MAYBE

Problem:
 g(c(x1)) -> g(f(c(x1)))
 g(f(c(x1))) -> g(f(f(c(x1))))
 g(g(x1)) -> g(f(g(x1)))
 f(f(g(x1))) -> g(f(x1))

Proof:
 Complexity Transformation Processor:
  strict:
   g(c(x1)) -> g(f(c(x1)))
   g(f(c(x1))) -> g(f(f(c(x1))))
   g(g(x1)) -> g(f(g(x1)))
   f(f(g(x1))) -> g(f(x1))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [f](x0) = x0 + 1,
     
     [g](x0) = x0 + 1,
     
     [c](x0) = x0
    orientation:
     g(c(x1)) = x1 + 1 >= x1 + 2 = g(f(c(x1)))
     
     g(f(c(x1))) = x1 + 2 >= x1 + 3 = g(f(f(c(x1))))
     
     g(g(x1)) = x1 + 2 >= x1 + 3 = g(f(g(x1)))
     
     f(f(g(x1))) = x1 + 3 >= x1 + 2 = g(f(x1))
    problem:
     strict:
      g(c(x1)) -> g(f(c(x1)))
      g(f(c(x1))) -> g(f(f(c(x1))))
      g(g(x1)) -> g(f(g(x1)))
     weak:
      f(f(g(x1))) -> g(f(x1))
    Bounds Processor:
     bound: 1
     enrichment: match
     automaton:
      final states: {4}
      transitions:
       g1(66) -> 67*
       g1(11) -> 12*
       f1(45) -> 46*
       f1(10) -> 11*
       f1(39) -> 40*
       f1(91) -> 92*
       c1(9) -> 10*
       g0(4) -> 4*
       c0(4) -> 4*
       f0(4) -> 4*
       4 -> 66,9
       11 -> 39*
       12 -> 92,40,67,45,4
       40 -> 11*
       46 -> 11*
       66 -> 91*
       67 -> 10*
       92 -> 11*
     problem:
      strict:
       g(f(c(x1))) -> g(f(f(c(x1))))
       g(g(x1)) -> g(f(g(x1)))
      weak:
       g(c(x1)) -> g(f(c(x1)))
       f(f(g(x1))) -> g(f(x1))
     Bounds Processor:
      bound: 2
      enrichment: match
      automaton:
       final states: {4}
       transitions:
        g1(47) -> 48*
        g1(111) -> 112*
        g1(33) -> 34*
        g1(13) -> 14*
        f1(65) -> 66*
        f1(27) -> 28*
        f1(12) -> 13*
        f1(164) -> 165*
        f1(144) -> 145*
        f1(211) -> 212*
        f1(11) -> 12*
        f1(118) -> 119*
        f1(190) -> 191*
        f1(150) -> 151*
        c1(10) -> 11*
        g2(304) -> 305*
        g2(77) -> 78*
        g2(61) -> 62*
        g2(193) -> 194*
        g2(98) -> 99*
        g2(83) -> 84*
        g2(125) -> 126*
        g0(4) -> 4*
        f2(60) -> 61*
        f2(192) -> 193*
        f2(172) -> 173*
        f2(254) -> 255*
        f2(209) -> 210*
        f2(291) -> 292*
        f2(281) -> 282*
        f2(59) -> 60*
        f2(231) -> 232*
        f2(303) -> 304*
        f2(76) -> 77*
        f2(248) -> 249*
        f2(238) -> 239*
        f2(340) -> 341*
        c0(4) -> 4*
        c2(58) -> 59*
        f0(4) -> 4*
        4 -> 33,10
        10 -> 58*
        12 -> 47*
        13 -> 209,98,65
        14 -> 249,193,165,151,194,66,126,34,27,4
        28 -> 13*
        33 -> 164,125
        34 -> 12*
        47 -> 254,150,83
        48 -> 126,34,118,4
        61 -> 238,144,111
        62 -> 305,84,76,48
        66 -> 13*
        77 -> 231,211
        78 -> 305,304,282,249,232,212,191,239,210,99,14,84,172,48,34
        83 -> 291*
        84 -> 76*
        98 -> 281*
        99 -> 76*
        111 -> 303,190
        112 -> 11*
        119 -> 13*
        125 -> 192*
        126 -> 60*
        145 -> 13*
        151 -> 13*
        165 -> 13*
        173 -> 61*
        191 -> 13*
        193 -> 248*
        194 -> 304,282,212,232,191,239,210,145
        210 -> 77*
        212 -> 13*
        232 -> 77*
        239 -> 77*
        249 -> 77*
        255 -> 77*
        282 -> 77*
        292 -> 77*
        304 -> 340*
        305 -> 292,255
        341 -> 77*
      problem:
       strict:
        g(g(x1)) -> g(f(g(x1)))
       weak:
        g(f(c(x1))) -> g(f(f(c(x1))))
        g(c(x1)) -> g(f(c(x1)))
        f(f(g(x1))) -> g(f(x1))
      Open