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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) QTRS
(1) FlatCCProof [EQUIVALENT, 0 ms]
(2) QTRS
(3) RootLabelingProof [EQUIVALENT, 11 ms]
(4) QTRS
(5) QTRSRRRProof [EQUIVALENT, 197 ms]
(6) QTRS
(7) QTRSRRRProof [EQUIVALENT, 49 ms]
(8) QTRS
(9) DependencyPairsProof [EQUIVALENT, 299 ms]
(10) QDP
(11) DependencyGraphProof [EQUIVALENT, 0 ms]
(12) QDP
(13) QDPOrderProof [EQUIVALENT, 385 ms]
(14) QDP
(15) PisEmptyProof [EQUIVALENT, 0 ms]
(16) YES


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

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

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

Q is empty.

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

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

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

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

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

Q is empty.

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

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

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

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

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

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

Q is empty.

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

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

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

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




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

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

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

Q is empty.

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

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

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

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




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

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

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

Q is empty.

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

(9) DependencyPairsProof (EQUIVALENT)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
----------------------------------------

(10)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(11) DependencyGraphProof (EQUIVALENT)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 292 less nodes.
----------------------------------------

(12)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(13) QDPOrderProof (EQUIVALENT)
We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.

   0_{0_1}^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_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x1))))))))))))) -> 0_{0_1}^1(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x1)))))))))
   0_{0_1}^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_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x1))))))))))))) -> 0_{0_1}^1(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x1)))))))))
The remaining pairs can at least be oriented weakly.
Used ordering:  Polynomial interpretation [POLO]:

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

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:

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


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

(14)
Obligation:
Q DP problem:
P is empty.
The TRS R consists of the following rules:

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

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
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(15) PisEmptyProof (EQUIVALENT)
The TRS P is empty. Hence, there is no (P,Q,R) chain.
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(16)
YES