YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) FlatCCProof [EQUIVALENT, 0 ms]
(2) QTRS
(3) RootLabelingProof [EQUIVALENT, 29 ms]
(4) QTRS
(5) QTRSRRRProof [EQUIVALENT, 2643 ms]
(6) QTRS
(7) QTRSRRRProof [EQUIVALENT, 20 ms]
(8) QTRS
(9) QTRSRRRProof [EQUIVALENT, 22 ms]
(10) QTRS
(11) QTRSRRRProof [EQUIVALENT, 11 ms]
(12) QTRS
(13) QTRSRRRProof [EQUIVALENT, 2 ms]
(14) QTRS
(15) RisEmptyProof [EQUIVALENT, 0 ms]
(16) YES


----------------------------------------

(0)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

Q is empty.

----------------------------------------

(1) FlatCCProof (EQUIVALENT)
We used flat context closure [ROOTLAB]
As Q is empty the flat context closure was sound AND complete.

----------------------------------------

(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

Q is empty.

----------------------------------------

(3) RootLabelingProof (EQUIVALENT)
We used plain root labeling [ROOTLAB] with the following heuristic:
LabelAll: All function symbols get labeled

As Q is empty the root labeling was sound AND complete.

----------------------------------------

(4)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{5_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{0_1}(0_{4_1}(4_{4_1}(4_{5_1}(5_{2_1}(2_{1_1}(1_{5_1}(x1))))))))))
   5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{0_1}(0_{4_1}(4_{4_1}(4_{5_1}(5_{2_1}(2_{1_1}(1_{1_1}(x1))))))))))
   5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{3_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{0_1}(0_{4_1}(4_{4_1}(4_{5_1}(5_{2_1}(2_{1_1}(1_{3_1}(x1))))))))))
   5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{0_1}(0_{4_1}(4_{4_1}(4_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(x1))))))))))
   5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{4_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{0_1}(0_{4_1}(4_{4_1}(4_{5_1}(5_{2_1}(2_{1_1}(1_{4_1}(x1))))))))))
   5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{0_1}(0_{4_1}(4_{4_1}(4_{5_1}(5_{2_1}(2_{1_1}(1_{2_1}(x1))))))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{5_1}(5_{4_1}(4_{5_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{1_1}(1_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{5_1}(5_{4_1}(4_{5_1}(x1))))))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{5_1}(5_{4_1}(4_{1_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{1_1}(1_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{5_1}(5_{4_1}(4_{1_1}(x1))))))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{1_1}(1_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{5_1}(5_{4_1}(4_{3_1}(x1))))))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{1_1}(1_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{5_1}(5_{4_1}(4_{0_1}(x1))))))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{5_1}(5_{4_1}(4_{4_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{1_1}(1_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{5_1}(5_{4_1}(4_{4_1}(x1))))))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{5_1}(5_{4_1}(4_{2_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{1_1}(1_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{5_1}(5_{4_1}(4_{2_1}(x1))))))))))
   3_{0_1}(0_{5_1}(5_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(x1)))))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{0_1}(0_{5_1}(x1))))))))))
   3_{0_1}(0_{5_1}(5_{5_1}(5_{4_1}(4_{3_1}(3_{1_1}(x1)))))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(x1))))))))))
   3_{0_1}(0_{5_1}(5_{5_1}(5_{4_1}(4_{3_1}(3_{3_1}(x1)))))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{0_1}(0_{3_1}(x1))))))))))
   3_{0_1}(0_{5_1}(5_{5_1}(5_{4_1}(4_{3_1}(3_{0_1}(x1)))))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{0_1}(0_{0_1}(x1))))))))))
   3_{0_1}(0_{5_1}(5_{5_1}(5_{4_1}(4_{3_1}(3_{4_1}(x1)))))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{0_1}(0_{4_1}(x1))))))))))
   3_{0_1}(0_{5_1}(5_{5_1}(5_{4_1}(4_{3_1}(3_{2_1}(x1)))))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{0_1}(0_{2_1}(x1))))))))))
   4_{4_1}(4_{2_1}(2_{5_1}(5_{5_1}(5_{0_1}(0_{5_1}(x1)))))) -> 4_{4_1}(4_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{5_1}(x1))))))))))
   4_{4_1}(4_{2_1}(2_{5_1}(5_{5_1}(5_{0_1}(0_{1_1}(x1)))))) -> 4_{4_1}(4_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{1_1}(x1))))))))))
   4_{4_1}(4_{2_1}(2_{5_1}(5_{5_1}(5_{0_1}(0_{3_1}(x1)))))) -> 4_{4_1}(4_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(x1))))))))))
   4_{4_1}(4_{2_1}(2_{5_1}(5_{5_1}(5_{0_1}(0_{0_1}(x1)))))) -> 4_{4_1}(4_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{0_1}(x1))))))))))
   4_{4_1}(4_{2_1}(2_{5_1}(5_{5_1}(5_{0_1}(0_{4_1}(x1)))))) -> 4_{4_1}(4_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(x1))))))))))
   4_{4_1}(4_{2_1}(2_{5_1}(5_{5_1}(5_{0_1}(0_{2_1}(x1)))))) -> 4_{4_1}(4_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(x1))))))))))
   4_{5_1}(5_{3_1}(3_{5_1}(5_{5_1}(5_{0_1}(0_{5_1}(x1)))))) -> 4_{2_1}(2_{2_1}(2_{3_1}(3_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(x1))))))))))
   4_{5_1}(5_{3_1}(3_{5_1}(5_{5_1}(5_{0_1}(0_{1_1}(x1)))))) -> 4_{2_1}(2_{2_1}(2_{3_1}(3_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(1_{5_1}(5_{1_1}(x1))))))))))
   4_{5_1}(5_{3_1}(3_{5_1}(5_{5_1}(5_{0_1}(0_{3_1}(x1)))))) -> 4_{2_1}(2_{2_1}(2_{3_1}(3_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(x1))))))))))
   4_{5_1}(5_{3_1}(3_{5_1}(5_{5_1}(5_{0_1}(0_{0_1}(x1)))))) -> 4_{2_1}(2_{2_1}(2_{3_1}(3_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(1_{5_1}(5_{0_1}(x1))))))))))
   4_{5_1}(5_{3_1}(3_{5_1}(5_{5_1}(5_{0_1}(0_{4_1}(x1)))))) -> 4_{2_1}(2_{2_1}(2_{3_1}(3_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(1_{5_1}(5_{4_1}(x1))))))))))
   4_{5_1}(5_{3_1}(3_{5_1}(5_{5_1}(5_{0_1}(0_{2_1}(x1)))))) -> 4_{2_1}(2_{2_1}(2_{3_1}(3_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(1_{5_1}(5_{2_1}(x1))))))))))
   5_{4_1}(4_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(2_{5_1}(x1)))))) -> 5_{4_1}(4_{0_1}(0_{3_1}(3_{3_1}(3_{3_1}(3_{3_1}(3_{2_1}(2_{5_1}(5_{5_1}(5_{5_1}(x1))))))))))
   5_{4_1}(4_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(x1)))))) -> 5_{4_1}(4_{0_1}(0_{3_1}(3_{3_1}(3_{3_1}(3_{3_1}(3_{2_1}(2_{5_1}(5_{5_1}(5_{1_1}(x1))))))))))
   5_{4_1}(4_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(2_{3_1}(x1)))))) -> 5_{4_1}(4_{0_1}(0_{3_1}(3_{3_1}(3_{3_1}(3_{3_1}(3_{2_1}(2_{5_1}(5_{5_1}(5_{3_1}(x1))))))))))
   5_{4_1}(4_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(x1)))))) -> 5_{4_1}(4_{0_1}(0_{3_1}(3_{3_1}(3_{3_1}(3_{3_1}(3_{2_1}(2_{5_1}(5_{5_1}(5_{0_1}(x1))))))))))
   5_{4_1}(4_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(2_{4_1}(x1)))))) -> 5_{4_1}(4_{0_1}(0_{3_1}(3_{3_1}(3_{3_1}(3_{3_1}(3_{2_1}(2_{5_1}(5_{5_1}(5_{4_1}(x1))))))))))
   5_{4_1}(4_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(x1)))))) -> 5_{4_1}(4_{0_1}(0_{3_1}(3_{3_1}(3_{3_1}(3_{3_1}(3_{2_1}(2_{5_1}(5_{5_1}(5_{2_1}(x1))))))))))
   5_{5_1}(5_{5_1}(5_{5_1}(5_{5_1}(5_{3_1}(3_{5_1}(x1)))))) -> 5_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(1_{5_1}(x1))))))))))
   5_{5_1}(5_{5_1}(5_{5_1}(5_{5_1}(5_{3_1}(3_{1_1}(x1)))))) -> 5_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(x1))))))))))
   5_{5_1}(5_{5_1}(5_{5_1}(5_{5_1}(5_{3_1}(3_{3_1}(x1)))))) -> 5_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(1_{3_1}(x1))))))))))
   5_{5_1}(5_{5_1}(5_{5_1}(5_{5_1}(5_{3_1}(3_{0_1}(x1)))))) -> 5_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(1_{0_1}(x1))))))))))
   5_{5_1}(5_{5_1}(5_{5_1}(5_{5_1}(5_{3_1}(3_{4_1}(x1)))))) -> 5_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(x1))))))))))
   5_{5_1}(5_{5_1}(5_{5_1}(5_{5_1}(5_{3_1}(3_{2_1}(x1)))))) -> 5_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(1_{2_1}(x1))))))))))
   2_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{5_1}(x1))))) -> 2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{5_1}(x1)))))))))))
   2_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(x1))))) -> 2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{1_1}(x1)))))))))))
   2_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{3_1}(x1))))) -> 2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{3_1}(x1)))))))))))
   2_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{0_1}(x1))))) -> 2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(x1)))))))))))
   2_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{4_1}(x1))))) -> 2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{4_1}(x1)))))))))))
   2_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{2_1}(x1))))) -> 2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{2_1}(x1)))))))))))
   5_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{5_1}(x1))))) -> 5_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{5_1}(x1)))))))))))
   5_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(x1))))) -> 5_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{1_1}(x1)))))))))))
   5_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{3_1}(x1))))) -> 5_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{3_1}(x1)))))))))))
   5_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{0_1}(x1))))) -> 5_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(x1)))))))))))
   5_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{4_1}(x1))))) -> 5_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{4_1}(x1)))))))))))
   5_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{2_1}(x1))))) -> 5_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{2_1}(x1)))))))))))
   3_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{5_1}(x1))))) -> 3_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{5_1}(x1)))))))))))
   3_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(x1))))) -> 3_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{1_1}(x1)))))))))))
   3_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{3_1}(x1))))) -> 3_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{3_1}(x1)))))))))))
   3_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{0_1}(x1))))) -> 3_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(x1)))))))))))
   3_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{4_1}(x1))))) -> 3_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{4_1}(x1)))))))))))
   3_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{2_1}(x1))))) -> 3_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{2_1}(x1)))))))))))
   0_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{5_1}(x1))))) -> 0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{5_1}(x1)))))))))))
   0_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(x1))))) -> 0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{1_1}(x1)))))))))))
   0_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{3_1}(x1))))) -> 0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{3_1}(x1)))))))))))
   0_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{0_1}(x1))))) -> 0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(x1)))))))))))
   0_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{4_1}(x1))))) -> 0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{4_1}(x1)))))))))))
   0_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{2_1}(x1))))) -> 0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{2_1}(x1)))))))))))
   1_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{5_1}(x1))))) -> 1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{5_1}(x1)))))))))))
   1_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(x1))))) -> 1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{1_1}(x1)))))))))))
   1_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{3_1}(x1))))) -> 1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{3_1}(x1)))))))))))
   1_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{0_1}(x1))))) -> 1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(x1)))))))))))
   1_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{4_1}(x1))))) -> 1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{4_1}(x1)))))))))))
   1_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{2_1}(x1))))) -> 1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{2_1}(x1)))))))))))
   4_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{5_1}(x1))))) -> 4_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{5_1}(x1)))))))))))
   4_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(x1))))) -> 4_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{1_1}(x1)))))))))))
   4_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{3_1}(x1))))) -> 4_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{3_1}(x1)))))))))))
   4_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{0_1}(x1))))) -> 4_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(x1)))))))))))
   4_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{4_1}(x1))))) -> 4_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{4_1}(x1)))))))))))
   4_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{2_1}(x1))))) -> 4_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{2_1}(x1)))))))))))
   2_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(x1)))))) -> 2_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))))))))))
   2_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{1_1}(x1)))))) -> 2_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))))))))))
   2_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{3_1}(x1)))))) -> 2_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))))))))))
   2_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{0_1}(x1)))))) -> 2_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))))))))))
   2_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{4_1}(x1)))))) -> 2_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))))))))))
   2_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{2_1}(x1)))))) -> 2_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))))))))))
   5_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(x1)))))) -> 5_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))))))))))
   5_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{1_1}(x1)))))) -> 5_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))))))))))
   5_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{3_1}(x1)))))) -> 5_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))))))))))
   5_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{0_1}(x1)))))) -> 5_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))))))))))
   5_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{4_1}(x1)))))) -> 5_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))))))))))
   5_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{2_1}(x1)))))) -> 5_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))))))))))
   3_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(x1)))))) -> 3_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))))))))))
   3_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{1_1}(x1)))))) -> 3_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))))))))))
   3_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{3_1}(x1)))))) -> 3_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))))))))))
   3_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{0_1}(x1)))))) -> 3_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))))))))))
   3_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{4_1}(x1)))))) -> 3_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))))))))))
   3_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{2_1}(x1)))))) -> 3_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))))))))))
   0_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(x1)))))) -> 0_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))))))))))
   0_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{1_1}(x1)))))) -> 0_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))))))))))
   0_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{3_1}(x1)))))) -> 0_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))))))))))
   0_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{0_1}(x1)))))) -> 0_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))))))))))
   0_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{4_1}(x1)))))) -> 0_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))))))))))
   0_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{2_1}(x1)))))) -> 0_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))))))))))
   1_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(x1)))))) -> 1_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))))))))))
   1_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{1_1}(x1)))))) -> 1_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))))))))))
   1_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{3_1}(x1)))))) -> 1_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))))))))))
   1_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{0_1}(x1)))))) -> 1_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))))))))))
   1_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{4_1}(x1)))))) -> 1_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))))))))))
   1_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{2_1}(x1)))))) -> 1_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))))))))))
   4_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(x1)))))) -> 4_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))))))))))
   4_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{1_1}(x1)))))) -> 4_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))))))))))
   4_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{3_1}(x1)))))) -> 4_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))))))))))
   4_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{0_1}(x1)))))) -> 4_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))))))))))
   4_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{4_1}(x1)))))) -> 4_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))))))))))
   4_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{2_1}(x1)))))) -> 4_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))))))))))
   2_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{5_1}(x1)))))) -> 2_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{5_1}(x1)))))))))))
   2_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{1_1}(x1)))))) -> 2_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(x1)))))))))))
   2_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{3_1}(x1)))))) -> 2_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{3_1}(x1)))))))))))
   2_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{0_1}(x1)))))) -> 2_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{0_1}(x1)))))))))))
   2_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{4_1}(x1)))))) -> 2_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{4_1}(x1)))))))))))
   2_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(x1)))))) -> 2_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{2_1}(x1)))))))))))
   5_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{5_1}(x1)))))) -> 5_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{5_1}(x1)))))))))))
   5_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{1_1}(x1)))))) -> 5_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(x1)))))))))))
   5_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{3_1}(x1)))))) -> 5_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{3_1}(x1)))))))))))
   5_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{0_1}(x1)))))) -> 5_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{0_1}(x1)))))))))))
   5_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{4_1}(x1)))))) -> 5_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{4_1}(x1)))))))))))
   5_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(x1)))))) -> 5_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{2_1}(x1)))))))))))
   3_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{5_1}(x1)))))) -> 3_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{5_1}(x1)))))))))))
   3_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{1_1}(x1)))))) -> 3_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(x1)))))))))))
   3_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{3_1}(x1)))))) -> 3_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{3_1}(x1)))))))))))
   3_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{0_1}(x1)))))) -> 3_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{0_1}(x1)))))))))))
   3_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{4_1}(x1)))))) -> 3_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{4_1}(x1)))))))))))
   3_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(x1)))))) -> 3_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{2_1}(x1)))))))))))
   0_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{5_1}(x1)))))) -> 0_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{5_1}(x1)))))))))))
   0_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{1_1}(x1)))))) -> 0_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(x1)))))))))))
   0_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{3_1}(x1)))))) -> 0_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{3_1}(x1)))))))))))
   0_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{0_1}(x1)))))) -> 0_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{0_1}(x1)))))))))))
   0_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{4_1}(x1)))))) -> 0_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{4_1}(x1)))))))))))
   0_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(x1)))))) -> 0_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{2_1}(x1)))))))))))
   1_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{5_1}(x1)))))) -> 1_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{5_1}(x1)))))))))))
   1_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{1_1}(x1)))))) -> 1_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(x1)))))))))))
   1_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{3_1}(x1)))))) -> 1_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{3_1}(x1)))))))))))
   1_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{0_1}(x1)))))) -> 1_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{0_1}(x1)))))))))))
   1_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{4_1}(x1)))))) -> 1_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{4_1}(x1)))))))))))
   1_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(x1)))))) -> 1_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{2_1}(x1)))))))))))
   4_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{5_1}(x1)))))) -> 4_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{5_1}(x1)))))))))))
   4_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{1_1}(x1)))))) -> 4_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(x1)))))))))))
   4_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{3_1}(x1)))))) -> 4_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{3_1}(x1)))))))))))
   4_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{0_1}(x1)))))) -> 4_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{0_1}(x1)))))))))))
   4_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{4_1}(x1)))))) -> 4_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{4_1}(x1)))))))))))
   4_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(x1)))))) -> 4_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{2_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{5_1}(x1))))))) -> 2_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{5_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(x1))))))) -> 2_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{1_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{3_1}(x1))))))) -> 2_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{3_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(x1))))))) -> 2_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{0_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{4_1}(x1))))))) -> 2_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{4_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{2_1}(x1))))))) -> 2_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{2_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{5_1}(x1))))))) -> 5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{5_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(x1))))))) -> 5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{1_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{3_1}(x1))))))) -> 5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{3_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(x1))))))) -> 5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{0_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{4_1}(x1))))))) -> 5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{4_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{2_1}(x1))))))) -> 5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{2_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{5_1}(x1))))))) -> 3_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{5_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(x1))))))) -> 3_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{1_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{3_1}(x1))))))) -> 3_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{3_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(x1))))))) -> 3_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{0_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{4_1}(x1))))))) -> 3_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{4_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{2_1}(x1))))))) -> 3_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{2_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{5_1}(x1))))))) -> 0_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{5_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(x1))))))) -> 0_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{1_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{3_1}(x1))))))) -> 0_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{3_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(x1))))))) -> 0_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{0_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{4_1}(x1))))))) -> 0_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{4_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{2_1}(x1))))))) -> 0_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{2_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{5_1}(x1))))))) -> 1_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{5_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(x1))))))) -> 1_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{1_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{3_1}(x1))))))) -> 1_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{3_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(x1))))))) -> 1_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{0_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{4_1}(x1))))))) -> 1_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{4_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{2_1}(x1))))))) -> 1_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{2_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{5_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{5_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{1_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{3_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{3_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{0_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{4_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{4_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{2_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{2_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(x1)))))))) -> 2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{5_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{1_1}(x1)))))))) -> 2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{3_1}(x1)))))))) -> 2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{3_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{0_1}(x1)))))))) -> 2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{4_1}(x1)))))))) -> 2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{4_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{2_1}(x1)))))))) -> 2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(x1)))))))) -> 5_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{5_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{1_1}(x1)))))))) -> 5_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{3_1}(x1)))))))) -> 5_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{3_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{0_1}(x1)))))))) -> 5_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{4_1}(x1)))))))) -> 5_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{4_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{2_1}(x1)))))))) -> 5_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(x1)))))))) -> 3_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{5_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{1_1}(x1)))))))) -> 3_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{3_1}(x1)))))))) -> 3_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{3_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{0_1}(x1)))))))) -> 3_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{4_1}(x1)))))))) -> 3_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{4_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{2_1}(x1)))))))) -> 3_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(x1)))))))) -> 0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{5_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{1_1}(x1)))))))) -> 0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{3_1}(x1)))))))) -> 0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{3_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{0_1}(x1)))))))) -> 0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{4_1}(x1)))))))) -> 0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{4_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{2_1}(x1)))))))) -> 0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(x1)))))))) -> 1_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{5_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{1_1}(x1)))))))) -> 1_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{3_1}(x1)))))))) -> 1_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{3_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{0_1}(x1)))))))) -> 1_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{4_1}(x1)))))))) -> 1_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{4_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{2_1}(x1)))))))) -> 1_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(x1)))))))) -> 4_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{5_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{1_1}(x1)))))))) -> 4_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{3_1}(x1)))))))) -> 4_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{3_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{0_1}(x1)))))))) -> 4_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{4_1}(x1)))))))) -> 4_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{4_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{2_1}(x1)))))))) -> 4_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{5_1}(x1)))))))) -> 2_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{5_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{1_1}(x1)))))))) -> 2_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{1_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{3_1}(x1)))))))) -> 2_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{3_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{0_1}(x1)))))))) -> 2_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{0_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{4_1}(x1)))))))) -> 2_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{4_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{2_1}(x1)))))))) -> 2_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{2_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{5_1}(x1)))))))) -> 5_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{5_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{1_1}(x1)))))))) -> 5_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{1_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{3_1}(x1)))))))) -> 5_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{3_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{0_1}(x1)))))))) -> 5_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{0_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{4_1}(x1)))))))) -> 5_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{4_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{2_1}(x1)))))))) -> 5_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{2_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{5_1}(x1)))))))) -> 3_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{5_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{1_1}(x1)))))))) -> 3_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{1_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{3_1}(x1)))))))) -> 3_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{3_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{0_1}(x1)))))))) -> 3_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{0_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{4_1}(x1)))))))) -> 3_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{4_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{2_1}(x1)))))))) -> 3_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{2_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{5_1}(x1)))))))) -> 0_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{5_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{1_1}(x1)))))))) -> 0_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{1_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{3_1}(x1)))))))) -> 0_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{3_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{0_1}(x1)))))))) -> 0_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{0_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{4_1}(x1)))))))) -> 0_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{4_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{2_1}(x1)))))))) -> 0_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{2_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{5_1}(x1)))))))) -> 1_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{5_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{1_1}(x1)))))))) -> 1_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{1_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{3_1}(x1)))))))) -> 1_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{3_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{0_1}(x1)))))))) -> 1_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{0_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{4_1}(x1)))))))) -> 1_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{4_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{2_1}(x1)))))))) -> 1_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{2_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{5_1}(x1)))))))) -> 4_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{5_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{1_1}(x1)))))))) -> 4_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{1_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{3_1}(x1)))))))) -> 4_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{3_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{0_1}(x1)))))))) -> 4_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{0_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{4_1}(x1)))))))) -> 4_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{4_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{2_1}(x1)))))))) -> 4_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{2_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{5_1}(x1)))))))) -> 2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{5_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{1_1}(x1)))))))) -> 2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(x1)))))))) -> 2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{3_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(x1)))))))) -> 2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{0_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{4_1}(x1)))))))) -> 2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{4_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{2_1}(x1)))))))) -> 2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{2_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{5_1}(x1)))))))) -> 5_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{5_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{1_1}(x1)))))))) -> 5_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(x1)))))))) -> 5_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{3_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(x1)))))))) -> 5_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{0_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{4_1}(x1)))))))) -> 5_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{4_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{2_1}(x1)))))))) -> 5_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{2_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{5_1}(x1)))))))) -> 3_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{5_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{1_1}(x1)))))))) -> 3_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(x1)))))))) -> 3_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{3_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(x1)))))))) -> 3_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{0_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{4_1}(x1)))))))) -> 3_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{4_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{2_1}(x1)))))))) -> 3_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{2_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{5_1}(x1)))))))) -> 0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{5_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{1_1}(x1)))))))) -> 0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(x1)))))))) -> 0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{3_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(x1)))))))) -> 0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{0_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{4_1}(x1)))))))) -> 0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{4_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{2_1}(x1)))))))) -> 0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{2_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{5_1}(x1)))))))) -> 1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{5_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{1_1}(x1)))))))) -> 1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(x1)))))))) -> 1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{3_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(x1)))))))) -> 1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{0_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{4_1}(x1)))))))) -> 1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{4_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{2_1}(x1)))))))) -> 1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{2_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{5_1}(x1)))))))) -> 4_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{5_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{1_1}(x1)))))))) -> 4_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(x1)))))))) -> 4_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{3_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(x1)))))))) -> 4_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{0_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{4_1}(x1)))))))) -> 4_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{4_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{2_1}(x1)))))))) -> 4_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{2_1}(x1)))))))))))

Q is empty.

----------------------------------------

(5) QTRSRRRProof (EQUIVALENT)
Used ordering:
Polynomial interpretation [POLO]:

   POL(0_{0_1}(x_1)) = x_1
   POL(0_{1_1}(x_1)) = x_1
   POL(0_{2_1}(x_1)) = x_1
   POL(0_{3_1}(x_1)) = x_1
   POL(0_{4_1}(x_1)) = x_1
   POL(0_{5_1}(x_1)) = 36 + x_1
   POL(1_{0_1}(x_1)) = x_1
   POL(1_{1_1}(x_1)) = 8 + x_1
   POL(1_{2_1}(x_1)) = 7 + x_1
   POL(1_{3_1}(x_1)) = 5 + x_1
   POL(1_{4_1}(x_1)) = x_1
   POL(1_{5_1}(x_1)) = x_1
   POL(2_{0_1}(x_1)) = 3 + x_1
   POL(2_{1_1}(x_1)) = 1 + x_1
   POL(2_{2_1}(x_1)) = x_1
   POL(2_{3_1}(x_1)) = 4 + x_1
   POL(2_{4_1}(x_1)) = x_1
   POL(2_{5_1}(x_1)) = 40 + x_1
   POL(3_{0_1}(x_1)) = x_1
   POL(3_{1_1}(x_1)) = x_1
   POL(3_{2_1}(x_1)) = x_1
   POL(3_{3_1}(x_1)) = x_1
   POL(3_{4_1}(x_1)) = x_1
   POL(3_{5_1}(x_1)) = 69 + x_1
   POL(4_{0_1}(x_1)) = x_1
   POL(4_{1_1}(x_1)) = 32 + x_1
   POL(4_{2_1}(x_1)) = 94 + x_1
   POL(4_{3_1}(x_1)) = x_1
   POL(4_{4_1}(x_1)) = x_1
   POL(4_{5_1}(x_1)) = 66 + x_1
   POL(5_{0_1}(x_1)) = 2 + x_1
   POL(5_{1_1}(x_1)) = x_1
   POL(5_{2_1}(x_1)) = x_1
   POL(5_{3_1}(x_1)) = 43 + x_1
   POL(5_{4_1}(x_1)) = 38 + x_1
   POL(5_{5_1}(x_1)) = 2 + x_1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{5_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{0_1}(0_{4_1}(4_{4_1}(4_{5_1}(5_{2_1}(2_{1_1}(1_{5_1}(x1))))))))))
   5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{0_1}(0_{4_1}(4_{4_1}(4_{5_1}(5_{2_1}(2_{1_1}(1_{1_1}(x1))))))))))
   5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{3_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{0_1}(0_{4_1}(4_{4_1}(4_{5_1}(5_{2_1}(2_{1_1}(1_{3_1}(x1))))))))))
   5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{0_1}(0_{4_1}(4_{4_1}(4_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(x1))))))))))
   5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{4_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{0_1}(0_{4_1}(4_{4_1}(4_{5_1}(5_{2_1}(2_{1_1}(1_{4_1}(x1))))))))))
   5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{0_1}(0_{4_1}(4_{4_1}(4_{5_1}(5_{2_1}(2_{1_1}(1_{2_1}(x1))))))))))
   3_{0_1}(0_{5_1}(5_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(x1)))))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{0_1}(0_{5_1}(x1))))))))))
   3_{0_1}(0_{5_1}(5_{5_1}(5_{4_1}(4_{3_1}(3_{1_1}(x1)))))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(x1))))))))))
   3_{0_1}(0_{5_1}(5_{5_1}(5_{4_1}(4_{3_1}(3_{3_1}(x1)))))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{0_1}(0_{3_1}(x1))))))))))
   3_{0_1}(0_{5_1}(5_{5_1}(5_{4_1}(4_{3_1}(3_{0_1}(x1)))))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{0_1}(0_{0_1}(x1))))))))))
   3_{0_1}(0_{5_1}(5_{5_1}(5_{4_1}(4_{3_1}(3_{4_1}(x1)))))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{0_1}(0_{4_1}(x1))))))))))
   3_{0_1}(0_{5_1}(5_{5_1}(5_{4_1}(4_{3_1}(3_{2_1}(x1)))))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{0_1}(0_{2_1}(x1))))))))))
   4_{4_1}(4_{2_1}(2_{5_1}(5_{5_1}(5_{0_1}(0_{5_1}(x1)))))) -> 4_{4_1}(4_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{5_1}(x1))))))))))
   4_{4_1}(4_{2_1}(2_{5_1}(5_{5_1}(5_{0_1}(0_{1_1}(x1)))))) -> 4_{4_1}(4_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{1_1}(x1))))))))))
   4_{4_1}(4_{2_1}(2_{5_1}(5_{5_1}(5_{0_1}(0_{3_1}(x1)))))) -> 4_{4_1}(4_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(x1))))))))))
   4_{4_1}(4_{2_1}(2_{5_1}(5_{5_1}(5_{0_1}(0_{0_1}(x1)))))) -> 4_{4_1}(4_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{0_1}(x1))))))))))
   4_{4_1}(4_{2_1}(2_{5_1}(5_{5_1}(5_{0_1}(0_{4_1}(x1)))))) -> 4_{4_1}(4_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(x1))))))))))
   4_{4_1}(4_{2_1}(2_{5_1}(5_{5_1}(5_{0_1}(0_{2_1}(x1)))))) -> 4_{4_1}(4_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(x1))))))))))
   4_{5_1}(5_{3_1}(3_{5_1}(5_{5_1}(5_{0_1}(0_{5_1}(x1)))))) -> 4_{2_1}(2_{2_1}(2_{3_1}(3_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(x1))))))))))
   4_{5_1}(5_{3_1}(3_{5_1}(5_{5_1}(5_{0_1}(0_{1_1}(x1)))))) -> 4_{2_1}(2_{2_1}(2_{3_1}(3_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(1_{5_1}(5_{1_1}(x1))))))))))
   4_{5_1}(5_{3_1}(3_{5_1}(5_{5_1}(5_{0_1}(0_{3_1}(x1)))))) -> 4_{2_1}(2_{2_1}(2_{3_1}(3_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(x1))))))))))
   4_{5_1}(5_{3_1}(3_{5_1}(5_{5_1}(5_{0_1}(0_{0_1}(x1)))))) -> 4_{2_1}(2_{2_1}(2_{3_1}(3_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(1_{5_1}(5_{0_1}(x1))))))))))
   4_{5_1}(5_{3_1}(3_{5_1}(5_{5_1}(5_{0_1}(0_{4_1}(x1)))))) -> 4_{2_1}(2_{2_1}(2_{3_1}(3_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(1_{5_1}(5_{4_1}(x1))))))))))
   4_{5_1}(5_{3_1}(3_{5_1}(5_{5_1}(5_{0_1}(0_{2_1}(x1)))))) -> 4_{2_1}(2_{2_1}(2_{3_1}(3_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(1_{5_1}(5_{2_1}(x1))))))))))
   5_{4_1}(4_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(2_{5_1}(x1)))))) -> 5_{4_1}(4_{0_1}(0_{3_1}(3_{3_1}(3_{3_1}(3_{3_1}(3_{2_1}(2_{5_1}(5_{5_1}(5_{5_1}(x1))))))))))
   5_{4_1}(4_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(x1)))))) -> 5_{4_1}(4_{0_1}(0_{3_1}(3_{3_1}(3_{3_1}(3_{3_1}(3_{2_1}(2_{5_1}(5_{5_1}(5_{1_1}(x1))))))))))
   5_{4_1}(4_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(x1)))))) -> 5_{4_1}(4_{0_1}(0_{3_1}(3_{3_1}(3_{3_1}(3_{3_1}(3_{2_1}(2_{5_1}(5_{5_1}(5_{0_1}(x1))))))))))
   5_{4_1}(4_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(2_{4_1}(x1)))))) -> 5_{4_1}(4_{0_1}(0_{3_1}(3_{3_1}(3_{3_1}(3_{3_1}(3_{2_1}(2_{5_1}(5_{5_1}(5_{4_1}(x1))))))))))
   5_{4_1}(4_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(x1)))))) -> 5_{4_1}(4_{0_1}(0_{3_1}(3_{3_1}(3_{3_1}(3_{3_1}(3_{2_1}(2_{5_1}(5_{5_1}(5_{2_1}(x1))))))))))
   5_{5_1}(5_{5_1}(5_{5_1}(5_{5_1}(5_{3_1}(3_{5_1}(x1)))))) -> 5_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(1_{5_1}(x1))))))))))
   5_{5_1}(5_{5_1}(5_{5_1}(5_{5_1}(5_{3_1}(3_{1_1}(x1)))))) -> 5_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(x1))))))))))
   5_{5_1}(5_{5_1}(5_{5_1}(5_{5_1}(5_{3_1}(3_{3_1}(x1)))))) -> 5_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(1_{3_1}(x1))))))))))
   5_{5_1}(5_{5_1}(5_{5_1}(5_{5_1}(5_{3_1}(3_{0_1}(x1)))))) -> 5_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(1_{0_1}(x1))))))))))
   5_{5_1}(5_{5_1}(5_{5_1}(5_{5_1}(5_{3_1}(3_{4_1}(x1)))))) -> 5_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(x1))))))))))
   5_{5_1}(5_{5_1}(5_{5_1}(5_{5_1}(5_{3_1}(3_{2_1}(x1)))))) -> 5_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(1_{2_1}(x1))))))))))
   2_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(x1))))) -> 2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{1_1}(x1)))))))))))
   2_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{0_1}(x1))))) -> 2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(x1)))))))))))
   2_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{4_1}(x1))))) -> 2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{4_1}(x1)))))))))))
   2_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{2_1}(x1))))) -> 2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{2_1}(x1)))))))))))
   5_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{5_1}(x1))))) -> 5_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{5_1}(x1)))))))))))
   5_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(x1))))) -> 5_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{1_1}(x1)))))))))))
   5_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{3_1}(x1))))) -> 5_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{3_1}(x1)))))))))))
   5_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{0_1}(x1))))) -> 5_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(x1)))))))))))
   5_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{4_1}(x1))))) -> 5_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{4_1}(x1)))))))))))
   5_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{2_1}(x1))))) -> 5_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{2_1}(x1)))))))))))
   3_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{5_1}(x1))))) -> 3_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{5_1}(x1)))))))))))
   3_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(x1))))) -> 3_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{1_1}(x1)))))))))))
   3_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{3_1}(x1))))) -> 3_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{3_1}(x1)))))))))))
   3_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{0_1}(x1))))) -> 3_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(x1)))))))))))
   3_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{4_1}(x1))))) -> 3_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{4_1}(x1)))))))))))
   3_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{2_1}(x1))))) -> 3_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{2_1}(x1)))))))))))
   0_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{5_1}(x1))))) -> 0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{5_1}(x1)))))))))))
   0_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(x1))))) -> 0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{1_1}(x1)))))))))))
   0_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{3_1}(x1))))) -> 0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{3_1}(x1)))))))))))
   0_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{0_1}(x1))))) -> 0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(x1)))))))))))
   0_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{4_1}(x1))))) -> 0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{4_1}(x1)))))))))))
   0_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{2_1}(x1))))) -> 0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{2_1}(x1)))))))))))
   1_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(x1))))) -> 1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{1_1}(x1)))))))))))
   1_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{0_1}(x1))))) -> 1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(x1)))))))))))
   1_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{4_1}(x1))))) -> 1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{4_1}(x1)))))))))))
   1_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{2_1}(x1))))) -> 1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{2_1}(x1)))))))))))
   4_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{5_1}(x1))))) -> 4_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{5_1}(x1)))))))))))
   4_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(x1))))) -> 4_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{1_1}(x1)))))))))))
   4_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{3_1}(x1))))) -> 4_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{3_1}(x1)))))))))))
   4_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{0_1}(x1))))) -> 4_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(x1)))))))))))
   4_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{4_1}(x1))))) -> 4_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{4_1}(x1)))))))))))
   4_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{2_1}(x1))))) -> 4_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{2_1}(x1)))))))))))
   2_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(x1)))))) -> 2_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))))))))))
   2_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{1_1}(x1)))))) -> 2_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))))))))))
   2_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{3_1}(x1)))))) -> 2_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))))))))))
   2_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{0_1}(x1)))))) -> 2_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))))))))))
   2_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{4_1}(x1)))))) -> 2_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))))))))))
   2_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{2_1}(x1)))))) -> 2_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))))))))))
   5_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(x1)))))) -> 5_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))))))))))
   5_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{1_1}(x1)))))) -> 5_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))))))))))
   5_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{3_1}(x1)))))) -> 5_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))))))))))
   5_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{0_1}(x1)))))) -> 5_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))))))))))
   5_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{4_1}(x1)))))) -> 5_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))))))))))
   5_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{2_1}(x1)))))) -> 5_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))))))))))
   3_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(x1)))))) -> 3_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))))))))))
   3_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{1_1}(x1)))))) -> 3_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))))))))))
   3_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{3_1}(x1)))))) -> 3_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))))))))))
   3_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{0_1}(x1)))))) -> 3_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))))))))))
   3_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{4_1}(x1)))))) -> 3_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))))))))))
   3_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{2_1}(x1)))))) -> 3_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))))))))))
   0_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(x1)))))) -> 0_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))))))))))
   0_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{1_1}(x1)))))) -> 0_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))))))))))
   0_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{3_1}(x1)))))) -> 0_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))))))))))
   0_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{0_1}(x1)))))) -> 0_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))))))))))
   0_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{4_1}(x1)))))) -> 0_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))))))))))
   0_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{2_1}(x1)))))) -> 0_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))))))))))
   1_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(x1)))))) -> 1_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))))))))))
   1_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{1_1}(x1)))))) -> 1_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))))))))))
   1_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{3_1}(x1)))))) -> 1_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))))))))))
   1_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{0_1}(x1)))))) -> 1_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))))))))))
   1_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{4_1}(x1)))))) -> 1_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))))))))))
   1_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{2_1}(x1)))))) -> 1_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))))))))))
   4_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(x1)))))) -> 4_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))))))))))
   4_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{1_1}(x1)))))) -> 4_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))))))))))
   4_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{3_1}(x1)))))) -> 4_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))))))))))
   4_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{0_1}(x1)))))) -> 4_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))))))))))
   4_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{4_1}(x1)))))) -> 4_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))))))))))
   4_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{2_1}(x1)))))) -> 4_{2_1}(2_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))))))))))
   2_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{5_1}(x1)))))) -> 2_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{5_1}(x1)))))))))))
   2_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{1_1}(x1)))))) -> 2_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(x1)))))))))))
   2_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{3_1}(x1)))))) -> 2_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{3_1}(x1)))))))))))
   2_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{0_1}(x1)))))) -> 2_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{0_1}(x1)))))))))))
   2_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{4_1}(x1)))))) -> 2_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{4_1}(x1)))))))))))
   2_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(x1)))))) -> 2_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{2_1}(x1)))))))))))
   3_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{5_1}(x1)))))) -> 3_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{5_1}(x1)))))))))))
   3_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{1_1}(x1)))))) -> 3_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(x1)))))))))))
   3_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{3_1}(x1)))))) -> 3_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{3_1}(x1)))))))))))
   3_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{0_1}(x1)))))) -> 3_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{0_1}(x1)))))))))))
   3_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{4_1}(x1)))))) -> 3_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{4_1}(x1)))))))))))
   3_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(x1)))))) -> 3_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{2_1}(x1)))))))))))
   0_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{5_1}(x1)))))) -> 0_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{5_1}(x1)))))))))))
   0_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{1_1}(x1)))))) -> 0_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(x1)))))))))))
   0_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{3_1}(x1)))))) -> 0_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{3_1}(x1)))))))))))
   0_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{0_1}(x1)))))) -> 0_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{0_1}(x1)))))))))))
   0_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{4_1}(x1)))))) -> 0_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{4_1}(x1)))))))))))
   0_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(x1)))))) -> 0_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{2_1}(x1)))))))))))
   1_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{5_1}(x1)))))) -> 1_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{5_1}(x1)))))))))))
   1_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{1_1}(x1)))))) -> 1_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(x1)))))))))))
   1_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{3_1}(x1)))))) -> 1_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{3_1}(x1)))))))))))
   1_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{0_1}(x1)))))) -> 1_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{0_1}(x1)))))))))))
   1_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{4_1}(x1)))))) -> 1_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{4_1}(x1)))))))))))
   1_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(x1)))))) -> 1_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{2_1}(x1)))))))))))
   4_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{5_1}(x1)))))) -> 4_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{5_1}(x1)))))))))))
   4_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{1_1}(x1)))))) -> 4_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(x1)))))))))))
   4_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{3_1}(x1)))))) -> 4_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{3_1}(x1)))))))))))
   4_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{0_1}(x1)))))) -> 4_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{0_1}(x1)))))))))))
   4_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{4_1}(x1)))))) -> 4_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{4_1}(x1)))))))))))
   4_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(x1)))))) -> 4_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{2_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{5_1}(x1))))))) -> 2_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{5_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(x1))))))) -> 2_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{1_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{3_1}(x1))))))) -> 2_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{3_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(x1))))))) -> 2_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{0_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{4_1}(x1))))))) -> 2_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{4_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{2_1}(x1))))))) -> 2_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{2_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{5_1}(x1))))))) -> 5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{5_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(x1))))))) -> 5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{1_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{3_1}(x1))))))) -> 5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{3_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(x1))))))) -> 5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{0_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{4_1}(x1))))))) -> 5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{4_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{2_1}(x1))))))) -> 5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{2_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{5_1}(x1))))))) -> 3_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{5_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(x1))))))) -> 3_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{1_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{3_1}(x1))))))) -> 3_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{3_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(x1))))))) -> 3_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{0_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{4_1}(x1))))))) -> 3_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{4_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{2_1}(x1))))))) -> 3_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{2_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{5_1}(x1))))))) -> 0_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{5_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(x1))))))) -> 0_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{1_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{3_1}(x1))))))) -> 0_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{3_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(x1))))))) -> 0_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{0_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{4_1}(x1))))))) -> 0_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{4_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{2_1}(x1))))))) -> 0_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{2_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{5_1}(x1))))))) -> 1_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{5_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(x1))))))) -> 1_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{1_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{3_1}(x1))))))) -> 1_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{3_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(x1))))))) -> 1_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{0_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{4_1}(x1))))))) -> 1_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{4_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{2_1}(x1))))))) -> 1_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{2_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(x1)))))))) -> 2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{5_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{1_1}(x1)))))))) -> 2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{3_1}(x1)))))))) -> 2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{3_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{0_1}(x1)))))))) -> 2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{4_1}(x1)))))))) -> 2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{4_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{2_1}(x1)))))))) -> 2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(x1)))))))) -> 5_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{5_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{1_1}(x1)))))))) -> 5_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{3_1}(x1)))))))) -> 5_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{3_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{0_1}(x1)))))))) -> 5_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{4_1}(x1)))))))) -> 5_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{4_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{2_1}(x1)))))))) -> 5_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(x1)))))))) -> 3_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{5_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{1_1}(x1)))))))) -> 3_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{3_1}(x1)))))))) -> 3_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{3_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{0_1}(x1)))))))) -> 3_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{4_1}(x1)))))))) -> 3_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{4_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{2_1}(x1)))))))) -> 3_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(x1)))))))) -> 0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{5_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{1_1}(x1)))))))) -> 0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{3_1}(x1)))))))) -> 0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{3_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{0_1}(x1)))))))) -> 0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{4_1}(x1)))))))) -> 0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{4_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{2_1}(x1)))))))) -> 0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(x1)))))))) -> 1_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{5_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{1_1}(x1)))))))) -> 1_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{3_1}(x1)))))))) -> 1_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{3_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{0_1}(x1)))))))) -> 1_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{4_1}(x1)))))))) -> 1_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{4_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{2_1}(x1)))))))) -> 1_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(x1)))))))) -> 4_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{5_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{1_1}(x1)))))))) -> 4_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{3_1}(x1)))))))) -> 4_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{3_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{0_1}(x1)))))))) -> 4_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{4_1}(x1)))))))) -> 4_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{4_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(3_{2_1}(x1)))))))) -> 4_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{5_1}(5_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{5_1}(x1)))))))) -> 2_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{5_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{1_1}(x1)))))))) -> 2_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{1_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{3_1}(x1)))))))) -> 2_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{3_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{0_1}(x1)))))))) -> 2_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{0_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{4_1}(x1)))))))) -> 2_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{4_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{2_1}(x1)))))))) -> 2_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{2_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{5_1}(x1)))))))) -> 5_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{5_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{1_1}(x1)))))))) -> 5_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{1_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{3_1}(x1)))))))) -> 5_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{3_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{0_1}(x1)))))))) -> 5_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{0_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{4_1}(x1)))))))) -> 5_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{4_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{2_1}(x1)))))))) -> 5_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{2_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{5_1}(x1)))))))) -> 3_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{5_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{1_1}(x1)))))))) -> 3_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{1_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{3_1}(x1)))))))) -> 3_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{3_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{0_1}(x1)))))))) -> 3_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{0_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{4_1}(x1)))))))) -> 3_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{4_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{2_1}(x1)))))))) -> 3_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{2_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{5_1}(x1)))))))) -> 0_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{5_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{1_1}(x1)))))))) -> 0_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{1_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{3_1}(x1)))))))) -> 0_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{3_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{0_1}(x1)))))))) -> 0_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{0_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{4_1}(x1)))))))) -> 0_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{4_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{2_1}(x1)))))))) -> 0_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{2_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{5_1}(x1)))))))) -> 1_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{5_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{1_1}(x1)))))))) -> 1_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{1_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{3_1}(x1)))))))) -> 1_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{3_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{0_1}(x1)))))))) -> 1_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{0_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{4_1}(x1)))))))) -> 1_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{4_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{2_1}(x1)))))))) -> 1_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{2_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{5_1}(x1)))))))) -> 4_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{5_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{1_1}(x1)))))))) -> 4_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{1_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{3_1}(x1)))))))) -> 4_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{3_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{0_1}(x1)))))))) -> 4_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{0_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{4_1}(x1)))))))) -> 4_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{4_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(2_{3_1}(3_{2_1}(x1)))))))) -> 4_{4_1}(4_{0_1}(0_{4_1}(4_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(3_{4_1}(4_{4_1}(4_{2_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{5_1}(x1)))))))) -> 2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{5_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{1_1}(x1)))))))) -> 2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(x1)))))))) -> 2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{3_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(x1)))))))) -> 2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{0_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{4_1}(x1)))))))) -> 2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{4_1}(x1)))))))))))
   2_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{2_1}(x1)))))))) -> 2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{2_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{5_1}(x1)))))))) -> 5_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{5_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{1_1}(x1)))))))) -> 5_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(x1)))))))) -> 5_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{3_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(x1)))))))) -> 5_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{0_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{4_1}(x1)))))))) -> 5_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{4_1}(x1)))))))))))
   5_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{2_1}(x1)))))))) -> 5_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{2_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{5_1}(x1)))))))) -> 3_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{5_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{1_1}(x1)))))))) -> 3_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(x1)))))))) -> 3_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{3_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(x1)))))))) -> 3_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{0_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{4_1}(x1)))))))) -> 3_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{4_1}(x1)))))))))))
   3_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{2_1}(x1)))))))) -> 3_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{2_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{5_1}(x1)))))))) -> 0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{5_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{1_1}(x1)))))))) -> 0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(x1)))))))) -> 0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{3_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(x1)))))))) -> 0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{0_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{4_1}(x1)))))))) -> 0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{4_1}(x1)))))))))))
   0_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{2_1}(x1)))))))) -> 0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{2_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{5_1}(x1)))))))) -> 1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{5_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{1_1}(x1)))))))) -> 1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(x1)))))))) -> 1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{3_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(x1)))))))) -> 1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{0_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{4_1}(x1)))))))) -> 1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{4_1}(x1)))))))))))
   1_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{2_1}(x1)))))))) -> 1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{2_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{5_1}(x1)))))))) -> 4_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{5_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{1_1}(x1)))))))) -> 4_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(x1)))))))) -> 4_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{3_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(x1)))))))) -> 4_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{0_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{4_1}(x1)))))))) -> 4_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{4_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{2_1}(x1)))))))) -> 4_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(3_{1_1}(1_{2_1}(2_{5_1}(5_{2_1}(x1)))))))))))




----------------------------------------

(6)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   2_{2_1}(2_{5_1}(5_{0_1}(0_{5_1}(5_{4_1}(4_{5_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{1_1}(1_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{5_1}(5_{4_1}(4_{5_1}(x1))))))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{5_1}(5_{4_1}(4_{1_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{1_1}(1_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{5_1}(5_{4_1}(4_{1_1}(x1))))))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{1_1}(1_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{5_1}(5_{4_1}(4_{3_1}(x1))))))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{1_1}(1_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{5_1}(5_{4_1}(4_{0_1}(x1))))))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{5_1}(5_{4_1}(4_{4_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{1_1}(1_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{5_1}(5_{4_1}(4_{4_1}(x1))))))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{5_1}(5_{4_1}(4_{2_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{1_1}(1_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{5_1}(5_{4_1}(4_{2_1}(x1))))))))))
   5_{4_1}(4_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(2_{3_1}(x1)))))) -> 5_{4_1}(4_{0_1}(0_{3_1}(3_{3_1}(3_{3_1}(3_{3_1}(3_{2_1}(2_{5_1}(5_{5_1}(5_{3_1}(x1))))))))))
   2_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{5_1}(x1))))) -> 2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{5_1}(x1)))))))))))
   2_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{3_1}(x1))))) -> 2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{3_1}(x1)))))))))))
   1_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{5_1}(x1))))) -> 1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{5_1}(x1)))))))))))
   1_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{3_1}(x1))))) -> 1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{3_1}(x1)))))))))))
   5_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{5_1}(x1)))))) -> 5_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{5_1}(x1)))))))))))
   5_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{1_1}(x1)))))) -> 5_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(x1)))))))))))
   5_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{3_1}(x1)))))) -> 5_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{3_1}(x1)))))))))))
   5_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{0_1}(x1)))))) -> 5_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{0_1}(x1)))))))))))
   5_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{4_1}(x1)))))) -> 5_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{4_1}(x1)))))))))))
   5_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(x1)))))) -> 5_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{2_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{5_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{5_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{1_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{3_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{3_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{0_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{4_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{4_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{2_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{2_1}(x1)))))))))))

Q is empty.

----------------------------------------

(7) QTRSRRRProof (EQUIVALENT)
Used ordering:
Polynomial interpretation [POLO]:

   POL(0_{0_1}(x_1)) = x_1
   POL(0_{1_1}(x_1)) = x_1
   POL(0_{3_1}(x_1)) = 1 + x_1
   POL(0_{4_1}(x_1)) = x_1
   POL(0_{5_1}(x_1)) = 1 + x_1
   POL(1_{0_1}(x_1)) = x_1
   POL(1_{1_1}(x_1)) = x_1
   POL(1_{2_1}(x_1)) = 2 + x_1
   POL(1_{3_1}(x_1)) = x_1
   POL(1_{4_1}(x_1)) = x_1
   POL(1_{5_1}(x_1)) = x_1
   POL(2_{0_1}(x_1)) = x_1
   POL(2_{1_1}(x_1)) = x_1
   POL(2_{2_1}(x_1)) = 2 + x_1
   POL(2_{3_1}(x_1)) = x_1
   POL(2_{4_1}(x_1)) = x_1
   POL(2_{5_1}(x_1)) = x_1
   POL(3_{0_1}(x_1)) = x_1
   POL(3_{1_1}(x_1)) = x_1
   POL(3_{2_1}(x_1)) = x_1
   POL(3_{3_1}(x_1)) = x_1
   POL(3_{5_1}(x_1)) = x_1
   POL(4_{0_1}(x_1)) = x_1
   POL(4_{1_1}(x_1)) = 1 + x_1
   POL(4_{2_1}(x_1)) = x_1
   POL(4_{3_1}(x_1)) = x_1
   POL(4_{4_1}(x_1)) = x_1
   POL(4_{5_1}(x_1)) = x_1
   POL(5_{0_1}(x_1)) = x_1
   POL(5_{1_1}(x_1)) = x_1
   POL(5_{2_1}(x_1)) = x_1
   POL(5_{3_1}(x_1)) = x_1
   POL(5_{4_1}(x_1)) = 4 + x_1
   POL(5_{5_1}(x_1)) = x_1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   5_{4_1}(4_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(2_{3_1}(x1)))))) -> 5_{4_1}(4_{0_1}(0_{3_1}(3_{3_1}(3_{3_1}(3_{3_1}(3_{2_1}(2_{5_1}(5_{5_1}(5_{3_1}(x1))))))))))
   2_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{5_1}(x1))))) -> 2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{5_1}(x1)))))))))))
   2_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{3_1}(x1))))) -> 2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{3_1}(x1)))))))))))
   1_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{5_1}(x1))))) -> 1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{5_1}(x1)))))))))))
   1_{2_1}(2_{5_1}(5_{3_1}(3_{0_1}(0_{3_1}(x1))))) -> 1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(2_{3_1}(x1)))))))))))




----------------------------------------

(8)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   2_{2_1}(2_{5_1}(5_{0_1}(0_{5_1}(5_{4_1}(4_{5_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{1_1}(1_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{5_1}(5_{4_1}(4_{5_1}(x1))))))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{5_1}(5_{4_1}(4_{1_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{1_1}(1_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{5_1}(5_{4_1}(4_{1_1}(x1))))))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{1_1}(1_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{5_1}(5_{4_1}(4_{3_1}(x1))))))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{1_1}(1_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{5_1}(5_{4_1}(4_{0_1}(x1))))))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{5_1}(5_{4_1}(4_{4_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{1_1}(1_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{5_1}(5_{4_1}(4_{4_1}(x1))))))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{5_1}(5_{4_1}(4_{2_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{1_1}(1_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{5_1}(5_{4_1}(4_{2_1}(x1))))))))))
   5_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{5_1}(x1)))))) -> 5_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{5_1}(x1)))))))))))
   5_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{1_1}(x1)))))) -> 5_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(x1)))))))))))
   5_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{3_1}(x1)))))) -> 5_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{3_1}(x1)))))))))))
   5_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{0_1}(x1)))))) -> 5_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{0_1}(x1)))))))))))
   5_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{4_1}(x1)))))) -> 5_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{4_1}(x1)))))))))))
   5_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(x1)))))) -> 5_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{2_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{5_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{5_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{1_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{3_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{3_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{0_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{4_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{4_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{2_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{2_1}(x1)))))))))))

Q is empty.

----------------------------------------

(9) QTRSRRRProof (EQUIVALENT)
Used ordering:
Polynomial interpretation [POLO]:

   POL(0_{5_1}(x_1)) = x_1
   POL(1_{1_1}(x_1)) = x_1
   POL(1_{3_1}(x_1)) = x_1
   POL(1_{4_1}(x_1)) = x_1
   POL(1_{5_1}(x_1)) = x_1
   POL(2_{0_1}(x_1)) = x_1
   POL(2_{1_1}(x_1)) = x_1
   POL(2_{2_1}(x_1)) = x_1
   POL(2_{3_1}(x_1)) = x_1
   POL(2_{4_1}(x_1)) = x_1
   POL(2_{5_1}(x_1)) = x_1
   POL(3_{1_1}(x_1)) = x_1
   POL(3_{2_1}(x_1)) = x_1
   POL(3_{3_1}(x_1)) = x_1
   POL(3_{5_1}(x_1)) = x_1
   POL(4_{0_1}(x_1)) = x_1
   POL(4_{1_1}(x_1)) = x_1
   POL(4_{2_1}(x_1)) = x_1
   POL(4_{3_1}(x_1)) = x_1
   POL(4_{4_1}(x_1)) = x_1
   POL(4_{5_1}(x_1)) = x_1
   POL(5_{0_1}(x_1)) = 1 + x_1
   POL(5_{1_1}(x_1)) = x_1
   POL(5_{2_1}(x_1)) = x_1
   POL(5_{3_1}(x_1)) = x_1
   POL(5_{4_1}(x_1)) = x_1
   POL(5_{5_1}(x_1)) = x_1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   2_{2_1}(2_{5_1}(5_{0_1}(0_{5_1}(5_{4_1}(4_{5_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{1_1}(1_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{5_1}(5_{4_1}(4_{5_1}(x1))))))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{5_1}(5_{4_1}(4_{1_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{1_1}(1_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{5_1}(5_{4_1}(4_{1_1}(x1))))))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{5_1}(5_{4_1}(4_{3_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{1_1}(1_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{5_1}(5_{4_1}(4_{3_1}(x1))))))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{1_1}(1_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{5_1}(5_{4_1}(4_{0_1}(x1))))))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{5_1}(5_{4_1}(4_{4_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{1_1}(1_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{5_1}(5_{4_1}(4_{4_1}(x1))))))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{5_1}(5_{4_1}(4_{2_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{1_1}(1_{3_1}(3_{3_1}(3_{2_1}(2_{2_1}(2_{5_1}(5_{4_1}(4_{2_1}(x1))))))))))




----------------------------------------

(10)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   5_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{5_1}(x1)))))) -> 5_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{5_1}(x1)))))))))))
   5_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{1_1}(x1)))))) -> 5_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(x1)))))))))))
   5_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{3_1}(x1)))))) -> 5_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{3_1}(x1)))))))))))
   5_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{0_1}(x1)))))) -> 5_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{0_1}(x1)))))))))))
   5_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{4_1}(x1)))))) -> 5_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{4_1}(x1)))))))))))
   5_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(x1)))))) -> 5_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{2_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{5_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{5_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{1_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{3_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{3_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{0_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{4_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{4_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{2_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{2_1}(x1)))))))))))

Q is empty.

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(11) QTRSRRRProof (EQUIVALENT)
Used ordering:
Polynomial interpretation [POLO]:

   POL(0_{5_1}(x_1)) = x_1
   POL(1_{1_1}(x_1)) = x_1
   POL(1_{5_1}(x_1)) = x_1
   POL(2_{0_1}(x_1)) = x_1
   POL(2_{1_1}(x_1)) = x_1
   POL(2_{2_1}(x_1)) = x_1
   POL(2_{3_1}(x_1)) = x_1
   POL(2_{4_1}(x_1)) = x_1
   POL(2_{5_1}(x_1)) = x_1
   POL(3_{1_1}(x_1)) = x_1
   POL(3_{2_1}(x_1)) = x_1
   POL(3_{3_1}(x_1)) = x_1
   POL(3_{5_1}(x_1)) = x_1
   POL(4_{2_1}(x_1)) = x_1
   POL(4_{3_1}(x_1)) = x_1
   POL(4_{4_1}(x_1)) = 1 + x_1
   POL(5_{0_1}(x_1)) = x_1
   POL(5_{1_1}(x_1)) = x_1
   POL(5_{2_1}(x_1)) = x_1
   POL(5_{3_1}(x_1)) = x_1
   POL(5_{4_1}(x_1)) = x_1
   POL(5_{5_1}(x_1)) = x_1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   5_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{5_1}(x1)))))) -> 5_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{5_1}(x1)))))))))))
   5_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{1_1}(x1)))))) -> 5_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(x1)))))))))))
   5_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{3_1}(x1)))))) -> 5_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{3_1}(x1)))))))))))
   5_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{0_1}(x1)))))) -> 5_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{0_1}(x1)))))))))))
   5_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{4_1}(x1)))))) -> 5_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{4_1}(x1)))))))))))
   5_{5_1}(5_{4_1}(4_{4_1}(4_{2_1}(2_{5_1}(5_{2_1}(x1)))))) -> 5_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{5_1}(5_{3_1}(3_{3_1}(3_{5_1}(5_{2_1}(x1)))))))))))




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(12)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{5_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{5_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{1_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{3_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{3_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{0_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{4_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{4_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{2_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{2_1}(x1)))))))))))

Q is empty.

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(13) QTRSRRRProof (EQUIVALENT)
Used ordering:
Polynomial interpretation [POLO]:

   POL(0_{5_1}(x_1)) = x_1
   POL(2_{0_1}(x_1)) = x_1
   POL(2_{1_1}(x_1)) = x_1
   POL(2_{2_1}(x_1)) = x_1
   POL(2_{3_1}(x_1)) = x_1
   POL(2_{4_1}(x_1)) = x_1
   POL(2_{5_1}(x_1)) = x_1
   POL(3_{2_1}(x_1)) = x_1
   POL(3_{5_1}(x_1)) = x_1
   POL(4_{2_1}(x_1)) = x_1
   POL(4_{3_1}(x_1)) = x_1
   POL(5_{2_1}(x_1)) = x_1
   POL(5_{4_1}(x_1)) = 1 + x_1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{5_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{5_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{1_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{3_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{3_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{0_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{4_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{4_1}(x1)))))))))))
   4_{3_1}(3_{5_1}(5_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{2_1}(x1))))))) -> 4_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(5_{2_1}(2_{2_1}(2_{3_1}(3_{2_1}(2_{2_1}(x1)))))))))))




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(14)
Obligation:
Q restricted rewrite system:
R is empty.
Q is empty.

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(15) RisEmptyProof (EQUIVALENT)
The TRS R is empty. Hence, termination is trivially proven.
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(16)
YES