MAYBE
Time: 0.096093
TRS:
 { cond2(true(), x, y) -> cond2(gr(y, 0()), p x, p y),
  cond2(false(), x, y) -> cond1(and(eq(x, y), gr(x, 0())), x, y),
            gr(0(), x) -> false(),
          gr(s x, 0()) -> true(),
          gr(s x, s y) -> gr(x, y),
   cond1(true(), x, y) -> cond2(gr(y, 0()), 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)}
 DP:
  DP:
   { cond2#(true(), x, y) -> cond2#(gr(y, 0()), p x, p y),
     cond2#(true(), x, y) -> gr#(y, 0()),
     cond2#(true(), x, y) -> p# y,
     cond2#(true(), x, y) -> p# x,
    cond2#(false(), x, y) -> gr#(x, 0()),
    cond2#(false(), x, y) -> cond1#(and(eq(x, y), gr(x, 0())), x, y),
    cond2#(false(), x, y) -> and#(eq(x, y), gr(x, 0())),
    cond2#(false(), x, y) -> eq#(x, y),
            gr#(s x, s y) -> gr#(x, y),
     cond1#(true(), x, y) -> cond2#(gr(y, 0()), x, y),
     cond1#(true(), x, y) -> gr#(y, 0()),
            eq#(s x, s y) -> eq#(x, y)}
  TRS:
  { cond2(true(), x, y) -> cond2(gr(y, 0()), p x, p y),
   cond2(false(), x, y) -> cond1(and(eq(x, y), gr(x, 0())), x, y),
             gr(0(), x) -> false(),
           gr(s x, 0()) -> true(),
           gr(s x, s y) -> gr(x, y),
    cond1(true(), x, y) -> cond2(gr(y, 0()), 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)}
  UR:
   {         gr(0(), x) -> false(),
           gr(s x, 0()) -> true(),
                  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(z, w) -> z,
                a(z, w) -> w}
   EDG:
    {(cond2#(false(), x, y) -> gr#(x, 0()), gr#(s x, s y) -> gr#(x, y))
     (cond2#(false(), x, y) -> eq#(x, y), eq#(s x, s y) -> eq#(x, y))
     (eq#(s x, s y) -> eq#(x, y), eq#(s x, s y) -> eq#(x, y))
     (cond2#(false(), x, y) -> cond1#(and(eq(x, y), gr(x, 0())), x, y), cond1#(true(), x, y) -> gr#(y, 0()))
     (cond2#(false(), x, y) -> cond1#(and(eq(x, y), gr(x, 0())), x, y), cond1#(true(), x, y) -> cond2#(gr(y, 0()), x, y))
     (cond1#(true(), x, y) -> cond2#(gr(y, 0()), x, y), cond2#(true(), x, y) -> cond2#(gr(y, 0()), p x, p y))
     (cond1#(true(), x, y) -> cond2#(gr(y, 0()), x, y), cond2#(true(), x, y) -> gr#(y, 0()))
     (cond1#(true(), x, y) -> cond2#(gr(y, 0()), x, y), cond2#(true(), x, y) -> p# y)
     (cond1#(true(), x, y) -> cond2#(gr(y, 0()), x, y), cond2#(true(), x, y) -> p# x)
     (cond1#(true(), x, y) -> cond2#(gr(y, 0()), x, y), cond2#(false(), x, y) -> gr#(x, 0()))
     (cond1#(true(), x, y) -> cond2#(gr(y, 0()), x, y), cond2#(false(), x, y) -> cond1#(and(eq(x, y), gr(x, 0())), x, y))
     (cond1#(true(), x, y) -> cond2#(gr(y, 0()), x, y), cond2#(false(), x, y) -> and#(eq(x, y), gr(x, 0())))
     (cond1#(true(), x, y) -> cond2#(gr(y, 0()), x, y), cond2#(false(), x, y) -> eq#(x, y))
     (gr#(s x, s y) -> gr#(x, y), gr#(s x, s y) -> gr#(x, y))
     (cond2#(true(), x, y) -> cond2#(gr(y, 0()), p x, p y), cond2#(true(), x, y) -> cond2#(gr(y, 0()), p x, p y))
     (cond2#(true(), x, y) -> cond2#(gr(y, 0()), p x, p y), cond2#(true(), x, y) -> gr#(y, 0()))
     (cond2#(true(), x, y) -> cond2#(gr(y, 0()), p x, p y), cond2#(true(), x, y) -> p# y)
     (cond2#(true(), x, y) -> cond2#(gr(y, 0()), p x, p y), cond2#(true(), x, y) -> p# x)
     (cond2#(true(), x, y) -> cond2#(gr(y, 0()), p x, p y), cond2#(false(), x, y) -> gr#(x, 0()))
     (cond2#(true(), x, y) -> cond2#(gr(y, 0()), p x, p y), cond2#(false(), x, y) -> cond1#(and(eq(x, y), gr(x, 0())), x, y))
     (cond2#(true(), x, y) -> cond2#(gr(y, 0()), p x, p y), cond2#(false(), x, y) -> and#(eq(x, y), gr(x, 0())))
     (cond2#(true(), x, y) -> cond2#(gr(y, 0()), p x, p y), cond2#(false(), x, y) -> eq#(x, y))
     (cond1#(true(), x, y) -> gr#(y, 0()), gr#(s x, s y) -> gr#(x, y))
     (cond2#(true(), x, y) -> gr#(y, 0()), gr#(s x, s y) -> gr#(x, y))}
    STATUS:
     arrows: 0.833333
     SCCS (3):
      Scc:
       { cond2#(true(), x, y) -> cond2#(gr(y, 0()), p x, p y),
        cond2#(false(), x, y) -> cond1#(and(eq(x, y), gr(x, 0())), x, y),
         cond1#(true(), x, y) -> cond2#(gr(y, 0()), x, y)}
      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) -> cond2#(gr(y, 0()), p x, p y),
         cond2#(false(), x, y) -> cond1#(and(eq(x, y), gr(x, 0())), x, y),
          cond1#(true(), x, y) -> cond2#(gr(y, 0()), x, y)}
       Weak:
       { cond2(true(), x, y) -> cond2(gr(y, 0()), p x, p y),
        cond2(false(), x, y) -> cond1(and(eq(x, y), gr(x, 0())), x, y),
                  gr(0(), x) -> false(),
                gr(s x, 0()) -> true(),
                gr(s x, s y) -> gr(x, y),
         cond1(true(), x, y) -> cond2(gr(y, 0()), 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)}
       Fail
      
      SCC (1):
       Strict:
        {eq#(s x, s y) -> eq#(x, y)}
       Weak:
       { cond2(true(), x, y) -> cond2(gr(y, 0()), p x, p y),
        cond2(false(), x, y) -> cond1(and(eq(x, y), gr(x, 0())), x, y),
                  gr(0(), x) -> false(),
                gr(s x, 0()) -> true(),
                gr(s x, s y) -> gr(x, y),
         cond1(true(), x, y) -> cond2(gr(y, 0()), 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)}
       POLY:
        Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
        Interpretation:
         [cond2](x0, x1, x2) = x0 + x1 + 1,
         
         [cond1](x0, x1, x2) = 0,
         
         [gr](x0, x1) = x0,
         
         [and](x0, x1) = x0 + x1,
         
         [eq](x0, x1) = x0 + x1,
         
         [p](x0) = 1,
         
         [s](x0) = x0 + 1,
         
         [0] = 1,
         
         [true] = 1,
         
         [false] = 1,
         
         [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)
         2 + 1y + 1x >= 0 + 1y + 1x
         eq(s x, 0()) -> false()
         2 + 1x >= 1
         eq(0(), s x) -> false()
         2 + 1x >= 1
         eq(0(), 0()) -> true()
         2 >= 1
         and(false(), x) -> false()
         1 + 1x >= 1
         and(true(), true()) -> true()
         2 >= 1
         and(x, false()) -> false()
         1 + 1x >= 1
         p s x -> x
         1 + 0x >= 1x
         p 0() -> 0()
         1 >= 1
         cond1(true(), x, y) -> cond2(gr(y, 0()), x, y)
         0 + 0y + 0x >= 1 + 2y + 0x
         gr(s x, s y) -> gr(x, y)
         1 + 0y + 1x >= 0 + 0y + 1x
         gr(s x, 0()) -> true()
         1 + 1x >= 1
         gr(0(), x) -> false()
         1 + 0x >= 1
         cond2(false(), x, y) -> cond1(and(eq(x, y), gr(x, 0())), x, y)
         2 + 1y + 0x >= 0 + 0y + 0x
         cond2(true(), x, y) -> cond2(gr(y, 0()), p x, p y)
         2 + 1y + 0x >= 2 + 1y + 0x
       Qed
     
     
     
     
     
     
     SCC (1):
      Strict:
       {gr#(s x, s y) -> gr#(x, y)}
      Weak:
      { cond2(true(), x, y) -> cond2(gr(y, 0()), p x, p y),
       cond2(false(), x, y) -> cond1(and(eq(x, y), gr(x, 0())), x, y),
                 gr(0(), x) -> false(),
               gr(s x, 0()) -> true(),
               gr(s x, s y) -> gr(x, y),
        cond1(true(), x, y) -> cond2(gr(y, 0()), 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)}
      POLY:
       Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
       Interpretation:
        [cond2](x0, x1, x2) = x0 + x1 + 1,
        
        [cond1](x0, x1, x2) = 0,
        
        [gr](x0, x1) = x0,
        
        [and](x0, x1) = x0 + x1,
        
        [eq](x0, x1) = x0 + x1,
        
        [p](x0) = 1,
        
        [s](x0) = x0 + 1,
        
        [0] = 1,
        
        [true] = 1,
        
        [false] = 1,
        
        [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)
        2 + 1y + 1x >= 0 + 1y + 1x
        eq(s x, 0()) -> false()
        2 + 1x >= 1
        eq(0(), s x) -> false()
        2 + 1x >= 1
        eq(0(), 0()) -> true()
        2 >= 1
        and(false(), x) -> false()
        1 + 1x >= 1
        and(true(), true()) -> true()
        2 >= 1
        and(x, false()) -> false()
        1 + 1x >= 1
        p s x -> x
        1 + 0x >= 1x
        p 0() -> 0()
        1 >= 1
        cond1(true(), x, y) -> cond2(gr(y, 0()), x, y)
        0 + 0y + 0x >= 1 + 2y + 0x
        gr(s x, s y) -> gr(x, y)
        1 + 0y + 1x >= 0 + 0y + 1x
        gr(s x, 0()) -> true()
        1 + 1x >= 1
        gr(0(), x) -> false()
        1 + 0x >= 1
        cond2(false(), x, y) -> cond1(and(eq(x, y), gr(x, 0())), x, y)
        2 + 1y + 0x >= 0 + 0y + 0x
        cond2(true(), x, y) -> cond2(gr(y, 0()), p x, p y)
        2 + 1y + 0x >= 2 + 1y + 0x
      Qed