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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {6,5,4,3}
   transitions:
    31(40) -> 41*
    31(31) -> 32*
    31(16) -> 17*
    51(39) -> 40*
    51(29) -> 30*
    51(38) -> 39*
    51(33) -> 34*
    11(15) -> 16*
    11(37) -> 38*
    11(32) -> 33*
    11(19) -> 20*
    11(13) -> 14*
    01(17) -> 18*
    01(36) -> 37*
    21(35) -> 36*
    21(30) -> 31*
    41(14) -> 15*
    00(2) -> 3*
    00(1) -> 3*
    10(2) -> 1*
    10(1) -> 1*
    20(2) -> 5*
    20(1) -> 5*
    30(2) -> 6*
    30(1) -> 6*
    40(2) -> 4*
    40(1) -> 4*
    50(2) -> 2*
    50(1) -> 2*
    1 -> 19*
    2 -> 13*
    14 -> 35,29
    18 -> 3*
    20 -> 14*
    34 -> 17*
    41 -> 3*
  problem:
   
  Qed