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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) QTRSRRRProof [EQUIVALENT, 650 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 678 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) QDP
(7) QDPOrderProof [EQUIVALENT, 963 ms]
(8) QDP
(9) PisEmptyProof [EQUIVALENT, 0 ms]
(10) YES


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

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

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

Q is empty.

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

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

   POL(0(x_1)) = 6 + x_1
   POL(1(x_1)) = 5 + x_1
   POL(2(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(2(1(x1)))) -> 0(2(2(2(1(x1)))))
   0(2(1(1(2(0(2(x1))))))) -> 2(2(2(0(2(1(2(2(x1))))))))
   2(0(0(0(0(1(0(x1))))))) -> 1(2(2(2(1(2(1(0(1(x1)))))))))
   0(0(0(1(1(0(0(1(0(1(1(0(0(x1))))))))))))) -> 2(2(1(2(0(2(2(1(1(1(2(2(1(0(x1))))))))))))))
   0(1(1(0(0(1(1(2(1(2(0(0(2(x1))))))))))))) -> 1(2(2(2(1(2(1(0(2(2(0(0(1(2(2(2(2(x1)))))))))))))))))
   1(0(0(0(1(0(1(1(0(1(1(0(1(2(0(1(x1)))))))))))))))) -> 2(2(1(1(2(1(2(0(0(1(2(0(0(1(1(0(0(0(x1))))))))))))))))))
   1(1(0(1(1(2(0(0(0(0(0(0(1(2(0(0(x1)))))))))))))))) -> 2(0(1(1(0(0(2(0(0(2(2(2(0(2(1(2(2(x1)))))))))))))))))
   2(0(0(2(2(2(0(1(2(1(2(0(1(1(0(0(x1)))))))))))))))) -> 2(2(2(2(2(2(2(1(2(0(0(2(1(0(1(0(1(2(1(2(x1))))))))))))))))))))
   1(1(1(1(1(1(2(1(0(1(2(1(0(2(2(0(1(x1))))))))))))))))) -> 1(1(2(2(0(2(2(2(2(1(0(1(2(0(2(1(0(0(0(x1)))))))))))))))))))
   0(2(0(0(2(1(0(0(0(0(1(0(2(1(1(1(0(1(x1)))))))))))))))))) -> 0(1(2(2(1(0(0(2(2(1(1(1(1(2(1(1(2(1(0(x1)))))))))))))))))))
   1(1(2(1(2(1(1(1(1(1(1(2(2(1(0(1(2(1(x1)))))))))))))))))) -> 2(0(2(2(2(2(2(1(1(1(2(0(1(0(2(1(2(2(1(2(2(2(1(2(2(2(x1))))))))))))))))))))))))))
   0(0(1(0(2(0(1(0(1(1(2(0(0(1(0(0(0(1(1(x1))))))))))))))))))) -> 0(2(2(2(0(2(0(1(2(1(1(0(1(2(2(0(1(0(0(2(2(2(2(x1)))))))))))))))))))))))
   0(2(0(2(1(0(2(2(1(0(0(2(0(0(0(2(0(0(1(x1))))))))))))))))))) -> 2(2(0(0(1(2(1(2(1(2(2(2(2(1(0(2(1(1(2(0(x1))))))))))))))))))))
   1(0(0(2(2(0(2(0(2(0(0(2(1(1(0(0(0(1(2(x1))))))))))))))))))) -> 2(2(1(0(2(1(0(2(1(2(1(2(1(0(2(2(2(1(2(2(1(2(x1))))))))))))))))))))))
   0(1(0(0(1(2(2(0(1(0(1(1(1(2(1(1(1(1(0(2(0(x1))))))))))))))))))))) -> 1(0(1(1(1(1(2(2(1(1(2(1(0(0(0(2(2(0(2(0(0(2(x1))))))))))))))))))))))
   1(1(0(1(0(1(1(2(1(0(0(0(1(0(2(0(1(0(0(1(0(1(x1)))))))))))))))))))))) -> 0(1(1(1(1(1(0(0(2(1(0(0(2(1(2(0(2(2(1(2(2(1(1(x1)))))))))))))))))))))))
   0(2(0(2(2(1(0(1(2(1(0(0(1(0(2(0(0(0(0(0(2(2(0(x1))))))))))))))))))))))) -> 2(1(1(2(2(1(2(2(2(1(0(0(2(2(0(1(0(1(2(0(0(2(1(1(x1))))))))))))))))))))))))
   1(0(0(1(2(1(2(0(0(0(2(1(0(2(0(2(0(0(0(0(0(1(1(2(2(x1))))))))))))))))))))))))) -> 1(1(1(1(2(0(1(2(2(2(1(2(1(0(1(2(2(0(2(2(2(0(0(1(0(2(x1))))))))))))))))))))))))))
   2(1(2(2(1(2(2(2(0(0(2(1(1(1(0(1(1(2(0(1(1(2(0(2(2(x1))))))))))))))))))))))))) -> 2(2(2(2(0(0(1(2(1(2(0(0(2(1(2(0(2(2(1(2(0(0(2(2(0(1(x1))))))))))))))))))))))))))
   1(0(0(2(1(1(1(1(1(2(2(1(1(1(0(2(1(0(1(2(1(2(0(0(1(2(x1)))))))))))))))))))))))))) -> 2(1(2(2(1(2(1(0(2(2(2(1(0(2(2(1(0(1(0(2(2(2(2(1(2(1(2(1(1(0(2(x1)))))))))))))))))))))))))))))))
   0(1(2(1(2(2(0(0(0(1(2(1(0(2(0(0(0(1(2(2(2(0(0(0(1(2(1(x1))))))))))))))))))))))))))) -> 2(2(1(2(2(2(1(2(2(2(2(1(2(2(0(2(1(1(1(0(1(0(2(2(1(1(0(1(x1))))))))))))))))))))))))))))
   1(2(2(0(2(0(1(2(1(2(2(0(2(1(1(1(1(2(0(1(0(0(1(2(0(1(2(x1))))))))))))))))))))))))))) -> 1(2(0(0(2(2(0(2(2(0(0(2(0(0(1(2(0(0(2(2(2(0(1(2(1(0(1(2(x1))))))))))))))))))))))))))))
   0(2(0(2(0(1(0(0(1(0(2(0(0(0(0(1(0(0(2(2(2(1(1(2(0(2(1(2(2(2(x1)))))))))))))))))))))))))))))) -> 2(2(1(2(0(1(1(1(2(2(1(2(2(2(0(1(2(2(2(1(2(1(1(1(0(0(1(2(2(0(0(x1)))))))))))))))))))))))))))))))
   1(0(2(0(2(0(2(0(0(1(1(1(2(0(1(0(0(0(1(2(0(1(1(2(0(0(2(1(0(0(x1)))))))))))))))))))))))))))))) -> 1(0(1(2(2(1(2(1(2(0(1(1(0(0(2(2(2(2(1(2(0(1(1(1(1(1(2(2(2(2(1(1(x1))))))))))))))))))))))))))))))))
   1(0(2(2(0(2(1(1(0(2(0(1(2(0(2(1(0(1(0(2(1(0(0(1(0(0(2(0(2(2(x1)))))))))))))))))))))))))))))) -> 1(1(0(1(2(2(1(1(1(2(1(2(2(0(0(2(2(1(1(2(0(1(2(1(2(0(2(0(2(0(0(2(x1))))))))))))))))))))))))))))))))
   1(2(0(2(0(0(1(2(2(1(1(0(1(2(0(1(0(1(0(0(2(0(1(0(1(0(1(0(2(0(x1)))))))))))))))))))))))))))))) -> 2(1(0(2(2(2(0(2(1(2(0(0(2(1(2(2(2(0(1(2(2(2(1(1(0(1(1(0(1(1(0(2(x1))))))))))))))))))))))))))))))))
   2(2(2(1(2(0(0(1(1(1(2(0(0(2(0(1(1(0(2(1(0(2(0(2(1(1(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 2(2(2(1(2(1(2(2(2(1(0(0(2(2(1(0(2(2(0(0(2(0(0(0(2(1(1(2(1(1(1(2(2(2(x1))))))))))))))))))))))))))))))))))
   0(1(1(0(0(2(2(1(0(1(1(1(2(2(1(2(0(0(1(1(0(0(2(0(2(2(0(1(1(1(1(x1))))))))))))))))))))))))))))))) -> 0(2(2(0(1(0(1(1(2(1(2(0(0(0(0(0(1(0(1(0(1(2(2(2(2(0(0(0(1(2(1(2(x1))))))))))))))))))))))))))))))))
   0(1(1(1(2(1(1(0(1(2(2(2(0(1(2(1(0(0(1(2(2(1(1(2(0(1(1(1(2(1(1(x1))))))))))))))))))))))))))))))) -> 2(2(1(1(2(1(2(1(2(2(1(0(0(2(1(2(2(2(0(0(0(2(2(0(2(1(1(1(0(2(2(2(x1))))))))))))))))))))))))))))))))
   1(2(1(1(1(1(2(1(0(1(0(2(2(0(0(1(0(1(0(1(2(1(1(1(1(0(2(2(2(2(1(x1))))))))))))))))))))))))))))))) -> 2(0(1(2(2(2(1(2(0(0(2(2(1(1(2(2(2(0(1(2(1(2(1(2(2(1(2(1(1(2(0(1(0(x1)))))))))))))))))))))))))))))))))
   2(0(1(0(1(2(1(2(2(2(0(1(0(0(0(1(2(0(1(1(1(1(2(2(0(0(0(1(0(0(0(x1))))))))))))))))))))))))))))))) -> 2(2(0(2(2(0(2(1(1(2(1(2(2(1(0(0(1(0(2(0(2(2(2(1(0(2(2(0(1(0(2(2(1(2(x1))))))))))))))))))))))))))))))))))
   1(0(0(2(2(1(0(2(1(2(0(2(0(2(0(2(0(1(1(2(2(1(0(0(0(1(0(1(2(1(2(0(x1)))))))))))))))))))))))))))))))) -> 2(2(0(1(0(1(1(1(2(2(1(2(1(0(2(2(2(2(1(2(1(1(2(0(2(2(2(0(0(0(1(1(1(x1)))))))))))))))))))))))))))))))))
   1(2(1(1(1(0(1(2(1(0(1(2(1(1(2(2(0(2(2(1(1(1(1(0(1(2(0(1(1(1(1(1(x1)))))))))))))))))))))))))))))))) -> 2(0(1(2(0(2(0(2(1(0(0(0(0(2(2(2(2(2(1(1(0(2(2(2(0(2(2(2(0(1(0(2(2(1(1(x1)))))))))))))))))))))))))))))))))))
   0(1(0(0(1(2(1(2(0(1(1(1(0(1(0(0(2(1(2(0(2(1(1(0(1(0(0(1(1(0(1(0(1(x1))))))))))))))))))))))))))))))))) -> 2(0(0(0(1(0(1(2(2(2(0(1(0(2(0(2(2(2(1(0(1(0(0(2(2(2(0(1(1(1(1(1(1(1(x1))))))))))))))))))))))))))))))))))
   0(2(0(0(2(1(1(0(0(0(2(2(1(0(2(1(0(1(0(0(1(1(2(0(1(1(2(2(0(1(1(1(0(x1))))))))))))))))))))))))))))))))) -> 0(1(2(1(2(2(1(0(2(1(1(2(2(1(2(1(1(0(2(1(0(0(0(2(2(1(2(2(2(2(1(0(0(2(x1))))))))))))))))))))))))))))))))))
   1(2(2(2(0(1(0(0(1(2(1(0(1(1(0(1(1(1(2(1(1(1(2(1(0(0(0(1(0(0(0(1(2(x1))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(1(0(1(0(2(2(0(0(2(2(2(0(0(0(2(0(0(1(1(2(2(1(2(2(2(1(0(1(0(1(0(2(0(x1))))))))))))))))))))))))))))))))))))))))
   1(1(0(2(0(2(0(0(0(1(1(0(1(0(1(0(1(1(2(1(0(2(0(0(2(2(1(0(0(2(0(2(0(2(x1)))))))))))))))))))))))))))))))))) -> 0(2(1(0(0(0(2(2(2(1(2(2(2(2(2(1(0(0(2(2(2(0(0(0(0(1(1(0(1(1(2(1(2(2(2(x1)))))))))))))))))))))))))))))))))))
   1(1(2(1(0(2(0(0(0(2(0(0(2(0(1(0(0(0(0(2(1(0(0(0(0(1(2(2(0(1(1(2(0(1(x1)))))))))))))))))))))))))))))))))) -> 2(2(1(2(2(2(2(1(0(2(1(2(2(2(1(1(2(2(1(2(0(1(0(1(1(2(2(1(1(1(0(2(1(2(2(0(0(2(x1))))))))))))))))))))))))))))))))))))))
   1(0(1(1(1(1(1(2(2(1(0(2(0(0(1(0(0(0(0(2(1(1(1(1(0(0(0(0(2(1(0(1(1(2(1(x1))))))))))))))))))))))))))))))))))) -> 0(2(0(1(1(2(1(1(1(2(2(0(2(0(2(2(1(2(1(1(2(0(1(2(1(1(2(1(2(1(1(0(1(0(2(1(x1))))))))))))))))))))))))))))))))))))
   1(1(2(0(0(0(1(1(0(1(0(2(2(1(2(1(0(2(2(2(0(2(1(1(2(0(0(0(2(0(1(2(0(0(1(x1))))))))))))))))))))))))))))))))))) -> 2(2(2(1(1(2(2(0(0(2(0(1(1(2(2(1(1(2(0(1(2(1(0(2(1(2(0(2(2(1(0(0(2(0(0(0(x1))))))))))))))))))))))))))))))))))))
   0(0(0(0(0(0(2(1(0(1(0(1(0(1(0(1(2(0(0(1(1(0(2(1(0(2(0(0(0(0(2(2(1(2(2(0(x1)))))))))))))))))))))))))))))))))))) -> 1(2(0(0(0(0(1(1(1(2(0(1(2(1(2(2(2(2(1(2(0(1(1(2(1(1(0(1(2(0(1(0(0(0(2(0(0(1(x1))))))))))))))))))))))))))))))))))))))
   0(0(1(2(2(1(1(2(0(0(1(0(2(2(0(0(2(0(1(0(1(0(1(2(2(1(0(2(1(1(0(1(0(0(0(1(x1)))))))))))))))))))))))))))))))))))) -> 1(1(2(2(1(2(0(2(2(2(1(2(1(2(0(0(1(2(2(0(0(1(0(1(2(0(0(1(0(1(1(0(1(1(1(1(1(0(x1))))))))))))))))))))))))))))))))))))))
   0(1(1(0(2(0(0(2(1(1(2(0(2(0(1(0(2(0(2(2(2(1(0(0(0(1(1(0(0(2(2(0(0(0(0(2(x1)))))))))))))))))))))))))))))))))))) -> 2(2(2(2(1(0(2(0(0(0(0(0(2(2(1(0(1(0(1(2(0(0(0(0(1(2(2(1(2(2(2(2(2(0(1(2(1(1(0(2(x1))))))))))))))))))))))))))))))))))))))))
   0(2(0(0(2(1(1(1(0(2(2(1(1(1(0(0(0(1(0(0(0(2(0(1(1(0(1(0(0(2(0(0(0(2(0(0(x1)))))))))))))))))))))))))))))))))))) -> 2(1(2(0(2(1(0(2(1(0(1(1(0(2(2(2(2(1(1(0(2(2(1(2(1(2(0(1(0(1(2(1(2(2(2(0(0(0(x1))))))))))))))))))))))))))))))))))))))
   0(2(0(0(2(0(0(1(0(2(0(0(0(0(2(1(0(0(0(2(2(0(1(0(2(2(0(0(2(0(2(0(0(1(0(1(2(x1))))))))))))))))))))))))))))))))))))) -> 2(2(1(2(1(0(1(1(2(2(2(2(1(0(2(0(0(1(1(2(2(1(0(1(1(1(0(1(1(0(2(1(0(2(2(0(1(2(2(2(x1))))))))))))))))))))))))))))))))))))))))
   0(2(0(2(0(2(1(0(0(0(1(1(1(2(1(0(1(2(1(2(0(1(1(2(0(2(0(0(1(0(2(2(2(2(0(0(2(x1))))))))))))))))))))))))))))))))))))) -> 2(2(1(0(1(2(0(1(2(1(2(2(2(2(2(1(0(2(1(2(0(2(1(1(2(1(1(1(0(0(0(2(0(2(0(2(2(1(x1))))))))))))))))))))))))))))))))))))))
   1(1(0(2(0(2(1(1(1(2(2(2(1(1(2(1(0(2(0(2(0(2(1(2(1(1(1(2(0(2(1(1(2(2(0(1(0(x1))))))))))))))))))))))))))))))))))))) -> 1(2(2(2(1(2(2(0(1(2(2(1(1(2(1(0(0(2(2(0(2(0(1(2(1(2(2(0(1(2(2(2(1(1(0(0(2(0(x1))))))))))))))))))))))))))))))))))))))
   2(1(0(1(0(0(1(0(0(0(1(1(2(2(1(0(0(1(1(1(0(1(0(1(2(1(2(1(0(1(2(1(0(2(0(0(1(x1))))))))))))))))))))))))))))))))))))) -> 1(1(2(2(0(0(2(0(2(1(2(0(2(0(1(2(2(2(1(1(1(0(0(1(0(0(1(1(1(1(1(1(2(1(0(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))
   2(1(0(0(1(1(1(1(0(1(1(0(1(2(0(0(2(2(0(2(1(2(1(2(2(2(0(0(1(0(2(1(2(1(0(2(1(2(x1)))))))))))))))))))))))))))))))))))))) -> 2(0(1(0(0(1(2(0(2(1(2(1(2(1(0(2(0(2(2(2(2(2(2(1(0(0(0(2(2(2(0(2(0(0(2(2(1(0(1(1(0(x1)))))))))))))))))))))))))))))))))))))))))
   1(1(0(0(0(2(1(2(1(1(0(0(1(1(1(2(2(0(0(0(1(0(1(0(1(0(2(1(0(0(1(0(1(1(1(2(2(1(0(x1))))))))))))))))))))))))))))))))))))))) -> 2(0(0(0(2(2(1(1(2(1(1(2(2(1(2(1(0(1(1(0(0(1(2(0(0(0(0(0(0(0(0(1(0(1(0(1(1(2(2(1(2(x1)))))))))))))))))))))))))))))))))))))))))
   2(0(2(0(2(1(2(1(1(0(1(1(2(1(2(2(0(1(0(0(2(2(0(1(1(0(1(1(1(2(2(0(1(0(0(1(2(0(2(x1))))))))))))))))))))))))))))))))))))))) -> 2(0(1(0(0(2(2(0(0(2(2(2(2(0(2(0(0(2(1(1(1(0(1(2(0(2(2(1(2(0(0(2(1(1(1(2(0(1(2(1(2(2(x1))))))))))))))))))))))))))))))))))))))))))
   0(1(1(0(2(1(0(2(1(2(0(0(1(0(2(0(0(2(0(2(1(0(1(0(1(2(2(0(1(0(0(1(2(2(0(1(0(0(0(0(x1)))))))))))))))))))))))))))))))))))))))) -> 0(2(2(2(2(2(2(1(1(2(2(1(1(2(0(1(1(2(1(2(2(1(2(0(1(1(2(0(1(1(2(1(1(0(1(2(0(1(1(2(2(x1)))))))))))))))))))))))))))))))))))))))))
   0(1(0(1(0(0(2(0(2(0(1(0(2(1(0(1(0(1(2(0(0(0(1(0(2(2(0(2(0(0(0(1(1(1(1(1(0(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))) -> 1(1(0(0(1(2(2(0(0(2(1(1(2(2(0(0(1(1(1(0(2(2(2(0(1(0(2(2(0(2(0(2(1(2(1(1(2(1(0(1(2(2(1(x1)))))))))))))))))))))))))))))))))))))))))))
   1(1(0(2(0(1(2(0(0(1(1(0(0(2(1(0(1(0(1(2(1(2(2(0(1(1(2(0(1(2(1(0(1(1(0(1(0(1(0(1(2(x1))))))))))))))))))))))))))))))))))))))))) -> 1(0(0(0(2(1(0(2(0(0(0(0(0(1(0(2(2(0(0(2(2(2(2(2(0(2(0(0(0(1(0(0(1(0(1(0(2(2(2(2(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))))
   1(1(0(2(2(1(0(2(2(2(1(0(0(0(2(0(0(2(2(0(1(2(1(2(2(1(1(0(0(1(2(0(0(2(2(2(0(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))) -> 1(1(1(2(2(2(2(2(2(1(1(2(0(2(0(1(0(2(1(0(0(0(1(2(2(2(1(2(2(2(0(2(2(0(1(1(2(2(2(2(2(1(2(2(x1))))))))))))))))))))))))))))))))))))))))))))
   2(2(1(2(0(0(0(0(0(1(2(2(0(1(0(0(2(1(1(0(1(2(1(0(0(1(0(1(0(2(0(0(1(0(2(2(2(1(1(0(2(x1))))))))))))))))))))))))))))))))))))))))) -> 2(1(1(2(1(1(2(1(1(0(2(0(0(0(1(2(2(2(0(2(0(0(2(0(1(0(0(2(1(1(1(1(2(2(2(0(0(2(0(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))
   2(0(1(2(1(1(1(2(1(2(1(2(0(0(0(0(1(2(2(1(1(1(0(2(1(1(0(0(0(0(1(0(0(0(1(1(0(2(0(1(1(1(x1)))))))))))))))))))))))))))))))))))))))))) -> 2(1(2(1(2(1(1(2(2(1(0(1(2(0(2(1(0(0(2(1(0(2(2(2(2(1(0(2(2(0(1(2(1(0(2(2(2(1(1(0(2(2(1(0(x1))))))))))))))))))))))))))))))))))))))))))))
   2(1(2(1(1(0(0(0(0(1(0(1(2(2(0(1(0(2(1(1(2(1(1(2(2(1(0(1(1(1(1(1(1(0(2(2(2(1(0(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))) -> 2(1(2(1(2(2(2(2(2(0(0(1(0(0(1(1(2(1(2(2(0(0(2(0(1(1(2(2(1(0(0(1(1(2(2(1(0(2(2(2(1(1(1(2(x1))))))))))))))))))))))))))))))))))))))))))))
   0(1(2(1(0(0(2(0(0(2(1(1(1(2(2(1(0(2(0(2(1(2(2(0(2(0(1(0(1(2(1(1(0(0(0(1(0(0(1(2(1(0(1(x1))))))))))))))))))))))))))))))))))))))))))) -> 0(1(2(0(2(1(0(2(2(1(2(1(1(0(1(1(0(1(2(2(2(0(1(0(1(2(2(2(2(0(1(1(2(2(0(1(1(2(1(2(0(2(1(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))
   0(0(2(1(0(0(2(1(2(2(0(1(2(0(0(0(2(0(0(0(0(0(0(0(1(0(0(2(0(2(0(0(2(2(0(2(1(1(1(1(2(1(0(2(0(x1))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(1(2(1(1(2(0(2(2(2(1(1(2(2(0(1(2(0(0(0(0(0(1(0(1(1(0(2(0(0(0(0(2(2(1(2(2(2(0(2(0(2(0(1(2(1(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))
   0(2(1(2(2(1(1(1(1(0(1(1(0(2(0(1(0(2(2(0(2(0(0(1(1(2(0(0(0(0(2(1(2(2(1(1(2(2(0(1(1(2(0(1(0(x1))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(0(2(2(1(1(0(2(2(0(0(2(1(0(0(1(1(0(0(2(1(2(1(1(1(2(1(0(1(2(2(2(2(2(1(1(1(2(2(0(2(2(0(1(2(x1))))))))))))))))))))))))))))))))))))))))))))))
   1(0(1(2(1(1(0(2(2(0(1(2(2(0(0(2(1(0(1(0(0(1(2(1(0(2(1(1(0(0(0(1(0(0(0(2(1(1(0(1(2(2(0(1(0(x1))))))))))))))))))))))))))))))))))))))))))))) -> 1(0(2(1(0(0(0(2(2(0(1(1(0(1(2(2(1(0(2(1(2(2(2(1(1(1(1(2(2(2(1(1(1(1(1(0(0(0(0(0(1(0(2(2(0(0(0(2(x1))))))))))))))))))))))))))))))))))))))))))))))))
   1(0(2(0(0(1(0(1(1(1(1(1(2(1(0(1(0(0(1(2(0(2(0(0(0(1(0(0(2(1(2(0(1(1(0(0(0(1(0(2(1(2(1(1(1(x1))))))))))))))))))))))))))))))))))))))))))))) -> 2(0(1(0(1(0(1(1(2(0(2(2(2(0(2(0(2(0(1(1(2(0(1(1(2(2(0(1(1(0(1(0(0(2(2(2(1(0(2(0(1(0(0(2(1(0(x1))))))))))))))))))))))))))))))))))))))))))))))
   1(1(1(0(0(2(1(0(2(2(0(2(0(0(1(1(0(1(2(2(1(0(1(1(2(0(0(2(2(1(1(2(0(0(0(1(1(0(0(0(0(0(1(2(0(x1))))))))))))))))))))))))))))))))))))))))))))) -> 1(0(0(2(1(0(2(0(1(1(1(1(2(0(1(2(0(2(0(0(2(2(2(1(2(1(2(2(1(2(0(0(2(0(1(1(1(2(0(1(1(1(1(0(0(1(2(x1)))))))))))))))))))))))))))))))))))))))))))))))
   0(0(2(0(2(0(2(0(2(0(2(0(0(2(2(2(1(1(1(0(0(1(1(1(1(1(1(2(1(2(1(2(0(1(0(1(1(1(1(2(0(1(2(1(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 1(1(2(2(0(2(0(2(1(2(2(1(2(0(2(1(2(1(1(2(2(2(2(1(0(1(1(1(0(1(0(0(1(0(2(0(2(1(2(2(0(2(1(2(1(2(1(2(x1))))))))))))))))))))))))))))))))))))))))))))))))
   0(2(0(2(2(0(2(0(1(2(1(2(0(0(0(1(0(1(1(2(1(1(2(0(0(0(0(1(1(1(1(2(1(0(2(0(1(1(0(1(0(1(0(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 2(1(1(2(0(1(2(0(2(0(1(2(0(1(2(2(2(2(1(1(1(2(2(2(0(2(1(2(2(0(0(1(0(0(0(0(2(0(1(2(1(1(2(1(2(0(1(0(x1))))))))))))))))))))))))))))))))))))))))))))))))
   1(1(0(2(2(2(1(1(0(1(0(0(0(2(1(1(1(1(1(1(0(2(0(0(0(0(2(2(0(1(1(0(1(1(1(0(1(2(1(1(0(0(1(2(0(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 1(2(2(2(2(2(1(0(2(0(0(0(1(1(2(2(2(1(2(1(0(0(0(0(0(2(2(0(0(0(0(0(0(1(2(2(2(0(2(1(0(1(1(0(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))
   2(0(2(2(2(1(2(2(2(2(2(2(2(0(0(1(0(0(2(2(2(1(1(0(0(2(2(0(0(1(0(2(2(0(2(1(2(2(0(1(0(1(2(0(0(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(1(0(2(0(0(1(2(2(2(1(2(0(1(2(2(1(1(2(0(0(1(0(2(2(1(1(2(0(1(0(1(0(2(2(2(1(1(2(0(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))
   2(1(0(2(0(0(0(2(0(2(2(1(1(2(2(1(1(2(1(0(1(1(0(0(2(0(0(1(0(2(1(1(0(0(2(2(1(1(1(1(0(2(2(0(1(0(2(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 2(1(2(2(0(1(0(1(0(0(0(0(0(1(2(1(1(1(2(1(2(0(2(1(0(1(0(2(1(1(2(0(1(1(0(1(0(2(1(2(0(0(2(2(2(2(1(1(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))




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

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

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

Q is empty.

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

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

(4)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

(5) DependencyGraphProof (EQUIVALENT)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 79 less nodes.
----------------------------------------

(6)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

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


The following pairs can be oriented strictly and are deleted.

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

   POL(0(x_1)) = 1 + x_1
   POL(0^1(x_1)) = x_1
   POL(1(x_1)) = x_1
   POL(1^1(x_1)) = 1 + x_1
   POL(2(x_1)) = x_1

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

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


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

(8)
Obligation:
Q DP problem:
P is empty.
The TRS R consists of the following rules:

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

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

(9) PisEmptyProof (EQUIVALENT)
The TRS P is empty. Hence, there is no (P,Q,R) chain.
----------------------------------------

(10)
YES