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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) QTRS
(1) FlatCCProof [EQUIVALENT, 0 ms]
(2) QTRS
(3) RootLabelingProof [EQUIVALENT, 36 ms]
(4) QTRS
(5) QTRSRRRProof [EQUIVALENT, 9910 ms]
(6) QTRS
(7) QTRSRRRProof [EQUIVALENT, 40 ms]
(8) QTRS
(9) QTRSRRRProof [EQUIVALENT, 12 ms]
(10) QTRS
(11) DependencyPairsProof [EQUIVALENT, 97 ms]
(12) QDP
(13) DependencyGraphProof [EQUIVALENT, 0 ms]
(14) AND
    (15) QDP
        (16) UsableRulesProof [EQUIVALENT, 0 ms]
        (17) QDP
        (18) DependencyGraphProof [EQUIVALENT, 0 ms]
        (19) QDP
        (20) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (21) YES
    (22) QDP
        (23) UsableRulesProof [EQUIVALENT, 0 ms]
        (24) QDP
        (25) DependencyGraphProof [EQUIVALENT, 0 ms]
        (26) QDP
        (27) QDPOrderProof [EQUIVALENT, 26 ms]
        (28) QDP
        (29) QDPOrderProof [EQUIVALENT, 23 ms]
        (30) QDP
        (31) DependencyGraphProof [EQUIVALENT, 0 ms]
        (32) TRUE
    (33) QDP
        (34) UsableRulesProof [EQUIVALENT, 0 ms]
        (35) QDP
        (36) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (37) YES


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

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

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

Q is empty.

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

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

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

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

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

Q is empty.

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

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

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

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

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

   0_{1_1}(1_{0_1}(0_{0_1}(x1))) -> 0_{1_1}(1_{3_1}(3_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(x1))))))
   0_{1_1}(1_{0_1}(0_{1_1}(x1))) -> 0_{1_1}(1_{3_1}(3_{4_1}(4_{0_1}(0_{3_1}(3_{1_1}(x1))))))
   0_{1_1}(1_{0_1}(0_{3_1}(x1))) -> 0_{1_1}(1_{3_1}(3_{4_1}(4_{0_1}(0_{3_1}(3_{3_1}(x1))))))
   0_{1_1}(1_{0_1}(0_{4_1}(x1))) -> 0_{1_1}(1_{3_1}(3_{4_1}(4_{0_1}(0_{3_1}(3_{4_1}(x1))))))
   0_{1_1}(1_{0_1}(0_{2_1}(x1))) -> 0_{1_1}(1_{3_1}(3_{4_1}(4_{0_1}(0_{3_1}(3_{2_1}(x1))))))
   0_{1_1}(1_{0_1}(0_{5_1}(x1))) -> 0_{1_1}(1_{3_1}(3_{4_1}(4_{0_1}(0_{3_1}(3_{5_1}(x1))))))
   0_{1_1}(1_{1_1}(1_{0_1}(x1))) -> 0_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{0_1}(x1)))))
   0_{1_1}(1_{1_1}(1_{1_1}(x1))) -> 0_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{1_1}(x1)))))
   0_{1_1}(1_{1_1}(1_{3_1}(x1))) -> 0_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(x1)))))
   0_{1_1}(1_{1_1}(1_{4_1}(x1))) -> 0_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{4_1}(x1)))))
   0_{1_1}(1_{1_1}(1_{2_1}(x1))) -> 0_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{2_1}(x1)))))
   0_{1_1}(1_{1_1}(1_{5_1}(x1))) -> 0_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{5_1}(x1)))))
   0_{1_1}(1_{1_1}(1_{0_1}(x1))) -> 0_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{0_1}(x1))))))
   0_{1_1}(1_{1_1}(1_{1_1}(x1))) -> 0_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{1_1}(x1))))))
   0_{1_1}(1_{1_1}(1_{3_1}(x1))) -> 0_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(x1))))))
   0_{1_1}(1_{1_1}(1_{4_1}(x1))) -> 0_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{4_1}(x1))))))
   0_{1_1}(1_{1_1}(1_{2_1}(x1))) -> 0_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{2_1}(x1))))))
   0_{1_1}(1_{1_1}(1_{5_1}(x1))) -> 0_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{5_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x1)))) -> 0_{2_1}(2_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{0_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x1)))) -> 0_{2_1}(2_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(x1)))) -> 0_{2_1}(2_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{1_1}(1_{4_1}(x1)))) -> 0_{2_1}(2_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x1)))) -> 0_{2_1}(2_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{2_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{1_1}(1_{5_1}(x1)))) -> 0_{2_1}(2_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{5_1}(x1))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 0_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(x1)))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 0_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(5_{1_1}(x1)))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 0_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(5_{3_1}(x1)))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 0_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(x1)))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 0_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(5_{2_1}(x1)))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 0_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(x1)))))
   0_{5_1}(5_{4_1}(4_{0_1}(0_{0_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(x1)))))
   0_{5_1}(5_{4_1}(4_{0_1}(0_{1_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(x1)))))
   0_{5_1}(5_{4_1}(4_{0_1}(0_{3_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(x1)))))
   0_{5_1}(5_{4_1}(4_{0_1}(0_{4_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{4_1}(x1)))))
   0_{5_1}(5_{4_1}(4_{0_1}(0_{2_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{2_1}(x1)))))
   0_{5_1}(5_{4_1}(4_{0_1}(0_{5_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(x1)))))
   2_{0_1}(0_{4_1}(4_{1_1}(1_{0_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(4_{0_1}(x1))))))
   2_{0_1}(0_{4_1}(4_{1_1}(1_{1_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(4_{1_1}(x1))))))
   2_{0_1}(0_{4_1}(4_{1_1}(1_{3_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(x1))))))
   2_{0_1}(0_{4_1}(4_{1_1}(1_{4_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(4_{4_1}(x1))))))
   2_{0_1}(0_{4_1}(4_{1_1}(1_{2_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(4_{2_1}(x1))))))
   2_{0_1}(0_{4_1}(4_{1_1}(1_{5_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(4_{5_1}(x1))))))
   5_{1_1}(1_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{0_1}(x1)))))
   5_{1_1}(1_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(x1)))))
   5_{1_1}(1_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{3_1}(x1)))))
   5_{1_1}(1_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(x1)))))
   5_{1_1}(1_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{2_1}(x1)))))
   5_{1_1}(1_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{5_1}(x1)))))
   5_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x1)))) -> 5_{1_1}(1_{0_1}(0_{3_1}(3_{2_1}(2_{0_1}(x1)))))
   5_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x1)))) -> 5_{1_1}(1_{0_1}(0_{3_1}(3_{2_1}(2_{1_1}(x1)))))
   5_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(x1)))) -> 5_{1_1}(1_{0_1}(0_{3_1}(3_{2_1}(2_{3_1}(x1)))))
   5_{2_1}(2_{0_1}(0_{1_1}(1_{4_1}(x1)))) -> 5_{1_1}(1_{0_1}(0_{3_1}(3_{2_1}(2_{4_1}(x1)))))
   5_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x1)))) -> 5_{1_1}(1_{0_1}(0_{3_1}(3_{2_1}(2_{2_1}(x1)))))
   5_{2_1}(2_{0_1}(0_{1_1}(1_{5_1}(x1)))) -> 5_{1_1}(1_{0_1}(0_{3_1}(3_{2_1}(2_{5_1}(x1)))))
   5_{3_1}(3_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 5_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{5_1}(5_{0_1}(x1))))))
   5_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 5_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(x1))))))
   5_{3_1}(3_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 5_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{5_1}(5_{3_1}(x1))))))
   5_{3_1}(3_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 5_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{5_1}(5_{4_1}(x1))))))
   5_{3_1}(3_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 5_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{5_1}(5_{2_1}(x1))))))
   5_{3_1}(3_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 5_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{5_1}(5_{5_1}(x1))))))
   5_{4_1}(4_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 5_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{5_1}(5_{0_1}(x1))))))
   5_{4_1}(4_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 5_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{5_1}(5_{1_1}(x1))))))
   5_{4_1}(4_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 5_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{5_1}(5_{3_1}(x1))))))
   5_{4_1}(4_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 5_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{5_1}(5_{4_1}(x1))))))
   5_{4_1}(4_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 5_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{5_1}(5_{2_1}(x1))))))
   5_{4_1}(4_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 5_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{5_1}(5_{5_1}(x1))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{3_1}(3_{0_1}(x1)))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{3_1}(3_{1_1}(x1)))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{3_1}(3_{3_1}(x1)))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{3_1}(3_{4_1}(x1)))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{3_1}(3_{2_1}(x1)))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(x1)))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{0_1}(x1))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(x1))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{3_1}(x1))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(x1))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{2_1}(x1))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{5_1}(x1))))))
   5_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{2_1}(2_{0_1}(x1))))))
   5_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{2_1}(2_{1_1}(x1))))))
   5_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{2_1}(2_{3_1}(x1))))))
   5_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{2_1}(2_{4_1}(x1))))))
   5_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{2_1}(2_{2_1}(x1))))))
   5_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{2_1}(2_{5_1}(x1))))))
   5_{3_1}(3_{0_1}(0_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 5_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{1_1}(1_{0_1}(x1))))))
   5_{3_1}(3_{0_1}(0_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 5_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{1_1}(1_{1_1}(x1))))))
   5_{3_1}(3_{0_1}(0_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 5_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{1_1}(1_{3_1}(x1))))))
   5_{3_1}(3_{0_1}(0_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 5_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(x1))))))
   5_{3_1}(3_{0_1}(0_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 5_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{1_1}(1_{2_1}(x1))))))
   5_{3_1}(3_{0_1}(0_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 5_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{1_1}(1_{5_1}(x1))))))
   0_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(x1)))) -> 0_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
   0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(x1)))) -> 0_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
   0_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(x1)))) -> 0_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
   0_{0_1}(0_{0_1}(0_{1_1}(1_{4_1}(x1)))) -> 0_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
   0_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(x1)))) -> 0_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
   0_{0_1}(0_{0_1}(0_{1_1}(1_{5_1}(x1)))) -> 0_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
   1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(x1)))) -> 1_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
   1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(x1)))) -> 1_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
   1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(x1)))) -> 1_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
   1_{0_1}(0_{0_1}(0_{1_1}(1_{4_1}(x1)))) -> 1_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
   1_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(x1)))) -> 1_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
   1_{0_1}(0_{0_1}(0_{1_1}(1_{5_1}(x1)))) -> 1_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
   2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(x1)))) -> 2_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
   2_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(x1)))) -> 2_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
   2_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(x1)))) -> 2_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
   2_{0_1}(0_{0_1}(0_{1_1}(1_{4_1}(x1)))) -> 2_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
   2_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(x1)))) -> 2_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
   2_{0_1}(0_{0_1}(0_{1_1}(1_{5_1}(x1)))) -> 2_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
   3_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(x1)))) -> 3_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
   3_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(x1)))) -> 3_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
   3_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(x1)))) -> 3_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
   3_{0_1}(0_{0_1}(0_{1_1}(1_{4_1}(x1)))) -> 3_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
   3_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(x1)))) -> 3_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
   3_{0_1}(0_{0_1}(0_{1_1}(1_{5_1}(x1)))) -> 3_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
   4_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(x1)))) -> 4_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
   4_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(x1)))) -> 4_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
   4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(x1)))) -> 4_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
   4_{0_1}(0_{0_1}(0_{1_1}(1_{4_1}(x1)))) -> 4_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
   4_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(x1)))) -> 4_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
   4_{0_1}(0_{0_1}(0_{1_1}(1_{5_1}(x1)))) -> 4_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
   5_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(x1)))) -> 5_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
   5_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(x1)))) -> 5_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
   5_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(x1)))) -> 5_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
   5_{0_1}(0_{0_1}(0_{1_1}(1_{4_1}(x1)))) -> 5_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
   5_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(x1)))) -> 5_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
   5_{0_1}(0_{0_1}(0_{1_1}(1_{5_1}(x1)))) -> 5_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 0_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 0_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 0_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 0_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 0_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 0_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 1_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 1_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 1_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 1_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 1_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 1_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 2_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 2_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 2_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 2_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 2_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 2_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 3_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 3_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 3_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 3_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 3_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 3_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 4_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 4_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 4_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 4_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 4_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 4_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 5_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 5_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 5_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 5_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 5_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 5_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(x1))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{1_1}(x1))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(x1))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(x1))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{2_1}(x1))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{5_1}(x1))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(x1))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{1_1}(x1))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(x1))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(x1))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{2_1}(x1))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{5_1}(x1))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(x1))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{1_1}(x1))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(x1))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(x1))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{2_1}(x1))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{5_1}(x1))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(x1))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{1_1}(x1))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(x1))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(x1))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{2_1}(x1))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{5_1}(x1))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(x1))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{1_1}(x1))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(x1))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(x1))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{2_1}(x1))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{5_1}(x1))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(x1))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{1_1}(x1))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(x1))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(x1))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{2_1}(x1))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{5_1}(x1))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{0_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{3_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{2_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{5_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{0_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{3_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{2_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{5_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{0_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{3_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{2_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{5_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{0_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{3_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{2_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{5_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{0_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{3_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{2_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{5_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{0_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{3_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{2_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{5_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{1_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{4_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{2_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{5_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{1_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{4_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{2_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{5_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{1_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{4_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{2_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{5_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{1_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{4_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{2_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{5_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{1_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{4_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{2_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{5_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{1_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{4_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{2_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{5_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{3_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{4_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{5_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{3_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{4_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{5_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{3_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{4_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{5_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{3_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{4_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{5_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{3_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{4_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{5_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{3_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{4_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{5_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{0_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{1_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{4_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{2_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{0_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{1_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{4_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{2_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{0_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{1_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{4_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{2_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{0_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{1_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{4_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{2_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{0_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{1_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{4_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{2_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{0_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{1_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{4_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{2_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{0_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{1_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{4_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{5_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{0_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{1_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{4_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{5_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{0_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{1_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{4_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{5_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{0_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{1_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{4_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{5_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{0_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{1_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{4_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{5_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{0_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{1_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{4_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{5_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{0_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{3_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{4_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{5_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{0_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{3_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{4_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{5_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{0_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{3_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{4_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{5_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{0_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{3_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{4_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{5_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{0_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{3_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{4_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{5_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{0_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{3_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{4_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{5_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{0_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{3_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{4_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{5_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 1_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{0_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 1_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 1_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{3_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 1_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{4_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 1_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 1_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{5_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 2_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{0_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 2_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 2_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{3_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 2_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{4_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 2_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 2_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{5_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 3_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{0_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 3_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 3_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{3_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 3_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{4_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 3_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 3_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{5_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 4_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{0_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 4_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 4_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{3_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 4_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{4_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 4_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 4_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{5_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 5_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{0_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 5_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 5_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{3_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 5_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{4_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 5_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 5_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{5_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{3_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{4_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{5_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 1_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 1_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 1_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{3_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 1_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{4_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 1_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 1_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{5_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 2_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 2_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 2_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{3_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 2_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{4_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 2_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 2_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{5_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 3_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 3_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 3_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{3_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 3_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{4_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 3_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 3_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{5_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 4_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 4_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 4_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{3_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 4_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{4_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 4_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 4_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{5_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 5_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 5_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 5_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{3_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 5_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{4_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 5_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 5_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{5_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 0_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{0_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 0_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 0_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{3_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 0_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 0_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{2_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 0_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{5_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 1_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{0_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 1_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 1_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{3_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 1_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 1_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{2_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 1_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{5_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 2_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{0_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 2_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 2_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{3_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 2_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 2_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{2_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 2_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{5_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 3_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{0_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 3_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 3_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{3_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 3_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 3_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{2_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 3_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{5_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 4_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{0_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 4_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 4_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{3_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 4_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 4_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{2_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 4_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{5_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 5_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{0_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 5_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 5_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{3_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 5_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 5_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{2_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 5_{5_1}(5_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(0_{5_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{0_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{1_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{3_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{4_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{2_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{5_1}(x1))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{0_1}(x1))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{1_1}(x1))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{3_1}(x1))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{4_1}(x1))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{2_1}(x1))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{5_1}(x1))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{0_1}(x1))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{1_1}(x1))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{3_1}(x1))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{4_1}(x1))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{2_1}(x1))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{5_1}(x1))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{0_1}(x1))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{1_1}(x1))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{3_1}(x1))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{4_1}(x1))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{2_1}(x1))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{5_1}(x1))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{0_1}(x1))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{1_1}(x1))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{3_1}(x1))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{4_1}(x1))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{2_1}(x1))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{5_1}(x1))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{0_1}(x1))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{1_1}(x1))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{3_1}(x1))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{4_1}(x1))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{2_1}(x1))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{5_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{0_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{1_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{3_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{2_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{5_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{0_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{1_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{3_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{2_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{5_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{0_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{1_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{3_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{2_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{5_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{0_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{1_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{3_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{2_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{5_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{0_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{1_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{3_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{2_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{5_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{0_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{1_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{3_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{2_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{5_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{1_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{4_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{2_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{5_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{1_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{4_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{2_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{5_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{1_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{4_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{2_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{5_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{1_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{4_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{2_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{5_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{1_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{4_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{2_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{5_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{1_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{4_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{2_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{5_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{0_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{3_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{4_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{2_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{0_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{3_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{4_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{2_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{0_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{3_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{4_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{2_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{0_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{3_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{4_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{2_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{0_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{3_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{4_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{2_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{0_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{3_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{4_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{2_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{1_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{3_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{4_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{2_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{5_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{1_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{3_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{4_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{2_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{5_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{1_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{3_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{4_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{2_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{5_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{1_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{3_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{4_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{2_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{5_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{1_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{3_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{4_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{2_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{5_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{1_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{3_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{4_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{2_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{5_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 1_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 1_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 1_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 1_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 1_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 1_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 2_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 2_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 2_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 2_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 2_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 2_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 3_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 3_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 3_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 3_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 3_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 3_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 4_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 4_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 4_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 4_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 4_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 4_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 5_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 5_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 5_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 5_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 5_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 5_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(x1))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{1_1}(x1))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{3_1}(x1))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(x1))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{2_1}(x1))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(x1))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(x1))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{1_1}(x1))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{3_1}(x1))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(x1))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{2_1}(x1))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(x1))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(x1))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{1_1}(x1))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{3_1}(x1))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(x1))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{2_1}(x1))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(x1))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(x1))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{1_1}(x1))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{3_1}(x1))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(x1))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{2_1}(x1))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(x1))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(x1))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{1_1}(x1))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{3_1}(x1))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(x1))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{2_1}(x1))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(x1))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(x1))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{1_1}(x1))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{3_1}(x1))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(x1))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{2_1}(x1))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(x1))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(x1))))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(x1))))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{3_1}(x1))))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{4_1}(x1))))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{4_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{2_1}(x1))))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{2_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{5_1}(x1))))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{5_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(x1))))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(x1))))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{3_1}(x1))))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{4_1}(x1))))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{4_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{2_1}(x1))))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{2_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{5_1}(x1))))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{5_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(x1))))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(x1))))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{3_1}(x1))))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{4_1}(x1))))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{4_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{2_1}(x1))))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{2_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{5_1}(x1))))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{5_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(x1))))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(x1))))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{3_1}(x1))))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{4_1}(x1))))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{4_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{2_1}(x1))))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{2_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{5_1}(x1))))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{5_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(x1))))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(x1))))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{3_1}(x1))))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{4_1}(x1))))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{4_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{2_1}(x1))))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{2_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{5_1}(x1))))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{5_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(x1))))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(x1))))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{3_1}(x1))))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{4_1}(x1))))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{4_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{2_1}(x1))))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{2_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{5_1}(x1))))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{5_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1))))) -> 0_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1))))) -> 0_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1))))) -> 0_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{3_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1))))) -> 0_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{4_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1))))) -> 0_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{2_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1))))) -> 0_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{5_1}(x1))))))
   1_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1))))) -> 1_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(x1))))))
   1_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1))))) -> 1_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(x1))))))
   1_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1))))) -> 1_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{3_1}(x1))))))
   1_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1))))) -> 1_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{4_1}(x1))))))
   1_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1))))) -> 1_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{2_1}(x1))))))
   1_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1))))) -> 1_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{5_1}(x1))))))
   2_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1))))) -> 2_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(x1))))))
   2_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1))))) -> 2_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(x1))))))
   2_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1))))) -> 2_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{3_1}(x1))))))
   2_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1))))) -> 2_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{4_1}(x1))))))
   2_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1))))) -> 2_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{2_1}(x1))))))
   2_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1))))) -> 2_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{5_1}(x1))))))
   3_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1))))) -> 3_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(x1))))))
   3_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1))))) -> 3_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(x1))))))
   3_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1))))) -> 3_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{3_1}(x1))))))
   3_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1))))) -> 3_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{4_1}(x1))))))
   3_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1))))) -> 3_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{2_1}(x1))))))
   3_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1))))) -> 3_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{5_1}(x1))))))
   4_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1))))) -> 4_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(x1))))))
   4_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1))))) -> 4_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(x1))))))
   4_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1))))) -> 4_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{3_1}(x1))))))
   4_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1))))) -> 4_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{4_1}(x1))))))
   4_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1))))) -> 4_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{2_1}(x1))))))
   4_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1))))) -> 4_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{5_1}(x1))))))
   5_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1))))) -> 5_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(x1))))))
   5_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1))))) -> 5_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(x1))))))
   5_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1))))) -> 5_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{3_1}(x1))))))
   5_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1))))) -> 5_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{4_1}(x1))))))
   5_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1))))) -> 5_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{2_1}(x1))))))
   5_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1))))) -> 5_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{5_1}(x1))))))
   0_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 0_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{0_1}(x1)))))))
   0_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 0_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{1_1}(x1)))))))
   0_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 0_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(x1)))))))
   0_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 0_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{4_1}(x1)))))))
   0_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 0_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{2_1}(x1)))))))
   0_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 0_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{5_1}(x1)))))))
   1_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{0_1}(x1)))))))
   1_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{1_1}(x1)))))))
   1_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(x1)))))))
   1_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{4_1}(x1)))))))
   1_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{2_1}(x1)))))))
   1_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{5_1}(x1)))))))
   2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 2_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{0_1}(x1)))))))
   2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 2_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{1_1}(x1)))))))
   2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 2_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(x1)))))))
   2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 2_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{4_1}(x1)))))))
   2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 2_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{2_1}(x1)))))))
   2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 2_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{5_1}(x1)))))))
   3_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 3_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{0_1}(x1)))))))
   3_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 3_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{1_1}(x1)))))))
   3_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 3_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(x1)))))))
   3_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 3_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{4_1}(x1)))))))
   3_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 3_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{2_1}(x1)))))))
   3_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 3_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{5_1}(x1)))))))
   4_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 4_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{0_1}(x1)))))))
   4_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 4_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{1_1}(x1)))))))
   4_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 4_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(x1)))))))
   4_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 4_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{4_1}(x1)))))))
   4_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 4_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{2_1}(x1)))))))
   4_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 4_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{5_1}(x1)))))))
   5_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 5_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{0_1}(x1)))))))
   5_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 5_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{1_1}(x1)))))))
   5_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 5_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(x1)))))))
   5_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 5_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{4_1}(x1)))))))
   5_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 5_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{2_1}(x1)))))))
   5_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 5_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{5_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x1))))) -> 0_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x1))))) -> 0_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{3_1}(x1))))) -> 0_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{3_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{4_1}(x1))))) -> 0_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x1))))) -> 0_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{2_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{5_1}(x1))))) -> 0_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{5_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x1))))) -> 1_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x1))))) -> 1_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{3_1}(x1))))) -> 1_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{3_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{4_1}(x1))))) -> 1_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x1))))) -> 1_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{2_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{5_1}(x1))))) -> 1_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{5_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x1))))) -> 2_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x1))))) -> 2_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{3_1}(x1))))) -> 2_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{3_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{4_1}(x1))))) -> 2_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x1))))) -> 2_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{2_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{5_1}(x1))))) -> 2_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{5_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x1))))) -> 3_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x1))))) -> 3_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{3_1}(x1))))) -> 3_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{3_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{4_1}(x1))))) -> 3_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x1))))) -> 3_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{2_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{5_1}(x1))))) -> 3_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{5_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x1))))) -> 4_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x1))))) -> 4_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{3_1}(x1))))) -> 4_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{3_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{4_1}(x1))))) -> 4_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x1))))) -> 4_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{2_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{5_1}(x1))))) -> 4_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{5_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x1))))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x1))))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{3_1}(x1))))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{3_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{4_1}(x1))))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x1))))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{2_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{5_1}(x1))))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{5_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x1))))) -> 0_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x1))))) -> 0_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{3_1}(x1))))) -> 0_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{4_1}(x1))))) -> 0_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x1))))) -> 0_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{5_1}(x1))))) -> 0_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x1))))) -> 1_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x1))))) -> 1_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{3_1}(x1))))) -> 1_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{4_1}(x1))))) -> 1_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x1))))) -> 1_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{5_1}(x1))))) -> 1_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x1))))) -> 2_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x1))))) -> 2_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{3_1}(x1))))) -> 2_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{4_1}(x1))))) -> 2_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x1))))) -> 2_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{5_1}(x1))))) -> 2_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x1))))) -> 3_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x1))))) -> 3_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{3_1}(x1))))) -> 3_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{4_1}(x1))))) -> 3_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x1))))) -> 3_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{5_1}(x1))))) -> 3_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x1))))) -> 4_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x1))))) -> 4_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{3_1}(x1))))) -> 4_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{4_1}(x1))))) -> 4_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x1))))) -> 4_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{5_1}(x1))))) -> 4_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x1))))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x1))))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{3_1}(x1))))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{4_1}(x1))))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x1))))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{5_1}(x1))))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1))))))
   0_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(x1))))) -> 0_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{0_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(x1))))) -> 0_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{1_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{3_1}(x1))))) -> 0_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{3_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{4_1}(x1))))) -> 0_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{4_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(x1))))) -> 0_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{2_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(x1))))) -> 0_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{5_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(x1))))) -> 1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{0_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(x1))))) -> 1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{1_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{3_1}(x1))))) -> 1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{3_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{4_1}(x1))))) -> 1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{4_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(x1))))) -> 1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{2_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(x1))))) -> 1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{5_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(x1))))) -> 2_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{0_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(x1))))) -> 2_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{1_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{3_1}(x1))))) -> 2_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{3_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{4_1}(x1))))) -> 2_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{4_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(x1))))) -> 2_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{2_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(x1))))) -> 2_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{5_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(x1))))) -> 3_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{0_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(x1))))) -> 3_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{1_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{3_1}(x1))))) -> 3_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{3_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{4_1}(x1))))) -> 3_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{4_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(x1))))) -> 3_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{2_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(x1))))) -> 3_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{5_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(x1))))) -> 4_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{0_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(x1))))) -> 4_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{1_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{3_1}(x1))))) -> 4_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{3_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{4_1}(x1))))) -> 4_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{4_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(x1))))) -> 4_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{2_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(x1))))) -> 4_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{5_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(x1))))) -> 5_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{0_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(x1))))) -> 5_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{1_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{3_1}(x1))))) -> 5_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{3_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{4_1}(x1))))) -> 5_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{4_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(x1))))) -> 5_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{2_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(x1))))) -> 5_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{5_1}(x1)))))))
   0_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{0_1}(x1)))))) -> 0_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(x1)))))))
   0_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{1_1}(x1)))))) -> 0_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{1_1}(x1)))))))
   0_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{3_1}(x1)))))) -> 0_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{3_1}(x1)))))))
   0_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{4_1}(x1)))))) -> 0_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{4_1}(x1)))))))
   0_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{2_1}(x1)))))) -> 0_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{2_1}(x1)))))))
   0_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{5_1}(x1)))))) -> 0_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(x1)))))))
   1_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{0_1}(x1)))))) -> 1_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(x1)))))))
   1_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{1_1}(x1)))))) -> 1_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{1_1}(x1)))))))
   1_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{3_1}(x1)))))) -> 1_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{3_1}(x1)))))))
   1_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{4_1}(x1)))))) -> 1_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{4_1}(x1)))))))
   1_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{2_1}(x1)))))) -> 1_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{2_1}(x1)))))))
   1_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{5_1}(x1)))))) -> 1_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(x1)))))))
   2_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{0_1}(x1)))))) -> 2_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(x1)))))))
   2_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{1_1}(x1)))))) -> 2_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{1_1}(x1)))))))
   2_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{3_1}(x1)))))) -> 2_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{3_1}(x1)))))))
   2_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{4_1}(x1)))))) -> 2_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{4_1}(x1)))))))
   2_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{2_1}(x1)))))) -> 2_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{2_1}(x1)))))))
   2_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{5_1}(x1)))))) -> 2_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(x1)))))))
   3_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{0_1}(x1)))))) -> 3_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(x1)))))))
   3_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{1_1}(x1)))))) -> 3_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{1_1}(x1)))))))
   3_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{3_1}(x1)))))) -> 3_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{3_1}(x1)))))))
   3_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{4_1}(x1)))))) -> 3_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{4_1}(x1)))))))
   3_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{2_1}(x1)))))) -> 3_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{2_1}(x1)))))))
   3_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{5_1}(x1)))))) -> 3_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(x1)))))))
   4_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{0_1}(x1)))))) -> 4_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(x1)))))))
   4_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{1_1}(x1)))))) -> 4_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{1_1}(x1)))))))
   4_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{3_1}(x1)))))) -> 4_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{3_1}(x1)))))))
   4_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{4_1}(x1)))))) -> 4_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{4_1}(x1)))))))
   4_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{2_1}(x1)))))) -> 4_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{2_1}(x1)))))))
   4_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{5_1}(x1)))))) -> 4_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(x1)))))))
   5_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{0_1}(x1)))))) -> 5_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(x1)))))))
   5_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{1_1}(x1)))))) -> 5_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{1_1}(x1)))))))
   5_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{3_1}(x1)))))) -> 5_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{3_1}(x1)))))))
   5_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{4_1}(x1)))))) -> 5_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{4_1}(x1)))))))
   5_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{2_1}(x1)))))) -> 5_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{2_1}(x1)))))))
   5_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{5_1}(x1)))))) -> 5_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 0_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 0_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 0_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 0_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 0_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 0_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 1_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 1_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 1_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 1_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 1_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 1_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 2_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 2_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 2_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 2_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 2_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 2_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 3_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 3_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 3_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 3_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 3_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 3_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 4_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 4_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 4_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 4_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 4_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 4_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 5_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 5_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 5_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 5_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 5_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 5_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
   0_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(x1)))))) -> 0_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{0_1}(x1)))))))
   0_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(x1)))))) -> 0_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{1_1}(x1)))))))
   0_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{3_1}(x1)))))) -> 0_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{3_1}(x1)))))))
   0_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{4_1}(x1)))))) -> 0_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{4_1}(x1)))))))
   0_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{2_1}(x1)))))) -> 0_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{2_1}(x1)))))))
   0_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{5_1}(x1)))))) -> 0_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{5_1}(x1)))))))
   1_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(x1)))))) -> 1_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{0_1}(x1)))))))
   1_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(x1)))))) -> 1_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{1_1}(x1)))))))
   1_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{3_1}(x1)))))) -> 1_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{3_1}(x1)))))))
   1_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{4_1}(x1)))))) -> 1_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{4_1}(x1)))))))
   1_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{2_1}(x1)))))) -> 1_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{2_1}(x1)))))))
   1_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{5_1}(x1)))))) -> 1_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{5_1}(x1)))))))
   2_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(x1)))))) -> 2_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{0_1}(x1)))))))
   2_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(x1)))))) -> 2_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{1_1}(x1)))))))
   2_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{3_1}(x1)))))) -> 2_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{3_1}(x1)))))))
   2_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{4_1}(x1)))))) -> 2_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{4_1}(x1)))))))
   2_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{2_1}(x1)))))) -> 2_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{2_1}(x1)))))))
   2_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{5_1}(x1)))))) -> 2_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{5_1}(x1)))))))
   3_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(x1)))))) -> 3_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{0_1}(x1)))))))
   3_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(x1)))))) -> 3_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{1_1}(x1)))))))
   3_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{3_1}(x1)))))) -> 3_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{3_1}(x1)))))))
   3_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{4_1}(x1)))))) -> 3_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{4_1}(x1)))))))
   3_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{2_1}(x1)))))) -> 3_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{2_1}(x1)))))))
   3_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{5_1}(x1)))))) -> 3_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{5_1}(x1)))))))
   4_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(x1)))))) -> 4_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{0_1}(x1)))))))
   4_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(x1)))))) -> 4_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{1_1}(x1)))))))
   4_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{3_1}(x1)))))) -> 4_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{3_1}(x1)))))))
   4_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{4_1}(x1)))))) -> 4_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{4_1}(x1)))))))
   4_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{2_1}(x1)))))) -> 4_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{2_1}(x1)))))))
   4_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{5_1}(x1)))))) -> 4_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{5_1}(x1)))))))
   5_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(x1)))))) -> 5_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{0_1}(x1)))))))
   5_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(x1)))))) -> 5_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{1_1}(x1)))))))
   5_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{3_1}(x1)))))) -> 5_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{3_1}(x1)))))))
   5_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{4_1}(x1)))))) -> 5_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{4_1}(x1)))))))
   5_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{2_1}(x1)))))) -> 5_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{2_1}(x1)))))))
   5_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{5_1}(x1)))))) -> 5_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{5_1}(x1)))))))
   0_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 0_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(x1)))))))
   0_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 0_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{1_1}(x1)))))))
   0_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 0_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{3_1}(x1)))))))
   0_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 0_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{4_1}(x1)))))))
   0_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 0_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{2_1}(x1)))))))
   0_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 0_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(x1)))))))
   1_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 1_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(x1)))))))
   1_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 1_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{1_1}(x1)))))))
   1_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 1_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{3_1}(x1)))))))
   1_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 1_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{4_1}(x1)))))))
   1_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 1_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{2_1}(x1)))))))
   1_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 1_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(x1)))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 2_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(x1)))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 2_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{1_1}(x1)))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 2_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{3_1}(x1)))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 2_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{4_1}(x1)))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 2_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{2_1}(x1)))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 2_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(x1)))))))
   3_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 3_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(x1)))))))
   3_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 3_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{1_1}(x1)))))))
   3_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 3_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{3_1}(x1)))))))
   3_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 3_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{4_1}(x1)))))))
   3_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 3_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{2_1}(x1)))))))
   3_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 3_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(x1)))))))
   4_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(x1)))))))
   4_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{1_1}(x1)))))))
   4_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{3_1}(x1)))))))
   4_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{4_1}(x1)))))))
   4_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{2_1}(x1)))))))
   4_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(x1)))))))
   5_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 5_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(x1)))))))
   5_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 5_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{1_1}(x1)))))))
   5_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 5_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{3_1}(x1)))))))
   5_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 5_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{4_1}(x1)))))))
   5_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 5_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{2_1}(x1)))))))
   5_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 5_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(x1)))))))
   0_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{0_1}(x1)))))) -> 0_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   0_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{1_1}(x1)))))) -> 0_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   0_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{3_1}(x1)))))) -> 0_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   0_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{4_1}(x1)))))) -> 0_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   0_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{2_1}(x1)))))) -> 0_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   0_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{5_1}(x1)))))) -> 0_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   1_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{0_1}(x1)))))) -> 1_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   1_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{1_1}(x1)))))) -> 1_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   1_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{3_1}(x1)))))) -> 1_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   1_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{4_1}(x1)))))) -> 1_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   1_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{2_1}(x1)))))) -> 1_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   1_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{5_1}(x1)))))) -> 1_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   2_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{0_1}(x1)))))) -> 2_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   2_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{1_1}(x1)))))) -> 2_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   2_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{3_1}(x1)))))) -> 2_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   2_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{4_1}(x1)))))) -> 2_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   2_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{2_1}(x1)))))) -> 2_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   2_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{5_1}(x1)))))) -> 2_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   3_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{0_1}(x1)))))) -> 3_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   3_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{1_1}(x1)))))) -> 3_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   3_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{3_1}(x1)))))) -> 3_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   3_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{4_1}(x1)))))) -> 3_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   3_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{2_1}(x1)))))) -> 3_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   3_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{5_1}(x1)))))) -> 3_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   4_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{0_1}(x1)))))) -> 4_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   4_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{1_1}(x1)))))) -> 4_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   4_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{3_1}(x1)))))) -> 4_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   4_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{4_1}(x1)))))) -> 4_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   4_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{2_1}(x1)))))) -> 4_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   4_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{5_1}(x1)))))) -> 4_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   5_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{0_1}(x1)))))) -> 5_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   5_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{1_1}(x1)))))) -> 5_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   5_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{3_1}(x1)))))) -> 5_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   5_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{4_1}(x1)))))) -> 5_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   5_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{2_1}(x1)))))) -> 5_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   5_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{5_1}(x1)))))) -> 5_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   0_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 0_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(x1)))))))
   0_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 0_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{1_1}(x1)))))))
   0_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 0_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{3_1}(x1)))))))
   0_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 0_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{4_1}(x1)))))))
   0_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 0_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{2_1}(x1)))))))
   0_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 0_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{5_1}(x1)))))))
   1_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 1_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(x1)))))))
   1_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 1_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{1_1}(x1)))))))
   1_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 1_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{3_1}(x1)))))))
   1_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 1_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{4_1}(x1)))))))
   1_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 1_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{2_1}(x1)))))))
   1_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 1_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{5_1}(x1)))))))
   2_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(x1)))))))
   2_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{1_1}(x1)))))))
   2_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{3_1}(x1)))))))
   2_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{4_1}(x1)))))))
   2_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{2_1}(x1)))))))
   2_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{5_1}(x1)))))))
   3_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 3_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(x1)))))))
   3_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 3_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{1_1}(x1)))))))
   3_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 3_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{3_1}(x1)))))))
   3_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 3_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{4_1}(x1)))))))
   3_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 3_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{2_1}(x1)))))))
   3_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 3_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{5_1}(x1)))))))
   4_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 4_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(x1)))))))
   4_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 4_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{1_1}(x1)))))))
   4_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 4_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{3_1}(x1)))))))
   4_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 4_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{4_1}(x1)))))))
   4_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 4_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{2_1}(x1)))))))
   4_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 4_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{5_1}(x1)))))))
   5_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(x1)))))))
   5_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{1_1}(x1)))))))
   5_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{3_1}(x1)))))))
   5_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{4_1}(x1)))))))
   5_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{2_1}(x1)))))))
   5_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{5_1}(x1)))))))

Q is empty.

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

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

   POL(0_{0_1}(x_1)) = 50 + x_1
   POL(0_{1_1}(x_1)) = 50 + x_1
   POL(0_{2_1}(x_1)) = 42 + x_1
   POL(0_{3_1}(x_1)) = 2 + x_1
   POL(0_{4_1}(x_1)) = 51 + x_1
   POL(0_{5_1}(x_1)) = 50 + x_1
   POL(1_{0_1}(x_1)) = 50 + x_1
   POL(1_{1_1}(x_1)) = 50 + x_1
   POL(1_{2_1}(x_1)) = 41 + x_1
   POL(1_{3_1}(x_1)) = x_1
   POL(1_{4_1}(x_1)) = 1 + x_1
   POL(1_{5_1}(x_1)) = 50 + x_1
   POL(2_{0_1}(x_1)) = 23 + x_1
   POL(2_{1_1}(x_1)) = x_1
   POL(2_{2_1}(x_1)) = 45 + x_1
   POL(2_{3_1}(x_1)) = 6 + x_1
   POL(2_{4_1}(x_1)) = 6 + x_1
   POL(2_{5_1}(x_1)) = 23 + x_1
   POL(3_{0_1}(x_1)) = x_1
   POL(3_{1_1}(x_1)) = x_1
   POL(3_{2_1}(x_1)) = 22 + x_1
   POL(3_{3_1}(x_1)) = x_1
   POL(3_{4_1}(x_1)) = x_1
   POL(3_{5_1}(x_1)) = x_1
   POL(4_{0_1}(x_1)) = 21 + x_1
   POL(4_{1_1}(x_1)) = 49 + x_1
   POL(4_{2_1}(x_1)) = 43 + x_1
   POL(4_{3_1}(x_1)) = x_1
   POL(4_{4_1}(x_1)) = 21 + x_1
   POL(4_{5_1}(x_1)) = 21 + x_1
   POL(5_{0_1}(x_1)) = x_1
   POL(5_{1_1}(x_1)) = x_1
   POL(5_{2_1}(x_1)) = 8 + x_1
   POL(5_{3_1}(x_1)) = x_1
   POL(5_{4_1}(x_1)) = 1 + x_1
   POL(5_{5_1}(x_1)) = x_1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   0_{1_1}(1_{0_1}(0_{0_1}(x1))) -> 0_{1_1}(1_{3_1}(3_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(x1))))))
   0_{1_1}(1_{0_1}(0_{1_1}(x1))) -> 0_{1_1}(1_{3_1}(3_{4_1}(4_{0_1}(0_{3_1}(3_{1_1}(x1))))))
   0_{1_1}(1_{0_1}(0_{3_1}(x1))) -> 0_{1_1}(1_{3_1}(3_{4_1}(4_{0_1}(0_{3_1}(3_{3_1}(x1))))))
   0_{1_1}(1_{0_1}(0_{4_1}(x1))) -> 0_{1_1}(1_{3_1}(3_{4_1}(4_{0_1}(0_{3_1}(3_{4_1}(x1))))))
   0_{1_1}(1_{0_1}(0_{2_1}(x1))) -> 0_{1_1}(1_{3_1}(3_{4_1}(4_{0_1}(0_{3_1}(3_{2_1}(x1))))))
   0_{1_1}(1_{0_1}(0_{5_1}(x1))) -> 0_{1_1}(1_{3_1}(3_{4_1}(4_{0_1}(0_{3_1}(3_{5_1}(x1))))))
   0_{1_1}(1_{1_1}(1_{0_1}(x1))) -> 0_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{0_1}(x1)))))
   0_{1_1}(1_{1_1}(1_{1_1}(x1))) -> 0_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{1_1}(x1)))))
   0_{1_1}(1_{1_1}(1_{3_1}(x1))) -> 0_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(x1)))))
   0_{1_1}(1_{1_1}(1_{4_1}(x1))) -> 0_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{4_1}(x1)))))
   0_{1_1}(1_{1_1}(1_{2_1}(x1))) -> 0_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{2_1}(x1)))))
   0_{1_1}(1_{1_1}(1_{5_1}(x1))) -> 0_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{5_1}(x1)))))
   0_{1_1}(1_{1_1}(1_{0_1}(x1))) -> 0_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{0_1}(x1))))))
   0_{1_1}(1_{1_1}(1_{1_1}(x1))) -> 0_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{1_1}(x1))))))
   0_{1_1}(1_{1_1}(1_{3_1}(x1))) -> 0_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(x1))))))
   0_{1_1}(1_{1_1}(1_{4_1}(x1))) -> 0_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{4_1}(x1))))))
   0_{1_1}(1_{1_1}(1_{2_1}(x1))) -> 0_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{2_1}(x1))))))
   0_{1_1}(1_{1_1}(1_{5_1}(x1))) -> 0_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{5_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x1)))) -> 0_{2_1}(2_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{0_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x1)))) -> 0_{2_1}(2_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(x1)))) -> 0_{2_1}(2_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{1_1}(1_{4_1}(x1)))) -> 0_{2_1}(2_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x1)))) -> 0_{2_1}(2_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{2_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{1_1}(1_{5_1}(x1)))) -> 0_{2_1}(2_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{5_1}(x1))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 0_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(x1)))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 0_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(5_{1_1}(x1)))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 0_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(5_{3_1}(x1)))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 0_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(x1)))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 0_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(5_{2_1}(x1)))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 0_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(x1)))))
   0_{5_1}(5_{4_1}(4_{0_1}(0_{0_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(x1)))))
   0_{5_1}(5_{4_1}(4_{0_1}(0_{1_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(x1)))))
   0_{5_1}(5_{4_1}(4_{0_1}(0_{4_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{4_1}(x1)))))
   0_{5_1}(5_{4_1}(4_{0_1}(0_{2_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{2_1}(x1)))))
   0_{5_1}(5_{4_1}(4_{0_1}(0_{5_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(x1)))))
   2_{0_1}(0_{4_1}(4_{1_1}(1_{0_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(4_{0_1}(x1))))))
   2_{0_1}(0_{4_1}(4_{1_1}(1_{1_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(4_{1_1}(x1))))))
   2_{0_1}(0_{4_1}(4_{1_1}(1_{3_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(4_{3_1}(x1))))))
   2_{0_1}(0_{4_1}(4_{1_1}(1_{4_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(4_{4_1}(x1))))))
   2_{0_1}(0_{4_1}(4_{1_1}(1_{2_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(4_{2_1}(x1))))))
   2_{0_1}(0_{4_1}(4_{1_1}(1_{5_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(4_{5_1}(x1))))))
   5_{1_1}(1_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{3_1}(x1)))))
   5_{1_1}(1_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(x1)))))
   5_{1_1}(1_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{2_1}(x1)))))
   5_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x1)))) -> 5_{1_1}(1_{0_1}(0_{3_1}(3_{2_1}(2_{0_1}(x1)))))
   5_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x1)))) -> 5_{1_1}(1_{0_1}(0_{3_1}(3_{2_1}(2_{1_1}(x1)))))
   5_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(x1)))) -> 5_{1_1}(1_{0_1}(0_{3_1}(3_{2_1}(2_{3_1}(x1)))))
   5_{2_1}(2_{0_1}(0_{1_1}(1_{4_1}(x1)))) -> 5_{1_1}(1_{0_1}(0_{3_1}(3_{2_1}(2_{4_1}(x1)))))
   5_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x1)))) -> 5_{1_1}(1_{0_1}(0_{3_1}(3_{2_1}(2_{2_1}(x1)))))
   5_{2_1}(2_{0_1}(0_{1_1}(1_{5_1}(x1)))) -> 5_{1_1}(1_{0_1}(0_{3_1}(3_{2_1}(2_{5_1}(x1)))))
   5_{3_1}(3_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 5_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{5_1}(5_{0_1}(x1))))))
   5_{3_1}(3_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 5_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(x1))))))
   5_{3_1}(3_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 5_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{5_1}(5_{2_1}(x1))))))
   5_{3_1}(3_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 5_{3_1}(3_{1_1}(1_{3_1}(3_{1_1}(1_{5_1}(5_{5_1}(x1))))))
   5_{4_1}(4_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 5_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{5_1}(5_{0_1}(x1))))))
   5_{4_1}(4_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 5_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{5_1}(5_{1_1}(x1))))))
   5_{4_1}(4_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 5_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{5_1}(5_{3_1}(x1))))))
   5_{4_1}(4_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 5_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{5_1}(5_{4_1}(x1))))))
   5_{4_1}(4_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 5_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{5_1}(5_{2_1}(x1))))))
   5_{4_1}(4_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 5_{1_1}(1_{4_1}(4_{1_1}(1_{4_1}(4_{5_1}(5_{5_1}(x1))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{3_1}(3_{0_1}(x1)))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{3_1}(3_{1_1}(x1)))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{3_1}(3_{3_1}(x1)))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{3_1}(3_{4_1}(x1)))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{3_1}(3_{2_1}(x1)))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(x1)))))
   5_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{2_1}(2_{0_1}(x1))))))
   5_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{2_1}(2_{1_1}(x1))))))
   5_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{2_1}(2_{3_1}(x1))))))
   5_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{2_1}(2_{4_1}(x1))))))
   5_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{2_1}(2_{2_1}(x1))))))
   5_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{2_1}(2_{5_1}(x1))))))
   0_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(x1)))) -> 0_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
   0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(x1)))) -> 0_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
   0_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(x1)))) -> 0_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
   0_{0_1}(0_{0_1}(0_{1_1}(1_{4_1}(x1)))) -> 0_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
   0_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(x1)))) -> 0_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
   0_{0_1}(0_{0_1}(0_{1_1}(1_{5_1}(x1)))) -> 0_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
   1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(x1)))) -> 1_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
   1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(x1)))) -> 1_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
   1_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(x1)))) -> 1_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
   1_{0_1}(0_{0_1}(0_{1_1}(1_{4_1}(x1)))) -> 1_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
   1_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(x1)))) -> 1_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
   1_{0_1}(0_{0_1}(0_{1_1}(1_{5_1}(x1)))) -> 1_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
   2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(x1)))) -> 2_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
   2_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(x1)))) -> 2_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
   2_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(x1)))) -> 2_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
   2_{0_1}(0_{0_1}(0_{1_1}(1_{4_1}(x1)))) -> 2_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
   2_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(x1)))) -> 2_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
   2_{0_1}(0_{0_1}(0_{1_1}(1_{5_1}(x1)))) -> 2_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
   3_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(x1)))) -> 3_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
   3_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(x1)))) -> 3_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
   3_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(x1)))) -> 3_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
   3_{0_1}(0_{0_1}(0_{1_1}(1_{4_1}(x1)))) -> 3_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
   3_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(x1)))) -> 3_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
   3_{0_1}(0_{0_1}(0_{1_1}(1_{5_1}(x1)))) -> 3_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
   4_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(x1)))) -> 4_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
   4_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(x1)))) -> 4_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
   4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(x1)))) -> 4_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
   4_{0_1}(0_{0_1}(0_{1_1}(1_{4_1}(x1)))) -> 4_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
   4_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(x1)))) -> 4_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
   4_{0_1}(0_{0_1}(0_{1_1}(1_{5_1}(x1)))) -> 4_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
   5_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(x1)))) -> 5_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
   5_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(x1)))) -> 5_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
   5_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(x1)))) -> 5_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
   5_{0_1}(0_{0_1}(0_{1_1}(1_{4_1}(x1)))) -> 5_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
   5_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(x1)))) -> 5_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
   5_{0_1}(0_{0_1}(0_{1_1}(1_{5_1}(x1)))) -> 5_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 0_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 0_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 0_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 0_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 0_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 0_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 1_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 1_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 1_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 1_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 1_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 1_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 2_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 2_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 2_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 2_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 2_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 2_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 3_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 3_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 3_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 3_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 3_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 3_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 4_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 4_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 4_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 4_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 4_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 4_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 5_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 5_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 5_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 5_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 5_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 5_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(x1))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{1_1}(x1))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(x1))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(x1))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{2_1}(x1))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{5_1}(x1))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(x1))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{1_1}(x1))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(x1))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(x1))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{2_1}(x1))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{5_1}(x1))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(x1))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{1_1}(x1))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(x1))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(x1))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{2_1}(x1))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{5_1}(x1))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(x1))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{1_1}(x1))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(x1))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(x1))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{2_1}(x1))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{5_1}(x1))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(x1))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{1_1}(x1))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(x1))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(x1))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{2_1}(x1))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{5_1}(x1))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{0_1}(x1))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{1_1}(x1))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(x1))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{4_1}(x1))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{2_1}(x1))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(1_{4_1}(4_{5_1}(x1))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{0_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{3_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{2_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{5_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{0_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{3_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{2_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{5_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{0_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{3_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{2_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{5_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{0_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{3_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{2_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{5_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{0_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{3_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{2_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{5_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{0_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{1_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{3_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{4_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{2_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(3_{0_1}(0_{5_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{1_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{4_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{2_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{5_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{1_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{4_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{2_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{5_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{1_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{4_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{2_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{5_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{1_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{4_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{2_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{5_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{1_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{2_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{5_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{0_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{1_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{4_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{2_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{3_1}(3_{1_1}(1_{4_1}(4_{0_1}(0_{5_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   0_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   1_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   2_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   3_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   4_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   5_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{3_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{4_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{5_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{3_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{4_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{5_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{3_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{4_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{5_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{3_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{4_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{5_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{3_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{4_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{5_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{3_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{4_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{5_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{0_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{1_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{4_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{2_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{0_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{1_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{4_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{2_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{0_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{1_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{4_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{2_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{0_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{1_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{4_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{2_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{0_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{1_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{3_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{4_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{2_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{0_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{1_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{4_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{2_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{0_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{1_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{4_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{5_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{0_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{1_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{4_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{5_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{0_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{1_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{4_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{5_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{0_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{1_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{4_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{5_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{0_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{1_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{4_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{5_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{0_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{1_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{4_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{5_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{0_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{3_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{4_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 0_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{5_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{0_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{3_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{4_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(x1))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 1_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{5_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{0_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{3_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{4_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(x1))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 2_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{5_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{0_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{3_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{4_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(x1))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 3_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{5_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{0_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{3_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{4_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(x1))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{5_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{0_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{3_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{4_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(x1))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 5_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{5_1}(x1))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{0_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{3_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{4_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{5_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 1_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{0_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 1_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 1_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{3_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 1_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{4_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 1_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 1_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{5_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 2_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{0_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 2_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 2_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{3_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 2_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{4_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 2_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 2_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{5_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 3_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{0_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 3_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 3_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{3_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 3_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{4_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 3_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 3_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{5_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 4_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{0_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 4_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 4_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{3_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 4_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{4_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 4_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 4_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{5_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 5_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{0_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 5_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{1_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 5_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{3_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 5_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{4_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 5_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 5_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{5_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{3_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{4_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 0_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{5_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 1_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 1_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 1_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{3_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 1_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{4_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 1_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 1_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{5_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 2_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 2_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 2_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{3_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 2_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{4_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 2_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 2_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{5_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 3_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 3_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 3_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{3_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 3_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{4_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 3_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 3_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{5_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 4_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 4_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 4_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{3_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 4_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{4_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 4_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 4_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{5_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1)))) -> 5_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{0_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1)))) -> 5_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1)))) -> 5_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{3_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1)))) -> 5_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{4_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1)))) -> 5_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 5_{4_1}(4_{5_1}(5_{0_1}(0_{3_1}(3_{5_1}(5_{0_1}(0_{5_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{0_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{1_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{3_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{4_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{2_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{5_1}(x1))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{0_1}(x1))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{1_1}(x1))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{3_1}(x1))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{4_1}(x1))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{2_1}(x1))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{5_1}(x1))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{0_1}(x1))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{1_1}(x1))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{3_1}(x1))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{4_1}(x1))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{2_1}(x1))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{5_1}(x1))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{0_1}(x1))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{1_1}(x1))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{3_1}(x1))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{4_1}(x1))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{2_1}(x1))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{5_1}(x1))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{0_1}(x1))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{1_1}(x1))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{3_1}(x1))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{4_1}(x1))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{2_1}(x1))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{5_1}(x1))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{0_1}(x1))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{1_1}(x1))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{3_1}(x1))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{4_1}(x1))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{2_1}(x1))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{0_1}(0_{3_1}(3_{2_1}(2_{5_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{0_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{1_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{3_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{2_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{5_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{0_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{1_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{3_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{2_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{5_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{0_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{1_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{3_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{2_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{5_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{0_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{1_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{3_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{2_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{5_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{0_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{1_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{3_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{2_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{5_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{0_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{1_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{3_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{2_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{3_1}(3_{0_1}(0_{2_1}(2_{3_1}(3_{5_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{1_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{4_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{2_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{5_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{1_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{4_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{2_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 1_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{5_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{1_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{4_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{2_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 2_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{5_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{1_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{4_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{2_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 3_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{5_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{1_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{4_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{2_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 4_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{5_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{0_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{1_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{3_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{3_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{4_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{4_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{2_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{0_1}(0_{5_1}(x1)))) -> 5_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(0_{3_1}(3_{5_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{0_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{3_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{4_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{2_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{0_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{3_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{4_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{2_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{0_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{3_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{4_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{2_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{0_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{3_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{4_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{2_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{0_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{3_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{4_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{2_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{0_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{3_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{4_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{2_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{1_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{3_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{4_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{2_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 0_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{5_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{1_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{3_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{4_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{2_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 1_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{5_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{1_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{3_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{4_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{2_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 2_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{5_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{1_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{3_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{4_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{2_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 3_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{5_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{1_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{3_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{4_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{2_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 4_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{5_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{0_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{0_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{1_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{3_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{3_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{4_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{4_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{2_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{2_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{5_1}(x1)))) -> 5_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(0_{3_1}(3_{5_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 0_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 1_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 1_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 1_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 1_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 1_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 1_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 2_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 2_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 2_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 2_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 2_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 2_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 4_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{0_1}(x1)))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 4_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{1_1}(x1)))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 4_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1)))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 4_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1)))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 4_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1)))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 4_{3_1}(3_{1_1}(1_{5_1}(5_{1_1}(1_{5_1}(x1)))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(x1))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{1_1}(x1))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{3_1}(x1))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(x1))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{2_1}(x1))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(x1))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(x1))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{1_1}(x1))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{3_1}(x1))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(x1))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{2_1}(x1))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(x1))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(x1))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{1_1}(x1))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{3_1}(x1))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(x1))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{2_1}(x1))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(x1))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(x1))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{1_1}(x1))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{3_1}(x1))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(x1))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{2_1}(x1))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(x1))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(x1))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{1_1}(x1))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{3_1}(x1))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(x1))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{2_1}(x1))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(x1))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(x1))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{1_1}(x1))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{3_1}(x1))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{4_1}(x1))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{2_1}(x1))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(x1))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{3_1}(3_{3_1}(3_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 0_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 1_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 2_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 3_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 4_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{0_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{1_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{4_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{2_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))) -> 5_{1_1}(1_{3_1}(3_{5_1}(5_{5_1}(5_{1_1}(1_{4_1}(4_{5_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(x1))))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(x1))))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{3_1}(x1))))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{4_1}(x1))))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{4_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{2_1}(x1))))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{2_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{5_1}(x1))))) -> 0_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{5_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(x1))))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(x1))))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{3_1}(x1))))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{4_1}(x1))))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{4_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{2_1}(x1))))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{2_1}(x1)))))))
   1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{5_1}(x1))))) -> 1_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{5_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(x1))))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(x1))))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{3_1}(x1))))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{4_1}(x1))))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{4_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{2_1}(x1))))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{2_1}(x1)))))))
   2_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{5_1}(x1))))) -> 2_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{5_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(x1))))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(x1))))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{3_1}(x1))))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{4_1}(x1))))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{4_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{2_1}(x1))))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{2_1}(x1)))))))
   3_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{5_1}(x1))))) -> 3_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{5_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(x1))))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(x1))))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{3_1}(x1))))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{4_1}(x1))))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{4_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{2_1}(x1))))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{2_1}(x1)))))))
   4_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{5_1}(x1))))) -> 4_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{5_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(x1))))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(x1))))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{3_1}(x1))))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{3_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{4_1}(x1))))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{4_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{2_1}(x1))))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{2_1}(x1)))))))
   5_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{5_1}(x1))))) -> 5_{3_1}(3_{0_1}(0_{3_1}(3_{0_1}(0_{2_1}(2_{2_1}(2_{5_1}(x1)))))))
   0_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1))))) -> 0_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1))))) -> 0_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1))))) -> 0_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{3_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1))))) -> 0_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{4_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1))))) -> 0_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{2_1}(x1))))))
   0_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1))))) -> 0_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{5_1}(x1))))))
   1_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1))))) -> 1_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(x1))))))
   1_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1))))) -> 1_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(x1))))))
   1_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1))))) -> 1_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{4_1}(x1))))))
   1_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1))))) -> 1_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{2_1}(x1))))))
   1_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1))))) -> 1_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{5_1}(x1))))))
   2_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1))))) -> 2_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(x1))))))
   2_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1))))) -> 2_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(x1))))))
   2_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1))))) -> 2_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{3_1}(x1))))))
   2_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1))))) -> 2_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{4_1}(x1))))))
   2_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1))))) -> 2_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{2_1}(x1))))))
   2_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1))))) -> 2_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{5_1}(x1))))))
   3_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1))))) -> 3_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(x1))))))
   3_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1))))) -> 3_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(x1))))))
   3_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1))))) -> 3_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{3_1}(x1))))))
   3_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1))))) -> 3_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{4_1}(x1))))))
   3_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1))))) -> 3_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{2_1}(x1))))))
   3_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1))))) -> 3_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{5_1}(x1))))))
   4_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1))))) -> 4_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(x1))))))
   4_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1))))) -> 4_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(x1))))))
   4_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1))))) -> 4_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{3_1}(x1))))))
   4_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1))))) -> 4_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{4_1}(x1))))))
   4_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1))))) -> 4_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{2_1}(x1))))))
   4_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1))))) -> 4_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{5_1}(x1))))))
   5_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{0_1}(x1))))) -> 5_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{0_1}(x1))))))
   5_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{1_1}(x1))))) -> 5_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(x1))))))
   5_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{3_1}(x1))))) -> 5_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{3_1}(x1))))))
   5_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{4_1}(x1))))) -> 5_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{4_1}(x1))))))
   5_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{2_1}(x1))))) -> 5_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{2_1}(x1))))))
   5_{2_1}(2_{0_1}(0_{5_1}(5_{0_1}(0_{5_1}(x1))))) -> 5_{0_1}(0_{0_1}(0_{3_1}(3_{5_1}(5_{2_1}(2_{5_1}(x1))))))
   0_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 0_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{0_1}(x1)))))))
   0_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 0_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{1_1}(x1)))))))
   0_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 0_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(x1)))))))
   0_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 0_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{4_1}(x1)))))))
   0_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 0_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{2_1}(x1)))))))
   0_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 0_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{5_1}(x1)))))))
   1_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{0_1}(x1)))))))
   1_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{1_1}(x1)))))))
   1_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(x1)))))))
   1_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{4_1}(x1)))))))
   1_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{2_1}(x1)))))))
   1_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 1_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{5_1}(x1)))))))
   2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 2_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{0_1}(x1)))))))
   2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 2_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{1_1}(x1)))))))
   2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 2_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(x1)))))))
   2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 2_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{4_1}(x1)))))))
   2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 2_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{2_1}(x1)))))))
   2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 2_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{5_1}(x1)))))))
   3_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 3_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{0_1}(x1)))))))
   3_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 3_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{1_1}(x1)))))))
   3_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 3_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(x1)))))))
   3_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 3_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{4_1}(x1)))))))
   3_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 3_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{2_1}(x1)))))))
   3_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 3_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{5_1}(x1)))))))
   4_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 4_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{0_1}(x1)))))))
   4_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 4_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{1_1}(x1)))))))
   4_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 4_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(x1)))))))
   4_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 4_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{4_1}(x1)))))))
   4_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 4_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{2_1}(x1)))))))
   4_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 4_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{5_1}(x1)))))))
   5_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(x1))))) -> 5_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{0_1}(x1)))))))
   5_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(x1))))) -> 5_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{1_1}(x1)))))))
   5_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{3_1}(x1))))) -> 5_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{3_1}(x1)))))))
   5_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{4_1}(x1))))) -> 5_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{4_1}(x1)))))))
   5_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{2_1}(x1))))) -> 5_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{2_1}(x1)))))))
   5_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{5_1}(x1))))) -> 5_{3_1}(3_{2_1}(2_{4_1}(4_{3_1}(3_{2_1}(2_{1_1}(1_{5_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x1))))) -> 0_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x1))))) -> 0_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{3_1}(x1))))) -> 0_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{3_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{4_1}(x1))))) -> 0_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x1))))) -> 0_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{2_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{5_1}(x1))))) -> 0_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{5_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x1))))) -> 1_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x1))))) -> 1_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{3_1}(x1))))) -> 1_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{3_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{4_1}(x1))))) -> 1_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x1))))) -> 1_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{2_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{5_1}(x1))))) -> 1_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{5_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x1))))) -> 2_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x1))))) -> 2_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{3_1}(x1))))) -> 2_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{3_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{4_1}(x1))))) -> 2_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x1))))) -> 2_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{2_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{5_1}(x1))))) -> 2_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{5_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x1))))) -> 3_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x1))))) -> 3_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{3_1}(x1))))) -> 3_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{3_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{4_1}(x1))))) -> 3_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x1))))) -> 3_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{2_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{5_1}(x1))))) -> 3_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{5_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x1))))) -> 4_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x1))))) -> 4_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{3_1}(x1))))) -> 4_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{3_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{4_1}(x1))))) -> 4_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x1))))) -> 4_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{2_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{5_1}(x1))))) -> 4_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{5_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x1))))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{0_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x1))))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{1_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{3_1}(x1))))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{3_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{4_1}(x1))))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{4_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x1))))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{2_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{0_1}(0_{1_1}(1_{5_1}(x1))))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{4_1}(4_{3_1}(3_{1_1}(1_{5_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{3_1}(x1))))) -> 0_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{4_1}(x1))))) -> 0_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1))))))
   0_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x1))))) -> 0_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{3_1}(x1))))) -> 1_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{4_1}(x1))))) -> 1_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1))))))
   1_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x1))))) -> 1_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{3_1}(x1))))) -> 2_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{4_1}(x1))))) -> 2_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1))))))
   2_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x1))))) -> 2_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{3_1}(x1))))) -> 3_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{4_1}(x1))))) -> 3_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1))))))
   3_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x1))))) -> 3_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{3_1}(x1))))) -> 4_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{4_1}(x1))))) -> 4_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1))))))
   4_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x1))))) -> 4_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{3_1}(x1))))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{3_1}(x1))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{4_1}(x1))))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{4_1}(x1))))))
   5_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x1))))) -> 5_{0_1}(0_{5_1}(5_{1_1}(1_{5_1}(5_{1_1}(1_{2_1}(x1))))))
   0_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(x1))))) -> 0_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{0_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(x1))))) -> 0_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{1_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{3_1}(x1))))) -> 0_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{3_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{4_1}(x1))))) -> 0_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{4_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(x1))))) -> 0_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{2_1}(x1)))))))
   0_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(x1))))) -> 0_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{5_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(x1))))) -> 1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{0_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(x1))))) -> 1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{1_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{3_1}(x1))))) -> 1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{3_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{4_1}(x1))))) -> 1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{4_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(x1))))) -> 1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{2_1}(x1)))))))
   1_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(x1))))) -> 1_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{5_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(x1))))) -> 2_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{0_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(x1))))) -> 2_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{1_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{3_1}(x1))))) -> 2_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{3_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{4_1}(x1))))) -> 2_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{4_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(x1))))) -> 2_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{2_1}(x1)))))))
   2_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(x1))))) -> 2_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{5_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(x1))))) -> 3_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{0_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(x1))))) -> 3_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{1_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{3_1}(x1))))) -> 3_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{3_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{4_1}(x1))))) -> 3_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{4_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(x1))))) -> 3_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{2_1}(x1)))))))
   3_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(x1))))) -> 3_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{5_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(x1))))) -> 4_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{0_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(x1))))) -> 4_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{1_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{3_1}(x1))))) -> 4_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{3_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{4_1}(x1))))) -> 4_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{4_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(x1))))) -> 4_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{2_1}(x1)))))))
   4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(x1))))) -> 4_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{5_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(x1))))) -> 5_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{0_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(x1))))) -> 5_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{1_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{3_1}(x1))))) -> 5_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{3_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{4_1}(x1))))) -> 5_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{4_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(x1))))) -> 5_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{2_1}(x1)))))))
   5_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{5_1}(x1))))) -> 5_{3_1}(3_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{2_1}(2_{5_1}(x1)))))))
   0_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{0_1}(x1)))))) -> 0_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(x1)))))))
   0_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{1_1}(x1)))))) -> 0_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{1_1}(x1)))))))
   0_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{3_1}(x1)))))) -> 0_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{3_1}(x1)))))))
   0_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{4_1}(x1)))))) -> 0_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{4_1}(x1)))))))
   0_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{2_1}(x1)))))) -> 0_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{2_1}(x1)))))))
   0_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{5_1}(x1)))))) -> 0_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(x1)))))))
   1_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{0_1}(x1)))))) -> 1_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(x1)))))))
   1_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{1_1}(x1)))))) -> 1_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{1_1}(x1)))))))
   1_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{3_1}(x1)))))) -> 1_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{3_1}(x1)))))))
   1_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{4_1}(x1)))))) -> 1_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{4_1}(x1)))))))
   1_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{2_1}(x1)))))) -> 1_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{2_1}(x1)))))))
   1_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{5_1}(x1)))))) -> 1_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(x1)))))))
   2_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{0_1}(x1)))))) -> 2_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(x1)))))))
   2_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{1_1}(x1)))))) -> 2_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{1_1}(x1)))))))
   2_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{4_1}(x1)))))) -> 2_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{4_1}(x1)))))))
   2_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{2_1}(x1)))))) -> 2_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{2_1}(x1)))))))
   2_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{5_1}(x1)))))) -> 2_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(x1)))))))
   3_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{0_1}(x1)))))) -> 3_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(x1)))))))
   3_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{1_1}(x1)))))) -> 3_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{1_1}(x1)))))))
   3_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{4_1}(x1)))))) -> 3_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{4_1}(x1)))))))
   3_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{2_1}(x1)))))) -> 3_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{2_1}(x1)))))))
   3_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{5_1}(x1)))))) -> 3_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(x1)))))))
   4_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{0_1}(x1)))))) -> 4_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(x1)))))))
   4_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{1_1}(x1)))))) -> 4_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{1_1}(x1)))))))
   4_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{4_1}(x1)))))) -> 4_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{4_1}(x1)))))))
   4_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{2_1}(x1)))))) -> 4_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{2_1}(x1)))))))
   4_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{5_1}(x1)))))) -> 4_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(x1)))))))
   5_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{0_1}(x1)))))) -> 5_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(x1)))))))
   5_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{1_1}(x1)))))) -> 5_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{1_1}(x1)))))))
   5_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{3_1}(x1)))))) -> 5_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{3_1}(x1)))))))
   5_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{4_1}(x1)))))) -> 5_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{4_1}(x1)))))))
   5_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{2_1}(x1)))))) -> 5_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{2_1}(x1)))))))
   5_{0_1}(0_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{5_1}(x1)))))) -> 5_{2_1}(2_{4_1}(4_{0_1}(0_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 0_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 0_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 0_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 0_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 0_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
   0_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 0_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 1_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 1_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 1_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 1_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 1_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
   1_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 1_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 2_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 2_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 2_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 2_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 2_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
   2_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 2_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 3_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 3_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 3_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 3_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 3_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
   3_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 3_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 4_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 4_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 4_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 4_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 4_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
   4_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 4_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 5_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{0_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 5_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 5_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{3_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 5_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{4_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 5_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{2_1}(x1)))))))
   5_{0_1}(0_{5_1}(5_{5_1}(5_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 5_{5_1}(5_{1_1}(1_{3_1}(3_{5_1}(5_{0_1}(0_{1_1}(1_{5_1}(x1)))))))
   0_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(x1)))))) -> 0_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{0_1}(x1)))))))
   0_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(x1)))))) -> 0_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{1_1}(x1)))))))
   0_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{3_1}(x1)))))) -> 0_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{3_1}(x1)))))))
   0_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{4_1}(x1)))))) -> 0_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{4_1}(x1)))))))
   0_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{2_1}(x1)))))) -> 0_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{2_1}(x1)))))))
   0_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{5_1}(x1)))))) -> 0_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{5_1}(x1)))))))
   1_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(x1)))))) -> 1_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{0_1}(x1)))))))
   1_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(x1)))))) -> 1_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{1_1}(x1)))))))
   1_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{4_1}(x1)))))) -> 1_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{4_1}(x1)))))))
   1_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{2_1}(x1)))))) -> 1_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{2_1}(x1)))))))
   1_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{5_1}(x1)))))) -> 1_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{5_1}(x1)))))))
   2_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(x1)))))) -> 2_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{0_1}(x1)))))))
   2_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(x1)))))) -> 2_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{1_1}(x1)))))))
   2_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{3_1}(x1)))))) -> 2_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{3_1}(x1)))))))
   2_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{4_1}(x1)))))) -> 2_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{4_1}(x1)))))))
   2_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{2_1}(x1)))))) -> 2_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{2_1}(x1)))))))
   2_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{5_1}(x1)))))) -> 2_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{5_1}(x1)))))))
   3_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(x1)))))) -> 3_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{0_1}(x1)))))))
   3_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(x1)))))) -> 3_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{1_1}(x1)))))))
   3_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{3_1}(x1)))))) -> 3_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{3_1}(x1)))))))
   3_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{4_1}(x1)))))) -> 3_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{4_1}(x1)))))))
   3_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{2_1}(x1)))))) -> 3_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{2_1}(x1)))))))
   3_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{5_1}(x1)))))) -> 3_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{5_1}(x1)))))))
   4_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(x1)))))) -> 4_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{0_1}(x1)))))))
   4_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(x1)))))) -> 4_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{1_1}(x1)))))))
   4_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{3_1}(x1)))))) -> 4_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{3_1}(x1)))))))
   4_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{4_1}(x1)))))) -> 4_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{4_1}(x1)))))))
   4_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{2_1}(x1)))))) -> 4_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{2_1}(x1)))))))
   4_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{5_1}(x1)))))) -> 4_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{5_1}(x1)))))))
   5_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(x1)))))) -> 5_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{0_1}(x1)))))))
   5_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{1_1}(x1)))))) -> 5_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{1_1}(x1)))))))
   5_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{3_1}(x1)))))) -> 5_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{3_1}(x1)))))))
   5_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{4_1}(x1)))))) -> 5_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{4_1}(x1)))))))
   5_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{2_1}(x1)))))) -> 5_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{2_1}(x1)))))))
   5_{2_1}(2_{2_1}(2_{2_1}(2_{4_1}(4_{1_1}(1_{5_1}(x1)))))) -> 5_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{4_1}(4_{2_1}(2_{5_1}(x1)))))))
   0_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 0_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(x1)))))))
   0_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 0_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{1_1}(x1)))))))
   0_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 0_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{3_1}(x1)))))))
   0_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 0_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{4_1}(x1)))))))
   0_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 0_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{2_1}(x1)))))))
   0_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 0_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(x1)))))))
   1_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 1_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(x1)))))))
   1_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 1_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{1_1}(x1)))))))
   1_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 1_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{4_1}(x1)))))))
   1_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 1_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{2_1}(x1)))))))
   1_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 1_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(x1)))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 2_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(x1)))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 2_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{1_1}(x1)))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 2_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{3_1}(x1)))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 2_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{4_1}(x1)))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 2_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{2_1}(x1)))))))
   2_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 2_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(x1)))))))
   3_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 3_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(x1)))))))
   3_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 3_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{1_1}(x1)))))))
   3_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 3_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{3_1}(x1)))))))
   3_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 3_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{4_1}(x1)))))))
   3_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 3_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{2_1}(x1)))))))
   3_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 3_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(x1)))))))
   4_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(x1)))))))
   4_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{1_1}(x1)))))))
   4_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{3_1}(x1)))))))
   4_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{4_1}(x1)))))))
   4_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{2_1}(x1)))))))
   4_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 4_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(x1)))))))
   5_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 5_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{0_1}(x1)))))))
   5_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 5_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{1_1}(x1)))))))
   5_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 5_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{3_1}(x1)))))))
   5_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 5_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{4_1}(x1)))))))
   5_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 5_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{2_1}(x1)))))))
   5_{2_1}(2_{5_1}(5_{0_1}(0_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 5_{5_1}(5_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{3_1}(3_{5_1}(x1)))))))
   0_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{0_1}(x1)))))) -> 0_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   0_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{1_1}(x1)))))) -> 0_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   0_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{3_1}(x1)))))) -> 0_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   0_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{4_1}(x1)))))) -> 0_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   0_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{2_1}(x1)))))) -> 0_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   0_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{5_1}(x1)))))) -> 0_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   1_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{0_1}(x1)))))) -> 1_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   1_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{1_1}(x1)))))) -> 1_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   1_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{3_1}(x1)))))) -> 1_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   1_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{4_1}(x1)))))) -> 1_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   1_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{2_1}(x1)))))) -> 1_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   1_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{5_1}(x1)))))) -> 1_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   2_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{0_1}(x1)))))) -> 2_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   2_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{1_1}(x1)))))) -> 2_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   2_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{3_1}(x1)))))) -> 2_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   2_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{4_1}(x1)))))) -> 2_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   2_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{2_1}(x1)))))) -> 2_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   2_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{5_1}(x1)))))) -> 2_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   3_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{0_1}(x1)))))) -> 3_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   3_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{1_1}(x1)))))) -> 3_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   3_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{3_1}(x1)))))) -> 3_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   3_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{4_1}(x1)))))) -> 3_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   3_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{2_1}(x1)))))) -> 3_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   3_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{5_1}(x1)))))) -> 3_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   4_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{0_1}(x1)))))) -> 4_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   4_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{1_1}(x1)))))) -> 4_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   4_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{3_1}(x1)))))) -> 4_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   4_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{4_1}(x1)))))) -> 4_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   4_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{2_1}(x1)))))) -> 4_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   4_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{5_1}(x1)))))) -> 4_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   5_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{0_1}(x1)))))) -> 5_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{0_1}(x1)))))))
   5_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{1_1}(x1)))))) -> 5_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{1_1}(x1)))))))
   5_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{3_1}(x1)))))) -> 5_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{3_1}(x1)))))))
   5_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{4_1}(x1)))))) -> 5_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{4_1}(x1)))))))
   5_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{2_1}(x1)))))) -> 5_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{2_1}(x1)))))))
   5_{5_1}(5_{2_1}(2_{4_1}(4_{1_1}(1_{0_1}(0_{5_1}(x1)))))) -> 5_{0_1}(0_{2_1}(2_{3_1}(3_{4_1}(4_{5_1}(5_{1_1}(1_{5_1}(x1)))))))
   0_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 0_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(x1)))))))
   0_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 0_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{1_1}(x1)))))))
   0_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 0_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{3_1}(x1)))))))
   0_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 0_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{4_1}(x1)))))))
   0_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 0_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{2_1}(x1)))))))
   0_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 0_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{5_1}(x1)))))))
   1_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 1_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(x1)))))))
   1_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 1_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{1_1}(x1)))))))
   1_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 1_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{3_1}(x1)))))))
   1_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 1_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{4_1}(x1)))))))
   1_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 1_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{2_1}(x1)))))))
   1_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 1_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{5_1}(x1)))))))
   2_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(x1)))))))
   2_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{1_1}(x1)))))))
   2_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{3_1}(x1)))))))
   2_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{4_1}(x1)))))))
   2_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{2_1}(x1)))))))
   2_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 2_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{5_1}(x1)))))))
   3_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 3_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(x1)))))))
   3_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 3_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{1_1}(x1)))))))
   3_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 3_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{3_1}(x1)))))))
   3_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 3_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{4_1}(x1)))))))
   3_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 3_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{2_1}(x1)))))))
   3_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 3_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{5_1}(x1)))))))
   4_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 4_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(x1)))))))
   4_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 4_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{1_1}(x1)))))))
   4_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 4_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{3_1}(x1)))))))
   4_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 4_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{4_1}(x1)))))))
   4_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 4_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{2_1}(x1)))))))
   4_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 4_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{5_1}(x1)))))))
   5_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{0_1}(x1)))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{0_1}(x1)))))))
   5_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{1_1}(x1)))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{1_1}(x1)))))))
   5_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{3_1}(x1)))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{3_1}(x1)))))))
   5_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{4_1}(x1)))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{4_1}(x1)))))))
   5_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{2_1}(x1)))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{2_1}(x1)))))))
   5_{5_1}(5_{3_1}(3_{4_1}(4_{1_1}(1_{1_1}(1_{5_1}(x1)))))) -> 5_{1_1}(1_{4_1}(4_{3_1}(3_{5_1}(5_{2_1}(2_{1_1}(1_{5_1}(x1)))))))




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

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

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

Q is empty.

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

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

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

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




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

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

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

Q is empty.

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

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

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

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




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

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

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

Q is empty.

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

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

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

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

The TRS R consists of the following rules:

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

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
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(13) DependencyGraphProof (EQUIVALENT)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 3 SCCs with 306 less nodes.
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(14)
Complex Obligation (AND)

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(15)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

(16) UsableRulesProof (EQUIVALENT)
We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R.
----------------------------------------

(17)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

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

(19)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

(20) QDPSizeChangeProof (EQUIVALENT)
By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 

From the DPs we obtained the following set of size-change graphs:
*3_{0_1}^1(0_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 3_{0_1}^1(0_{5_1}(x1))
The graph contains the following edges 1 > 1


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

(21)
YES

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

(22)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   1_{5_1}^1(5_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x1))))) -> 5_{1_1}^1(1_{5_1}(5_{1_1}(1_{0_1}(x1))))
   5_{1_1}^1(1_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 1_{5_1}^1(x1)
   1_{5_1}^1(5_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x1))))) -> 5_{1_1}^1(1_{0_1}(x1))
   1_{5_1}^1(5_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x1))))) -> 5_{1_1}^1(1_{5_1}(5_{1_1}(1_{1_1}(x1))))
   1_{5_1}^1(5_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x1))))) -> 1_{5_1}^1(5_{1_1}(1_{1_1}(x1)))
   1_{5_1}^1(5_{1_1}(1_{1_1}(1_{0_1}(0_{5_1}(x1))))) -> 5_{1_1}^1(1_{5_1}(5_{1_1}(1_{5_1}(x1))))
   1_{5_1}^1(5_{1_1}(1_{1_1}(1_{0_1}(0_{5_1}(x1))))) -> 5_{1_1}^1(1_{5_1}(x1))
   1_{5_1}^1(5_{1_1}(1_{1_1}(1_{0_1}(0_{5_1}(x1))))) -> 1_{5_1}^1(x1)

The TRS R consists of the following rules:

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

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

(23) UsableRulesProof (EQUIVALENT)
We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R.
----------------------------------------

(24)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   1_{5_1}^1(5_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x1))))) -> 5_{1_1}^1(1_{5_1}(5_{1_1}(1_{0_1}(x1))))
   5_{1_1}^1(1_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 1_{5_1}^1(x1)
   1_{5_1}^1(5_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x1))))) -> 5_{1_1}^1(1_{0_1}(x1))
   1_{5_1}^1(5_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x1))))) -> 5_{1_1}^1(1_{5_1}(5_{1_1}(1_{1_1}(x1))))
   1_{5_1}^1(5_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x1))))) -> 1_{5_1}^1(5_{1_1}(1_{1_1}(x1)))
   1_{5_1}^1(5_{1_1}(1_{1_1}(1_{0_1}(0_{5_1}(x1))))) -> 5_{1_1}^1(1_{5_1}(5_{1_1}(1_{5_1}(x1))))
   1_{5_1}^1(5_{1_1}(1_{1_1}(1_{0_1}(0_{5_1}(x1))))) -> 5_{1_1}^1(1_{5_1}(x1))
   1_{5_1}^1(5_{1_1}(1_{1_1}(1_{0_1}(0_{5_1}(x1))))) -> 1_{5_1}^1(x1)

The TRS R consists of the following rules:

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

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

(25) DependencyGraphProof (EQUIVALENT)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 4 less nodes.
----------------------------------------

(26)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   1_{5_1}^1(5_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x1))))) -> 1_{5_1}^1(5_{1_1}(1_{1_1}(x1)))
   1_{5_1}^1(5_{1_1}(1_{1_1}(1_{0_1}(0_{5_1}(x1))))) -> 5_{1_1}^1(1_{5_1}(x1))
   5_{1_1}^1(1_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 1_{5_1}^1(x1)
   1_{5_1}^1(5_{1_1}(1_{1_1}(1_{0_1}(0_{5_1}(x1))))) -> 1_{5_1}^1(x1)

The TRS R consists of the following rules:

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

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

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


The following pairs can be oriented strictly and are deleted.

   1_{5_1}^1(5_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x1))))) -> 1_{5_1}^1(5_{1_1}(1_{1_1}(x1)))
The remaining pairs can at least be oriented weakly.
Used ordering:  Polynomial interpretation [POLO]:

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

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

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


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

(28)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   1_{5_1}^1(5_{1_1}(1_{1_1}(1_{0_1}(0_{5_1}(x1))))) -> 5_{1_1}^1(1_{5_1}(x1))
   5_{1_1}^1(1_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 1_{5_1}^1(x1)
   1_{5_1}^1(5_{1_1}(1_{1_1}(1_{0_1}(0_{5_1}(x1))))) -> 1_{5_1}^1(x1)

The TRS R consists of the following rules:

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

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

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


The following pairs can be oriented strictly and are deleted.

   1_{5_1}^1(5_{1_1}(1_{1_1}(1_{0_1}(0_{5_1}(x1))))) -> 5_{1_1}^1(1_{5_1}(x1))
   1_{5_1}^1(5_{1_1}(1_{1_1}(1_{0_1}(0_{5_1}(x1))))) -> 1_{5_1}^1(x1)
The remaining pairs can at least be oriented weakly.
Used ordering:  Polynomial interpretation [POLO]:

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

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

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


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

(30)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   5_{1_1}^1(1_{5_1}(5_{0_1}(0_{5_1}(x1)))) -> 1_{5_1}^1(x1)

The TRS R consists of the following rules:

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

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

(31) DependencyGraphProof (EQUIVALENT)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.
----------------------------------------

(32)
TRUE

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

(33)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   5_{3_1}^1(3_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 5_{3_1}^1(x1)

The TRS R consists of the following rules:

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

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
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(34) UsableRulesProof (EQUIVALENT)
We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R.
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(35)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   5_{3_1}^1(3_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 5_{3_1}^1(x1)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
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(36) QDPSizeChangeProof (EQUIVALENT)
By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 

From the DPs we obtained the following set of size-change graphs:
*5_{3_1}^1(3_{1_1}(1_{1_1}(1_{3_1}(x1)))) -> 5_{3_1}^1(x1)
The graph contains the following edges 1 > 1


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(37)
YES