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(174) -> 175*
        g1(33) -> 34*
        g1(13) -> 14*
        f1(65) -> 66*
        f1(137) -> 138*
        f1(27) -> 28*
        f1(12) -> 13*
        f1(154) -> 155*
        f1(129) -> 130*
        f1(11) -> 12*
        f1(173) -> 174*
        c1(10) -> 11*
        g2(77) -> 78*
        g2(189) -> 190*
        g2(116) -> 117*
        g2(61) -> 62*
        g2(98) -> 99*
        g2(83) -> 84*
        g2(220) -> 221*
        g0(4) -> 4*
        f2(60) -> 61*
        f2(264) -> 265*
        f2(249) -> 250*
        f2(199) -> 200*
        f2(59) -> 60*
        f2(251) -> 252*
        f2(76) -> 77*
        f2(213) -> 214*
        f2(188) -> 189*
        f2(260) -> 261*
        f2(240) -> 241*
        f2(205) -> 206*
        f2(292) -> 293*
        c0(4) -> 4*
        c2(58) -> 59*
        f0(4) -> 4*
        4 -> 33,10
        10 -> 58*
        12 -> 47*
        13 -> 199,98,65
        14 -> 250,189,190,155,66,117,34,27,4
        28 -> 13*
        33 -> 154,116
        34 -> 12*
        47 -> 240,137,83
        48 -> 117,34,4
        61 -> 213,129
        62 -> 175,221,84,76,48
        66 -> 13*
        77 -> 205,173
        78 -> 293,175,221,250,252,261,200,189,174,206,214,84,14,99,48,4,34
        83 -> 264*
        84 -> 76*
        98 -> 260*
        99 -> 76*
        116 -> 188*
        117 -> 60*
        130 -> 13*
        138 -> 13*
        155 -> 13*
        174 -> 251,220
        175 -> 4,155
        189 -> 249*
        190 -> 206,174,261,200,214,130
        200 -> 77*
        206 -> 77*
        214 -> 77*
        220 -> 292*
        221 -> 76*
        241 -> 77*
        250 -> 77*
        252 -> 77*
        261 -> 77*
        265 -> 77*
        293 -> 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