Problem:
 0(0(1(x1))) -> 0(0(2(1(x1))))
 0(1(3(x1))) -> 0(3(4(1(x1))))
 3(1(1(x1))) -> 3(1(4(1(x1))))
 3(1(1(x1))) -> 3(4(1(4(4(1(x1))))))
 3(1(1(x1))) -> 3(4(4(1(2(4(1(x1)))))))
 3(3(1(x1))) -> 3(2(1(3(x1))))
 5(0(4(x1))) -> 4(0(5(4(x1))))
 0(0(0(1(x1)))) -> 0(0(0(2(1(x1)))))
 0(0(1(5(x1)))) -> 0(0(5(1(2(4(x1))))))
 0(0(5(3(x1)))) -> 0(0(5(4(3(x1)))))
 0(4(1(1(x1)))) -> 0(5(4(1(2(1(x1))))))
 0(4(3(1(x1)))) -> 0(3(5(4(1(x1)))))
 0(4(3(4(x1)))) -> 0(3(2(4(4(x1)))))
 3(0(1(1(x1)))) -> 0(2(1(3(1(x1)))))
 3(1(1(5(x1)))) -> 3(1(2(1(5(x1)))))
 5(0(1(5(x1)))) -> 0(5(4(1(5(x1)))))
 5(2(3(1(x1)))) -> 4(5(2(1(3(x1)))))
 5(2(3(5(x1)))) -> 2(4(5(3(5(x1)))))
 5(2(5(4(x1)))) -> 2(4(5(4(5(x1)))))
 0(1(2(2(1(x1))))) -> 2(4(0(1(2(1(x1))))))
 0(1(5(0(4(x1))))) -> 0(2(1(5(4(0(x1))))))
 0(1(5(5(3(x1))))) -> 0(5(4(5(1(3(x1))))))
 0(2(2(1(5(x1))))) -> 0(2(1(5(4(2(4(4(2(x1)))))))))
 0(2(2(3(4(x1))))) -> 0(3(4(4(2(4(4(2(x1))))))))
 0(2(5(1(1(x1))))) -> 5(0(1(2(4(1(x1))))))
 0(3(3(2(3(x1))))) -> 0(3(3(2(4(3(x1))))))
 0(4(4(3(4(x1))))) -> 4(4(4(4(0(3(x1))))))
 3(0(1(4(3(x1))))) -> 3(2(0(3(4(1(x1))))))
 3(0(4(5(1(x1))))) -> 3(5(4(4(1(0(x1))))))
 3(1(1(1(2(x1))))) -> 3(2(1(4(1(2(1(2(x1))))))))
 5(2(3(1(4(x1))))) -> 5(2(1(2(1(3(4(x1)))))))
 5(3(0(0(4(x1))))) -> 0(0(3(5(4(4(x1))))))
 0(1(3(4(3(4(x1)))))) -> 0(3(4(3(4(1(2(x1)))))))
 0(1(5(0(4(2(x1)))))) -> 0(5(2(4(1(0(2(x1)))))))
 0(2(2(2(3(1(x1)))))) -> 0(2(2(4(2(3(1(x1)))))))
 0(4(1(1(0(4(x1)))))) -> 0(4(4(1(4(1(0(x1)))))))
 0(4(3(2(2(3(x1)))))) -> 0(2(3(2(4(2(3(x1)))))))
 3(0(4(1(2(2(x1)))))) -> 3(2(1(0(4(4(2(x1)))))))
 3(1(0(3(5(4(x1)))))) -> 3(0(3(2(1(5(4(x1)))))))
 3(2(2(1(1(3(x1)))))) -> 1(2(1(3(2(4(3(x1)))))))
 3(3(3(1(3(5(x1)))))) -> 3(2(1(3(3(3(5(x1)))))))
 3(4(3(0(4(5(x1)))))) -> 3(5(0(3(4(4(4(x1)))))))
 3(4(3(1(4(2(x1)))))) -> 3(4(2(1(3(2(2(4(2(4(x1))))))))))
 3(5(0(2(1(4(x1)))))) -> 3(2(4(0(5(1(2(x1)))))))
 3(5(5(2(3(1(x1)))))) -> 5(5(4(3(3(2(1(x1)))))))
 5(0(1(2(3(1(x1)))))) -> 2(1(0(3(4(5(4(4(4(1(x1))))))))))
 5(0(4(3(3(1(x1)))))) -> 0(3(5(1(5(4(4(3(x1))))))))
 0(0(1(1(3(3(3(x1))))))) -> 0(3(0(1(3(3(4(1(x1))))))))
 0(0(2(5(1(4(2(x1))))))) -> 0(2(1(0(5(4(2(2(x1))))))))
 0(2(5(4(4(1(5(x1))))))) -> 1(2(4(5(0(5(4(4(x1))))))))
 0(4(2(3(4(5(4(x1))))))) -> 3(0(5(4(4(2(4(0(x1))))))))
 0(5(2(1(2(1(4(x1))))))) -> 2(1(2(1(0(5(2(4(x1))))))))
 3(2(5(0(4(0(1(x1))))))) -> 0(0(5(4(2(2(4(4(1(3(x1))))))))))
 3(4(3(4(0(1(4(x1))))))) -> 3(4(2(4(4(4(0(5(1(2(3(x1)))))))))))
 3(5(2(1(0(2(2(x1))))))) -> 2(1(3(0(5(2(2(4(x1))))))))
 3(5(2(2(0(1(1(x1))))))) -> 3(2(4(5(0(2(1(2(1(x1)))))))))
 3(5(3(4(0(1(4(x1))))))) -> 2(1(5(4(3(4(0(3(x1))))))))
 5(1(5(3(1(1(3(x1))))))) -> 2(1(5(1(5(1(3(3(x1))))))))
 5(2(0(0(1(0(3(x1))))))) -> 0(5(3(4(2(1(0(0(x1))))))))
 5(2(0(4(0(4(3(x1))))))) -> 2(0(5(1(0(4(4(3(x1))))))))
 5(2(3(0(0(4(3(x1))))))) -> 0(5(4(2(4(3(0(3(3(x1)))))))))
 5(2(3(3(2(0(5(x1))))))) -> 2(0(3(3(5(2(4(5(x1))))))))
 5(5(5(0(1(4(3(x1))))))) -> 0(5(4(4(3(4(5(5(1(x1)))))))))
 0(2(0(5(5(2(2(3(x1)))))))) -> 5(2(2(4(5(3(2(0(0(x1)))))))))
 0(2(5(2(4(0(1(4(x1)))))))) -> 0(3(0(5(2(1(2(2(4(4(x1))))))))))
 0(4(1(5(3(2(3(3(x1)))))))) -> 0(5(4(1(2(3(3(4(3(x1)))))))))
 0(4(5(0(1(5(2(3(x1)))))))) -> 2(1(2(4(2(5(3(0(5(0(x1))))))))))
 0(5(5(1(4(2(0(3(x1)))))))) -> 0(3(5(1(2(0(5(1(2(4(x1))))))))))
 3(0(1(3(2(0(4(2(x1)))))))) -> 0(4(2(2(2(4(1(0(3(3(4(x1)))))))))))
 3(3(1(1(2(5(5(2(x1)))))))) -> 3(2(1(5(1(2(5(3(1(x1)))))))))
 3(5(4(2(5(1(0(4(x1)))))))) -> 4(2(4(2(1(3(5(0(5(4(x1))))))))))
 5(0(4(3(0(2(2(3(x1)))))))) -> 0(2(4(4(0(3(2(5(3(x1)))))))))
 5(2(2(0(4(0(1(4(x1)))))))) -> 4(2(4(0(0(5(1(0(2(x1)))))))))
 5(2(2(0(4(1(5(4(x1)))))))) -> 2(5(2(4(5(0(2(1(4(x1)))))))))
 5(3(2(2(1(1(0(5(x1)))))))) -> 0(3(2(5(2(1(5(1(2(x1)))))))))
 0(0(4(4(5(3(1(1(5(x1))))))))) -> 2(1(5(4(4(4(1(0(0(3(5(x1)))))))))))
 0(1(2(5(1(4(0(3(4(x1))))))))) -> 0(2(4(0(3(1(2(1(2(4(5(x1)))))))))))
 0(1(3(1(2(0(1(1(5(x1))))))))) -> 0(5(1(0(1(4(1(1(2(3(x1))))))))))
 0(2(0(4(1(5(3(0(4(x1))))))))) -> 4(1(0(3(5(0(0(2(2(4(x1))))))))))
 0(4(3(3(4(2(5(0(5(x1))))))))) -> 0(5(0(4(3(2(4(5(3(2(x1))))))))))
 3(0(4(3(5(4(3(0(1(x1))))))))) -> 0(3(0(3(4(3(2(4(5(1(x1))))))))))
 3(1(5(3(1(1(0(3(2(x1))))))))) -> 5(1(0(3(2(1(3(3(2(1(x1))))))))))
 3(3(0(0(1(5(4(0(4(x1))))))))) -> 1(0(2(4(4(0(3(5(0(3(x1))))))))))
 5(2(0(3(1(2(5(0(4(x1))))))))) -> 5(1(0(3(5(2(4(2(4(0(x1))))))))))
 5(2(0(3(2(0(4(4(1(x1))))))))) -> 0(5(3(0(5(2(2(4(2(4(1(x1)))))))))))
 5(5(0(1(1(3(2(5(2(x1))))))))) -> 3(5(1(2(2(0(5(1(5(4(x1))))))))))
 5(5(3(2(1(0(1(0(4(x1))))))))) -> 0(2(1(3(5(0(5(4(2(4(1(x1)))))))))))
 0(1(3(1(4(2(0(4(5(2(x1)))))))))) -> 4(0(1(2(4(0(2(1(5(1(3(x1)))))))))))
 0(4(3(1(3(5(2(5(4(4(x1)))))))))) -> 0(5(5(2(4(4(1(5(4(3(3(x1)))))))))))
 3(2(0(2(0(5(2(3(4(5(x1)))))))))) -> 3(5(4(4(2(0(3(2(5(2(0(x1)))))))))))

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {6,5,4}
   transitions:
    31(15) -> 16*
    21(67) -> 68*
    21(37) -> 38*
    21(79) -> 80*
    21(59) -> 60*
    21(81) -> 82*
    21(61) -> 62*
    21(41) -> 42*
    21(63) -> 64*
    11(62) -> 63*
    11(42) -> 43*
    11(17) -> 18*
    11(12) -> 13*
    11(64) -> 65*
    11(14) -> 15*
    11(66) -> 67*
    11(26) -> 27*
    11(38) -> 39*
    11(23) -> 24*
    41(65) -> 66*
    41(25) -> 26*
    41(27) -> 28*
    41(39) -> 40*
    41(58) -> 59*
    41(43) -> 44*
    41(13) -> 14*
    01(45) -> 46*
    01(57) -> 58*
    51(44) -> 45*
    00(2) -> 4*
    00(1) -> 4*
    00(3) -> 4*
    10(2) -> 1*
    10(1) -> 1*
    10(3) -> 1*
    20(2) -> 2*
    20(1) -> 2*
    20(3) -> 2*
    30(2) -> 5*
    30(1) -> 5*
    30(3) -> 5*
    40(2) -> 3*
    40(1) -> 3*
    40(3) -> 3*
    50(2) -> 6*
    50(1) -> 6*
    50(3) -> 6*
    1 -> 79,17
    2 -> 61,12
    3 -> 81,23
    13 -> 41*
    14 -> 37,25
    16 -> 5*
    18 -> 13*
    24 -> 13*
    28 -> 15*
    40 -> 27*
    43 -> 57*
    46 -> 4*
    60 -> 4*
    68 -> 15*
    80 -> 62*
    82 -> 62*
  problem:
   
  Qed