MAYBE

Problem:
 a(l(x1)) -> l(a(x1))
 r(a(a(x1))) -> a(a(r(x1)))
 b(l(x1)) -> b(a(r(x1)))
 r(b(x1)) -> l(b(x1))

Proof:
 Complexity Transformation Processor:
  strict:
   a(l(x1)) -> l(a(x1))
   r(a(a(x1))) -> a(a(r(x1)))
   b(l(x1)) -> b(a(r(x1)))
   r(b(x1)) -> l(b(x1))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [b](x0) = x0,
     
     [r](x0) = x0 + 1,
     
     [a](x0) = x0,
     
     [l](x0) = x0
    orientation:
     a(l(x1)) = x1 >= x1 = l(a(x1))
     
     r(a(a(x1))) = x1 + 1 >= x1 + 1 = a(a(r(x1)))
     
     b(l(x1)) = x1 >= x1 + 1 = b(a(r(x1)))
     
     r(b(x1)) = x1 + 1 >= x1 = l(b(x1))
    problem:
     strict:
      a(l(x1)) -> l(a(x1))
      r(a(a(x1))) -> a(a(r(x1)))
      b(l(x1)) -> b(a(r(x1)))
     weak:
      r(b(x1)) -> l(b(x1))
    Bounds Processor:
     bound: 3
     enrichment: match
     automaton:
      final states: {5}
      transitions:
       b3(223) -> 224*
       a3(429) -> 430*
       a3(222) -> 223*
       a3(329) -> 330*
       a3(398) -> 399*
       a3(368) -> 369*
       a3(430) -> 431*
       a3(400) -> 401*
       a3(397) -> 398*
       l1(51) -> 52*
       r3(396) -> 397*
       r3(428) -> 429*
       r3(221) -> 222*
       r3(332) -> 333*
       a1(252) -> 253*
       a1(25) -> 26*
       a1(112) -> 113*
       a1(251) -> 252*
       a1(28) -> 29*
       b2(94) -> 95*
       b2(185) -> 186*
       b2(165) -> 166*
       r1(24) -> 25*
       r1(53) -> 54*
       r1(250) -> 251*
       b1(72) -> 73*
       b1(26) -> 27*
       a2(267) -> 268*
       a2(264) -> 265*
       a2(199) -> 200*
       a2(386) -> 387*
       a2(385) -> 386*
       a2(340) -> 341*
       a2(93) -> 94*
       a2(265) -> 266*
       a0(5) -> 5*
       r2(384) -> 385*
       r2(92) -> 93*
       r2(219) -> 220*
       r2(263) -> 264*
       l0(5) -> 5*
       l2(131) -> 132*
       l2(268) -> 269*
       l2(200) -> 201*
       r0(5) -> 5*
       l3(369) -> 370*
       l3(298) -> 299*
       l3(330) -> 331*
       b0(5) -> 5*
       5 -> 72,24
       26 -> 185,28
       27 -> 166,73,51,5
       29 -> 25*
       51 -> 112,92,53
       52 -> 29,54,26,25,5
       54 -> 25*
       72 -> 165*
       73 -> 51*
       95 -> 186,166,131,27,73
       112 -> 263,250
       113 -> 51*
       131 -> 199*
       132 -> 251,264,93,54
       166 -> 131*
       186 -> 131*
       200 -> 267,221,219
       201 -> 265,252,94,26
       220 -> 93*
       224 -> 298,95,186
       253 -> 251,54
       266 -> 264,93
       267 -> 396,384
       268 -> 340*
       269 -> 266,253,29
       298 -> 329*
       299 -> 93,264
       330 -> 368,332
       331 -> 265,94
       333 -> 222*
       341 -> 200*
       368 -> 428*
       369 -> 400*
       370 -> 266*
       387 -> 385,220
       399 -> 397,222
       401 -> 330*
       431 -> 429,333
     problem:
      strict:
       a(l(x1)) -> l(a(x1))
       r(a(a(x1))) -> a(a(r(x1)))
      weak:
       b(l(x1)) -> b(a(r(x1)))
       r(b(x1)) -> l(b(x1))
     Open