WORST_CASE(?, O(n^1))
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 82 ms]
(4) CpxRelTRS
(5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(6) CpxTRS
(7) CpxTrsMatchBoundsProof [FINISHED, 436 ms]
(8) BOUNDS(1, n^1)


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

(0)
Obligation:
The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).


The TRS R consists of the following rules:

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

S is empty.
Rewrite Strategy: FULL
----------------------------------------

(1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID))
The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem:

   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(2(x_1)) -> 2(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_3(x_1)) -> 3(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))
   encode_2(x_1) -> 2(encArg(x_1))
   encode_3(x_1) -> 3(encArg(x_1))
   encode_4(x_1) -> 4(encArg(x_1))
   encode_5(x_1) -> 5(encArg(x_1))


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

(2)
Obligation:
The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1).


The TRS R consists of the following rules:

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

The (relative) TRS S consists of the following rules:

   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(2(x_1)) -> 2(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_3(x_1)) -> 3(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))
   encode_2(x_1) -> 2(encArg(x_1))
   encode_3(x_1) -> 3(encArg(x_1))
   encode_4(x_1) -> 4(encArg(x_1))
   encode_5(x_1) -> 5(encArg(x_1))

Rewrite Strategy: FULL
----------------------------------------

(3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID))
proved innermost termination of relative rules
----------------------------------------

(4)
Obligation:
The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1).


The TRS R consists of the following rules:

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

The (relative) TRS S consists of the following rules:

   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(2(x_1)) -> 2(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_3(x_1)) -> 3(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))
   encode_2(x_1) -> 2(encArg(x_1))
   encode_3(x_1) -> 3(encArg(x_1))
   encode_4(x_1) -> 4(encArg(x_1))
   encode_5(x_1) -> 5(encArg(x_1))

Rewrite Strategy: FULL
----------------------------------------

(5) RelTrsToTrsProof (UPPER BOUND(ID))
transformed relative TRS to TRS
----------------------------------------

(6)
Obligation:
The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1).


The TRS R consists of the following rules:

   0(0(1(x1))) -> 0(0(2(1(x1))))
   0(1(3(x1))) -> 0(3(4(1(x1))))
   3(1(1(x1))) -> 3(1(4(1(x1))))
   3(1(1(x1))) -> 3(4(1(4(4(1(x1))))))
   3(1(1(x1))) -> 3(4(4(1(2(4(1(x1)))))))
   3(3(1(x1))) -> 3(2(1(3(x1))))
   5(0(4(x1))) -> 4(0(5(4(x1))))
   0(0(0(1(x1)))) -> 0(0(0(2(1(x1)))))
   0(0(1(5(x1)))) -> 0(0(5(1(2(4(x1))))))
   0(0(5(3(x1)))) -> 0(0(5(4(3(x1)))))
   0(4(1(1(x1)))) -> 0(5(4(1(2(1(x1))))))
   0(4(3(1(x1)))) -> 0(3(5(4(1(x1)))))
   0(4(3(4(x1)))) -> 0(3(2(4(4(x1)))))
   3(0(1(1(x1)))) -> 0(2(1(3(1(x1)))))
   3(1(1(5(x1)))) -> 3(1(2(1(5(x1)))))
   5(0(1(5(x1)))) -> 0(5(4(1(5(x1)))))
   5(2(3(1(x1)))) -> 4(5(2(1(3(x1)))))
   5(2(3(5(x1)))) -> 2(4(5(3(5(x1)))))
   5(2(5(4(x1)))) -> 2(4(5(4(5(x1)))))
   0(1(2(2(1(x1))))) -> 2(4(0(1(2(1(x1))))))
   0(1(5(0(4(x1))))) -> 0(2(1(5(4(0(x1))))))
   0(1(5(5(3(x1))))) -> 0(5(4(5(1(3(x1))))))
   0(2(2(1(5(x1))))) -> 0(2(1(5(4(2(4(4(2(x1)))))))))
   0(2(2(3(4(x1))))) -> 0(3(4(4(2(4(4(2(x1))))))))
   0(2(5(1(1(x1))))) -> 5(0(1(2(4(1(x1))))))
   0(3(3(2(3(x1))))) -> 0(3(3(2(4(3(x1))))))
   0(4(4(3(4(x1))))) -> 4(4(4(4(0(3(x1))))))
   3(0(1(4(3(x1))))) -> 3(2(0(3(4(1(x1))))))
   3(0(4(5(1(x1))))) -> 3(5(4(4(1(0(x1))))))
   3(1(1(1(2(x1))))) -> 3(2(1(4(1(2(1(2(x1))))))))
   5(2(3(1(4(x1))))) -> 5(2(1(2(1(3(4(x1)))))))
   5(3(0(0(4(x1))))) -> 0(0(3(5(4(4(x1))))))
   0(1(3(4(3(4(x1)))))) -> 0(3(4(3(4(1(2(x1)))))))
   0(1(5(0(4(2(x1)))))) -> 0(5(2(4(1(0(2(x1)))))))
   0(2(2(2(3(1(x1)))))) -> 0(2(2(4(2(3(1(x1)))))))
   0(4(1(1(0(4(x1)))))) -> 0(4(4(1(4(1(0(x1)))))))
   0(4(3(2(2(3(x1)))))) -> 0(2(3(2(4(2(3(x1)))))))
   3(0(4(1(2(2(x1)))))) -> 3(2(1(0(4(4(2(x1)))))))
   3(1(0(3(5(4(x1)))))) -> 3(0(3(2(1(5(4(x1)))))))
   3(2(2(1(1(3(x1)))))) -> 1(2(1(3(2(4(3(x1)))))))
   3(3(3(1(3(5(x1)))))) -> 3(2(1(3(3(3(5(x1)))))))
   3(4(3(0(4(5(x1)))))) -> 3(5(0(3(4(4(4(x1)))))))
   3(4(3(1(4(2(x1)))))) -> 3(4(2(1(3(2(2(4(2(4(x1))))))))))
   3(5(0(2(1(4(x1)))))) -> 3(2(4(0(5(1(2(x1)))))))
   3(5(5(2(3(1(x1)))))) -> 5(5(4(3(3(2(1(x1)))))))
   5(0(1(2(3(1(x1)))))) -> 2(1(0(3(4(5(4(4(4(1(x1))))))))))
   5(0(4(3(3(1(x1)))))) -> 0(3(5(1(5(4(4(3(x1))))))))
   0(0(1(1(3(3(3(x1))))))) -> 0(3(0(1(3(3(4(1(x1))))))))
   0(0(2(5(1(4(2(x1))))))) -> 0(2(1(0(5(4(2(2(x1))))))))
   0(2(5(4(4(1(5(x1))))))) -> 1(2(4(5(0(5(4(4(x1))))))))
   0(4(2(3(4(5(4(x1))))))) -> 3(0(5(4(4(2(4(0(x1))))))))
   0(5(2(1(2(1(4(x1))))))) -> 2(1(2(1(0(5(2(4(x1))))))))
   3(2(5(0(4(0(1(x1))))))) -> 0(0(5(4(2(2(4(4(1(3(x1))))))))))
   3(4(3(4(0(1(4(x1))))))) -> 3(4(2(4(4(4(0(5(1(2(3(x1)))))))))))
   3(5(2(1(0(2(2(x1))))))) -> 2(1(3(0(5(2(2(4(x1))))))))
   3(5(2(2(0(1(1(x1))))))) -> 3(2(4(5(0(2(1(2(1(x1)))))))))
   3(5(3(4(0(1(4(x1))))))) -> 2(1(5(4(3(4(0(3(x1))))))))
   5(1(5(3(1(1(3(x1))))))) -> 2(1(5(1(5(1(3(3(x1))))))))
   5(2(0(0(1(0(3(x1))))))) -> 0(5(3(4(2(1(0(0(x1))))))))
   5(2(0(4(0(4(3(x1))))))) -> 2(0(5(1(0(4(4(3(x1))))))))
   5(2(3(0(0(4(3(x1))))))) -> 0(5(4(2(4(3(0(3(3(x1)))))))))
   5(2(3(3(2(0(5(x1))))))) -> 2(0(3(3(5(2(4(5(x1))))))))
   5(5(5(0(1(4(3(x1))))))) -> 0(5(4(4(3(4(5(5(1(x1)))))))))
   0(2(0(5(5(2(2(3(x1)))))))) -> 5(2(2(4(5(3(2(0(0(x1)))))))))
   0(2(5(2(4(0(1(4(x1)))))))) -> 0(3(0(5(2(1(2(2(4(4(x1))))))))))
   0(4(1(5(3(2(3(3(x1)))))))) -> 0(5(4(1(2(3(3(4(3(x1)))))))))
   0(4(5(0(1(5(2(3(x1)))))))) -> 2(1(2(4(2(5(3(0(5(0(x1))))))))))
   0(5(5(1(4(2(0(3(x1)))))))) -> 0(3(5(1(2(0(5(1(2(4(x1))))))))))
   3(0(1(3(2(0(4(2(x1)))))))) -> 0(4(2(2(2(4(1(0(3(3(4(x1)))))))))))
   3(3(1(1(2(5(5(2(x1)))))))) -> 3(2(1(5(1(2(5(3(1(x1)))))))))
   3(5(4(2(5(1(0(4(x1)))))))) -> 4(2(4(2(1(3(5(0(5(4(x1))))))))))
   5(0(4(3(0(2(2(3(x1)))))))) -> 0(2(4(4(0(3(2(5(3(x1)))))))))
   5(2(2(0(4(0(1(4(x1)))))))) -> 4(2(4(0(0(5(1(0(2(x1)))))))))
   5(2(2(0(4(1(5(4(x1)))))))) -> 2(5(2(4(5(0(2(1(4(x1)))))))))
   5(3(2(2(1(1(0(5(x1)))))))) -> 0(3(2(5(2(1(5(1(2(x1)))))))))
   0(0(4(4(5(3(1(1(5(x1))))))))) -> 2(1(5(4(4(4(1(0(0(3(5(x1)))))))))))
   0(1(2(5(1(4(0(3(4(x1))))))))) -> 0(2(4(0(3(1(2(1(2(4(5(x1)))))))))))
   0(1(3(1(2(0(1(1(5(x1))))))))) -> 0(5(1(0(1(4(1(1(2(3(x1))))))))))
   0(2(0(4(1(5(3(0(4(x1))))))))) -> 4(1(0(3(5(0(0(2(2(4(x1))))))))))
   0(4(3(3(4(2(5(0(5(x1))))))))) -> 0(5(0(4(3(2(4(5(3(2(x1))))))))))
   3(0(4(3(5(4(3(0(1(x1))))))))) -> 0(3(0(3(4(3(2(4(5(1(x1))))))))))
   3(1(5(3(1(1(0(3(2(x1))))))))) -> 5(1(0(3(2(1(3(3(2(1(x1))))))))))
   3(3(0(0(1(5(4(0(4(x1))))))))) -> 1(0(2(4(4(0(3(5(0(3(x1))))))))))
   5(2(0(3(1(2(5(0(4(x1))))))))) -> 5(1(0(3(5(2(4(2(4(0(x1))))))))))
   5(2(0(3(2(0(4(4(1(x1))))))))) -> 0(5(3(0(5(2(2(4(2(4(1(x1)))))))))))
   5(5(0(1(1(3(2(5(2(x1))))))))) -> 3(5(1(2(2(0(5(1(5(4(x1))))))))))
   5(5(3(2(1(0(1(0(4(x1))))))))) -> 0(2(1(3(5(0(5(4(2(4(1(x1)))))))))))
   0(1(3(1(4(2(0(4(5(2(x1)))))))))) -> 4(0(1(2(4(0(2(1(5(1(3(x1)))))))))))
   0(4(3(1(3(5(2(5(4(4(x1)))))))))) -> 0(5(5(2(4(4(1(5(4(3(3(x1)))))))))))
   3(2(0(2(0(5(2(3(4(5(x1)))))))))) -> 3(5(4(4(2(0(3(2(5(2(0(x1)))))))))))
   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(2(x_1)) -> 2(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_3(x_1)) -> 3(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))
   encode_2(x_1) -> 2(encArg(x_1))
   encode_3(x_1) -> 3(encArg(x_1))
   encode_4(x_1) -> 4(encArg(x_1))
   encode_5(x_1) -> 5(encArg(x_1))

S is empty.
Rewrite Strategy: FULL
----------------------------------------

(7) CpxTrsMatchBoundsProof (FINISHED)
A linear upper bound on the runtime complexity of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. 
The certificate found is represented by the following graph.

"[57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 780, 781, 782, 783, 784]
{(57,58,[0_1|0, 3_1|0, 5_1|0, encArg_1|0, encode_0_1|0, encode_1_1|0, encode_2_1|0, encode_3_1|0, encode_4_1|0, encode_5_1|0]), (57,59,[2_1|1]), (57,64,[0_1|1]), (57,69,[3_1|1]), (57,72,[3_1|1]), (57,77,[3_1|1]), (57,83,[3_1|1]), (57,90,[1_1|1, 2_1|1, 4_1|1, 0_1|1, 3_1|1, 5_1|1]), (57,91,[0_1|2]), (57,94,[0_1|2]), (57,99,[0_1|2]), (57,106,[0_1|2]), (57,110,[0_1|2]), (57,114,[0_1|2]), (57,121,[2_1|2]), (57,131,[0_1|2]), (57,134,[0_1|2]), (57,140,[0_1|2]), (57,149,[4_1|2]), (57,159,[2_1|2]), (57,164,[0_1|2]), (57,174,[0_1|2]), (57,179,[0_1|2]), (57,185,[0_1|2]), (57,190,[0_1|2]), (57,195,[0_1|2]), (57,201,[0_1|2]), (57,209,[0_1|2]), (57,213,[0_1|2]), (57,223,[0_1|2]), (57,227,[0_1|2]), (57,233,[0_1|2]), (57,242,[4_1|2]), (57,247,[3_1|2]), (57,254,[2_1|2]), (57,263,[0_1|2]), (57,271,[0_1|2]), (57,278,[0_1|2]), (57,284,[5_1|2]), (57,289,[1_1|2]), (57,296,[0_1|2]), (57,305,[5_1|2]), (57,313,[4_1|2]), (57,322,[0_1|2]), (57,327,[2_1|2]), (57,334,[0_1|2]), (57,343,[3_1|2]), (57,346,[3_1|2]), (57,351,[3_1|2]), (57,357,[3_1|2]), (57,361,[3_1|2]), (57,368,[3_1|2]), (57,374,[5_1|2]), (57,383,[3_1|2]), (57,386,[3_1|2]), (57,394,[3_1|2]), (57,400,[1_1|2]), (57,409,[0_1|2]), (57,413,[3_1|2]), (57,418,[0_1|2]), (57,428,[3_1|2]), (57,433,[3_1|2]), (57,439,[0_1|2]), (57,448,[1_1|2]), (57,454,[0_1|2]), (57,463,[3_1|2]), (57,473,[3_1|2]), (57,479,[3_1|2]), (57,488,[3_1|2]), (57,498,[3_1|2]), (57,504,[5_1|2]), (57,510,[2_1|2]), (57,517,[3_1|2]), (57,525,[2_1|2]), (57,532,[4_1|2]), (57,541,[4_1|2]), (57,544,[0_1|2]), (57,551,[0_1|2]), (57,559,[0_1|2]), (57,563,[2_1|2]), (57,572,[4_1|2]), (57,576,[5_1|2]), (57,582,[2_1|2]), (57,586,[0_1|2]), (57,594,[2_1|2]), (57,601,[2_1|2]), (57,605,[0_1|2]), (57,612,[2_1|2]), (57,619,[5_1|2]), (57,628,[0_1|2]), (57,638,[4_1|2]), (57,646,[2_1|2]), (57,654,[0_1|2]), (57,659,[0_1|2]), (57,667,[2_1|2]), (57,674,[0_1|2]), (57,682,[3_1|2]), (57,691,[0_1|2]), (58,58,[1_1|0, 2_1|0, 4_1|0, cons_0_1|0, cons_3_1|0, cons_5_1|0]), (59,60,[4_1|1]), (60,61,[0_1|1]), (61,62,[1_1|1]), (62,63,[2_1|1]), (63,58,[1_1|1]), (64,65,[5_1|1]), (65,66,[4_1|1]), (66,67,[1_1|1]), (67,68,[2_1|1]), (68,58,[1_1|1]), (69,70,[1_1|1]), (70,71,[4_1|1]), (71,58,[1_1|1]), (72,73,[4_1|1]), (73,74,[1_1|1]), (74,75,[4_1|1]), (75,76,[4_1|1]), (76,58,[1_1|1]), (77,78,[4_1|1]), (78,79,[4_1|1]), (79,80,[1_1|1]), (80,81,[2_1|1]), (81,82,[4_1|1]), (82,58,[1_1|1]), (83,84,[2_1|1]), (84,85,[1_1|1]), (85,86,[4_1|1]), (86,87,[1_1|1]), (87,88,[2_1|1]), (88,89,[1_1|1]), (89,58,[2_1|1]), (90,58,[encArg_1|1]), (90,90,[1_1|1, 2_1|1, 4_1|1, 0_1|1, 3_1|1, 5_1|1]), (90,91,[0_1|2]), (90,94,[0_1|2]), (90,99,[0_1|2]), (90,106,[0_1|2]), (90,110,[0_1|2]), (90,114,[0_1|2]), (90,121,[2_1|2]), (90,131,[0_1|2]), (90,134,[0_1|2]), (90,140,[0_1|2]), (90,149,[4_1|2]), (90,159,[2_1|2]), (90,164,[0_1|2]), (90,174,[0_1|2]), (90,179,[0_1|2]), (90,185,[0_1|2]), (90,190,[0_1|2]), (90,195,[0_1|2]), (90,201,[0_1|2]), (90,209,[0_1|2]), (90,213,[0_1|2]), (90,223,[0_1|2]), (90,227,[0_1|2]), (90,233,[0_1|2]), (90,242,[4_1|2]), (90,247,[3_1|2]), (90,254,[2_1|2]), (90,263,[0_1|2]), (90,271,[0_1|2]), (90,278,[0_1|2]), (90,284,[5_1|2]), (90,289,[1_1|2]), (90,296,[0_1|2]), (90,305,[5_1|2]), (90,313,[4_1|2]), (90,322,[0_1|2]), (90,327,[2_1|2]), (90,334,[0_1|2]), (90,343,[3_1|2]), (90,346,[3_1|2]), (90,351,[3_1|2]), (90,357,[3_1|2]), (90,361,[3_1|2]), (90,368,[3_1|2]), (90,374,[5_1|2]), (90,383,[3_1|2]), (90,386,[3_1|2]), (90,394,[3_1|2]), (90,400,[1_1|2]), (90,409,[0_1|2]), (90,413,[3_1|2]), (90,418,[0_1|2]), (90,428,[3_1|2]), (90,433,[3_1|2]), (90,439,[0_1|2]), (90,448,[1_1|2]), (90,454,[0_1|2]), (90,463,[3_1|2]), (90,473,[3_1|2]), (90,479,[3_1|2]), (90,488,[3_1|2]), (90,498,[3_1|2]), (90,504,[5_1|2]), (90,510,[2_1|2]), (90,517,[3_1|2]), (90,525,[2_1|2]), (90,532,[4_1|2]), (90,541,[4_1|2]), (90,544,[0_1|2]), (90,551,[0_1|2]), (90,559,[0_1|2]), (90,563,[2_1|2]), (90,572,[4_1|2]), (90,576,[5_1|2]), (90,582,[2_1|2]), (90,586,[0_1|2]), (90,594,[2_1|2]), (90,601,[2_1|2]), (90,605,[0_1|2]), (90,612,[2_1|2]), (90,619,[5_1|2]), (90,628,[0_1|2]), (90,638,[4_1|2]), (90,646,[2_1|2]), (90,654,[0_1|2]), (90,659,[0_1|2]), (90,667,[2_1|2]), (90,674,[0_1|2]), (90,682,[3_1|2]), (90,691,[0_1|2]), (91,92,[0_1|2]), (92,93,[2_1|2]), (93,90,[1_1|2]), (93,289,[1_1|2]), (93,400,[1_1|2]), (93,448,[1_1|2]), (94,95,[0_1|2]), (95,96,[5_1|2]), (96,97,[1_1|2]), (97,98,[2_1|2]), (98,90,[4_1|2]), (98,284,[4_1|2]), (98,305,[4_1|2]), (98,374,[4_1|2]), (98,504,[4_1|2]), (98,576,[4_1|2]), (98,619,[4_1|2]), (99,100,[3_1|2]), (100,101,[0_1|2]), (100,701,[0_1|3]), (101,102,[1_1|2]), (102,103,[3_1|2]), (103,104,[3_1|2]), (104,105,[4_1|2]), (105,90,[1_1|2]), (105,247,[1_1|2]), (105,343,[1_1|2]), (105,346,[1_1|2]), (105,351,[1_1|2]), (105,357,[1_1|2]), (105,361,[1_1|2]), (105,368,[1_1|2]), (105,383,[1_1|2]), (105,386,[1_1|2]), (105,394,[1_1|2]), (105,413,[1_1|2]), (105,428,[1_1|2]), (105,433,[1_1|2]), (105,463,[1_1|2]), (105,473,[1_1|2]), (105,479,[1_1|2]), (105,488,[1_1|2]), (105,498,[1_1|2]), (105,517,[1_1|2]), (105,682,[1_1|2]), (106,107,[0_1|2]), (107,108,[0_1|2]), (108,109,[2_1|2]), (109,90,[1_1|2]), (109,289,[1_1|2]), (109,400,[1_1|2]), (109,448,[1_1|2]), (110,111,[0_1|2]), (111,112,[5_1|2]), (112,113,[4_1|2]), (113,90,[3_1|2]), (113,247,[3_1|2]), (113,343,[3_1|2]), (113,346,[3_1|2]), (113,351,[3_1|2]), (113,357,[3_1|2]), (113,361,[3_1|2]), (113,368,[3_1|2]), (113,383,[3_1|2]), (113,386,[3_1|2]), (113,394,[3_1|2]), (113,413,[3_1|2]), (113,428,[3_1|2]), (113,433,[3_1|2]), (113,463,[3_1|2]), (113,473,[3_1|2]), (113,479,[3_1|2]), (113,488,[3_1|2]), (113,498,[3_1|2]), (113,517,[3_1|2]), (113,682,[3_1|2]), (113,607,[3_1|2]), (113,630,[3_1|2]), (113,374,[5_1|2]), (113,400,[1_1|2]), (113,409,[0_1|2]), (113,418,[0_1|2]), (113,439,[0_1|2]), (113,448,[1_1|2]), (113,454,[0_1|2]), (113,504,[5_1|2]), (113,510,[2_1|2]), (113,525,[2_1|2]), (113,532,[4_1|2]), (113,704,[3_1|3]), (114,115,[2_1|2]), (115,116,[1_1|2]), (116,117,[0_1|2]), (117,118,[5_1|2]), (118,119,[4_1|2]), (119,120,[2_1|2]), (120,90,[2_1|2]), (120,121,[2_1|2]), (120,159,[2_1|2]), (120,254,[2_1|2]), (120,327,[2_1|2]), (120,510,[2_1|2]), (120,525,[2_1|2]), (120,563,[2_1|2]), (120,582,[2_1|2]), (120,594,[2_1|2]), (120,601,[2_1|2]), (120,612,[2_1|2]), (120,646,[2_1|2]), (120,667,[2_1|2]), (120,533,[2_1|2]), (120,639,[2_1|2]), (121,122,[1_1|2]), (122,123,[5_1|2]), (123,124,[4_1|2]), (124,125,[4_1|2]), (125,126,[4_1|2]), (126,127,[1_1|2]), (127,128,[0_1|2]), (128,129,[0_1|2]), (129,130,[3_1|2]), (129,498,[3_1|2]), (129,504,[5_1|2]), (129,510,[2_1|2]), (129,517,[3_1|2]), (129,525,[2_1|2]), (129,532,[4_1|2]), (130,90,[5_1|2]), (130,284,[5_1|2]), (130,305,[5_1|2]), (130,374,[5_1|2]), (130,504,[5_1|2]), (130,576,[5_1|2]), (130,619,[5_1|2]), (130,541,[4_1|2]), (130,544,[0_1|2]), (130,551,[0_1|2]), (130,559,[0_1|2]), (130,563,[2_1|2]), (130,572,[4_1|2]), (130,582,[2_1|2]), (130,586,[0_1|2]), (130,594,[2_1|2]), (130,601,[2_1|2]), (130,605,[0_1|2]), (130,612,[2_1|2]), (130,628,[0_1|2]), (130,638,[4_1|2]), (130,646,[2_1|2]), (130,654,[0_1|2]), (130,659,[0_1|2]), (130,667,[2_1|2]), (130,674,[0_1|2]), (130,682,[3_1|2]), (130,691,[0_1|2]), (130,707,[4_1|3]), (131,132,[3_1|2]), (132,133,[4_1|2]), (133,90,[1_1|2]), (133,247,[1_1|2]), (133,343,[1_1|2]), (133,346,[1_1|2]), (133,351,[1_1|2]), (133,357,[1_1|2]), (133,361,[1_1|2]), (133,368,[1_1|2]), (133,383,[1_1|2]), (133,386,[1_1|2]), (133,394,[1_1|2]), (133,413,[1_1|2]), (133,428,[1_1|2]), (133,433,[1_1|2]), (133,463,[1_1|2]), (133,473,[1_1|2]), (133,479,[1_1|2]), (133,488,[1_1|2]), (133,498,[1_1|2]), (133,517,[1_1|2]), (133,682,[1_1|2]), (134,135,[3_1|2]), (135,136,[4_1|2]), (136,137,[3_1|2]), (137,138,[4_1|2]), (138,139,[1_1|2]), (139,90,[2_1|2]), (139,149,[2_1|2]), (139,242,[2_1|2]), (139,313,[2_1|2]), (139,532,[2_1|2]), (139,541,[2_1|2]), (139,572,[2_1|2]), (139,638,[2_1|2]), (139,347,[2_1|2]), (139,352,[2_1|2]), (139,480,[2_1|2]), (139,489,[2_1|2]), (140,141,[5_1|2]), (141,142,[1_1|2]), (142,143,[0_1|2]), 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(739,578,[1_1|3]), (740,741,[4_1|3]), (741,742,[1_1|3]), (742,743,[4_1|3]), (743,744,[4_1|3]), (744,289,[1_1|3]), (744,400,[1_1|3]), (744,448,[1_1|3]), (744,122,[1_1|3]), (744,255,[1_1|3]), (744,328,[1_1|3]), (744,511,[1_1|3]), (744,526,[1_1|3]), (744,564,[1_1|3]), (744,668,[1_1|3]), (744,578,[1_1|3]), (745,746,[4_1|3]), (746,747,[4_1|3]), (747,748,[1_1|3]), (748,749,[2_1|3]), (749,750,[4_1|3]), (750,289,[1_1|3]), (750,400,[1_1|3]), (750,448,[1_1|3]), (750,122,[1_1|3]), (750,255,[1_1|3]), (750,328,[1_1|3]), (750,511,[1_1|3]), (750,526,[1_1|3]), (750,564,[1_1|3]), (750,668,[1_1|3]), (750,578,[1_1|3]), (751,752,[0_1|3]), (752,753,[2_1|3]), (753,289,[1_1|3]), (753,400,[1_1|3]), (753,448,[1_1|3]), (753,344,[1_1|3]), (753,358,[1_1|3]), (754,755,[4_1|3]), (755,756,[4_1|3]), (756,757,[4_1|3]), (757,758,[0_1|3]), (758,149,[3_1|3]), (758,242,[3_1|3]), (758,313,[3_1|3]), (758,532,[3_1|3]), (758,541,[3_1|3]), (758,572,[3_1|3]), (758,638,[3_1|3]), (758,347,[3_1|3]), (758,352,[3_1|3]), (758,480,[3_1|3]), (758,489,[3_1|3]), (759,760,[0_1|3]), (760,761,[2_1|3]), (761,151,[1_1|3]), (762,763,[1_1|3]), (763,764,[2_1|3]), (764,765,[1_1|3]), (765,123,[5_1|3]), (765,527,[5_1|3]), (765,669,[5_1|3]), (766,767,[0_1|3]), (767,768,[2_1|3]), (768,286,[1_1|3]), (769,770,[0_1|3]), (770,771,[0_1|3]), (771,772,[2_1|3]), (772,102,[1_1|3]), (773,774,[0_1|3]), (774,775,[2_1|3]), (775,102,[1_1|3]), (776,777,[5_1|3]), (777,778,[4_1|3]), (778,779,[1_1|3]), (779,780,[2_1|3]), (780,289,[1_1|3]), (780,400,[1_1|3]), (780,448,[1_1|3]), (780,344,[1_1|3]), (780,358,[1_1|3]), (781,782,[3_1|3]), (782,783,[2_1|3]), (783,784,[4_1|3]), (784,138,[4_1|3])}"
----------------------------------------

(8)
BOUNDS(1, n^1)