (cond2#(false(), x, y, z) -> gr#(x, z), gr#(s x, s y) -> gr#(x, y))
     (cond2#(true(), x, y, z) -> cond2#(gr(y, z), p x, p y, z), cond2#(true(), x, y, z) -> cond2#(gr(y, z), p x, p y, z))
     (cond2#(true(), x, y, z) -> cond2#(gr(y, z), p x, p y, z), cond2#(true(), x, y, z) -> gr#(y, z))
     (cond2#(true(), x, y, z) -> cond2#(gr(y, z), p x, p y, z), cond2#(true(), x, y, z) -> p# y)
     (cond2#(true(), x, y, z) -> cond2#(gr(y, z), p x, p y, z), cond2#(true(), x, y, z) -> p# x)
     (cond2#(true(), x, y, z) -> cond2#(gr(y, z), p x, p y, z), cond2#(false(), x, y, z) -> gr#(x, z))
     (cond2#(true(), x, y, z) -> cond2#(gr(y, z), p x, p y, z), cond2#(false(), x, y, z) -> cond1#(and(eq(x, y), gr(x, z)), x, y, z))
     (cond2#(true(), x, y, z) -> cond2#(gr(y, z), p x, p y, z), cond2#(false(), x, y, z) -> and#(eq(x, y), gr(x, z)))
     (cond2#(true(), x, y, z) -> cond2#(gr(y, z), p x, p y, z), cond2#(false(), x, y, z) -> eq#(x, y))}
    STATUS:
     arrows: 0.833333
     SCCS (3):
      Scc:
       { cond2#(true(), x, y, z) -> cond2#(gr(y, z), p x, p y, z),
        cond2#(false(), x, y, z) -> cond1#(and(eq(x, y), gr(x, z)), x, y, z),
         cond1#(true(), x, y, z) -> cond2#(gr(y, z), x, y, z)}
      Scc:
       {eq#(s x, s y) -> eq#(x, y)}
      Scc:
       {gr#(s x, s y) -> gr#(x, y)}
      
      SCC (3):
       Strict:
        { cond2#(true(), x, y, z) -> cond2#(gr(y, z), p x, p y, z),
         cond2#(false(), x, y, z) -> cond1#(and(eq(x, y), gr(x, z)), x, y, z),
          cond1#(true(), x, y, z) -> cond2#(gr(y, z), x, y, z)}
       Weak:
       { cond2(true(), x, y, z) -> cond2(gr(y, z), p x, p y, z),
        cond2(false(), x, y, z) -> cond1(and(eq(x, y), gr(x, z)), x, y, z),
                     gr(0(), x) -> false(),
                   gr(s x, 0()) -> true(),
                   gr(s x, s y) -> gr(x, y),
         cond1(true(), x, y, z) -> cond2(gr(y, z), x, y, z),
                          p 0() -> 0(),
                          p s x -> x,
                and(x, false()) -> false(),
            and(true(), true()) -> true(),
                and(false(), x) -> false(),
                   eq(0(), 0()) -> true(),
                   eq(0(), s x) -> false(),
                   eq(s x, 0()) -> false(),
                   eq(s x, s y) -> eq(x, y)}
       Fail
      
      
      SCC (1):
       Strict:
        {eq#(s x, s y) -> eq#(x, y)}
       Weak:
       { cond2(true(), x, y, z) -> cond2(gr(y, z), p x, p y, z),
        cond2(false(), x, y, z) -> cond1(and(eq(x, y), gr(x, z)), x, y, z),
                     gr(0(), x) -> false(),
                   gr(s x, 0()) -> true(),
                   gr(s x, s y) -> gr(x, y),
         cond1(true(), x, y, z) -> cond2(gr(y, z), x, y, z),
                          p 0() -> 0(),
                          p s x -> x,
                and(x, false()) -> false(),
            and(true(), true()) -> true(),
                and(false(), x) -> false(),
                   eq(0(), 0()) -> true(),
                   eq(0(), s x) -> false(),
                   eq(s x, 0()) -> false(),
                   eq(s x, s y) -> eq(x, y)}
       POLY:
        Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
        Interpretation:
         [cond2](x0, x1, x2, x3) = x0 + x1 + x2 + 1,
         
         [cond1](x0, x1, x2, x3) = x0 + x1,
         
         [gr](x0, x1) = x0,
         
         [and](x0, x1) = x0,
         
         [eq](x0, x1) = 0,
         
         [p](x0) = 1,
         
         [s](x0) = x0 + 1,
         
         [true] = 1,
         
         [false] = 1,
         
         [0] = 0,
         
         [eq#](x0, x1) = x0 + 1
        Strict:
         eq#(s x, s y) -> eq#(x, y)
         2 + 0y + 1x >= 1 + 0y + 1x
        Weak:
         eq(s x, s y) -> eq(x, y)
         0 + 0y + 0x >= 0 + 0y + 0x
         eq(s x, 0()) -> false()
         0 + 0x >= 1
         eq(0(), s x) -> false()
         0 + 0x >= 1
         eq(0(), 0()) -> true()
         0 >= 1
         and(false(), x) -> false()
         0 + 1x >= 1
         and(true(), true()) -> true()
         1 >= 1
         and(x, false()) -> false()
         1 + 0x >= 1
         p s x -> x
         1 + 0x >= 1x
         p 0() -> 0()
         1 >= 0
         cond1(true(), x, y, z) -> cond2(gr(y, z), x, y, z)
         1 + 0y + 1z + 0x >= 1 + 0y + 2z + 1x
         gr(s x, s y) -> gr(x, y)
         1 + 1y + 0x >= 0 + 1y + 0x
         gr(s x, 0()) -> true()
         0 + 0x >= 1
         gr(0(), x) -> false()
         0 + 1x >= 1
         cond2(false(), x, y, z) -> cond1(and(eq(x, y), gr(x, z)), x, y, z)
         2 + 0y + 1z + 1x >= 0 + 0y + 2z + 0x
         cond2(true(), x, y, z) -> cond2(gr(y, z), p x, p y, z)
         2 + 0y + 1z + 1x >= 2 + 0y + 2z + 0x
       Qed
     
     
     
     SCC (1):
      Strict:
       {gr#(s x, s y) -> gr#(x, y)}
      Weak:
      { cond2(true(), x, y, z) -> cond2(gr(y, z), p x, p y, z),
       cond2(false(), x, y, z) -> cond1(and(eq(x, y), gr(x, z)), x, y, z),
                    gr(0(), x) -> false(),
                  gr(s x, 0()) -> true(),
                  gr(s x, s y) -> gr(x, y),
        cond1(true(), x, y, z) -> cond2(gr(y, z), x, y, z),
                         p 0() -> 0(),
                         p s x -> x,
               and(x, false()) -> false(),
           and(true(), true()) -> true(),
               and(false(), x) -> false(),
                  eq(0(), 0()) -> true(),
                  eq(0(), s x) -> false(),
                  eq(s x, 0()) -> false(),
                  eq(s x, s y) -> eq(x, y)}
      POLY:
       Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
       Interpretation:
        [cond2](x0, x1, x2, x3) = x0 + x1 + x2 + 1,
        
        [cond1](x0, x1, x2, x3) = x0 + x1,
        
        [gr](x0, x1) = x0,
        
        [and](x0, x1) = x0,
        
        [eq](x0, x1) = 0,
        
        [p](x0) = 1,
        
        [s](x0) = x0 + 1,
        
        [true] = 1,
        
        [false] = 1,
        
        [0] = 0,
        
        [gr#](x0, x1) = x0 + 1
       Strict:
        gr#(s x, s y) -> gr#(x, y)
        2 + 0y + 1x >= 1 + 0y + 1x
       Weak:
        eq(s x, s y) -> eq(x, y)
        0 + 0y + 0x >= 0 + 0y + 0x
        eq(s x, 0()) -> false()
        0 + 0x >= 1
        eq(0(), s x) -> false()
        0 + 0x >= 1
        eq(0(), 0()) -> true()
        0 >= 1
        and(false(), x) -> false()
        0 + 1x >= 1
        and(true(), true()) -> true()
        1 >= 1
        and(x, false()) -> false()
        1 + 0x >= 1
        p s x -> x
        1 + 0x >= 1x
        p 0() -> 0()
        1 >= 0
        cond1(true(), x, y, z) -> cond2(gr(y, z), x, y, z)
        1 + 0y + 1z + 0x >= 1 + 0y + 2z + 1x
        gr(s x, s y) -> gr(x, y)
        1 + 1y + 0x >= 0 + 1y + 0x
        gr(s x, 0()) -> true()
        0 + 0x >= 1
        gr(0(), x) -> false()
        0 + 1x >= 1
        cond2(false(), x, y, z) -> cond1(and(eq(x, y), gr(x, z)), x, y, z)
        2 + 0y + 1z + 1x >= 0 + 0y + 2z + 0x
        cond2(true(), x, y, z) -> cond2(gr(y, z), p x, p y, z)
        2 + 0y + 1z + 1x >= 2 + 0y + 2z + 0x
      Qed