47.29/12.92	YES
47.45/12.97	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
47.45/12.97	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
47.45/12.97	
47.45/12.97	
47.45/12.97	Termination w.r.t. Q of the given QTRS could be proven:
47.45/12.97	
47.45/12.97	(0) QTRS
47.45/12.97	(1) QTRS Reverse [EQUIVALENT, 0 ms]
47.45/12.97	(2) QTRS
47.45/12.97	(3) FlatCCProof [EQUIVALENT, 0 ms]
47.45/12.97	(4) QTRS
47.45/12.97	(5) RootLabelingProof [EQUIVALENT, 0 ms]
47.45/12.97	(6) QTRS
47.45/12.97	(7) QTRSRRRProof [EQUIVALENT, 1438 ms]
47.45/12.97	(8) QTRS
47.45/12.97	(9) QTRSRRRProof [EQUIVALENT, 4 ms]
47.45/12.97	(10) QTRS
47.45/12.97	(11) QTRSRRRProof [EQUIVALENT, 2 ms]
47.45/12.97	(12) QTRS
47.45/12.97	(13) QTRSRRRProof [EQUIVALENT, 2 ms]
47.45/12.97	(14) QTRS
47.45/12.97	(15) RisEmptyProof [EQUIVALENT, 0 ms]
47.45/12.97	(16) YES
47.45/12.97	
47.45/12.97	
47.45/12.97	----------------------------------------
47.45/12.97	
47.45/12.97	(0)
47.45/12.97	Obligation:
47.45/12.97	Q restricted rewrite system:
47.45/12.97	The TRS R consists of the following rules:
47.45/12.97	
47.45/12.97	   1(4(x1)) -> 3(1(1(2(2(4(x1))))))
47.45/12.97	   5(4(x1)) -> 4(2(3(1(1(1(x1))))))
47.45/12.97	   0(3(0(x1))) -> 2(1(1(0(2(0(x1))))))
47.45/12.97	   0(5(5(x1))) -> 1(0(1(3(4(2(x1))))))
47.45/12.97	   1(5(4(x1))) -> 0(2(5(2(0(4(x1))))))
47.45/12.97	   3(5(4(x1))) -> 4(1(3(4(2(3(x1))))))
47.45/12.97	   4(1(4(x1))) -> 3(3(2(2(3(1(x1))))))
47.45/12.97	   5(4(0(x1))) -> 2(4(0(4(4(0(x1))))))
47.45/12.97	   5(4(0(x1))) -> 5(1(5(2(1(0(x1))))))
47.45/12.97	   5(4(4(x1))) -> 4(1(1(3(2(4(x1))))))
47.45/12.97	   5(5(4(x1))) -> 3(4(4(1(2(2(x1))))))
47.45/12.97	   0(5(5(0(x1)))) -> 0(2(0(0(3(0(x1))))))
47.45/12.97	   0(5(5(4(x1)))) -> 0(1(3(4(3(4(x1))))))
47.45/12.97	   1(4(5(4(x1)))) -> 0(4(5(0(2(1(x1))))))
47.45/12.97	   1(4(5(5(x1)))) -> 0(0(1(3(4(1(x1))))))
47.45/12.97	   2(5(4(0(x1)))) -> 0(4(1(2(4(0(x1))))))
47.45/12.97	   4(3(0(5(x1)))) -> 3(3(2(3(5(5(x1))))))
47.45/12.97	   5(4(0(0(x1)))) -> 1(0(4(0(2(2(x1))))))
47.45/12.97	   5(4(0(2(x1)))) -> 3(0(4(5(0(2(x1))))))
47.45/12.97	
47.45/12.97	Q is empty.
47.45/12.97	
47.45/12.97	----------------------------------------
47.45/12.97	
47.45/12.97	(1) QTRS Reverse (EQUIVALENT)
47.45/12.97	We applied the QTRS Reverse Processor [REVERSE].
47.45/12.97	----------------------------------------
47.45/12.97	
47.45/12.97	(2)
47.45/12.97	Obligation:
47.45/12.97	Q restricted rewrite system:
47.45/12.97	The TRS R consists of the following rules:
47.45/12.97	
47.45/12.97	   4(1(x1)) -> 4(2(2(1(1(3(x1))))))
47.45/12.97	   4(5(x1)) -> 1(1(1(3(2(4(x1))))))
47.45/12.97	   0(3(0(x1))) -> 0(2(0(1(1(2(x1))))))
47.45/12.97	   5(5(0(x1))) -> 2(4(3(1(0(1(x1))))))
47.45/12.97	   4(5(1(x1))) -> 4(0(2(5(2(0(x1))))))
47.45/12.97	   4(5(3(x1))) -> 3(2(4(3(1(4(x1))))))
47.45/12.97	   4(1(4(x1))) -> 1(3(2(2(3(3(x1))))))
47.45/12.97	   0(4(5(x1))) -> 0(4(4(0(4(2(x1))))))
47.45/12.97	   0(4(5(x1))) -> 0(1(2(5(1(5(x1))))))
47.45/12.97	   4(4(5(x1))) -> 4(2(3(1(1(4(x1))))))
47.45/12.97	   4(5(5(x1))) -> 2(2(1(4(4(3(x1))))))
47.45/12.97	   0(5(5(0(x1)))) -> 0(3(0(0(2(0(x1))))))
47.45/12.97	   4(5(5(0(x1)))) -> 4(3(4(3(1(0(x1))))))
47.45/12.97	   4(5(4(1(x1)))) -> 1(2(0(5(4(0(x1))))))
47.45/12.97	   5(5(4(1(x1)))) -> 1(4(3(1(0(0(x1))))))
47.45/12.97	   0(4(5(2(x1)))) -> 0(4(2(1(4(0(x1))))))
47.45/12.97	   5(0(3(4(x1)))) -> 5(5(3(2(3(3(x1))))))
47.45/12.97	   0(0(4(5(x1)))) -> 2(2(0(4(0(1(x1))))))
47.45/12.97	   2(0(4(5(x1)))) -> 2(0(5(4(0(3(x1))))))
47.45/12.97	
47.45/12.97	Q is empty.
47.45/12.97	
47.45/12.97	----------------------------------------
47.45/12.97	
47.45/12.97	(3) FlatCCProof (EQUIVALENT)
47.45/12.97	We used flat context closure [ROOTLAB]
47.45/12.97	As Q is empty the flat context closure was sound AND complete.
47.45/12.97	
47.45/12.97	----------------------------------------
47.45/12.97	
47.45/12.97	(4)
47.45/12.97	Obligation:
47.45/12.97	Q restricted rewrite system:
47.45/12.97	The TRS R consists of the following rules:
47.45/12.97	
47.45/12.97	   4(1(x1)) -> 4(2(2(1(1(3(x1))))))
47.45/12.97	   0(3(0(x1))) -> 0(2(0(1(1(2(x1))))))
47.45/12.97	   4(5(1(x1))) -> 4(0(2(5(2(0(x1))))))
47.45/12.97	   0(4(5(x1))) -> 0(4(4(0(4(2(x1))))))
47.45/12.97	   0(4(5(x1))) -> 0(1(2(5(1(5(x1))))))
47.45/12.97	   4(4(5(x1))) -> 4(2(3(1(1(4(x1))))))
47.45/12.97	   0(5(5(0(x1)))) -> 0(3(0(0(2(0(x1))))))
47.45/12.97	   4(5(5(0(x1)))) -> 4(3(4(3(1(0(x1))))))
47.45/12.97	   0(4(5(2(x1)))) -> 0(4(2(1(4(0(x1))))))
47.45/12.97	   5(0(3(4(x1)))) -> 5(5(3(2(3(3(x1))))))
47.45/12.97	   2(0(4(5(x1)))) -> 2(0(5(4(0(3(x1))))))
47.45/12.97	   4(4(5(x1))) -> 4(1(1(1(3(2(4(x1)))))))
47.45/12.97	   1(4(5(x1))) -> 1(1(1(1(3(2(4(x1)))))))
47.45/12.97	   2(4(5(x1))) -> 2(1(1(1(3(2(4(x1)))))))
47.45/12.97	   3(4(5(x1))) -> 3(1(1(1(3(2(4(x1)))))))
47.45/12.97	   5(4(5(x1))) -> 5(1(1(1(3(2(4(x1)))))))
47.45/12.97	   0(4(5(x1))) -> 0(1(1(1(3(2(4(x1)))))))
47.45/12.97	   4(5(5(0(x1)))) -> 4(2(4(3(1(0(1(x1)))))))
47.45/12.97	   1(5(5(0(x1)))) -> 1(2(4(3(1(0(1(x1)))))))
47.45/12.97	   2(5(5(0(x1)))) -> 2(2(4(3(1(0(1(x1)))))))
47.45/12.97	   3(5(5(0(x1)))) -> 3(2(4(3(1(0(1(x1)))))))
47.45/12.97	   5(5(5(0(x1)))) -> 5(2(4(3(1(0(1(x1)))))))
47.45/12.97	   0(5(5(0(x1)))) -> 0(2(4(3(1(0(1(x1)))))))
47.45/12.97	   4(4(5(3(x1)))) -> 4(3(2(4(3(1(4(x1)))))))
47.45/12.97	   1(4(5(3(x1)))) -> 1(3(2(4(3(1(4(x1)))))))
47.45/12.97	   2(4(5(3(x1)))) -> 2(3(2(4(3(1(4(x1)))))))
47.45/12.97	   3(4(5(3(x1)))) -> 3(3(2(4(3(1(4(x1)))))))
47.45/12.97	   5(4(5(3(x1)))) -> 5(3(2(4(3(1(4(x1)))))))
47.45/12.97	   0(4(5(3(x1)))) -> 0(3(2(4(3(1(4(x1)))))))
47.45/12.97	   4(4(1(4(x1)))) -> 4(1(3(2(2(3(3(x1)))))))
47.45/12.97	   1(4(1(4(x1)))) -> 1(1(3(2(2(3(3(x1)))))))
47.45/12.97	   2(4(1(4(x1)))) -> 2(1(3(2(2(3(3(x1)))))))
47.45/12.97	   3(4(1(4(x1)))) -> 3(1(3(2(2(3(3(x1)))))))
47.45/12.97	   5(4(1(4(x1)))) -> 5(1(3(2(2(3(3(x1)))))))
47.45/12.97	   0(4(1(4(x1)))) -> 0(1(3(2(2(3(3(x1)))))))
47.45/12.97	   4(4(5(5(x1)))) -> 4(2(2(1(4(4(3(x1)))))))
47.45/12.97	   1(4(5(5(x1)))) -> 1(2(2(1(4(4(3(x1)))))))
47.45/12.97	   2(4(5(5(x1)))) -> 2(2(2(1(4(4(3(x1)))))))
47.45/12.97	   3(4(5(5(x1)))) -> 3(2(2(1(4(4(3(x1)))))))
47.45/12.97	   5(4(5(5(x1)))) -> 5(2(2(1(4(4(3(x1)))))))
47.45/12.97	   0(4(5(5(x1)))) -> 0(2(2(1(4(4(3(x1)))))))
47.45/12.97	   4(4(5(4(1(x1))))) -> 4(1(2(0(5(4(0(x1)))))))
47.45/12.97	   1(4(5(4(1(x1))))) -> 1(1(2(0(5(4(0(x1)))))))
47.45/12.97	   2(4(5(4(1(x1))))) -> 2(1(2(0(5(4(0(x1)))))))
47.45/12.97	   3(4(5(4(1(x1))))) -> 3(1(2(0(5(4(0(x1)))))))
47.45/12.97	   5(4(5(4(1(x1))))) -> 5(1(2(0(5(4(0(x1)))))))
47.45/12.97	   0(4(5(4(1(x1))))) -> 0(1(2(0(5(4(0(x1)))))))
47.45/12.97	   4(5(5(4(1(x1))))) -> 4(1(4(3(1(0(0(x1)))))))
47.45/12.97	   1(5(5(4(1(x1))))) -> 1(1(4(3(1(0(0(x1)))))))
47.45/12.97	   2(5(5(4(1(x1))))) -> 2(1(4(3(1(0(0(x1)))))))
47.45/12.97	   3(5(5(4(1(x1))))) -> 3(1(4(3(1(0(0(x1)))))))
47.45/12.97	   5(5(5(4(1(x1))))) -> 5(1(4(3(1(0(0(x1)))))))
47.45/12.97	   0(5(5(4(1(x1))))) -> 0(1(4(3(1(0(0(x1)))))))
47.45/12.97	   4(0(0(4(5(x1))))) -> 4(2(2(0(4(0(1(x1)))))))
47.45/12.97	   1(0(0(4(5(x1))))) -> 1(2(2(0(4(0(1(x1)))))))
47.45/12.97	   2(0(0(4(5(x1))))) -> 2(2(2(0(4(0(1(x1)))))))
47.45/12.97	   3(0(0(4(5(x1))))) -> 3(2(2(0(4(0(1(x1)))))))
47.45/12.97	   5(0(0(4(5(x1))))) -> 5(2(2(0(4(0(1(x1)))))))
47.45/12.97	   0(0(0(4(5(x1))))) -> 0(2(2(0(4(0(1(x1)))))))
47.45/12.97	
47.45/12.97	Q is empty.
47.45/12.97	
47.45/12.97	----------------------------------------
47.45/12.97	
47.45/12.97	(5) RootLabelingProof (EQUIVALENT)
47.45/12.97	We used plain root labeling [ROOTLAB] with the following heuristic:
47.45/12.97	LabelAll: All function symbols get labeled
47.45/12.97	
47.45/12.97	As Q is empty the root labeling was sound AND complete.
47.45/12.97	
47.45/12.97	----------------------------------------
47.45/12.97	
47.45/12.97	(6)
47.45/12.97	Obligation:
47.45/12.97	Q restricted rewrite system:
47.45/12.97	The TRS R consists of the following rules:
47.45/12.97	
47.45/12.97	   4_{1_1}(1_{4_1}(x1)) -> 4_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{3_1}(3_{4_1}(x1))))))
47.45/12.97	   4_{1_1}(1_{1_1}(x1)) -> 4_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{3_1}(3_{1_1}(x1))))))
47.45/12.97	   4_{1_1}(1_{2_1}(x1)) -> 4_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(x1))))))
47.45/12.97	   4_{1_1}(1_{3_1}(x1)) -> 4_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{3_1}(3_{3_1}(x1))))))
47.45/12.97	   4_{1_1}(1_{0_1}(x1)) -> 4_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{3_1}(3_{0_1}(x1))))))
47.45/12.97	   4_{1_1}(1_{5_1}(x1)) -> 4_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{3_1}(3_{5_1}(x1))))))
47.45/12.97	   0_{3_1}(3_{0_1}(0_{4_1}(x1))) -> 0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{4_1}(x1))))))
47.45/12.97	   0_{3_1}(3_{0_1}(0_{1_1}(x1))) -> 0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(x1))))))
47.45/12.97	   0_{3_1}(3_{0_1}(0_{2_1}(x1))) -> 0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(x1))))))
47.45/12.97	   0_{3_1}(3_{0_1}(0_{3_1}(x1))) -> 0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{3_1}(x1))))))
47.45/12.97	   0_{3_1}(3_{0_1}(0_{0_1}(x1))) -> 0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(x1))))))
47.45/12.97	   0_{3_1}(3_{0_1}(0_{5_1}(x1))) -> 0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{5_1}(x1))))))
47.45/12.97	   4_{5_1}(5_{1_1}(1_{4_1}(x1))) -> 4_{0_1}(0_{2_1}(2_{5_1}(5_{2_1}(2_{0_1}(0_{4_1}(x1))))))
47.45/12.97	   4_{5_1}(5_{1_1}(1_{1_1}(x1))) -> 4_{0_1}(0_{2_1}(2_{5_1}(5_{2_1}(2_{0_1}(0_{1_1}(x1))))))
47.45/12.97	   4_{5_1}(5_{1_1}(1_{2_1}(x1))) -> 4_{0_1}(0_{2_1}(2_{5_1}(5_{2_1}(2_{0_1}(0_{2_1}(x1))))))
47.45/12.98	   4_{5_1}(5_{1_1}(1_{3_1}(x1))) -> 4_{0_1}(0_{2_1}(2_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(x1))))))
47.45/12.98	   4_{5_1}(5_{1_1}(1_{0_1}(x1))) -> 4_{0_1}(0_{2_1}(2_{5_1}(5_{2_1}(2_{0_1}(0_{0_1}(x1))))))
47.45/12.98	   4_{5_1}(5_{1_1}(1_{5_1}(x1))) -> 4_{0_1}(0_{2_1}(2_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(x1))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{4_1}(x1))) -> 0_{4_1}(4_{4_1}(4_{0_1}(0_{4_1}(4_{2_1}(2_{4_1}(x1))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{1_1}(x1))) -> 0_{4_1}(4_{4_1}(4_{0_1}(0_{4_1}(4_{2_1}(2_{1_1}(x1))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{2_1}(x1))) -> 0_{4_1}(4_{4_1}(4_{0_1}(0_{4_1}(4_{2_1}(2_{2_1}(x1))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{3_1}(x1))) -> 0_{4_1}(4_{4_1}(4_{0_1}(0_{4_1}(4_{2_1}(2_{3_1}(x1))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{0_1}(x1))) -> 0_{4_1}(4_{4_1}(4_{0_1}(0_{4_1}(4_{2_1}(2_{0_1}(x1))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{5_1}(x1))) -> 0_{4_1}(4_{4_1}(4_{0_1}(0_{4_1}(4_{2_1}(2_{5_1}(x1))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{4_1}(x1))) -> 0_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(1_{5_1}(5_{4_1}(x1))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{1_1}(x1))) -> 0_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(x1))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{2_1}(x1))) -> 0_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(1_{5_1}(5_{2_1}(x1))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{3_1}(x1))) -> 0_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(1_{5_1}(5_{3_1}(x1))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{0_1}(x1))) -> 0_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(1_{5_1}(5_{0_1}(x1))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{5_1}(x1))) -> 0_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(1_{5_1}(5_{5_1}(x1))))))
47.45/12.98	   4_{4_1}(4_{5_1}(5_{4_1}(x1))) -> 4_{2_1}(2_{3_1}(3_{1_1}(1_{1_1}(1_{4_1}(4_{4_1}(x1))))))
47.45/12.98	   4_{4_1}(4_{5_1}(5_{1_1}(x1))) -> 4_{2_1}(2_{3_1}(3_{1_1}(1_{1_1}(1_{4_1}(4_{1_1}(x1))))))
47.45/12.98	   4_{4_1}(4_{5_1}(5_{2_1}(x1))) -> 4_{2_1}(2_{3_1}(3_{1_1}(1_{1_1}(1_{4_1}(4_{2_1}(x1))))))
47.45/12.98	   4_{4_1}(4_{5_1}(5_{3_1}(x1))) -> 4_{2_1}(2_{3_1}(3_{1_1}(1_{1_1}(1_{4_1}(4_{3_1}(x1))))))
47.45/12.98	   4_{4_1}(4_{5_1}(5_{0_1}(x1))) -> 4_{2_1}(2_{3_1}(3_{1_1}(1_{1_1}(1_{4_1}(4_{0_1}(x1))))))
47.45/12.98	   4_{4_1}(4_{5_1}(5_{5_1}(x1))) -> 4_{2_1}(2_{3_1}(3_{1_1}(1_{1_1}(1_{4_1}(4_{5_1}(x1))))))
47.45/12.98	   0_{5_1}(5_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{4_1}(x1))))))
47.45/12.98	   0_{5_1}(5_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(x1))))))
47.45/12.98	   0_{5_1}(5_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{2_1}(x1))))))
47.45/12.98	   0_{5_1}(5_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{3_1}(x1))))))
47.45/12.98	   0_{5_1}(5_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(x1))))))
47.45/12.98	   0_{5_1}(5_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{5_1}(x1))))))
47.45/12.98	   4_{5_1}(5_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 4_{3_1}(3_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{4_1}(x1))))))
47.45/12.98	   4_{5_1}(5_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 4_{3_1}(3_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(x1))))))
47.45/12.98	   4_{5_1}(5_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 4_{3_1}(3_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{2_1}(x1))))))
47.45/12.98	   4_{5_1}(5_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 4_{3_1}(3_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{3_1}(x1))))))
47.45/12.98	   4_{5_1}(5_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 4_{3_1}(3_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(x1))))))
47.45/12.98	   4_{5_1}(5_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 4_{3_1}(3_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{5_1}(x1))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{2_1}(2_{4_1}(x1)))) -> 0_{4_1}(4_{2_1}(2_{1_1}(1_{4_1}(4_{0_1}(0_{4_1}(x1))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{2_1}(2_{1_1}(x1)))) -> 0_{4_1}(4_{2_1}(2_{1_1}(1_{4_1}(4_{0_1}(0_{1_1}(x1))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{2_1}(2_{2_1}(x1)))) -> 0_{4_1}(4_{2_1}(2_{1_1}(1_{4_1}(4_{0_1}(0_{2_1}(x1))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{2_1}(2_{3_1}(x1)))) -> 0_{4_1}(4_{2_1}(2_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(x1))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{2_1}(2_{0_1}(x1)))) -> 0_{4_1}(4_{2_1}(2_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(x1))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{2_1}(2_{5_1}(x1)))) -> 0_{4_1}(4_{2_1}(2_{1_1}(1_{4_1}(4_{0_1}(0_{5_1}(x1))))))
47.45/12.98	   5_{0_1}(0_{3_1}(3_{4_1}(4_{4_1}(x1)))) -> 5_{5_1}(5_{3_1}(3_{2_1}(2_{3_1}(3_{3_1}(3_{4_1}(x1))))))
47.45/12.98	   5_{0_1}(0_{3_1}(3_{4_1}(4_{1_1}(x1)))) -> 5_{5_1}(5_{3_1}(3_{2_1}(2_{3_1}(3_{3_1}(3_{1_1}(x1))))))
47.45/12.98	   5_{0_1}(0_{3_1}(3_{4_1}(4_{2_1}(x1)))) -> 5_{5_1}(5_{3_1}(3_{2_1}(2_{3_1}(3_{3_1}(3_{2_1}(x1))))))
47.45/12.98	   5_{0_1}(0_{3_1}(3_{4_1}(4_{3_1}(x1)))) -> 5_{5_1}(5_{3_1}(3_{2_1}(2_{3_1}(3_{3_1}(3_{3_1}(x1))))))
47.45/12.98	   5_{0_1}(0_{3_1}(3_{4_1}(4_{0_1}(x1)))) -> 5_{5_1}(5_{3_1}(3_{2_1}(2_{3_1}(3_{3_1}(3_{0_1}(x1))))))
47.45/12.98	   5_{0_1}(0_{3_1}(3_{4_1}(4_{5_1}(x1)))) -> 5_{5_1}(5_{3_1}(3_{2_1}(2_{3_1}(3_{3_1}(3_{5_1}(x1))))))
47.45/12.98	   2_{0_1}(0_{4_1}(4_{5_1}(5_{4_1}(x1)))) -> 2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{3_1}(3_{4_1}(x1))))))
47.45/12.98	   2_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(x1)))) -> 2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{3_1}(3_{1_1}(x1))))))
47.45/12.98	   2_{0_1}(0_{4_1}(4_{5_1}(5_{2_1}(x1)))) -> 2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{3_1}(3_{2_1}(x1))))))
47.45/12.98	   2_{0_1}(0_{4_1}(4_{5_1}(5_{3_1}(x1)))) -> 2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{3_1}(3_{3_1}(x1))))))
47.45/12.98	   2_{0_1}(0_{4_1}(4_{5_1}(5_{0_1}(x1)))) -> 2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(x1))))))
47.45/12.98	   2_{0_1}(0_{4_1}(4_{5_1}(5_{5_1}(x1)))) -> 2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{3_1}(3_{5_1}(x1))))))
47.45/12.98	   4_{4_1}(4_{5_1}(5_{4_1}(x1))) -> 4_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{4_1}(x1)))))))
47.45/12.98	   4_{4_1}(4_{5_1}(5_{1_1}(x1))) -> 4_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{1_1}(x1)))))))
47.45/12.98	   4_{4_1}(4_{5_1}(5_{2_1}(x1))) -> 4_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{2_1}(x1)))))))
47.45/12.98	   4_{4_1}(4_{5_1}(5_{3_1}(x1))) -> 4_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(x1)))))))
47.45/12.98	   4_{4_1}(4_{5_1}(5_{0_1}(x1))) -> 4_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{0_1}(x1)))))))
47.45/12.98	   4_{4_1}(4_{5_1}(5_{5_1}(x1))) -> 4_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{5_1}(x1)))))))
47.45/12.98	   1_{4_1}(4_{5_1}(5_{4_1}(x1))) -> 1_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{4_1}(x1)))))))
47.45/12.98	   1_{4_1}(4_{5_1}(5_{1_1}(x1))) -> 1_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{1_1}(x1)))))))
47.45/12.98	   1_{4_1}(4_{5_1}(5_{2_1}(x1))) -> 1_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{2_1}(x1)))))))
47.45/12.98	   1_{4_1}(4_{5_1}(5_{3_1}(x1))) -> 1_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(x1)))))))
47.45/12.98	   1_{4_1}(4_{5_1}(5_{0_1}(x1))) -> 1_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{0_1}(x1)))))))
47.45/12.98	   1_{4_1}(4_{5_1}(5_{5_1}(x1))) -> 1_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{5_1}(x1)))))))
47.45/12.98	   2_{4_1}(4_{5_1}(5_{4_1}(x1))) -> 2_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{4_1}(x1)))))))
47.45/12.98	   2_{4_1}(4_{5_1}(5_{1_1}(x1))) -> 2_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{1_1}(x1)))))))
47.45/12.98	   2_{4_1}(4_{5_1}(5_{2_1}(x1))) -> 2_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{2_1}(x1)))))))
47.45/12.98	   2_{4_1}(4_{5_1}(5_{3_1}(x1))) -> 2_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(x1)))))))
47.45/12.98	   2_{4_1}(4_{5_1}(5_{0_1}(x1))) -> 2_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{0_1}(x1)))))))
47.45/12.98	   2_{4_1}(4_{5_1}(5_{5_1}(x1))) -> 2_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{5_1}(x1)))))))
47.45/12.98	   3_{4_1}(4_{5_1}(5_{4_1}(x1))) -> 3_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{4_1}(x1)))))))
47.45/12.98	   3_{4_1}(4_{5_1}(5_{1_1}(x1))) -> 3_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{1_1}(x1)))))))
47.45/12.98	   3_{4_1}(4_{5_1}(5_{2_1}(x1))) -> 3_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{2_1}(x1)))))))
47.45/12.98	   3_{4_1}(4_{5_1}(5_{3_1}(x1))) -> 3_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(x1)))))))
47.45/12.98	   3_{4_1}(4_{5_1}(5_{0_1}(x1))) -> 3_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{0_1}(x1)))))))
47.45/12.98	   3_{4_1}(4_{5_1}(5_{5_1}(x1))) -> 3_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{5_1}(x1)))))))
47.45/12.98	   5_{4_1}(4_{5_1}(5_{4_1}(x1))) -> 5_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{4_1}(x1)))))))
47.45/12.98	   5_{4_1}(4_{5_1}(5_{1_1}(x1))) -> 5_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{1_1}(x1)))))))
47.45/12.98	   5_{4_1}(4_{5_1}(5_{2_1}(x1))) -> 5_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{2_1}(x1)))))))
47.45/12.98	   5_{4_1}(4_{5_1}(5_{3_1}(x1))) -> 5_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(x1)))))))
47.45/12.98	   5_{4_1}(4_{5_1}(5_{0_1}(x1))) -> 5_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{0_1}(x1)))))))
47.45/12.98	   5_{4_1}(4_{5_1}(5_{5_1}(x1))) -> 5_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{5_1}(x1)))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{4_1}(x1))) -> 0_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{4_1}(x1)))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{1_1}(x1))) -> 0_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{1_1}(x1)))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{2_1}(x1))) -> 0_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{2_1}(x1)))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{3_1}(x1))) -> 0_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(x1)))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{0_1}(x1))) -> 0_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{0_1}(x1)))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{5_1}(x1))) -> 0_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{5_1}(x1)))))))
47.45/12.98	   4_{5_1}(5_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 4_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
47.45/12.98	   4_{5_1}(5_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 4_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
47.45/12.98	   4_{5_1}(5_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 4_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
47.45/12.98	   4_{5_1}(5_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 4_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
47.45/12.98	   4_{5_1}(5_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 4_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
47.45/12.98	   4_{5_1}(5_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 4_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
47.45/12.98	   1_{5_1}(5_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 1_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
47.45/12.98	   1_{5_1}(5_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 1_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
47.45/12.98	   1_{5_1}(5_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 1_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
47.45/12.98	   1_{5_1}(5_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 1_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
47.45/12.98	   1_{5_1}(5_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 1_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
47.45/12.98	   1_{5_1}(5_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 1_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
47.45/12.98	   2_{5_1}(5_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 2_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
47.45/12.98	   2_{5_1}(5_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 2_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
47.45/12.98	   2_{5_1}(5_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 2_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
47.45/12.98	   2_{5_1}(5_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 2_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
47.45/12.98	   2_{5_1}(5_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 2_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
47.45/12.98	   2_{5_1}(5_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 2_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
47.45/12.98	   3_{5_1}(5_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
47.45/12.98	   3_{5_1}(5_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
47.45/12.98	   3_{5_1}(5_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
47.45/12.98	   3_{5_1}(5_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
47.45/12.98	   3_{5_1}(5_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
47.45/12.98	   3_{5_1}(5_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
47.45/12.98	   5_{5_1}(5_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 5_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
47.45/12.98	   5_{5_1}(5_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 5_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
47.45/12.98	   5_{5_1}(5_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 5_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
47.45/12.98	   5_{5_1}(5_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 5_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
47.45/12.98	   5_{5_1}(5_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 5_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
47.45/12.98	   5_{5_1}(5_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 5_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
47.45/12.98	   0_{5_1}(5_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 0_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
47.45/12.98	   0_{5_1}(5_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 0_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
47.45/12.98	   0_{5_1}(5_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 0_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
47.45/12.98	   0_{5_1}(5_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 0_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
47.45/12.98	   0_{5_1}(5_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 0_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
47.45/12.98	   0_{5_1}(5_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 0_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
47.45/12.98	   4_{4_1}(4_{5_1}(5_{3_1}(3_{4_1}(x1)))) -> 4_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
47.45/12.98	   4_{4_1}(4_{5_1}(5_{3_1}(3_{1_1}(x1)))) -> 4_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
47.45/12.98	   4_{4_1}(4_{5_1}(5_{3_1}(3_{2_1}(x1)))) -> 4_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
47.45/12.98	   4_{4_1}(4_{5_1}(5_{3_1}(3_{3_1}(x1)))) -> 4_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
47.45/12.98	   4_{4_1}(4_{5_1}(5_{3_1}(3_{0_1}(x1)))) -> 4_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
47.45/12.98	   4_{4_1}(4_{5_1}(5_{3_1}(3_{5_1}(x1)))) -> 4_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
47.45/12.98	   1_{4_1}(4_{5_1}(5_{3_1}(3_{4_1}(x1)))) -> 1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
47.45/12.98	   1_{4_1}(4_{5_1}(5_{3_1}(3_{1_1}(x1)))) -> 1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
47.45/12.98	   1_{4_1}(4_{5_1}(5_{3_1}(3_{2_1}(x1)))) -> 1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
47.45/12.98	   1_{4_1}(4_{5_1}(5_{3_1}(3_{3_1}(x1)))) -> 1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
47.45/12.98	   1_{4_1}(4_{5_1}(5_{3_1}(3_{0_1}(x1)))) -> 1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
47.45/12.98	   1_{4_1}(4_{5_1}(5_{3_1}(3_{5_1}(x1)))) -> 1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
47.45/12.98	   2_{4_1}(4_{5_1}(5_{3_1}(3_{4_1}(x1)))) -> 2_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
47.45/12.98	   2_{4_1}(4_{5_1}(5_{3_1}(3_{1_1}(x1)))) -> 2_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
47.45/12.98	   2_{4_1}(4_{5_1}(5_{3_1}(3_{2_1}(x1)))) -> 2_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
47.45/12.98	   2_{4_1}(4_{5_1}(5_{3_1}(3_{3_1}(x1)))) -> 2_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
47.45/12.98	   2_{4_1}(4_{5_1}(5_{3_1}(3_{0_1}(x1)))) -> 2_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
47.45/12.98	   2_{4_1}(4_{5_1}(5_{3_1}(3_{5_1}(x1)))) -> 2_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
47.45/12.98	   3_{4_1}(4_{5_1}(5_{3_1}(3_{4_1}(x1)))) -> 3_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
47.45/12.98	   3_{4_1}(4_{5_1}(5_{3_1}(3_{1_1}(x1)))) -> 3_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
47.45/12.98	   3_{4_1}(4_{5_1}(5_{3_1}(3_{2_1}(x1)))) -> 3_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
47.45/12.98	   3_{4_1}(4_{5_1}(5_{3_1}(3_{3_1}(x1)))) -> 3_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
47.45/12.98	   3_{4_1}(4_{5_1}(5_{3_1}(3_{0_1}(x1)))) -> 3_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
47.45/12.98	   3_{4_1}(4_{5_1}(5_{3_1}(3_{5_1}(x1)))) -> 3_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
47.45/12.98	   5_{4_1}(4_{5_1}(5_{3_1}(3_{4_1}(x1)))) -> 5_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
47.45/12.98	   5_{4_1}(4_{5_1}(5_{3_1}(3_{1_1}(x1)))) -> 5_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
47.45/12.98	   5_{4_1}(4_{5_1}(5_{3_1}(3_{2_1}(x1)))) -> 5_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
47.45/12.98	   5_{4_1}(4_{5_1}(5_{3_1}(3_{3_1}(x1)))) -> 5_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
47.45/12.98	   5_{4_1}(4_{5_1}(5_{3_1}(3_{0_1}(x1)))) -> 5_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
47.45/12.98	   5_{4_1}(4_{5_1}(5_{3_1}(3_{5_1}(x1)))) -> 5_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{3_1}(3_{4_1}(x1)))) -> 0_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{3_1}(3_{1_1}(x1)))) -> 0_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{3_1}(3_{2_1}(x1)))) -> 0_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{3_1}(3_{3_1}(x1)))) -> 0_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{3_1}(3_{0_1}(x1)))) -> 0_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{3_1}(3_{5_1}(x1)))) -> 0_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
47.45/12.98	   4_{4_1}(4_{1_1}(1_{4_1}(4_{4_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{4_1}(x1)))))))
47.45/12.98	   4_{4_1}(4_{1_1}(1_{4_1}(4_{1_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{1_1}(x1)))))))
47.45/12.98	   4_{4_1}(4_{1_1}(1_{4_1}(4_{2_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{2_1}(x1)))))))
47.45/12.98	   4_{4_1}(4_{1_1}(1_{4_1}(4_{3_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{3_1}(x1)))))))
47.45/12.98	   4_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{0_1}(x1)))))))
47.45/12.98	   4_{4_1}(4_{1_1}(1_{4_1}(4_{5_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{5_1}(x1)))))))
47.45/12.98	   1_{4_1}(4_{1_1}(1_{4_1}(4_{4_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{4_1}(x1)))))))
47.45/12.98	   1_{4_1}(4_{1_1}(1_{4_1}(4_{1_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{1_1}(x1)))))))
47.45/12.98	   1_{4_1}(4_{1_1}(1_{4_1}(4_{2_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{2_1}(x1)))))))
47.45/12.98	   1_{4_1}(4_{1_1}(1_{4_1}(4_{3_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{3_1}(x1)))))))
47.45/12.98	   1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{0_1}(x1)))))))
47.45/12.98	   1_{4_1}(4_{1_1}(1_{4_1}(4_{5_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{5_1}(x1)))))))
47.45/12.98	   2_{4_1}(4_{1_1}(1_{4_1}(4_{4_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{4_1}(x1)))))))
47.45/12.98	   2_{4_1}(4_{1_1}(1_{4_1}(4_{1_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{1_1}(x1)))))))
47.45/12.98	   2_{4_1}(4_{1_1}(1_{4_1}(4_{2_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{2_1}(x1)))))))
47.45/12.98	   2_{4_1}(4_{1_1}(1_{4_1}(4_{3_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{3_1}(x1)))))))
47.45/12.98	   2_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{0_1}(x1)))))))
47.45/12.98	   2_{4_1}(4_{1_1}(1_{4_1}(4_{5_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{5_1}(x1)))))))
47.45/12.98	   3_{4_1}(4_{1_1}(1_{4_1}(4_{4_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{4_1}(x1)))))))
47.45/12.98	   3_{4_1}(4_{1_1}(1_{4_1}(4_{1_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{1_1}(x1)))))))
47.45/12.98	   3_{4_1}(4_{1_1}(1_{4_1}(4_{2_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{2_1}(x1)))))))
47.45/12.98	   3_{4_1}(4_{1_1}(1_{4_1}(4_{3_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{3_1}(x1)))))))
47.45/12.98	   3_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{0_1}(x1)))))))
47.45/12.98	   3_{4_1}(4_{1_1}(1_{4_1}(4_{5_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{5_1}(x1)))))))
47.45/12.98	   5_{4_1}(4_{1_1}(1_{4_1}(4_{4_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{4_1}(x1)))))))
47.45/12.98	   5_{4_1}(4_{1_1}(1_{4_1}(4_{1_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{1_1}(x1)))))))
47.45/12.98	   5_{4_1}(4_{1_1}(1_{4_1}(4_{2_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{2_1}(x1)))))))
47.45/12.98	   5_{4_1}(4_{1_1}(1_{4_1}(4_{3_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{3_1}(x1)))))))
47.45/12.98	   5_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{0_1}(x1)))))))
47.45/12.98	   5_{4_1}(4_{1_1}(1_{4_1}(4_{5_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{5_1}(x1)))))))
47.45/12.98	   0_{4_1}(4_{1_1}(1_{4_1}(4_{4_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{4_1}(x1)))))))
47.45/12.98	   0_{4_1}(4_{1_1}(1_{4_1}(4_{1_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{1_1}(x1)))))))
47.45/12.98	   0_{4_1}(4_{1_1}(1_{4_1}(4_{2_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{2_1}(x1)))))))
47.45/12.98	   0_{4_1}(4_{1_1}(1_{4_1}(4_{3_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{3_1}(x1)))))))
47.45/12.98	   0_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{0_1}(x1)))))))
47.45/12.98	   0_{4_1}(4_{1_1}(1_{4_1}(4_{5_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{5_1}(x1)))))))
47.45/12.98	   4_{4_1}(4_{5_1}(5_{5_1}(5_{4_1}(x1)))) -> 4_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{4_1}(x1)))))))
47.45/12.98	   4_{4_1}(4_{5_1}(5_{5_1}(5_{1_1}(x1)))) -> 4_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{1_1}(x1)))))))
47.45/12.98	   4_{4_1}(4_{5_1}(5_{5_1}(5_{2_1}(x1)))) -> 4_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{2_1}(x1)))))))
47.45/12.98	   4_{4_1}(4_{5_1}(5_{5_1}(5_{3_1}(x1)))) -> 4_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{3_1}(x1)))))))
47.45/12.98	   4_{4_1}(4_{5_1}(5_{5_1}(5_{0_1}(x1)))) -> 4_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{0_1}(x1)))))))
47.45/12.98	   4_{4_1}(4_{5_1}(5_{5_1}(5_{5_1}(x1)))) -> 4_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{5_1}(x1)))))))
47.45/12.98	   1_{4_1}(4_{5_1}(5_{5_1}(5_{4_1}(x1)))) -> 1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{4_1}(x1)))))))
47.45/12.98	   1_{4_1}(4_{5_1}(5_{5_1}(5_{1_1}(x1)))) -> 1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{1_1}(x1)))))))
47.45/12.98	   1_{4_1}(4_{5_1}(5_{5_1}(5_{2_1}(x1)))) -> 1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{2_1}(x1)))))))
47.45/12.98	   1_{4_1}(4_{5_1}(5_{5_1}(5_{3_1}(x1)))) -> 1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{3_1}(x1)))))))
47.45/12.98	   1_{4_1}(4_{5_1}(5_{5_1}(5_{0_1}(x1)))) -> 1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{0_1}(x1)))))))
47.45/12.98	   1_{4_1}(4_{5_1}(5_{5_1}(5_{5_1}(x1)))) -> 1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{5_1}(x1)))))))
47.45/12.98	   2_{4_1}(4_{5_1}(5_{5_1}(5_{4_1}(x1)))) -> 2_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{4_1}(x1)))))))
47.45/12.98	   2_{4_1}(4_{5_1}(5_{5_1}(5_{1_1}(x1)))) -> 2_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{1_1}(x1)))))))
47.45/12.98	   2_{4_1}(4_{5_1}(5_{5_1}(5_{2_1}(x1)))) -> 2_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{2_1}(x1)))))))
47.45/12.98	   2_{4_1}(4_{5_1}(5_{5_1}(5_{3_1}(x1)))) -> 2_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{3_1}(x1)))))))
47.45/12.98	   2_{4_1}(4_{5_1}(5_{5_1}(5_{0_1}(x1)))) -> 2_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{0_1}(x1)))))))
47.45/12.98	   2_{4_1}(4_{5_1}(5_{5_1}(5_{5_1}(x1)))) -> 2_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{5_1}(x1)))))))
47.45/12.98	   3_{4_1}(4_{5_1}(5_{5_1}(5_{4_1}(x1)))) -> 3_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{4_1}(x1)))))))
47.45/12.98	   3_{4_1}(4_{5_1}(5_{5_1}(5_{1_1}(x1)))) -> 3_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{1_1}(x1)))))))
47.45/12.98	   3_{4_1}(4_{5_1}(5_{5_1}(5_{2_1}(x1)))) -> 3_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{2_1}(x1)))))))
47.45/12.98	   3_{4_1}(4_{5_1}(5_{5_1}(5_{3_1}(x1)))) -> 3_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{3_1}(x1)))))))
47.45/12.98	   3_{4_1}(4_{5_1}(5_{5_1}(5_{0_1}(x1)))) -> 3_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{0_1}(x1)))))))
47.45/12.98	   3_{4_1}(4_{5_1}(5_{5_1}(5_{5_1}(x1)))) -> 3_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{5_1}(x1)))))))
47.45/12.98	   5_{4_1}(4_{5_1}(5_{5_1}(5_{4_1}(x1)))) -> 5_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{4_1}(x1)))))))
47.45/12.98	   5_{4_1}(4_{5_1}(5_{5_1}(5_{1_1}(x1)))) -> 5_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{1_1}(x1)))))))
47.45/12.98	   5_{4_1}(4_{5_1}(5_{5_1}(5_{2_1}(x1)))) -> 5_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{2_1}(x1)))))))
47.45/12.98	   5_{4_1}(4_{5_1}(5_{5_1}(5_{3_1}(x1)))) -> 5_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{3_1}(x1)))))))
47.45/12.98	   5_{4_1}(4_{5_1}(5_{5_1}(5_{0_1}(x1)))) -> 5_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{0_1}(x1)))))))
47.45/12.98	   5_{4_1}(4_{5_1}(5_{5_1}(5_{5_1}(x1)))) -> 5_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{5_1}(x1)))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{5_1}(5_{4_1}(x1)))) -> 0_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{4_1}(x1)))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{5_1}(5_{1_1}(x1)))) -> 0_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{1_1}(x1)))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{5_1}(5_{2_1}(x1)))) -> 0_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{2_1}(x1)))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{5_1}(5_{3_1}(x1)))) -> 0_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{3_1}(x1)))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{5_1}(5_{0_1}(x1)))) -> 0_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{0_1}(x1)))))))
47.45/12.98	   0_{4_1}(4_{5_1}(5_{5_1}(5_{5_1}(x1)))) -> 0_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{5_1}(x1)))))))
47.45/12.98	   4_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 4_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{4_1}(x1)))))))
47.45/12.98	   4_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 4_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{1_1}(x1)))))))
47.45/12.98	   4_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 4_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{2_1}(x1)))))))
47.45/12.98	   4_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 4_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{3_1}(x1)))))))
47.45/12.98	   4_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 4_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{0_1}(x1)))))))
47.45/12.98	   4_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 4_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{5_1}(x1)))))))
47.45/12.98	   1_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 1_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{4_1}(x1)))))))
47.45/12.98	   1_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 1_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{1_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 1_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{2_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 1_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{3_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 1_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{0_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 1_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{5_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 2_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{4_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 2_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{1_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 2_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{2_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 2_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{3_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 2_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{0_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 2_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{5_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 3_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{4_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 3_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{1_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 3_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{2_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 3_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{3_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 3_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{0_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 3_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{5_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 5_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{4_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 5_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{1_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 5_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{2_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 5_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{3_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 5_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{0_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 5_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{5_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 0_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{4_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 0_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{1_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 0_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{2_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 0_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{3_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 0_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{0_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 0_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{5_1}(x1)))))))
47.45/12.99	   4_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 4_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{4_1}(x1)))))))
47.45/12.99	   4_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 4_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(x1)))))))
47.45/12.99	   4_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 4_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{2_1}(x1)))))))
47.45/12.99	   4_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 4_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(x1)))))))
47.45/12.99	   4_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 4_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(x1)))))))
47.45/12.99	   4_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 4_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{5_1}(x1)))))))
47.45/12.99	   1_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 1_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{4_1}(x1)))))))
47.45/12.99	   1_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 1_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(x1)))))))
47.45/12.99	   1_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 1_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{2_1}(x1)))))))
47.45/12.99	   1_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 1_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(x1)))))))
47.45/12.99	   1_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 1_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(x1)))))))
47.45/12.99	   1_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 1_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{5_1}(x1)))))))
47.45/12.99	   2_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 2_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{4_1}(x1)))))))
47.45/12.99	   2_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 2_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(x1)))))))
47.45/12.99	   2_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 2_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{2_1}(x1)))))))
47.45/12.99	   2_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 2_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(x1)))))))
47.45/12.99	   2_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 2_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(x1)))))))
47.45/12.99	   2_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 2_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{5_1}(x1)))))))
47.45/12.99	   3_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 3_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{4_1}(x1)))))))
47.45/12.99	   3_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 3_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(x1)))))))
47.45/12.99	   3_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 3_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{2_1}(x1)))))))
47.45/12.99	   3_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 3_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(x1)))))))
47.45/12.99	   3_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 3_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(x1)))))))
47.45/12.99	   3_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 3_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{5_1}(x1)))))))
47.45/12.99	   5_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{4_1}(x1)))))))
47.45/12.99	   5_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(x1)))))))
47.45/12.99	   5_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{2_1}(x1)))))))
47.45/12.99	   5_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(x1)))))))
47.45/12.99	   5_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(x1)))))))
47.45/12.99	   5_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{5_1}(x1)))))))
47.45/12.99	   0_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 0_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{4_1}(x1)))))))
47.45/12.99	   0_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 0_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(x1)))))))
47.45/12.99	   0_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 0_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{2_1}(x1)))))))
47.45/12.99	   0_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 0_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(x1)))))))
47.45/12.99	   0_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 0_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(x1)))))))
47.45/12.99	   0_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 0_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{5_1}(x1)))))))
47.45/12.99	   4_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{4_1}(x1))))) -> 4_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
47.45/12.99	   4_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(x1))))) -> 4_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
47.45/12.99	   4_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{2_1}(x1))))) -> 4_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
47.45/12.99	   4_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{3_1}(x1))))) -> 4_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
47.45/12.99	   4_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{0_1}(x1))))) -> 4_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
47.45/12.99	   4_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{5_1}(x1))))) -> 4_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
47.45/12.99	   1_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{4_1}(x1))))) -> 1_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
47.45/12.99	   1_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(x1))))) -> 1_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
47.45/12.99	   1_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{2_1}(x1))))) -> 1_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
47.45/12.99	   1_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{3_1}(x1))))) -> 1_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
47.45/12.99	   1_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{0_1}(x1))))) -> 1_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
47.45/12.99	   1_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{5_1}(x1))))) -> 1_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
47.45/12.99	   2_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{4_1}(x1))))) -> 2_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
47.45/12.99	   2_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(x1))))) -> 2_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
47.45/12.99	   2_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{2_1}(x1))))) -> 2_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
47.45/12.99	   2_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{3_1}(x1))))) -> 2_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
47.45/12.99	   2_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{0_1}(x1))))) -> 2_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
47.45/12.99	   2_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{5_1}(x1))))) -> 2_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
47.45/12.99	   3_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{4_1}(x1))))) -> 3_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
47.45/12.99	   3_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(x1))))) -> 3_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
47.45/12.99	   3_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{2_1}(x1))))) -> 3_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
47.45/12.99	   3_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{3_1}(x1))))) -> 3_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
47.45/12.99	   3_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{0_1}(x1))))) -> 3_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
47.45/12.99	   3_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{5_1}(x1))))) -> 3_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
47.45/12.99	   5_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{4_1}(x1))))) -> 5_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
47.45/12.99	   5_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(x1))))) -> 5_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
47.45/12.99	   5_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{2_1}(x1))))) -> 5_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
47.45/12.99	   5_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{3_1}(x1))))) -> 5_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
47.45/12.99	   5_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{0_1}(x1))))) -> 5_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
47.45/12.99	   5_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{5_1}(x1))))) -> 5_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
47.45/12.99	   0_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{4_1}(x1))))) -> 0_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
47.45/12.99	   0_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(x1))))) -> 0_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
47.45/12.99	   0_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{2_1}(x1))))) -> 0_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
47.45/12.99	   0_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{3_1}(x1))))) -> 0_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
47.45/12.99	   0_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{0_1}(x1))))) -> 0_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
47.45/12.99	   0_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{5_1}(x1))))) -> 0_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
47.45/12.99	
47.45/12.99	Q is empty.
47.45/12.99	
47.45/12.99	----------------------------------------
47.45/12.99	
47.45/12.99	(7) QTRSRRRProof (EQUIVALENT)
47.45/12.99	Used ordering:
47.45/12.99	Polynomial interpretation [POLO]:
47.45/12.99	
47.45/12.99	   POL(0_{0_1}(x_1)) = 60 + x_1
47.45/12.99	   POL(0_{1_1}(x_1)) = 10 + x_1
47.45/12.99	   POL(0_{2_1}(x_1)) = x_1
47.45/12.99	   POL(0_{3_1}(x_1)) = x_1
47.45/12.99	   POL(0_{4_1}(x_1)) = 1 + x_1
47.45/12.99	   POL(0_{5_1}(x_1)) = 2 + x_1
47.45/12.99	   POL(1_{0_1}(x_1)) = 59 + x_1
47.45/12.99	   POL(1_{1_1}(x_1)) = 9 + x_1
47.45/12.99	   POL(1_{2_1}(x_1)) = x_1
47.45/12.99	   POL(1_{3_1}(x_1)) = 1 + x_1
47.45/12.99	   POL(1_{4_1}(x_1)) = 1 + x_1
47.45/12.99	   POL(1_{5_1}(x_1)) = 1 + x_1
47.45/12.99	   POL(2_{0_1}(x_1)) = 15 + x_1
47.45/12.99	   POL(2_{1_1}(x_1)) = x_1
47.45/12.99	   POL(2_{2_1}(x_1)) = x_1
47.45/12.99	   POL(2_{3_1}(x_1)) = 1 + x_1
47.45/12.99	   POL(2_{4_1}(x_1)) = x_1
47.45/12.99	   POL(2_{5_1}(x_1)) = x_1
47.45/12.99	   POL(3_{0_1}(x_1)) = 35 + x_1
47.45/12.99	   POL(3_{1_1}(x_1)) = 103 + x_1
47.45/12.99	   POL(3_{2_1}(x_1)) = x_1
47.45/12.99	   POL(3_{3_1}(x_1)) = 3 + x_1
47.45/12.99	   POL(3_{4_1}(x_1)) = 23 + x_1
47.45/12.99	   POL(3_{5_1}(x_1)) = 96 + x_1
47.45/12.99	   POL(4_{0_1}(x_1)) = 53 + x_1
47.45/12.99	   POL(4_{1_1}(x_1)) = 124 + x_1
47.45/12.99	   POL(4_{2_1}(x_1)) = 18 + x_1
47.45/12.99	   POL(4_{3_1}(x_1)) = 20 + x_1
47.45/12.99	   POL(4_{4_1}(x_1)) = 44 + x_1
47.45/12.99	   POL(4_{5_1}(x_1)) = 117 + x_1
47.45/12.99	   POL(5_{0_1}(x_1)) = 93 + x_1
47.45/12.99	   POL(5_{1_1}(x_1)) = 107 + x_1
47.45/12.99	   POL(5_{2_1}(x_1)) = x_1
47.45/12.99	   POL(5_{3_1}(x_1)) = 29 + x_1
47.45/12.99	   POL(5_{4_1}(x_1)) = 28 + x_1
47.45/12.99	   POL(5_{5_1}(x_1)) = 100 + x_1
47.45/12.99	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
47.45/12.99	
47.45/12.99	   4_{1_1}(1_{4_1}(x1)) -> 4_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{3_1}(3_{4_1}(x1))))))
47.45/12.99	   4_{1_1}(1_{1_1}(x1)) -> 4_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{3_1}(3_{1_1}(x1))))))
47.45/12.99	   4_{1_1}(1_{2_1}(x1)) -> 4_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(x1))))))
47.45/12.99	   4_{1_1}(1_{3_1}(x1)) -> 4_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{3_1}(3_{3_1}(x1))))))
47.45/12.99	   4_{1_1}(1_{0_1}(x1)) -> 4_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{3_1}(3_{0_1}(x1))))))
47.45/12.99	   4_{1_1}(1_{5_1}(x1)) -> 4_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{3_1}(3_{5_1}(x1))))))
47.45/12.99	   0_{3_1}(3_{0_1}(0_{4_1}(x1))) -> 0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{4_1}(x1))))))
47.45/12.99	   0_{3_1}(3_{0_1}(0_{1_1}(x1))) -> 0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(x1))))))
47.45/12.99	   0_{3_1}(3_{0_1}(0_{2_1}(x1))) -> 0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(x1))))))
47.45/12.99	   0_{3_1}(3_{0_1}(0_{0_1}(x1))) -> 0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(x1))))))
47.45/12.99	   0_{3_1}(3_{0_1}(0_{5_1}(x1))) -> 0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{5_1}(x1))))))
47.45/12.99	   4_{5_1}(5_{1_1}(1_{4_1}(x1))) -> 4_{0_1}(0_{2_1}(2_{5_1}(5_{2_1}(2_{0_1}(0_{4_1}(x1))))))
47.45/12.99	   4_{5_1}(5_{1_1}(1_{1_1}(x1))) -> 4_{0_1}(0_{2_1}(2_{5_1}(5_{2_1}(2_{0_1}(0_{1_1}(x1))))))
47.45/12.99	   4_{5_1}(5_{1_1}(1_{2_1}(x1))) -> 4_{0_1}(0_{2_1}(2_{5_1}(5_{2_1}(2_{0_1}(0_{2_1}(x1))))))
47.45/12.99	   4_{5_1}(5_{1_1}(1_{3_1}(x1))) -> 4_{0_1}(0_{2_1}(2_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(x1))))))
47.45/12.99	   4_{5_1}(5_{1_1}(1_{0_1}(x1))) -> 4_{0_1}(0_{2_1}(2_{5_1}(5_{2_1}(2_{0_1}(0_{0_1}(x1))))))
47.45/12.99	   4_{5_1}(5_{1_1}(1_{5_1}(x1))) -> 4_{0_1}(0_{2_1}(2_{5_1}(5_{2_1}(2_{0_1}(0_{5_1}(x1))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{4_1}(x1))) -> 0_{4_1}(4_{4_1}(4_{0_1}(0_{4_1}(4_{2_1}(2_{4_1}(x1))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{1_1}(x1))) -> 0_{4_1}(4_{4_1}(4_{0_1}(0_{4_1}(4_{2_1}(2_{1_1}(x1))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{2_1}(x1))) -> 0_{4_1}(4_{4_1}(4_{0_1}(0_{4_1}(4_{2_1}(2_{2_1}(x1))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{3_1}(x1))) -> 0_{4_1}(4_{4_1}(4_{0_1}(0_{4_1}(4_{2_1}(2_{3_1}(x1))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{0_1}(x1))) -> 0_{4_1}(4_{4_1}(4_{0_1}(0_{4_1}(4_{2_1}(2_{0_1}(x1))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{5_1}(x1))) -> 0_{4_1}(4_{4_1}(4_{0_1}(0_{4_1}(4_{2_1}(2_{5_1}(x1))))))
47.45/12.99	   4_{4_1}(4_{5_1}(5_{4_1}(x1))) -> 4_{2_1}(2_{3_1}(3_{1_1}(1_{1_1}(1_{4_1}(4_{4_1}(x1))))))
47.45/12.99	   4_{4_1}(4_{5_1}(5_{1_1}(x1))) -> 4_{2_1}(2_{3_1}(3_{1_1}(1_{1_1}(1_{4_1}(4_{1_1}(x1))))))
47.45/12.99	   4_{4_1}(4_{5_1}(5_{2_1}(x1))) -> 4_{2_1}(2_{3_1}(3_{1_1}(1_{1_1}(1_{4_1}(4_{2_1}(x1))))))
47.45/12.99	   4_{4_1}(4_{5_1}(5_{3_1}(x1))) -> 4_{2_1}(2_{3_1}(3_{1_1}(1_{1_1}(1_{4_1}(4_{3_1}(x1))))))
47.45/12.99	   4_{4_1}(4_{5_1}(5_{0_1}(x1))) -> 4_{2_1}(2_{3_1}(3_{1_1}(1_{1_1}(1_{4_1}(4_{0_1}(x1))))))
47.45/12.99	   4_{4_1}(4_{5_1}(5_{5_1}(x1))) -> 4_{2_1}(2_{3_1}(3_{1_1}(1_{1_1}(1_{4_1}(4_{5_1}(x1))))))
47.45/12.99	   0_{5_1}(5_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{4_1}(x1))))))
47.45/12.99	   0_{5_1}(5_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(x1))))))
47.45/12.99	   0_{5_1}(5_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{2_1}(x1))))))
47.45/12.99	   0_{5_1}(5_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{3_1}(x1))))))
47.45/12.99	   0_{5_1}(5_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(x1))))))
47.45/12.99	   0_{5_1}(5_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{5_1}(x1))))))
47.45/12.99	   4_{5_1}(5_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 4_{3_1}(3_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{4_1}(x1))))))
47.45/12.99	   4_{5_1}(5_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 4_{3_1}(3_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(x1))))))
47.45/12.99	   4_{5_1}(5_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 4_{3_1}(3_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{2_1}(x1))))))
47.45/12.99	   4_{5_1}(5_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 4_{3_1}(3_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{3_1}(x1))))))
47.45/12.99	   4_{5_1}(5_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 4_{3_1}(3_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(x1))))))
47.45/12.99	   4_{5_1}(5_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 4_{3_1}(3_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{5_1}(x1))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{2_1}(2_{4_1}(x1)))) -> 0_{4_1}(4_{2_1}(2_{1_1}(1_{4_1}(4_{0_1}(0_{4_1}(x1))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{2_1}(2_{1_1}(x1)))) -> 0_{4_1}(4_{2_1}(2_{1_1}(1_{4_1}(4_{0_1}(0_{1_1}(x1))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{2_1}(2_{2_1}(x1)))) -> 0_{4_1}(4_{2_1}(2_{1_1}(1_{4_1}(4_{0_1}(0_{2_1}(x1))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{2_1}(2_{3_1}(x1)))) -> 0_{4_1}(4_{2_1}(2_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(x1))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{2_1}(2_{5_1}(x1)))) -> 0_{4_1}(4_{2_1}(2_{1_1}(1_{4_1}(4_{0_1}(0_{5_1}(x1))))))
47.45/12.99	   5_{0_1}(0_{3_1}(3_{4_1}(4_{4_1}(x1)))) -> 5_{5_1}(5_{3_1}(3_{2_1}(2_{3_1}(3_{3_1}(3_{4_1}(x1))))))
47.45/12.99	   5_{0_1}(0_{3_1}(3_{4_1}(4_{1_1}(x1)))) -> 5_{5_1}(5_{3_1}(3_{2_1}(2_{3_1}(3_{3_1}(3_{1_1}(x1))))))
47.45/12.99	   5_{0_1}(0_{3_1}(3_{4_1}(4_{2_1}(x1)))) -> 5_{5_1}(5_{3_1}(3_{2_1}(2_{3_1}(3_{3_1}(3_{2_1}(x1))))))
47.45/12.99	   5_{0_1}(0_{3_1}(3_{4_1}(4_{0_1}(x1)))) -> 5_{5_1}(5_{3_1}(3_{2_1}(2_{3_1}(3_{3_1}(3_{0_1}(x1))))))
47.45/12.99	   5_{0_1}(0_{3_1}(3_{4_1}(4_{5_1}(x1)))) -> 5_{5_1}(5_{3_1}(3_{2_1}(2_{3_1}(3_{3_1}(3_{5_1}(x1))))))
47.45/12.99	   2_{0_1}(0_{4_1}(4_{5_1}(5_{4_1}(x1)))) -> 2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{3_1}(3_{4_1}(x1))))))
47.45/12.99	   2_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(x1)))) -> 2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{3_1}(3_{1_1}(x1))))))
47.45/12.99	   2_{0_1}(0_{4_1}(4_{5_1}(5_{2_1}(x1)))) -> 2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{3_1}(3_{2_1}(x1))))))
47.45/12.99	   2_{0_1}(0_{4_1}(4_{5_1}(5_{3_1}(x1)))) -> 2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{3_1}(3_{3_1}(x1))))))
47.45/12.99	   2_{0_1}(0_{4_1}(4_{5_1}(5_{0_1}(x1)))) -> 2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(x1))))))
47.45/12.99	   2_{0_1}(0_{4_1}(4_{5_1}(5_{5_1}(x1)))) -> 2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{3_1}(3_{5_1}(x1))))))
47.45/12.99	   4_{4_1}(4_{5_1}(5_{4_1}(x1))) -> 4_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{4_1}(x1)))))))
47.45/12.99	   4_{4_1}(4_{5_1}(5_{1_1}(x1))) -> 4_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{1_1}(x1)))))))
47.45/12.99	   4_{4_1}(4_{5_1}(5_{3_1}(x1))) -> 4_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(x1)))))))
47.45/12.99	   4_{4_1}(4_{5_1}(5_{0_1}(x1))) -> 4_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{0_1}(x1)))))))
47.45/12.99	   4_{4_1}(4_{5_1}(5_{5_1}(x1))) -> 4_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{5_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{5_1}(5_{4_1}(x1))) -> 1_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{4_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{5_1}(5_{1_1}(x1))) -> 1_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{1_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{5_1}(5_{2_1}(x1))) -> 1_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{2_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{5_1}(5_{3_1}(x1))) -> 1_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{5_1}(5_{0_1}(x1))) -> 1_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{0_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{5_1}(5_{5_1}(x1))) -> 1_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{5_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{4_1}(x1))) -> 2_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{4_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{1_1}(x1))) -> 2_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{1_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{2_1}(x1))) -> 2_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{2_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{3_1}(x1))) -> 2_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{0_1}(x1))) -> 2_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{0_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{5_1}(x1))) -> 2_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{5_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{5_1}(5_{4_1}(x1))) -> 3_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{4_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{5_1}(5_{1_1}(x1))) -> 3_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{1_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{5_1}(5_{3_1}(x1))) -> 3_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{5_1}(5_{0_1}(x1))) -> 3_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{0_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{5_1}(5_{5_1}(x1))) -> 3_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{5_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{4_1}(x1))) -> 5_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{4_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{1_1}(x1))) -> 5_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{1_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{2_1}(x1))) -> 5_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{2_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{3_1}(x1))) -> 5_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{0_1}(x1))) -> 5_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{0_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{5_1}(x1))) -> 5_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{5_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{4_1}(x1))) -> 0_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{4_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{1_1}(x1))) -> 0_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{1_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{2_1}(x1))) -> 0_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{2_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{3_1}(x1))) -> 0_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{0_1}(x1))) -> 0_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{0_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{5_1}(x1))) -> 0_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{5_1}(x1)))))))
47.45/12.99	   4_{5_1}(5_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 4_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
47.45/12.99	   4_{5_1}(5_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 4_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
47.45/12.99	   4_{5_1}(5_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 4_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
47.45/12.99	   4_{5_1}(5_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 4_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
47.45/12.99	   4_{5_1}(5_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 4_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
47.45/12.99	   4_{5_1}(5_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 4_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
47.45/12.99	   1_{5_1}(5_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 1_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
47.45/12.99	   1_{5_1}(5_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 1_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
47.45/12.99	   1_{5_1}(5_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 1_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
47.45/12.99	   1_{5_1}(5_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 1_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
47.45/12.99	   1_{5_1}(5_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 1_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
47.45/12.99	   1_{5_1}(5_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 1_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
47.45/12.99	   2_{5_1}(5_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 2_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
47.45/12.99	   2_{5_1}(5_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 2_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
47.45/12.99	   2_{5_1}(5_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 2_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
47.45/12.99	   2_{5_1}(5_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 2_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
47.45/12.99	   2_{5_1}(5_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 2_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
47.45/12.99	   3_{5_1}(5_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
47.45/12.99	   3_{5_1}(5_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
47.45/12.99	   3_{5_1}(5_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
47.45/12.99	   3_{5_1}(5_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
47.45/12.99	   3_{5_1}(5_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
47.45/12.99	   3_{5_1}(5_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
47.45/12.99	   5_{5_1}(5_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 5_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
47.45/12.99	   5_{5_1}(5_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 5_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
47.45/12.99	   5_{5_1}(5_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 5_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
47.45/12.99	   5_{5_1}(5_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 5_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
47.45/12.99	   5_{5_1}(5_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 5_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
47.45/12.99	   5_{5_1}(5_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 5_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
47.45/12.99	   0_{5_1}(5_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 0_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
47.45/12.99	   0_{5_1}(5_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 0_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
47.45/12.99	   0_{5_1}(5_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 0_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
47.45/12.99	   0_{5_1}(5_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 0_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
47.45/12.99	   0_{5_1}(5_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 0_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
47.45/12.99	   0_{5_1}(5_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 0_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
47.45/12.99	   4_{4_1}(4_{5_1}(5_{3_1}(3_{4_1}(x1)))) -> 4_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
47.45/12.99	   4_{4_1}(4_{5_1}(5_{3_1}(3_{1_1}(x1)))) -> 4_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
47.45/12.99	   4_{4_1}(4_{5_1}(5_{3_1}(3_{2_1}(x1)))) -> 4_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
47.45/12.99	   4_{4_1}(4_{5_1}(5_{3_1}(3_{3_1}(x1)))) -> 4_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
47.45/12.99	   4_{4_1}(4_{5_1}(5_{3_1}(3_{0_1}(x1)))) -> 4_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
47.45/12.99	   4_{4_1}(4_{5_1}(5_{3_1}(3_{5_1}(x1)))) -> 4_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{5_1}(5_{3_1}(3_{4_1}(x1)))) -> 1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{5_1}(5_{3_1}(3_{1_1}(x1)))) -> 1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{5_1}(5_{3_1}(3_{2_1}(x1)))) -> 1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{5_1}(5_{3_1}(3_{3_1}(x1)))) -> 1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{5_1}(5_{3_1}(3_{0_1}(x1)))) -> 1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{5_1}(5_{3_1}(3_{5_1}(x1)))) -> 1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{3_1}(3_{2_1}(x1)))) -> 2_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{3_1}(3_{3_1}(x1)))) -> 2_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{3_1}(3_{0_1}(x1)))) -> 2_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{5_1}(5_{3_1}(3_{4_1}(x1)))) -> 3_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{5_1}(5_{3_1}(3_{1_1}(x1)))) -> 3_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{5_1}(5_{3_1}(3_{2_1}(x1)))) -> 3_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{5_1}(5_{3_1}(3_{3_1}(x1)))) -> 3_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{5_1}(5_{3_1}(3_{0_1}(x1)))) -> 3_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{5_1}(5_{3_1}(3_{5_1}(x1)))) -> 3_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{3_1}(3_{2_1}(x1)))) -> 5_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{3_1}(3_{3_1}(x1)))) -> 5_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{3_1}(3_{0_1}(x1)))) -> 5_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{3_1}(3_{4_1}(x1)))) -> 0_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{3_1}(3_{1_1}(x1)))) -> 0_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{3_1}(3_{2_1}(x1)))) -> 0_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{3_1}(3_{3_1}(x1)))) -> 0_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{3_1}(3_{0_1}(x1)))) -> 0_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{3_1}(3_{5_1}(x1)))) -> 0_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
47.45/12.99	   4_{4_1}(4_{1_1}(1_{4_1}(4_{4_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{4_1}(x1)))))))
47.45/12.99	   4_{4_1}(4_{1_1}(1_{4_1}(4_{1_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{1_1}(x1)))))))
47.45/12.99	   4_{4_1}(4_{1_1}(1_{4_1}(4_{2_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{2_1}(x1)))))))
47.45/12.99	   4_{4_1}(4_{1_1}(1_{4_1}(4_{3_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{3_1}(x1)))))))
47.45/12.99	   4_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{0_1}(x1)))))))
47.45/12.99	   4_{4_1}(4_{1_1}(1_{4_1}(4_{5_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{5_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{1_1}(1_{4_1}(4_{4_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{4_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{1_1}(1_{4_1}(4_{1_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{1_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{1_1}(1_{4_1}(4_{2_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{2_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{1_1}(1_{4_1}(4_{3_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{3_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{0_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{1_1}(1_{4_1}(4_{5_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{5_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{1_1}(1_{4_1}(4_{4_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{4_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{1_1}(1_{4_1}(4_{1_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{1_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{1_1}(1_{4_1}(4_{2_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{2_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{1_1}(1_{4_1}(4_{3_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{3_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{0_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{1_1}(1_{4_1}(4_{5_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{5_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{1_1}(1_{4_1}(4_{4_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{4_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{1_1}(1_{4_1}(4_{1_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{1_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{1_1}(1_{4_1}(4_{2_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{2_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{1_1}(1_{4_1}(4_{3_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{3_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{0_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{1_1}(1_{4_1}(4_{5_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{5_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{1_1}(1_{4_1}(4_{4_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{4_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{1_1}(1_{4_1}(4_{1_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{1_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{1_1}(1_{4_1}(4_{2_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{2_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{1_1}(1_{4_1}(4_{3_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{3_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{0_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{1_1}(1_{4_1}(4_{5_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{5_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{1_1}(1_{4_1}(4_{4_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{4_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{1_1}(1_{4_1}(4_{1_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{1_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{1_1}(1_{4_1}(4_{2_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{2_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{1_1}(1_{4_1}(4_{3_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{3_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{1_1}(1_{4_1}(4_{0_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{0_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{1_1}(1_{4_1}(4_{5_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{2_1}(2_{2_1}(2_{3_1}(3_{3_1}(3_{5_1}(x1)))))))
47.45/12.99	   4_{4_1}(4_{5_1}(5_{5_1}(5_{4_1}(x1)))) -> 4_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{4_1}(x1)))))))
47.45/12.99	   4_{4_1}(4_{5_1}(5_{5_1}(5_{1_1}(x1)))) -> 4_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{1_1}(x1)))))))
47.45/12.99	   4_{4_1}(4_{5_1}(5_{5_1}(5_{2_1}(x1)))) -> 4_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{2_1}(x1)))))))
47.45/12.99	   4_{4_1}(4_{5_1}(5_{5_1}(5_{3_1}(x1)))) -> 4_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{3_1}(x1)))))))
47.45/12.99	   4_{4_1}(4_{5_1}(5_{5_1}(5_{0_1}(x1)))) -> 4_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{0_1}(x1)))))))
47.45/12.99	   4_{4_1}(4_{5_1}(5_{5_1}(5_{5_1}(x1)))) -> 4_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{5_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{5_1}(5_{5_1}(5_{4_1}(x1)))) -> 1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{4_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{5_1}(5_{5_1}(5_{1_1}(x1)))) -> 1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{1_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{5_1}(5_{5_1}(5_{2_1}(x1)))) -> 1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{2_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{5_1}(5_{5_1}(5_{3_1}(x1)))) -> 1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{3_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{5_1}(5_{5_1}(5_{0_1}(x1)))) -> 1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{0_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{5_1}(5_{5_1}(5_{5_1}(x1)))) -> 1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{5_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{5_1}(5_{4_1}(x1)))) -> 2_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{4_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{5_1}(5_{1_1}(x1)))) -> 2_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{1_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{5_1}(5_{2_1}(x1)))) -> 2_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{2_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{5_1}(5_{3_1}(x1)))) -> 2_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{3_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{5_1}(5_{0_1}(x1)))) -> 2_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{0_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{5_1}(5_{5_1}(x1)))) -> 2_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{5_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{5_1}(5_{5_1}(5_{4_1}(x1)))) -> 3_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{4_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{5_1}(5_{5_1}(5_{1_1}(x1)))) -> 3_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{1_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{5_1}(5_{5_1}(5_{2_1}(x1)))) -> 3_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{2_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{5_1}(5_{5_1}(5_{3_1}(x1)))) -> 3_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{3_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{5_1}(5_{5_1}(5_{0_1}(x1)))) -> 3_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{0_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{5_1}(5_{5_1}(5_{5_1}(x1)))) -> 3_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{5_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{5_1}(5_{4_1}(x1)))) -> 5_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{4_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{5_1}(5_{1_1}(x1)))) -> 5_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{1_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{5_1}(5_{2_1}(x1)))) -> 5_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{2_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{5_1}(5_{3_1}(x1)))) -> 5_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{3_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{5_1}(5_{0_1}(x1)))) -> 5_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{0_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{5_1}(5_{5_1}(x1)))) -> 5_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{5_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{5_1}(5_{4_1}(x1)))) -> 0_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{4_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{5_1}(5_{1_1}(x1)))) -> 0_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{1_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{5_1}(5_{2_1}(x1)))) -> 0_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{2_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{5_1}(5_{3_1}(x1)))) -> 0_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{3_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{5_1}(5_{0_1}(x1)))) -> 0_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{0_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{5_1}(5_{5_1}(x1)))) -> 0_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(3_{5_1}(x1)))))))
47.45/12.99	   4_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 4_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{4_1}(x1)))))))
47.45/12.99	   4_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 4_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{1_1}(x1)))))))
47.45/12.99	   4_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 4_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{2_1}(x1)))))))
47.45/12.99	   4_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 4_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{3_1}(x1)))))))
47.45/12.99	   4_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 4_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{0_1}(x1)))))))
47.45/12.99	   4_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 4_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{5_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 1_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{4_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 1_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{1_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 1_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{2_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 1_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{3_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 1_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{0_1}(x1)))))))
47.45/12.99	   1_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 1_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{5_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 2_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{4_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 2_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{1_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 2_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{2_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 2_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{3_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 2_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{0_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 2_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{5_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 3_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{4_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 3_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{1_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 3_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{2_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 3_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{3_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 3_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{0_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 3_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{5_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 5_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{4_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 5_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{1_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 5_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{2_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 5_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{3_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 5_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{0_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 5_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{5_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 0_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{4_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 0_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{1_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 0_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{2_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 0_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{3_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 0_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{0_1}(x1)))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 0_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(5_{4_1}(4_{0_1}(0_{5_1}(x1)))))))
47.45/12.99	   4_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 4_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{4_1}(x1)))))))
47.45/12.99	   4_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 4_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(x1)))))))
47.45/12.99	   4_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 4_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{2_1}(x1)))))))
47.45/12.99	   4_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 4_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(x1)))))))
47.45/12.99	   4_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 4_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(x1)))))))
47.45/12.99	   4_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 4_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{5_1}(x1)))))))
47.45/12.99	   1_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 1_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{4_1}(x1)))))))
47.45/12.99	   1_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 1_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{2_1}(x1)))))))
47.45/12.99	   1_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 1_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(x1)))))))
47.45/12.99	   2_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 2_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{4_1}(x1)))))))
47.45/12.99	   2_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 2_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(x1)))))))
47.45/12.99	   2_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 2_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{2_1}(x1)))))))
47.45/12.99	   2_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 2_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(x1)))))))
47.45/12.99	   2_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 2_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(x1)))))))
47.45/12.99	   2_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 2_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{5_1}(x1)))))))
47.45/12.99	   3_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 3_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{4_1}(x1)))))))
47.45/12.99	   3_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 3_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(x1)))))))
47.45/12.99	   3_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 3_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{2_1}(x1)))))))
47.45/12.99	   3_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 3_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(x1)))))))
47.45/12.99	   3_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 3_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(x1)))))))
47.45/12.99	   3_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 3_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{5_1}(x1)))))))
47.45/12.99	   5_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{4_1}(x1)))))))
47.45/12.99	   5_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(x1)))))))
47.45/12.99	   5_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{2_1}(x1)))))))
47.45/12.99	   5_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(x1)))))))
47.45/12.99	   5_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(x1)))))))
47.45/12.99	   5_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{5_1}(x1)))))))
47.45/12.99	   0_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 0_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{4_1}(x1)))))))
47.45/12.99	   0_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 0_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{2_1}(x1)))))))
47.45/12.99	   0_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 0_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{3_1}(x1)))))))
47.45/12.99	   4_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{4_1}(x1))))) -> 4_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
47.45/12.99	   4_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(x1))))) -> 4_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
47.45/12.99	   4_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{2_1}(x1))))) -> 4_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
47.45/12.99	   4_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{3_1}(x1))))) -> 4_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
47.45/12.99	   4_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{0_1}(x1))))) -> 4_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
47.45/12.99	   4_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{5_1}(x1))))) -> 4_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
47.45/12.99	   1_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{4_1}(x1))))) -> 1_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
47.45/12.99	   1_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(x1))))) -> 1_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
47.45/12.99	   1_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{2_1}(x1))))) -> 1_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
47.45/12.99	   1_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{3_1}(x1))))) -> 1_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
47.45/12.99	   1_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{0_1}(x1))))) -> 1_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
47.45/12.99	   1_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{5_1}(x1))))) -> 1_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
47.45/12.99	   2_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{4_1}(x1))))) -> 2_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
47.45/12.99	   2_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(x1))))) -> 2_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
47.45/12.99	   2_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{2_1}(x1))))) -> 2_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
47.45/12.99	   2_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{3_1}(x1))))) -> 2_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
47.45/12.99	   2_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{0_1}(x1))))) -> 2_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
47.45/12.99	   2_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{5_1}(x1))))) -> 2_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
47.45/12.99	   3_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{4_1}(x1))))) -> 3_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
47.45/12.99	   3_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(x1))))) -> 3_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
47.45/12.99	   3_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{2_1}(x1))))) -> 3_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
47.45/12.99	   3_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{3_1}(x1))))) -> 3_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
47.45/12.99	   3_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{0_1}(x1))))) -> 3_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
47.45/12.99	   3_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{5_1}(x1))))) -> 3_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
47.45/12.99	   5_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{4_1}(x1))))) -> 5_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
47.45/12.99	   5_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(x1))))) -> 5_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
47.45/12.99	   5_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{2_1}(x1))))) -> 5_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
47.45/12.99	   5_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{3_1}(x1))))) -> 5_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
47.45/12.99	   5_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{0_1}(x1))))) -> 5_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
47.45/12.99	   5_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{5_1}(x1))))) -> 5_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
47.45/12.99	   0_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{4_1}(x1))))) -> 0_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
47.45/12.99	   0_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{1_1}(x1))))) -> 0_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
47.45/12.99	   0_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{2_1}(x1))))) -> 0_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
47.45/12.99	   0_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{3_1}(x1))))) -> 0_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
47.45/12.99	   0_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{0_1}(x1))))) -> 0_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
47.45/12.99	   0_{0_1}(0_{0_1}(0_{4_1}(4_{5_1}(5_{5_1}(x1))))) -> 0_{2_1}(2_{2_1}(2_{0_1}(0_{4_1}(4_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
47.45/12.99	
47.45/12.99	
47.45/12.99	
47.45/12.99	
47.45/12.99	----------------------------------------
47.45/12.99	
47.45/12.99	(8)
47.45/12.99	Obligation:
47.45/12.99	Q restricted rewrite system:
47.45/12.99	The TRS R consists of the following rules:
47.45/12.99	
47.45/12.99	   0_{3_1}(3_{0_1}(0_{3_1}(x1))) -> 0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{3_1}(x1))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{4_1}(x1))) -> 0_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(1_{5_1}(5_{4_1}(x1))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{1_1}(x1))) -> 0_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(x1))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{2_1}(x1))) -> 0_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(1_{5_1}(5_{2_1}(x1))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{3_1}(x1))) -> 0_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(1_{5_1}(5_{3_1}(x1))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{0_1}(x1))) -> 0_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(1_{5_1}(5_{0_1}(x1))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{5_1}(x1))) -> 0_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(1_{5_1}(5_{5_1}(x1))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{2_1}(2_{0_1}(x1)))) -> 0_{4_1}(4_{2_1}(2_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(x1))))))
47.45/12.99	   5_{0_1}(0_{3_1}(3_{4_1}(4_{3_1}(x1)))) -> 5_{5_1}(5_{3_1}(3_{2_1}(2_{3_1}(3_{3_1}(3_{3_1}(x1))))))
47.45/12.99	   4_{4_1}(4_{5_1}(5_{2_1}(x1))) -> 4_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{2_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{5_1}(5_{2_1}(x1))) -> 3_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{2_1}(x1)))))))
47.45/12.99	   2_{5_1}(5_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 2_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{3_1}(3_{4_1}(x1)))) -> 2_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{3_1}(3_{1_1}(x1)))) -> 2_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{3_1}(3_{5_1}(x1)))) -> 2_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{3_1}(3_{4_1}(x1)))) -> 5_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{3_1}(3_{1_1}(x1)))) -> 5_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{3_1}(3_{5_1}(x1)))) -> 5_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
47.45/12.99	   1_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 1_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(x1)))))))
47.45/12.99	   1_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 1_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(x1)))))))
47.45/12.99	   1_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 1_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{5_1}(x1)))))))
47.45/12.99	   0_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 0_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(x1)))))))
47.45/12.99	   0_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 0_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(x1)))))))
47.45/12.99	   0_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 0_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{5_1}(x1)))))))
47.45/12.99	
47.45/12.99	Q is empty.
47.45/12.99	
47.45/12.99	----------------------------------------
47.45/12.99	
47.45/12.99	(9) QTRSRRRProof (EQUIVALENT)
47.45/12.99	Used ordering:
47.45/12.99	Polynomial interpretation [POLO]:
47.45/12.99	
47.45/12.99	   POL(0_{0_1}(x_1)) = x_1
47.45/12.99	   POL(0_{1_1}(x_1)) = x_1
47.45/12.99	   POL(0_{2_1}(x_1)) = x_1
47.45/12.99	   POL(0_{3_1}(x_1)) = x_1
47.45/12.99	   POL(0_{4_1}(x_1)) = x_1
47.45/12.99	   POL(0_{5_1}(x_1)) = x_1
47.45/12.99	   POL(1_{0_1}(x_1)) = 1 + x_1
47.45/12.99	   POL(1_{1_1}(x_1)) = x_1
47.45/12.99	   POL(1_{2_1}(x_1)) = x_1
47.45/12.99	   POL(1_{3_1}(x_1)) = x_1
47.45/12.99	   POL(1_{4_1}(x_1)) = x_1
47.45/12.99	   POL(1_{5_1}(x_1)) = x_1
47.45/12.99	   POL(2_{0_1}(x_1)) = x_1
47.45/12.99	   POL(2_{1_1}(x_1)) = x_1
47.45/12.99	   POL(2_{2_1}(x_1)) = x_1
47.45/12.99	   POL(2_{3_1}(x_1)) = x_1
47.45/12.99	   POL(2_{4_1}(x_1)) = x_1
47.45/12.99	   POL(2_{5_1}(x_1)) = x_1
47.45/12.99	   POL(3_{0_1}(x_1)) = 1 + x_1
47.45/12.99	   POL(3_{1_1}(x_1)) = x_1
47.45/12.99	   POL(3_{2_1}(x_1)) = x_1
47.45/12.99	   POL(3_{3_1}(x_1)) = x_1
47.45/12.99	   POL(3_{4_1}(x_1)) = x_1
47.45/12.99	   POL(3_{5_1}(x_1)) = x_1
47.45/12.99	   POL(4_{0_1}(x_1)) = x_1
47.45/12.99	   POL(4_{1_1}(x_1)) = x_1
47.45/12.99	   POL(4_{2_1}(x_1)) = x_1
47.45/12.99	   POL(4_{3_1}(x_1)) = x_1
47.45/12.99	   POL(4_{4_1}(x_1)) = x_1
47.45/12.99	   POL(4_{5_1}(x_1)) = x_1
47.45/12.99	   POL(5_{0_1}(x_1)) = 2 + x_1
47.45/12.99	   POL(5_{1_1}(x_1)) = x_1
47.45/12.99	   POL(5_{2_1}(x_1)) = 1 + x_1
47.45/12.99	   POL(5_{3_1}(x_1)) = 1 + x_1
47.45/12.99	   POL(5_{4_1}(x_1)) = 1 + x_1
47.45/12.99	   POL(5_{5_1}(x_1)) = x_1
47.45/12.99	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
47.45/12.99	
47.45/12.99	   0_{3_1}(3_{0_1}(0_{3_1}(x1))) -> 0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{3_1}(x1))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{2_1}(2_{0_1}(x1)))) -> 0_{4_1}(4_{2_1}(2_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(x1))))))
47.45/12.99	   5_{0_1}(0_{3_1}(3_{4_1}(4_{3_1}(x1)))) -> 5_{5_1}(5_{3_1}(3_{2_1}(2_{3_1}(3_{3_1}(3_{3_1}(x1))))))
47.45/12.99	   4_{4_1}(4_{5_1}(5_{2_1}(x1))) -> 4_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{2_1}(x1)))))))
47.45/12.99	   3_{4_1}(4_{5_1}(5_{2_1}(x1))) -> 3_{1_1}(1_{1_1}(1_{1_1}(1_{3_1}(3_{2_1}(2_{4_1}(4_{2_1}(x1)))))))
47.45/12.99	   2_{5_1}(5_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 2_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{3_1}(3_{4_1}(x1)))) -> 2_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{3_1}(3_{1_1}(x1)))) -> 2_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
47.45/12.99	   2_{4_1}(4_{5_1}(5_{3_1}(3_{5_1}(x1)))) -> 2_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{3_1}(3_{4_1}(x1)))) -> 5_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{3_1}(3_{1_1}(x1)))) -> 5_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
47.45/12.99	   5_{4_1}(4_{5_1}(5_{3_1}(3_{5_1}(x1)))) -> 5_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
47.45/12.99	   1_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 1_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(x1)))))))
47.45/12.99	   0_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 0_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(x1)))))))
47.45/12.99	
47.45/12.99	
47.45/12.99	
47.45/12.99	
47.45/12.99	----------------------------------------
47.45/12.99	
47.45/12.99	(10)
47.45/12.99	Obligation:
47.45/12.99	Q restricted rewrite system:
47.45/12.99	The TRS R consists of the following rules:
47.45/12.99	
47.45/12.99	   0_{4_1}(4_{5_1}(5_{4_1}(x1))) -> 0_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(1_{5_1}(5_{4_1}(x1))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{1_1}(x1))) -> 0_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(x1))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{2_1}(x1))) -> 0_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(1_{5_1}(5_{2_1}(x1))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{3_1}(x1))) -> 0_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(1_{5_1}(5_{3_1}(x1))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{0_1}(x1))) -> 0_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(1_{5_1}(5_{0_1}(x1))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{5_1}(x1))) -> 0_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(1_{5_1}(5_{5_1}(x1))))))
47.45/12.99	   1_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 1_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(x1)))))))
47.45/12.99	   1_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 1_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{5_1}(x1)))))))
47.45/12.99	   0_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 0_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(x1)))))))
47.45/12.99	   0_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 0_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{5_1}(x1)))))))
47.45/12.99	
47.45/12.99	Q is empty.
47.45/12.99	
47.45/12.99	----------------------------------------
47.45/12.99	
47.45/12.99	(11) QTRSRRRProof (EQUIVALENT)
47.45/12.99	Used ordering:
47.45/12.99	Polynomial interpretation [POLO]:
47.45/12.99	
47.45/12.99	   POL(0_{0_1}(x_1)) = x_1
47.45/12.99	   POL(0_{1_1}(x_1)) = x_1
47.45/12.99	   POL(0_{4_1}(x_1)) = 1 + x_1
47.45/12.99	   POL(0_{5_1}(x_1)) = x_1
47.45/12.99	   POL(1_{0_1}(x_1)) = x_1
47.45/12.99	   POL(1_{1_1}(x_1)) = x_1
47.45/12.99	   POL(1_{2_1}(x_1)) = x_1
47.45/12.99	   POL(1_{4_1}(x_1)) = x_1
47.45/12.99	   POL(1_{5_1}(x_1)) = x_1
47.45/12.99	   POL(2_{5_1}(x_1)) = x_1
47.45/12.99	   POL(3_{1_1}(x_1)) = x_1
47.45/12.99	   POL(4_{1_1}(x_1)) = x_1
47.45/12.99	   POL(4_{3_1}(x_1)) = x_1
47.45/12.99	   POL(4_{5_1}(x_1)) = x_1
47.45/12.99	   POL(5_{0_1}(x_1)) = x_1
47.45/12.99	   POL(5_{1_1}(x_1)) = x_1
47.45/12.99	   POL(5_{2_1}(x_1)) = x_1
47.45/12.99	   POL(5_{3_1}(x_1)) = x_1
47.45/12.99	   POL(5_{4_1}(x_1)) = x_1
47.45/12.99	   POL(5_{5_1}(x_1)) = x_1
47.45/12.99	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
47.45/12.99	
47.45/12.99	   0_{4_1}(4_{5_1}(5_{4_1}(x1))) -> 0_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(1_{5_1}(5_{4_1}(x1))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{1_1}(x1))) -> 0_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(x1))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{2_1}(x1))) -> 0_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(1_{5_1}(5_{2_1}(x1))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{3_1}(x1))) -> 0_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(1_{5_1}(5_{3_1}(x1))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{0_1}(x1))) -> 0_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(1_{5_1}(5_{0_1}(x1))))))
47.45/12.99	   0_{4_1}(4_{5_1}(5_{5_1}(x1))) -> 0_{1_1}(1_{2_1}(2_{5_1}(5_{1_1}(1_{5_1}(5_{5_1}(x1))))))
47.45/12.99	
47.45/12.99	
47.45/12.99	
47.45/12.99	
47.45/12.99	----------------------------------------
47.45/12.99	
47.45/12.99	(12)
47.45/12.99	Obligation:
47.45/12.99	Q restricted rewrite system:
47.45/12.99	The TRS R consists of the following rules:
47.45/12.99	
47.45/12.99	   1_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 1_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(x1)))))))
47.45/12.99	   1_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 1_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{5_1}(x1)))))))
47.45/12.99	   0_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 0_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(x1)))))))
47.45/12.99	   0_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 0_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{5_1}(x1)))))))
47.45/12.99	
47.45/12.99	Q is empty.
47.45/12.99	
47.45/12.99	----------------------------------------
47.45/12.99	
47.45/12.99	(13) QTRSRRRProof (EQUIVALENT)
47.45/12.99	Used ordering:
47.45/12.99	Polynomial interpretation [POLO]:
47.45/12.99	
47.45/12.99	   POL(0_{0_1}(x_1)) = x_1
47.45/12.99	   POL(0_{1_1}(x_1)) = x_1
47.45/12.99	   POL(0_{5_1}(x_1)) = x_1
47.45/12.99	   POL(1_{0_1}(x_1)) = x_1
47.45/12.99	   POL(1_{1_1}(x_1)) = 1 + x_1
47.45/12.99	   POL(1_{4_1}(x_1)) = x_1
47.45/12.99	   POL(1_{5_1}(x_1)) = 1 + x_1
47.45/12.99	   POL(3_{1_1}(x_1)) = x_1
47.45/12.99	   POL(4_{1_1}(x_1)) = x_1
47.45/12.99	   POL(4_{3_1}(x_1)) = x_1
47.45/12.99	   POL(5_{4_1}(x_1)) = x_1
47.45/12.99	   POL(5_{5_1}(x_1)) = x_1
47.45/12.99	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
47.45/12.99	
47.45/12.99	   1_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 1_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(x1)))))))
47.45/12.99	   1_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 1_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{5_1}(x1)))))))
47.45/12.99	   0_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 0_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(x1)))))))
47.45/12.99	   0_{5_1}(5_{5_1}(5_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 0_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(0_{0_1}(0_{5_1}(x1)))))))
47.45/12.99	
47.45/12.99	
47.45/12.99	
47.45/12.99	
47.45/12.99	----------------------------------------
47.45/12.99	
47.45/12.99	(14)
47.45/12.99	Obligation:
47.45/12.99	Q restricted rewrite system:
47.45/12.99	R is empty.
47.45/12.99	Q is empty.
47.45/12.99	
47.45/12.99	----------------------------------------
47.45/12.99	
47.45/12.99	(15) RisEmptyProof (EQUIVALENT)
47.45/12.99	The TRS R is empty. Hence, termination is trivially proven.
47.45/12.99	----------------------------------------
47.45/12.99	
47.45/12.99	(16)
47.45/12.99	YES
47.71/13.11	EOF