YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) QTRS Reverse [EQUIVALENT, 0 ms]
(2) QTRS
(3) FlatCCProof [EQUIVALENT, 0 ms]
(4) QTRS
(5) RootLabelingProof [EQUIVALENT, 17 ms]
(6) QTRS
(7) QTRSRRRProof [EQUIVALENT, 687 ms]
(8) QTRS
(9) QTRSRRRProof [EQUIVALENT, 3 ms]
(10) QTRS
(11) QTRSRRRProof [EQUIVALENT, 16 ms]
(12) QTRS
(13) QTRSRRRProof [EQUIVALENT, 2 ms]
(14) QTRS
(15) QTRSRRRProof [EQUIVALENT, 2 ms]
(16) QTRS
(17) RisEmptyProof [EQUIVALENT, 0 ms]
(18) YES


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

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

   0(0(0(0(0(0(1(1(1(2(2(2(1(x1))))))))))))) -> 0(1(1(0(0(1(1(1(0(1(1(1(1(1(1(2(1(x1)))))))))))))))))
   0(0(0(1(1(1(2(0(2(0(1(1(1(x1))))))))))))) -> 1(1(1(1(2(1(1(0(1(1(1(0(1(1(1(0(1(x1)))))))))))))))))
   0(0(1(0(0(1(2(2(1(0(1(0(1(x1))))))))))))) -> 0(0(1(1(1(0(0(0(1(0(0(1(1(2(1(1(1(x1)))))))))))))))))
   0(0(1(0(1(0(1(1(2(0(1(2(1(x1))))))))))))) -> 0(0(0(0(1(1(1(2(1(0(0(0(0(0(1(0(1(x1)))))))))))))))))
   0(0(1(1(1(1(0(0(0(0(2(2(2(x1))))))))))))) -> 0(1(0(0(1(1(1(0(0(1(1(0(2(0(0(1(1(x1)))))))))))))))))
   0(0(1(1(2(2(0(0(0(1(2(1(2(x1))))))))))))) -> 0(0(0(1(1(0(1(0(0(0(1(2(1(0(2(1(2(x1)))))))))))))))))
   0(0(1(2(1(1(1(1(0(2(0(1(2(x1))))))))))))) -> 1(0(0(1(1(1(2(0(0(0(1(1(2(0(0(1(2(x1)))))))))))))))))
   0(0(1(2(2(2(0(1(0(0(0(0(1(x1))))))))))))) -> 0(1(0(1(1(1(2(0(1(0(1(1(0(0(1(1(1(x1)))))))))))))))))
   0(0(2(1(0(0(1(0(1(0(1(0(0(x1))))))))))))) -> 0(0(0(0(1(0(1(0(1(0(1(0(0(1(1(1(1(x1)))))))))))))))))
   0(1(0(0(1(0(0(2(0(1(0(1(2(x1))))))))))))) -> 0(0(0(0(1(0(0(0(0(0(1(0(0(2(1(1(1(x1)))))))))))))))))
   0(1(0(1(0(2(0(1(1(0(1(0(2(x1))))))))))))) -> 0(1(2(0(1(0(0(0(1(0(0(0(1(0(1(0(2(x1)))))))))))))))))
   0(1(0(2(2(0(0(1(0(1(0(0(1(x1))))))))))))) -> 0(1(1(1(1(2(0(1(1(0(1(0(1(0(1(0(1(x1)))))))))))))))))
   0(1(1(0(1(0(2(1(1(0(0(2(1(x1))))))))))))) -> 1(1(2(0(0(0(0(0(1(0(1(1(2(2(0(0(1(x1)))))))))))))))))
   0(1(1(0(1(1(1(1(0(2(0(1(0(x1))))))))))))) -> 0(1(0(0(0(0(0(0(1(0(1(1(2(0(0(0(1(x1)))))))))))))))))
   0(1(1(1(2(1(0(0(1(1(2(2(1(x1))))))))))))) -> 1(1(0(1(1(2(0(1(1(1(1(0(1(1(2(0(1(x1)))))))))))))))))
   0(1(2(0(1(1(2(0(0(1(0(1(0(x1))))))))))))) -> 0(1(2(0(0(0(0(0(0(1(2(1(0(0(1(0(0(x1)))))))))))))))))
   0(1(2(0(2(1(1(2(2(2(1(0(1(x1))))))))))))) -> 0(1(2(0(0(2(1(1(1(2(0(1(1(2(0(1(1(x1)))))))))))))))))
   0(1(2(2(0(0(2(0(0(1(0(0(0(x1))))))))))))) -> 1(1(2(0(0(1(0(1(2(0(1(0(1(0(0(0(0(x1)))))))))))))))))
   0(2(1(0(0(0(1(1(2(1(0(1(1(x1))))))))))))) -> 1(1(1(1(0(0(1(1(0(1(2(1(0(1(0(0(1(x1)))))))))))))))))
   0(2(1(0(1(0(1(0(0(0(2(0(1(x1))))))))))))) -> 0(0(0(0(0(1(0(0(1(1(2(0(1(1(0(0(1(x1)))))))))))))))))
   0(2(2(0(0(0(0(1(1(1(0(1(1(x1))))))))))))) -> 1(1(1(1(1(1(0(1(0(0(1(1(1(0(1(1(1(x1)))))))))))))))))
   1(0(0(0(0(0(1(0(2(0(1(2(0(x1))))))))))))) -> 1(0(1(1(1(0(1(1(1(0(0(1(2(2(0(0(0(x1)))))))))))))))))
   1(0(0(1(0(1(2(0(1(0(1(2(0(x1))))))))))))) -> 0(0(0(1(1(0(1(0(1(2(0(1(0(1(0(1(0(x1)))))))))))))))))
   1(0(0(1(1(0(0(2(2(0(1(0(1(x1))))))))))))) -> 0(0(0(1(1(1(1(1(0(0(0(0(0(2(1(1(1(x1)))))))))))))))))
   1(0(1(0(1(0(1(1(1(0(1(2(2(x1))))))))))))) -> 0(1(0(1(1(1(0(0(1(1(0(1(0(0(1(2(1(x1)))))))))))))))))
   1(0(1(1(2(0(1(2(2(0(0(0(0(x1))))))))))))) -> 1(0(0(0(0(1(0(1(1(2(2(2(0(0(0(0(0(x1)))))))))))))))))
   1(0(1(2(2(0(1(1(0(2(0(1(1(x1))))))))))))) -> 0(0(1(0(0(1(1(1(0(2(2(2(0(0(0(1(1(x1)))))))))))))))))
   1(1(0(0(0(0(1(1(1(0(0(2(1(x1))))))))))))) -> 0(1(0(1(1(0(0(0(0(1(1(0(0(0(0(0(1(x1)))))))))))))))))
   1(1(0(0(1(0(1(1(1(0(1(0(2(x1))))))))))))) -> 0(1(1(1(1(1(0(1(0(0(0(1(1(1(1(1(2(x1)))))))))))))))))
   1(1(0(1(0(0(1(2(1(0(2(1(1(x1))))))))))))) -> 0(1(0(1(0(0(1(0(1(0(2(2(0(1(0(0(1(x1)))))))))))))))))
   1(1(0(1(1(0(2(0(0(1(0(1(0(x1))))))))))))) -> 0(1(1(0(1(1(0(1(0(0(0(1(1(1(0(0(0(x1)))))))))))))))))
   1(1(1(1(2(0(1(1(2(0(0(0(0(x1))))))))))))) -> 1(1(0(1(1(0(0(1(1(0(1(1(0(1(0(0(1(x1)))))))))))))))))
   1(1(1(2(0(0(0(0(1(1(2(1(1(x1))))))))))))) -> 1(1(1(1(1(0(0(0(1(1(0(2(1(0(0(0(1(x1)))))))))))))))))
   1(1(2(1(0(1(1(1(2(1(0(0(1(x1))))))))))))) -> 0(1(2(2(0(0(0(1(1(0(0(0(0(0(0(1(1(x1)))))))))))))))))
   1(2(0(0(1(0(1(1(1(0(1(0(0(x1))))))))))))) -> 0(1(0(1(1(0(0(1(1(0(0(0(0(0(0(0(1(x1)))))))))))))))))
   1(2(0(0(1(1(0(1(1(0(0(0(2(x1))))))))))))) -> 0(0(1(1(0(0(1(1(1(1(0(1(1(0(1(1(1(x1)))))))))))))))))
   1(2(1(0(1(1(1(0(1(1(0(0(2(x1))))))))))))) -> 0(0(1(0(0(0(1(1(0(0(0(2(0(0(0(1(2(x1)))))))))))))))))
   1(2(1(2(2(0(1(1(1(0(1(0(0(x1))))))))))))) -> 0(1(2(1(0(1(0(0(2(1(1(0(0(1(1(0(0(x1)))))))))))))))))
   1(2(2(2(1(1(0(1(1(0(2(0(0(x1))))))))))))) -> 1(0(0(0(0(0(1(2(2(1(2(1(0(0(2(0(0(x1)))))))))))))))))
   1(2(2(2(1(2(0(0(0(1(2(1(0(x1))))))))))))) -> 1(1(1(0(0(2(1(1(0(2(0(1(1(2(0(1(0(x1)))))))))))))))))
   2(0(0(0(0(1(2(1(2(0(1(2(0(x1))))))))))))) -> 2(0(0(1(1(0(1(0(0(2(1(0(1(1(2(0(0(x1)))))))))))))))))
   2(0(0(1(1(2(0(1(0(1(1(0(1(x1))))))))))))) -> 0(1(0(0(0(2(0(0(0(1(0(1(0(1(1(0(1(x1)))))))))))))))))
   2(0(1(0(0(1(0(0(1(2(1(0(0(x1))))))))))))) -> 1(1(1(0(0(0(1(0(0(1(0(0(0(1(0(1(0(x1)))))))))))))))))
   2(0(1(0(0(2(1(1(0(2(1(2(2(x1))))))))))))) -> 2(1(1(0(0(1(1(0(1(1(1(0(2(1(2(2(2(x1)))))))))))))))))
   2(0(1(0(2(0(1(1(1(1(0(0(1(x1))))))))))))) -> 0(2(1(1(1(0(1(0(1(0(1(1(1(1(1(0(1(x1)))))))))))))))))
   2(0(1(1(0(0(0(1(0(0(2(2(1(x1))))))))))))) -> 2(0(0(0(1(1(2(1(0(0(0(0(1(2(0(0(1(x1)))))))))))))))))
   2(0(1(1(0(0(1(1(1(1(2(0(0(x1))))))))))))) -> 2(0(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(x1)))))))))))))))))
   2(1(2(2(0(0(0(1(0(1(0(1(0(x1))))))))))))) -> 2(1(1(1(0(1(0(0(0(0(0(1(2(1(1(1(0(x1)))))))))))))))))
   2(2(0(0(0(1(1(0(1(1(1(0(0(x1))))))))))))) -> 1(0(1(1(0(0(1(1(0(0(0(0(0(0(1(1(1(x1)))))))))))))))))
   2(2(0(1(1(0(0(1(0(1(1(1(1(x1))))))))))))) -> 2(1(0(0(0(0(0(1(1(1(0(1(0(1(1(0(1(x1)))))))))))))))))

Q is empty.

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

(1) QTRS Reverse (EQUIVALENT)
We applied the QTRS Reverse Processor [REVERSE].
----------------------------------------

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

   1(2(2(2(1(1(1(0(0(0(0(0(0(x1))))))))))))) -> 1(2(1(1(1(1(1(1(0(1(1(1(0(0(1(1(0(x1)))))))))))))))))
   1(1(1(0(2(0(2(1(1(1(0(0(0(x1))))))))))))) -> 1(0(1(1(1(0(1(1(1(0(1(1(2(1(1(1(1(x1)))))))))))))))))
   1(0(1(0(1(2(2(1(0(0(1(0(0(x1))))))))))))) -> 1(1(1(2(1(1(0(0(1(0(0(0(1(1(1(0(0(x1)))))))))))))))))
   1(2(1(0(2(1(1(0(1(0(1(0(0(x1))))))))))))) -> 1(0(1(0(0(0(0(0(1(2(1(1(1(0(0(0(0(x1)))))))))))))))))
   2(2(2(0(0(0(0(1(1(1(1(0(0(x1))))))))))))) -> 1(1(0(0(2(0(1(1(0(0(1(1(1(0(0(1(0(x1)))))))))))))))))
   2(1(2(1(0(0(0(2(2(1(1(0(0(x1))))))))))))) -> 2(1(2(0(1(2(1(0(0(0(1(0(1(1(0(0(0(x1)))))))))))))))))
   2(1(0(2(0(1(1(1(1(2(1(0(0(x1))))))))))))) -> 2(1(0(0(2(1(1(0(0(0(2(1(1(1(0(0(1(x1)))))))))))))))))
   1(0(0(0(0(1(0(2(2(2(1(0(0(x1))))))))))))) -> 1(1(1(0(0(1(1(0(1(0(2(1(1(1(0(1(0(x1)))))))))))))))))
   0(0(1(0(1(0(1(0(0(1(2(0(0(x1))))))))))))) -> 1(1(1(1(0(0(1(0(1(0(1(0(1(0(0(0(0(x1)))))))))))))))))
   2(1(0(1(0(2(0(0(1(0(0(1(0(x1))))))))))))) -> 1(1(1(2(0(0(1(0(0(0(0(0(1(0(0(0(0(x1)))))))))))))))))
   2(0(1(0(1(1(0(2(0(1(0(1(0(x1))))))))))))) -> 2(0(1(0(1(0(0(0(1(0(0(0(1(0(2(1(0(x1)))))))))))))))))
   1(0(0(1(0(1(0(0(2(2(0(1(0(x1))))))))))))) -> 1(0(1(0(1(0(1(0(1(1(0(2(1(1(1(1(0(x1)))))))))))))))))
   1(2(0(0(1(1(2(0(1(0(1(1(0(x1))))))))))))) -> 1(0(0(2(2(1(1(0(1(0(0(0(0(0(2(1(1(x1)))))))))))))))))
   0(1(0(2(0(1(1(1(1(0(1(1(0(x1))))))))))))) -> 1(0(0(0(2(1(1(0(1(0(0(0(0(0(0(1(0(x1)))))))))))))))))
   1(2(2(1(1(0(0(1(2(1(1(1(0(x1))))))))))))) -> 1(0(2(1(1(0(1(1(1(1(0(2(1(1(0(1(1(x1)))))))))))))))))
   0(1(0(1(0(0(2(1(1(0(2(1(0(x1))))))))))))) -> 0(0(1(0(0(1(2(1(0(0(0(0(0(0(2(1(0(x1)))))))))))))))))
   1(0(1(2(2(2(1(1(2(0(2(1(0(x1))))))))))))) -> 1(1(0(2(1(1(0(2(1(1(1(2(0(0(2(1(0(x1)))))))))))))))))
   0(0(0(1(0(0(2(0(0(2(2(1(0(x1))))))))))))) -> 0(0(0(0(1(0(1(0(2(1(0(1(0(0(2(1(1(x1)))))))))))))))))
   1(1(0(1(2(1(1(0(0(0(1(2(0(x1))))))))))))) -> 1(0(0(1(0(1(2(1(0(1(1(0(0(1(1(1(1(x1)))))))))))))))))
   1(0(2(0(0(0(1(0(1(0(1(2(0(x1))))))))))))) -> 1(0(0(1(1(0(2(1(1(0(0(1(0(0(0(0(0(x1)))))))))))))))))
   1(1(0(1(1(1(0(0(0(0(2(2(0(x1))))))))))))) -> 1(1(1(0(1(1(1(0(0(1(0(1(1(1(1(1(1(x1)))))))))))))))))
   0(2(1(0(2(0(1(0(0(0(0(0(1(x1))))))))))))) -> 0(0(0(2(2(1(0(0(1(1(1(0(1(1(1(0(1(x1)))))))))))))))))
   0(2(1(0(1(0(2(1(0(1(0(0(1(x1))))))))))))) -> 0(1(0(1(0(1(0(2(1(0(1(0(1(1(0(0(0(x1)))))))))))))))))
   1(0(1(0(2(2(0(0(1(1(0(0(1(x1))))))))))))) -> 1(1(1(2(0(0(0(0(0(1(1(1(1(1(0(0(0(x1)))))))))))))))))
   2(2(1(0(1(1(1(0(1(0(1(0(1(x1))))))))))))) -> 1(2(1(0(0(1(0(1(1(0(0(1(1(1(0(1(0(x1)))))))))))))))))
   0(0(0(0(2(2(1(0(2(1(1(0(1(x1))))))))))))) -> 0(0(0(0(0(2(2(2(1(1(0(1(0(0(0(0(1(x1)))))))))))))))))
   1(1(0(2(0(1(1(0(2(2(1(0(1(x1))))))))))))) -> 1(1(0(0(0(2(2(2(0(1(1(1(0(0(1(0(0(x1)))))))))))))))))
   1(2(0(0(1(1(1(0(0(0(0(1(1(x1))))))))))))) -> 1(0(0(0(0(0(1(1(0(0(0(0(1(1(0(1(0(x1)))))))))))))))))
   2(0(1(0(1(1(1(0(1(0(0(1(1(x1))))))))))))) -> 2(1(1(1(1(1(0(0(0(1(0(1(1(1(1(1(0(x1)))))))))))))))))
   1(1(2(0(1(2(1(0(0(1(0(1(1(x1))))))))))))) -> 1(0(0(1(0(2(2(0(1(0(1(0(0(1(0(1(0(x1)))))))))))))))))
   0(1(0(1(0(0(2(0(1(1(0(1(1(x1))))))))))))) -> 0(0(0(1(1(1(0(0(0(1(0(1(1(0(1(1(0(x1)))))))))))))))))
   0(0(0(0(2(1(1(0(2(1(1(1(1(x1))))))))))))) -> 1(0(0(1(0(1(1(0(1(1(0(0(1(1(0(1(1(x1)))))))))))))))))
   1(1(2(1(1(0(0(0(0(2(1(1(1(x1))))))))))))) -> 1(0(0(0(1(2(0(1(1(0(0(0(1(1(1(1(1(x1)))))))))))))))))
   1(0(0(1(2(1(1(1(0(1(2(1(1(x1))))))))))))) -> 1(1(0(0(0(0(0(0(1(1(0(0(0(2(2(1(0(x1)))))))))))))))))
   0(0(1(0(1(1(1(0(1(0(0(2(1(x1))))))))))))) -> 1(0(0(0(0(0(0(0(1(1(0(0(1(1(0(1(0(x1)))))))))))))))))
   2(0(0(0(1(1(0(1(1(0(0(2(1(x1))))))))))))) -> 1(1(1(0(1(1(0(1(1(1(1(0(0(1(1(0(0(x1)))))))))))))))))
   2(0(0(1(1(0(1(1(1(0(1(2(1(x1))))))))))))) -> 2(1(0(0(0(2(0(0(0(1(1(0(0(0(1(0(0(x1)))))))))))))))))
   0(0(1(0(1(1(1(0(2(2(1(2(1(x1))))))))))))) -> 0(0(1(1(0(0(1(1(2(0(0(1(0(1(2(1(0(x1)))))))))))))))))
   0(0(2(0(1(1(0(1(1(2(2(2(1(x1))))))))))))) -> 0(0(2(0(0(1(2(1(2(2(1(0(0(0(0(0(1(x1)))))))))))))))))
   0(1(2(1(0(0(0(2(1(2(2(2(1(x1))))))))))))) -> 0(1(0(2(1(1(0(2(0(1(1(2(0(0(1(1(1(x1)))))))))))))))))
   0(2(1(0(2(1(2(1(0(0(0(0(2(x1))))))))))))) -> 0(0(2(1(1(0(1(2(0(0(1(0(1(1(0(0(2(x1)))))))))))))))))
   1(0(1(1(0(1(0(2(1(1(0(0(2(x1))))))))))))) -> 1(0(1(1(0(1(0(1(0(0(0(2(0(0(0(1(0(x1)))))))))))))))))
   0(0(1(2(1(0(0(1(0(0(1(0(2(x1))))))))))))) -> 0(1(0(1(0(0(0(1(0(0(1(0(0(0(1(1(1(x1)))))))))))))))))
   2(2(1(2(0(1(1(2(0(0(1(0(2(x1))))))))))))) -> 2(2(2(1(2(0(1(1(1(0(1(1(0(0(1(1(2(x1)))))))))))))))))
   1(0(0(1(1(1(1(0(2(0(1(0(2(x1))))))))))))) -> 1(0(1(1(1(1(1(0(1(0(1(0(1(1(1(2(0(x1)))))))))))))))))
   1(2(2(0(0(1(0(0(0(1(1(0(2(x1))))))))))))) -> 1(0(0(2(1(0(0(0(0(1(2(1(1(0(0(0(2(x1)))))))))))))))))
   0(0(2(1(1(1(1(0(0(1(1(0(2(x1))))))))))))) -> 0(0(0(0(0(1(0(1(0(0(0(0(1(1(0(0(2(x1)))))))))))))))))
   0(1(0(1(0(1(0(0(0(2(2(1(2(x1))))))))))))) -> 0(1(1(1(2(1(0(0(0(0(0(1(0(1(1(1(2(x1)))))))))))))))))
   0(0(1(1(1(0(1(1(0(0(0(2(2(x1))))))))))))) -> 1(1(1(0(0(0(0(0(0(1(1(0(0(1(1(0(1(x1)))))))))))))))))
   1(1(1(1(0(1(0(0(1(1(0(2(2(x1))))))))))))) -> 1(0(1(1(0(1(0(1(1(1(0(0(0(0(0(1(2(x1)))))))))))))))))

Q is empty.

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

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

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

   1(2(2(2(1(1(1(0(0(0(0(0(0(x1))))))))))))) -> 1(2(1(1(1(1(1(1(0(1(1(1(0(0(1(1(0(x1)))))))))))))))))
   1(1(1(0(2(0(2(1(1(1(0(0(0(x1))))))))))))) -> 1(0(1(1(1(0(1(1(1(0(1(1(2(1(1(1(1(x1)))))))))))))))))
   1(0(1(0(1(2(2(1(0(0(1(0(0(x1))))))))))))) -> 1(1(1(2(1(1(0(0(1(0(0(0(1(1(1(0(0(x1)))))))))))))))))
   1(2(1(0(2(1(1(0(1(0(1(0(0(x1))))))))))))) -> 1(0(1(0(0(0(0(0(1(2(1(1(1(0(0(0(0(x1)))))))))))))))))
   2(1(2(1(0(0(0(2(2(1(1(0(0(x1))))))))))))) -> 2(1(2(0(1(2(1(0(0(0(1(0(1(1(0(0(0(x1)))))))))))))))))
   2(1(0(2(0(1(1(1(1(2(1(0(0(x1))))))))))))) -> 2(1(0(0(2(1(1(0(0(0(2(1(1(1(0(0(1(x1)))))))))))))))))
   1(0(0(0(0(1(0(2(2(2(1(0(0(x1))))))))))))) -> 1(1(1(0(0(1(1(0(1(0(2(1(1(1(0(1(0(x1)))))))))))))))))
   2(0(1(0(1(1(0(2(0(1(0(1(0(x1))))))))))))) -> 2(0(1(0(1(0(0(0(1(0(0(0(1(0(2(1(0(x1)))))))))))))))))
   1(0(0(1(0(1(0(0(2(2(0(1(0(x1))))))))))))) -> 1(0(1(0(1(0(1(0(1(1(0(2(1(1(1(1(0(x1)))))))))))))))))
   1(2(0(0(1(1(2(0(1(0(1(1(0(x1))))))))))))) -> 1(0(0(2(2(1(1(0(1(0(0(0(0(0(2(1(1(x1)))))))))))))))))
   1(2(2(1(1(0(0(1(2(1(1(1(0(x1))))))))))))) -> 1(0(2(1(1(0(1(1(1(1(0(2(1(1(0(1(1(x1)))))))))))))))))
   0(1(0(1(0(0(2(1(1(0(2(1(0(x1))))))))))))) -> 0(0(1(0(0(1(2(1(0(0(0(0(0(0(2(1(0(x1)))))))))))))))))
   1(0(1(2(2(2(1(1(2(0(2(1(0(x1))))))))))))) -> 1(1(0(2(1(1(0(2(1(1(1(2(0(0(2(1(0(x1)))))))))))))))))
   0(0(0(1(0(0(2(0(0(2(2(1(0(x1))))))))))))) -> 0(0(0(0(1(0(1(0(2(1(0(1(0(0(2(1(1(x1)))))))))))))))))
   1(1(0(1(2(1(1(0(0(0(1(2(0(x1))))))))))))) -> 1(0(0(1(0(1(2(1(0(1(1(0(0(1(1(1(1(x1)))))))))))))))))
   1(0(2(0(0(0(1(0(1(0(1(2(0(x1))))))))))))) -> 1(0(0(1(1(0(2(1(1(0(0(1(0(0(0(0(0(x1)))))))))))))))))
   1(1(0(1(1(1(0(0(0(0(2(2(0(x1))))))))))))) -> 1(1(1(0(1(1(1(0(0(1(0(1(1(1(1(1(1(x1)))))))))))))))))
   0(2(1(0(2(0(1(0(0(0(0(0(1(x1))))))))))))) -> 0(0(0(2(2(1(0(0(1(1(1(0(1(1(1(0(1(x1)))))))))))))))))
   0(2(1(0(1(0(2(1(0(1(0(0(1(x1))))))))))))) -> 0(1(0(1(0(1(0(2(1(0(1(0(1(1(0(0(0(x1)))))))))))))))))
   1(0(1(0(2(2(0(0(1(1(0(0(1(x1))))))))))))) -> 1(1(1(2(0(0(0(0(0(1(1(1(1(1(0(0(0(x1)))))))))))))))))
   0(0(0(0(2(2(1(0(2(1(1(0(1(x1))))))))))))) -> 0(0(0(0(0(2(2(2(1(1(0(1(0(0(0(0(1(x1)))))))))))))))))
   1(1(0(2(0(1(1(0(2(2(1(0(1(x1))))))))))))) -> 1(1(0(0(0(2(2(2(0(1(1(1(0(0(1(0(0(x1)))))))))))))))))
   1(2(0(0(1(1(1(0(0(0(0(1(1(x1))))))))))))) -> 1(0(0(0(0(0(1(1(0(0(0(0(1(1(0(1(0(x1)))))))))))))))))
   2(0(1(0(1(1(1(0(1(0(0(1(1(x1))))))))))))) -> 2(1(1(1(1(1(0(0(0(1(0(1(1(1(1(1(0(x1)))))))))))))))))
   1(1(2(0(1(2(1(0(0(1(0(1(1(x1))))))))))))) -> 1(0(0(1(0(2(2(0(1(0(1(0(0(1(0(1(0(x1)))))))))))))))))
   0(1(0(1(0(0(2(0(1(1(0(1(1(x1))))))))))))) -> 0(0(0(1(1(1(0(0(0(1(0(1(1(0(1(1(0(x1)))))))))))))))))
   1(1(2(1(1(0(0(0(0(2(1(1(1(x1))))))))))))) -> 1(0(0(0(1(2(0(1(1(0(0(0(1(1(1(1(1(x1)))))))))))))))))
   1(0(0(1(2(1(1(1(0(1(2(1(1(x1))))))))))))) -> 1(1(0(0(0(0(0(0(1(1(0(0(0(2(2(1(0(x1)))))))))))))))))
   2(0(0(1(1(0(1(1(1(0(1(2(1(x1))))))))))))) -> 2(1(0(0(0(2(0(0(0(1(1(0(0(0(1(0(0(x1)))))))))))))))))
   0(0(1(0(1(1(1(0(2(2(1(2(1(x1))))))))))))) -> 0(0(1(1(0(0(1(1(2(0(0(1(0(1(2(1(0(x1)))))))))))))))))
   0(0(2(0(1(1(0(1(1(2(2(2(1(x1))))))))))))) -> 0(0(2(0(0(1(2(1(2(2(1(0(0(0(0(0(1(x1)))))))))))))))))
   0(1(2(1(0(0(0(2(1(2(2(2(1(x1))))))))))))) -> 0(1(0(2(1(1(0(2(0(1(1(2(0(0(1(1(1(x1)))))))))))))))))
   0(2(1(0(2(1(2(1(0(0(0(0(2(x1))))))))))))) -> 0(0(2(1(1(0(1(2(0(0(1(0(1(1(0(0(2(x1)))))))))))))))))
   1(0(1(1(0(1(0(2(1(1(0(0(2(x1))))))))))))) -> 1(0(1(1(0(1(0(1(0(0(0(2(0(0(0(1(0(x1)))))))))))))))))
   0(0(1(2(1(0(0(1(0(0(1(0(2(x1))))))))))))) -> 0(1(0(1(0(0(0(1(0(0(1(0(0(0(1(1(1(x1)))))))))))))))))
   2(2(1(2(0(1(1(2(0(0(1(0(2(x1))))))))))))) -> 2(2(2(1(2(0(1(1(1(0(1(1(0(0(1(1(2(x1)))))))))))))))))
   1(0(0(1(1(1(1(0(2(0(1(0(2(x1))))))))))))) -> 1(0(1(1(1(1(1(0(1(0(1(0(1(1(1(2(0(x1)))))))))))))))))
   1(2(2(0(0(1(0(0(0(1(1(0(2(x1))))))))))))) -> 1(0(0(2(1(0(0(0(0(1(2(1(1(0(0(0(2(x1)))))))))))))))))
   0(0(2(1(1(1(1(0(0(1(1(0(2(x1))))))))))))) -> 0(0(0(0(0(1(0(1(0(0(0(0(1(1(0(0(2(x1)))))))))))))))))
   0(1(0(1(0(1(0(0(0(2(2(1(2(x1))))))))))))) -> 0(1(1(1(2(1(0(0(0(0(0(1(0(1(1(1(2(x1)))))))))))))))))
   1(1(1(1(0(1(0(0(1(1(0(2(2(x1))))))))))))) -> 1(0(1(1(0(1(0(1(1(1(0(0(0(0(0(1(2(x1)))))))))))))))))
   1(2(2(2(0(0(0(0(1(1(1(1(0(0(x1)))))))))))))) -> 1(1(1(0(0(2(0(1(1(0(0(1(1(1(0(0(1(0(x1))))))))))))))))))
   2(2(2(2(0(0(0(0(1(1(1(1(0(0(x1)))))))))))))) -> 2(1(1(0(0(2(0(1(1(0(0(1(1(1(0(0(1(0(x1))))))))))))))))))
   0(2(2(2(0(0(0(0(1(1(1(1(0(0(x1)))))))))))))) -> 0(1(1(0(0(2(0(1(1(0(0(1(1(1(0(0(1(0(x1))))))))))))))))))
   1(0(0(1(0(1(0(1(0(0(1(2(0(0(x1)))))))))))))) -> 1(1(1(1(1(0(0(1(0(1(0(1(0(1(0(0(0(0(x1))))))))))))))))))
   2(0(0(1(0(1(0(1(0(0(1(2(0(0(x1)))))))))))))) -> 2(1(1(1(1(0(0(1(0(1(0(1(0(1(0(0(0(0(x1))))))))))))))))))
   0(0(0(1(0(1(0(1(0(0(1(2(0(0(x1)))))))))))))) -> 0(1(1(1(1(0(0(1(0(1(0(1(0(1(0(0(0(0(x1))))))))))))))))))
   1(2(1(0(1(0(2(0(0(1(0(0(1(0(x1)))))))))))))) -> 1(1(1(1(2(0(0(1(0(0(0(0(0(1(0(0(0(0(x1))))))))))))))))))
   2(2(1(0(1(0(2(0(0(1(0(0(1(0(x1)))))))))))))) -> 2(1(1(1(2(0(0(1(0(0(0(0(0(1(0(0(0(0(x1))))))))))))))))))
   0(2(1(0(1(0(2(0(0(1(0(0(1(0(x1)))))))))))))) -> 0(1(1(1(2(0(0(1(0(0(0(0(0(1(0(0(0(0(x1))))))))))))))))))
   1(0(1(0(2(0(1(1(1(1(0(1(1(0(x1)))))))))))))) -> 1(1(0(0(0(2(1(1(0(1(0(0(0(0(0(0(1(0(x1))))))))))))))))))
   2(0(1(0(2(0(1(1(1(1(0(1(1(0(x1)))))))))))))) -> 2(1(0(0(0(2(1(1(0(1(0(0(0(0(0(0(1(0(x1))))))))))))))))))
   0(0(1(0(2(0(1(1(1(1(0(1(1(0(x1)))))))))))))) -> 0(1(0(0(0(2(1(1(0(1(0(0(0(0(0(0(1(0(x1))))))))))))))))))
   1(2(2(1(0(1(1(1(0(1(0(1(0(1(x1)))))))))))))) -> 1(1(2(1(0(0(1(0(1(1(0(0(1(1(1(0(1(0(x1))))))))))))))))))
   2(2(2(1(0(1(1(1(0(1(0(1(0(1(x1)))))))))))))) -> 2(1(2(1(0(0(1(0(1(1(0(0(1(1(1(0(1(0(x1))))))))))))))))))
   0(2(2(1(0(1(1(1(0(1(0(1(0(1(x1)))))))))))))) -> 0(1(2(1(0(0(1(0(1(1(0(0(1(1(1(0(1(0(x1))))))))))))))))))
   1(0(0(0(0(2(1(1(0(2(1(1(1(1(x1)))))))))))))) -> 1(1(0(0(1(0(1(1(0(1(1(0(0(1(1(0(1(1(x1))))))))))))))))))
   2(0(0(0(0(2(1(1(0(2(1(1(1(1(x1)))))))))))))) -> 2(1(0(0(1(0(1(1(0(1(1(0(0(1(1(0(1(1(x1))))))))))))))))))
   0(0(0(0(0(2(1(1(0(2(1(1(1(1(x1)))))))))))))) -> 0(1(0(0(1(0(1(1(0(1(1(0(0(1(1(0(1(1(x1))))))))))))))))))
   1(0(0(1(0(1(1(1(0(1(0(0(2(1(x1)))))))))))))) -> 1(1(0(0(0(0(0(0(0(1(1(0(0(1(1(0(1(0(x1))))))))))))))))))
   2(0(0(1(0(1(1(1(0(1(0(0(2(1(x1)))))))))))))) -> 2(1(0(0(0(0(0(0(0(1(1(0(0(1(1(0(1(0(x1))))))))))))))))))
   0(0(0(1(0(1(1(1(0(1(0(0(2(1(x1)))))))))))))) -> 0(1(0(0(0(0(0(0(0(1(1(0(0(1(1(0(1(0(x1))))))))))))))))))
   1(2(0(0(0(1(1(0(1(1(0(0(2(1(x1)))))))))))))) -> 1(1(1(1(0(1(1(0(1(1(1(1(0(0(1(1(0(0(x1))))))))))))))))))
   2(2(0(0(0(1(1(0(1(1(0(0(2(1(x1)))))))))))))) -> 2(1(1(1(0(1(1(0(1(1(1(1(0(0(1(1(0(0(x1))))))))))))))))))
   0(2(0(0(0(1(1(0(1(1(0(0(2(1(x1)))))))))))))) -> 0(1(1(1(0(1(1(0(1(1(1(1(0(0(1(1(0(0(x1))))))))))))))))))
   1(0(0(1(1(1(0(1(1(0(0(0(2(2(x1)))))))))))))) -> 1(1(1(1(0(0(0(0(0(0(1(1(0(0(1(1(0(1(x1))))))))))))))))))
   2(0(0(1(1(1(0(1(1(0(0(0(2(2(x1)))))))))))))) -> 2(1(1(1(0(0(0(0(0(0(1(1(0(0(1(1(0(1(x1))))))))))))))))))
   0(0(0(1(1(1(0(1(1(0(0(0(2(2(x1)))))))))))))) -> 0(1(1(1(0(0(0(0(0(0(1(1(0(0(1(1(0(1(x1))))))))))))))))))

Q is empty.

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(5) 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.

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

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

Q is empty.

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

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

   POL(0_{0_1}(x_1)) = 1 + x_1
   POL(0_{1_1}(x_1)) = 9 + x_1
   POL(0_{2_1}(x_1)) = 1 + x_1
   POL(1_{0_1}(x_1)) = x_1
   POL(1_{1_1}(x_1)) = 9 + x_1
   POL(1_{2_1}(x_1)) = x_1
   POL(2_{0_1}(x_1)) = 104 + x_1
   POL(2_{1_1}(x_1)) = 74 + x_1
   POL(2_{2_1}(x_1)) = 61 + x_1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

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




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

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

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

Q is empty.

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

(9) 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)) = 3 + x_1
   POL(1_{0_1}(x_1)) = x_1
   POL(1_{1_1}(x_1)) = 1 + x_1
   POL(1_{2_1}(x_1)) = 2 + x_1
   POL(2_{0_1}(x_1)) = 1 + x_1
   POL(2_{1_1}(x_1)) = x_1
   POL(2_{2_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:

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




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

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

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

Q is empty.

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

(11) 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(1_{0_1}(x_1)) = x_1
   POL(1_{1_1}(x_1)) = x_1
   POL(1_{2_1}(x_1)) = x_1
   POL(2_{0_1}(x_1)) = 2 + x_1
   POL(2_{1_1}(x_1)) = 1 + x_1
   POL(2_{2_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:

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




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

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

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

Q is empty.

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

(13) 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(1_{0_1}(x_1)) = x_1
   POL(1_{1_1}(x_1)) = x_1
   POL(1_{2_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)) = 1 + x_1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

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




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

(14)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

Q is empty.

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(15) 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)) = 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)) = 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
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

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




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(16)
Obligation:
Q restricted rewrite system:
R is empty.
Q is empty.

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(17) RisEmptyProof (EQUIVALENT)
The TRS R is empty. Hence, termination is trivially proven.
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(18)
YES