/export/starexec/sandbox/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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


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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 50 ms]
(4) CpxRelTRS
(5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(6) CpxTRS
(7) CpxTrsMatchBoundsProof [FINISHED, 521 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.

"[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, 785, 786]
{(59,60,[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]), (59,61,[2_1|1]), (59,66,[0_1|1]), (59,71,[3_1|1]), (59,74,[3_1|1]), (59,79,[3_1|1]), (59,85,[3_1|1]), (59,92,[1_1|1, 2_1|1, 4_1|1, 0_1|1, 3_1|1, 5_1|1]), (59,93,[0_1|2]), (59,96,[0_1|2]), (59,101,[0_1|2]), (59,108,[0_1|2]), (59,112,[0_1|2]), (59,116,[0_1|2]), (59,123,[2_1|2]), (59,133,[0_1|2]), (59,136,[0_1|2]), (59,142,[0_1|2]), (59,151,[4_1|2]), (59,161,[2_1|2]), (59,166,[0_1|2]), (59,176,[0_1|2]), (59,181,[0_1|2]), (59,187,[0_1|2]), (59,192,[0_1|2]), (59,197,[0_1|2]), (59,203,[0_1|2]), (59,211,[0_1|2]), (59,215,[0_1|2]), (59,225,[0_1|2]), (59,229,[0_1|2]), (59,235,[0_1|2]), (59,244,[4_1|2]), (59,249,[3_1|2]), (59,256,[2_1|2]), (59,265,[0_1|2]), (59,273,[0_1|2]), (59,280,[0_1|2]), (59,286,[5_1|2]), (59,291,[1_1|2]), (59,298,[0_1|2]), (59,307,[5_1|2]), (59,315,[4_1|2]), (59,324,[0_1|2]), (59,329,[2_1|2]), (59,336,[0_1|2]), (59,345,[3_1|2]), (59,348,[3_1|2]), (59,353,[3_1|2]), (59,359,[3_1|2]), (59,363,[3_1|2]), (59,370,[3_1|2]), (59,376,[5_1|2]), (59,385,[3_1|2]), (59,388,[3_1|2]), (59,396,[3_1|2]), (59,402,[1_1|2]), (59,411,[0_1|2]), (59,415,[3_1|2]), (59,420,[0_1|2]), (59,430,[3_1|2]), (59,435,[3_1|2]), (59,441,[0_1|2]), (59,450,[1_1|2]), (59,456,[0_1|2]), (59,465,[3_1|2]), (59,475,[3_1|2]), (59,481,[3_1|2]), (59,490,[3_1|2]), (59,500,[3_1|2]), (59,506,[5_1|2]), (59,512,[2_1|2]), (59,519,[3_1|2]), (59,527,[2_1|2]), (59,534,[4_1|2]), (59,543,[4_1|2]), (59,546,[0_1|2]), (59,553,[0_1|2]), (59,561,[0_1|2]), (59,565,[2_1|2]), (59,574,[4_1|2]), (59,578,[5_1|2]), (59,584,[2_1|2]), (59,588,[0_1|2]), (59,596,[2_1|2]), (59,603,[2_1|2]), (59,607,[0_1|2]), (59,614,[2_1|2]), (59,621,[5_1|2]), (59,630,[0_1|2]), (59,640,[4_1|2]), (59,648,[2_1|2]), (59,656,[0_1|2]), (59,661,[0_1|2]), (59,669,[2_1|2]), (59,676,[0_1|2]), (59,684,[3_1|2]), (59,693,[0_1|2]), (60,60,[1_1|0, 2_1|0, 4_1|0, cons_0_1|0, cons_3_1|0, cons_5_1|0]), (61,62,[4_1|1]), (62,63,[0_1|1]), (63,64,[1_1|1]), (64,65,[2_1|1]), (65,60,[1_1|1]), (66,67,[5_1|1]), (67,68,[4_1|1]), (68,69,[1_1|1]), (69,70,[2_1|1]), (70,60,[1_1|1]), (71,72,[1_1|1]), (72,73,[4_1|1]), (73,60,[1_1|1]), (74,75,[4_1|1]), (75,76,[1_1|1]), (76,77,[4_1|1]), (77,78,[4_1|1]), (78,60,[1_1|1]), (79,80,[4_1|1]), (80,81,[4_1|1]), (81,82,[1_1|1]), (82,83,[2_1|1]), (83,84,[4_1|1]), (84,60,[1_1|1]), (85,86,[2_1|1]), (86,87,[1_1|1]), (87,88,[4_1|1]), (88,89,[1_1|1]), (89,90,[2_1|1]), (90,91,[1_1|1]), (91,60,[2_1|1]), (92,60,[encArg_1|1]), (92,92,[1_1|1, 2_1|1, 4_1|1, 0_1|1, 3_1|1, 5_1|1]), (92,93,[0_1|2]), (92,96,[0_1|2]), (92,101,[0_1|2]), (92,108,[0_1|2]), (92,112,[0_1|2]), (92,116,[0_1|2]), (92,123,[2_1|2]), (92,133,[0_1|2]), (92,136,[0_1|2]), (92,142,[0_1|2]), (92,151,[4_1|2]), (92,161,[2_1|2]), (92,166,[0_1|2]), (92,176,[0_1|2]), (92,181,[0_1|2]), (92,187,[0_1|2]), (92,192,[0_1|2]), (92,197,[0_1|2]), (92,203,[0_1|2]), (92,211,[0_1|2]), (92,215,[0_1|2]), (92,225,[0_1|2]), (92,229,[0_1|2]), (92,235,[0_1|2]), (92,244,[4_1|2]), (92,249,[3_1|2]), (92,256,[2_1|2]), (92,265,[0_1|2]), (92,273,[0_1|2]), (92,280,[0_1|2]), (92,286,[5_1|2]), (92,291,[1_1|2]), (92,298,[0_1|2]), (92,307,[5_1|2]), (92,315,[4_1|2]), (92,324,[0_1|2]), (92,329,[2_1|2]), (92,336,[0_1|2]), (92,345,[3_1|2]), (92,348,[3_1|2]), (92,353,[3_1|2]), (92,359,[3_1|2]), (92,363,[3_1|2]), (92,370,[3_1|2]), (92,376,[5_1|2]), (92,385,[3_1|2]), (92,388,[3_1|2]), (92,396,[3_1|2]), (92,402,[1_1|2]), (92,411,[0_1|2]), (92,415,[3_1|2]), (92,420,[0_1|2]), (92,430,[3_1|2]), (92,435,[3_1|2]), (92,441,[0_1|2]), (92,450,[1_1|2]), (92,456,[0_1|2]), (92,465,[3_1|2]), (92,475,[3_1|2]), (92,481,[3_1|2]), (92,490,[3_1|2]), (92,500,[3_1|2]), (92,506,[5_1|2]), (92,512,[2_1|2]), (92,519,[3_1|2]), (92,527,[2_1|2]), (92,534,[4_1|2]), (92,543,[4_1|2]), (92,546,[0_1|2]), (92,553,[0_1|2]), (92,561,[0_1|2]), (92,565,[2_1|2]), (92,574,[4_1|2]), (92,578,[5_1|2]), (92,584,[2_1|2]), (92,588,[0_1|2]), (92,596,[2_1|2]), (92,603,[2_1|2]), (92,607,[0_1|2]), (92,614,[2_1|2]), (92,621,[5_1|2]), (92,630,[0_1|2]), (92,640,[4_1|2]), (92,648,[2_1|2]), (92,656,[0_1|2]), (92,661,[0_1|2]), (92,669,[2_1|2]), (92,676,[0_1|2]), (92,684,[3_1|2]), (92,693,[0_1|2]), (93,94,[0_1|2]), (94,95,[2_1|2]), (95,92,[1_1|2]), (95,291,[1_1|2]), (95,402,[1_1|2]), (95,450,[1_1|2]), (96,97,[0_1|2]), (97,98,[5_1|2]), (98,99,[1_1|2]), (99,100,[2_1|2]), (100,92,[4_1|2]), (100,286,[4_1|2]), (100,307,[4_1|2]), (100,376,[4_1|2]), (100,506,[4_1|2]), (100,578,[4_1|2]), (100,621,[4_1|2]), (101,102,[3_1|2]), (102,103,[0_1|2]), (102,703,[0_1|3]), (103,104,[1_1|2]), (104,105,[3_1|2]), (105,106,[3_1|2]), (106,107,[4_1|2]), (107,92,[1_1|2]), (107,249,[1_1|2]), (107,345,[1_1|2]), (107,348,[1_1|2]), (107,353,[1_1|2]), (107,359,[1_1|2]), (107,363,[1_1|2]), (107,370,[1_1|2]), (107,385,[1_1|2]), (107,388,[1_1|2]), (107,396,[1_1|2]), (107,415,[1_1|2]), (107,430,[1_1|2]), (107,435,[1_1|2]), (107,465,[1_1|2]), (107,475,[1_1|2]), (107,481,[1_1|2]), (107,490,[1_1|2]), (107,500,[1_1|2]), (107,519,[1_1|2]), (107,684,[1_1|2]), (108,109,[0_1|2]), (109,110,[0_1|2]), (110,111,[2_1|2]), (111,92,[1_1|2]), (111,291,[1_1|2]), (111,402,[1_1|2]), (111,450,[1_1|2]), (112,113,[0_1|2]), (113,114,[5_1|2]), (114,115,[4_1|2]), (115,92,[3_1|2]), (115,249,[3_1|2]), (115,345,[3_1|2]), (115,348,[3_1|2]), (115,353,[3_1|2]), (115,359,[3_1|2]), (115,363,[3_1|2]), (115,370,[3_1|2]), (115,385,[3_1|2]), (115,388,[3_1|2]), (115,396,[3_1|2]), (115,415,[3_1|2]), (115,430,[3_1|2]), (115,435,[3_1|2]), (115,465,[3_1|2]), (115,475,[3_1|2]), (115,481,[3_1|2]), (115,490,[3_1|2]), (115,500,[3_1|2]), (115,519,[3_1|2]), (115,684,[3_1|2]), (115,609,[3_1|2]), (115,632,[3_1|2]), (115,376,[5_1|2]), (115,402,[1_1|2]), (115,411,[0_1|2]), (115,420,[0_1|2]), (115,441,[0_1|2]), (115,450,[1_1|2]), (115,456,[0_1|2]), (115,506,[5_1|2]), (115,512,[2_1|2]), (115,527,[2_1|2]), (115,534,[4_1|2]), (115,706,[3_1|3]), (116,117,[2_1|2]), (117,118,[1_1|2]), (118,119,[0_1|2]), (119,120,[5_1|2]), (120,121,[4_1|2]), (121,122,[2_1|2]), (122,92,[2_1|2]), (122,123,[2_1|2]), (122,161,[2_1|2]), (122,256,[2_1|2]), (122,329,[2_1|2]), (122,512,[2_1|2]), (122,527,[2_1|2]), (122,565,[2_1|2]), (122,584,[2_1|2]), (122,596,[2_1|2]), (122,603,[2_1|2]), (122,614,[2_1|2]), (122,648,[2_1|2]), (122,669,[2_1|2]), (122,535,[2_1|2]), (122,641,[2_1|2]), (123,124,[1_1|2]), (124,125,[5_1|2]), (125,126,[4_1|2]), (126,127,[4_1|2]), (127,128,[4_1|2]), (128,129,[1_1|2]), (129,130,[0_1|2]), (130,131,[0_1|2]), (131,132,[3_1|2]), (131,500,[3_1|2]), (131,506,[5_1|2]), (131,512,[2_1|2]), (131,519,[3_1|2]), (131,527,[2_1|2]), (131,534,[4_1|2]), (132,92,[5_1|2]), (132,286,[5_1|2]), (132,307,[5_1|2]), (132,376,[5_1|2]), (132,506,[5_1|2]), (132,578,[5_1|2]), (132,621,[5_1|2]), (132,543,[4_1|2]), (132,546,[0_1|2]), (132,553,[0_1|2]), (132,561,[0_1|2]), (132,565,[2_1|2]), (132,574,[4_1|2]), (132,584,[2_1|2]), (132,588,[0_1|2]), (132,596,[2_1|2]), (132,603,[2_1|2]), (132,607,[0_1|2]), (132,614,[2_1|2]), (132,630,[0_1|2]), (132,640,[4_1|2]), (132,648,[2_1|2]), (132,656,[0_1|2]), (132,661,[0_1|2]), (132,669,[2_1|2]), (132,676,[0_1|2]), (132,684,[3_1|2]), (132,693,[0_1|2]), (132,709,[4_1|3]), (133,134,[3_1|2]), (134,135,[4_1|2]), (135,92,[1_1|2]), (135,249,[1_1|2]), (135,345,[1_1|2]), (135,348,[1_1|2]), (135,353,[1_1|2]), (135,359,[1_1|2]), (135,363,[1_1|2]), (135,370,[1_1|2]), (135,385,[1_1|2]), (135,388,[1_1|2]), (135,396,[1_1|2]), (135,415,[1_1|2]), (135,430,[1_1|2]), (135,435,[1_1|2]), (135,465,[1_1|2]), (135,475,[1_1|2]), (135,481,[1_1|2]), (135,490,[1_1|2]), (135,500,[1_1|2]), (135,519,[1_1|2]), (135,684,[1_1|2]), (136,137,[3_1|2]), (137,138,[4_1|2]), (138,139,[3_1|2]), (139,140,[4_1|2]), (140,141,[1_1|2]), (141,92,[2_1|2]), (141,151,[2_1|2]), (141,244,[2_1|2]), (141,315,[2_1|2]), (141,534,[2_1|2]), (141,543,[2_1|2]), (141,574,[2_1|2]), (141,640,[2_1|2]), (141,349,[2_1|2]), (141,354,[2_1|2]), (141,482,[2_1|2]), (141,491,[2_1|2]), (142,143,[5_1|2]), (143,144,[1_1|2]), (144,145,[0_1|2]), 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(718,719,[5_1|3]), (719,720,[4_1|3]), (720,721,[2_1|3]), (721,722,[4_1|3]), (722,723,[4_1|3]), (723,125,[2_1|3]), (723,529,[2_1|3]), (723,671,[2_1|3]), (724,725,[2_1|3]), (725,726,[1_1|3]), (726,291,[3_1|3]), (726,402,[3_1|3]), (726,450,[3_1|3]), (726,316,[3_1|3]), (726,346,[3_1|3]), (726,360,[3_1|3]), (727,728,[0_1|3]), (728,729,[5_1|3]), (729,238,[4_1|3]), (730,731,[0_1|3]), (731,732,[5_1|3]), (732,151,[4_1|3]), (732,244,[4_1|3]), (732,315,[4_1|3]), (732,534,[4_1|3]), (732,543,[4_1|3]), (732,574,[4_1|3]), (732,640,[4_1|3]), (732,349,[4_1|3]), (732,354,[4_1|3]), (732,482,[4_1|3]), (732,491,[4_1|3]), (732,198,[4_1|3]), (732,727,[4_1|3]), (733,734,[0_1|3]), (734,735,[3_1|3]), (735,736,[2_1|3]), (736,737,[1_1|3]), (737,738,[5_1|3]), (738,214,[4_1|3]), (739,740,[1_1|3]), (740,741,[4_1|3]), (741,291,[1_1|3]), (741,402,[1_1|3]), (741,450,[1_1|3]), (741,124,[1_1|3]), (741,257,[1_1|3]), (741,330,[1_1|3]), (741,513,[1_1|3]), (741,528,[1_1|3]), (741,566,[1_1|3]), (741,670,[1_1|3]), (741,580,[1_1|3]), (742,743,[4_1|3]), (743,744,[1_1|3]), (744,745,[4_1|3]), (745,746,[4_1|3]), (746,291,[1_1|3]), (746,402,[1_1|3]), (746,450,[1_1|3]), (746,124,[1_1|3]), (746,257,[1_1|3]), (746,330,[1_1|3]), (746,513,[1_1|3]), (746,528,[1_1|3]), (746,566,[1_1|3]), (746,670,[1_1|3]), (746,580,[1_1|3]), (747,748,[4_1|3]), (748,749,[4_1|3]), (749,750,[1_1|3]), (750,751,[2_1|3]), (751,752,[4_1|3]), (752,291,[1_1|3]), (752,402,[1_1|3]), (752,450,[1_1|3]), (752,124,[1_1|3]), (752,257,[1_1|3]), (752,330,[1_1|3]), (752,513,[1_1|3]), (752,528,[1_1|3]), (752,566,[1_1|3]), (752,670,[1_1|3]), (752,580,[1_1|3]), (753,754,[0_1|3]), (754,755,[2_1|3]), (755,291,[1_1|3]), (755,402,[1_1|3]), (755,450,[1_1|3]), (755,346,[1_1|3]), (755,360,[1_1|3]), (756,757,[4_1|3]), (757,758,[4_1|3]), (758,759,[4_1|3]), (759,760,[0_1|3]), (760,151,[3_1|3]), (760,244,[3_1|3]), (760,315,[3_1|3]), (760,534,[3_1|3]), (760,543,[3_1|3]), (760,574,[3_1|3]), (760,640,[3_1|3]), (760,349,[3_1|3]), (760,354,[3_1|3]), (760,482,[3_1|3]), (760,491,[3_1|3]), (761,762,[0_1|3]), (762,763,[2_1|3]), (763,153,[1_1|3]), (764,765,[1_1|3]), (765,766,[2_1|3]), (766,767,[1_1|3]), (767,125,[5_1|3]), (767,529,[5_1|3]), (767,671,[5_1|3]), (768,769,[0_1|3]), (769,770,[2_1|3]), (770,288,[1_1|3]), (771,772,[0_1|3]), (772,773,[0_1|3]), (773,774,[2_1|3]), (774,104,[1_1|3]), (775,776,[0_1|3]), (776,777,[2_1|3]), (777,104,[1_1|3]), (778,779,[5_1|3]), (779,780,[4_1|3]), (780,781,[1_1|3]), (781,782,[2_1|3]), (782,291,[1_1|3]), (782,402,[1_1|3]), (782,450,[1_1|3]), (782,346,[1_1|3]), (782,360,[1_1|3]), (783,784,[3_1|3]), (784,785,[2_1|3]), (785,786,[4_1|3]), (786,140,[4_1|3])}"
----------------------------------------

(8)
BOUNDS(1, n^1)