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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) QTRS
(1) FlatCCProof [EQUIVALENT, 0 ms]
(2) QTRS
(3) RootLabelingProof [EQUIVALENT, 26 ms]
(4) QTRS
(5) QTRSRRRProof [EQUIVALENT, 851 ms]
(6) QTRS
(7) QTRSRRRProof [EQUIVALENT, 175 ms]
(8) QTRS
(9) QTRSRRRProof [EQUIVALENT, 112 ms]
(10) QTRS
(11) QTRSRRRProof [EQUIVALENT, 116 ms]
(12) QTRS
(13) QTRSRRRProof [EQUIVALENT, 70 ms]
(14) QTRS
(15) QTRSRRRProof [EQUIVALENT, 85 ms]
(16) QTRS
(17) QTRSRRRProof [EQUIVALENT, 74 ms]
(18) QTRS
(19) QTRSRRRProof [EQUIVALENT, 62 ms]
(20) QTRS
(21) QTRSRRRProof [EQUIVALENT, 27 ms]
(22) QTRS
(23) QTRSRRRProof [EQUIVALENT, 2 ms]
(24) QTRS
(25) QTRSRRRProof [EQUIVALENT, 0 ms]
(26) QTRS
(27) QTRSRRRProof [EQUIVALENT, 2 ms]
(28) QTRS
(29) QTRSRRRProof [EQUIVALENT, 1 ms]
(30) QTRS
(31) QTRSRRRProof [EQUIVALENT, 0 ms]
(32) QTRS
(33) QTRSRRRProof [EQUIVALENT, 0 ms]
(34) QTRS
(35) RisEmptyProof [EQUIVALENT, 0 ms]
(36) YES


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

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

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

Q is empty.

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

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

   POL(0_{0_1}(x_1)) = 145 + x_1
   POL(0_{1_1}(x_1)) = 132 + x_1
   POL(0_{2_1}(x_1)) = 114 + x_1
   POL(0_{3_1}(x_1)) = 234 + x_1
   POL(0_{4_1}(x_1)) = 286 + x_1
   POL(0_{5_1}(x_1)) = 132 + x_1
   POL(1_{0_1}(x_1)) = x_1
   POL(1_{1_1}(x_1)) = x_1
   POL(1_{2_1}(x_1)) = 44 + x_1
   POL(1_{3_1}(x_1)) = 173 + x_1
   POL(1_{4_1}(x_1)) = x_1
   POL(1_{5_1}(x_1)) = x_1
   POL(2_{0_1}(x_1)) = 19 + x_1
   POL(2_{1_1}(x_1)) = 2 + x_1
   POL(2_{2_1}(x_1)) = 16 + x_1
   POL(2_{3_1}(x_1)) = x_1
   POL(2_{4_1}(x_1)) = 37 + x_1
   POL(2_{5_1}(x_1)) = 2 + x_1
   POL(3_{0_1}(x_1)) = x_1
   POL(3_{1_1}(x_1)) = x_1
   POL(3_{2_1}(x_1)) = x_1
   POL(3_{3_1}(x_1)) = 95 + x_1
   POL(3_{4_1}(x_1)) = 52 + x_1
   POL(3_{5_1}(x_1)) = x_1
   POL(4_{0_1}(x_1)) = 13 + x_1
   POL(4_{1_1}(x_1)) = x_1
   POL(4_{2_1}(x_1)) = 24 + x_1
   POL(4_{3_1}(x_1)) = 61 + x_1
   POL(4_{4_1}(x_1)) = 17 + x_1
   POL(4_{5_1}(x_1)) = x_1
   POL(5_{0_1}(x_1)) = 2 + x_1
   POL(5_{1_1}(x_1)) = 2 + x_1
   POL(5_{2_1}(x_1)) = x_1
   POL(5_{3_1}(x_1)) = x_1
   POL(5_{4_1}(x_1)) = 21 + x_1
   POL(5_{5_1}(x_1)) = 2 + x_1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

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




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

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

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

Q is empty.

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

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

   POL(0_{1_1}(x_1)) = 4 + x_1
   POL(0_{2_1}(x_1)) = x_1
   POL(0_{3_1}(x_1)) = x_1
   POL(0_{4_1}(x_1)) = 2 + x_1
   POL(0_{5_1}(x_1)) = 4 + x_1
   POL(1_{0_1}(x_1)) = 5 + x_1
   POL(1_{1_1}(x_1)) = 1 + x_1
   POL(1_{2_1}(x_1)) = x_1
   POL(1_{3_1}(x_1)) = x_1
   POL(1_{4_1}(x_1)) = x_1
   POL(1_{5_1}(x_1)) = 1 + x_1
   POL(2_{0_1}(x_1)) = 4 + x_1
   POL(2_{1_1}(x_1)) = x_1
   POL(2_{2_1}(x_1)) = 3 + x_1
   POL(2_{3_1}(x_1)) = x_1
   POL(2_{4_1}(x_1)) = x_1
   POL(2_{5_1}(x_1)) = x_1
   POL(3_{0_1}(x_1)) = 4 + x_1
   POL(3_{1_1}(x_1)) = x_1
   POL(3_{2_1}(x_1)) = x_1
   POL(3_{3_1}(x_1)) = x_1
   POL(3_{4_1}(x_1)) = x_1
   POL(3_{5_1}(x_1)) = x_1
   POL(4_{0_1}(x_1)) = x_1
   POL(4_{1_1}(x_1)) = x_1
   POL(4_{2_1}(x_1)) = x_1
   POL(4_{3_1}(x_1)) = x_1
   POL(4_{4_1}(x_1)) = 3 + x_1
   POL(4_{5_1}(x_1)) = x_1
   POL(5_{0_1}(x_1)) = 6 + x_1
   POL(5_{1_1}(x_1)) = 2 + x_1
   POL(5_{2_1}(x_1)) = x_1
   POL(5_{4_1}(x_1)) = x_1
   POL(5_{5_1}(x_1)) = 2 + x_1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

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




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

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

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

Q is empty.

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

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

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

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




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

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

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

Q is empty.

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

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

   POL(0_{1_1}(x_1)) = x_1
   POL(0_{2_1}(x_1)) = 1 + x_1
   POL(0_{3_1}(x_1)) = x_1
   POL(0_{4_1}(x_1)) = 1 + x_1
   POL(0_{5_1}(x_1)) = x_1
   POL(1_{0_1}(x_1)) = x_1
   POL(1_{1_1}(x_1)) = x_1
   POL(1_{3_1}(x_1)) = 1 + x_1
   POL(1_{5_1}(x_1)) = x_1
   POL(2_{0_1}(x_1)) = x_1
   POL(2_{1_1}(x_1)) = x_1
   POL(2_{2_1}(x_1)) = x_1
   POL(2_{3_1}(x_1)) = x_1
   POL(2_{4_1}(x_1)) = x_1
   POL(2_{5_1}(x_1)) = x_1
   POL(3_{0_1}(x_1)) = x_1
   POL(3_{1_1}(x_1)) = 1 + x_1
   POL(3_{2_1}(x_1)) = 1 + x_1
   POL(3_{3_1}(x_1)) = x_1
   POL(3_{4_1}(x_1)) = x_1
   POL(3_{5_1}(x_1)) = 1 + x_1
   POL(4_{0_1}(x_1)) = x_1
   POL(4_{1_1}(x_1)) = x_1
   POL(4_{2_1}(x_1)) = x_1
   POL(4_{3_1}(x_1)) = x_1
   POL(4_{4_1}(x_1)) = x_1
   POL(4_{5_1}(x_1)) = x_1
   POL(5_{0_1}(x_1)) = x_1
   POL(5_{1_1}(x_1)) = 1 + x_1
   POL(5_{2_1}(x_1)) = x_1
   POL(5_{4_1}(x_1)) = x_1
   POL(5_{5_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:

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




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

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

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

Q is empty.

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

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

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

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




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

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

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

Q is empty.

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

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

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

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




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

(16)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

Q is empty.

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

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

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

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




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

(18)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

Q is empty.

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

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

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

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




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

(20)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

Q is empty.

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

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

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

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




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

(22)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

Q is empty.

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

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

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

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




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

(24)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

Q is empty.

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

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

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

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




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

(26)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

Q is empty.

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

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

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

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




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

(28)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

Q is empty.

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

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

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

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




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

(30)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

Q is empty.

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

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

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




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(32)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

Q is empty.

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

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

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




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(34)
Obligation:
Q restricted rewrite system:
R is empty.
Q is empty.

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(35) RisEmptyProof (EQUIVALENT)
The TRS R is empty. Hence, termination is trivially proven.
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(36)
YES