/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 (innermost) 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), 42 ms]
(4) CpxRelTRS
(5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(6) CpxTRS
(7) CpxTrsMatchBoundsProof [FINISHED, 657 ms]
(8) BOUNDS(1, n^1)


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

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


The TRS R consists of the following rules:

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

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

(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(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_1(x_1)) -> 1(encArg(x_1))
   encArg(cons_2(x_1)) -> 2(encArg(x_1))
   encArg(cons_3(x_1)) -> 3(encArg(x_1))
   encArg(cons_4(x_1)) -> 4(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_3(x_1) -> 3(encArg(x_1))
   encode_5(x_1) -> 5(encArg(x_1))
   encode_2(x_1) -> 2(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))
   encode_4(x_1) -> 4(encArg(x_1))


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

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


The TRS R consists of the following rules:

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

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

   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_1(x_1)) -> 1(encArg(x_1))
   encArg(cons_2(x_1)) -> 2(encArg(x_1))
   encArg(cons_3(x_1)) -> 3(encArg(x_1))
   encArg(cons_4(x_1)) -> 4(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_3(x_1) -> 3(encArg(x_1))
   encode_5(x_1) -> 5(encArg(x_1))
   encode_2(x_1) -> 2(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))
   encode_4(x_1) -> 4(encArg(x_1))

Rewrite Strategy: INNERMOST
----------------------------------------

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

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


The TRS R consists of the following rules:

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

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

   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_1(x_1)) -> 1(encArg(x_1))
   encArg(cons_2(x_1)) -> 2(encArg(x_1))
   encArg(cons_3(x_1)) -> 3(encArg(x_1))
   encArg(cons_4(x_1)) -> 4(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_3(x_1) -> 3(encArg(x_1))
   encode_5(x_1) -> 5(encArg(x_1))
   encode_2(x_1) -> 2(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))
   encode_4(x_1) -> 4(encArg(x_1))

Rewrite Strategy: INNERMOST
----------------------------------------

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

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


The TRS R consists of the following rules:

   0(0(0(0(0(0(3(5(3(0(0(2(x1)))))))))))) -> 1(4(4(1(4(4(0(1(1(3(3(1(4(4(1(1(0(x1)))))))))))))))))
   0(0(2(3(1(5(5(0(5(2(4(1(x1)))))))))))) -> 3(4(1(4(4(4(4(1(0(0(4(5(4(4(3(0(4(3(x1))))))))))))))))))
   0(0(3(0(5(5(0(0(3(3(0(5(x1)))))))))))) -> 0(1(0(5(4(2(3(3(5(4(5(4(4(0(x1))))))))))))))
   0(0(3(2(0(3(4(2(2(3(0(5(x1)))))))))))) -> 4(1(5(5(0(0(1(4(4(4(1(1(3(0(x1))))))))))))))
   0(0(3(4(2(3(0(0(5(5(2(3(x1)))))))))))) -> 4(4(2(4(0(1(1(0(4(0(2(0(5(5(4(x1)))))))))))))))
   0(1(5(3(0(5(3(2(5(5(1(1(x1)))))))))))) -> 3(4(0(1(4(4(4(2(4(1(4(2(3(0(1(5(1(x1)))))))))))))))))
   0(2(0(3(5(0(5(5(3(1(3(5(x1)))))))))))) -> 4(3(1(4(3(0(4(3(4(4(1(0(4(2(x1))))))))))))))
   0(2(1(0(0(1(3(2(0(2(1(5(x1)))))))))))) -> 2(2(4(3(3(4(5(4(4(0(0(1(4(4(x1))))))))))))))
   0(3(0(0(1(5(5(2(4(5(5(5(x1)))))))))))) -> 1(4(2(4(5(0(4(4(4(4(2(4(0(1(4(4(3(x1)))))))))))))))))
   0(3(2(0(3(2(0(3(5(2(4(1(x1)))))))))))) -> 0(3(4(1(1(3(3(4(4(4(4(0(1(1(1(3(4(4(x1))))))))))))))))))
   0(3(2(5(3(4(0(0(5(5(3(4(x1)))))))))))) -> 4(4(1(2(4(4(0(4(2(0(4(5(4(5(2(4(4(x1)))))))))))))))))
   0(5(0(1(2(5(1(1(2(1(4(2(x1)))))))))))) -> 3(4(4(1(3(0(4(3(3(1(0(1(3(4(4(x1)))))))))))))))
   0(5(1(0(5(0(5(3(4(0(5(5(x1)))))))))))) -> 4(1(2(2(4(5(1(3(4(1(0(4(4(2(0(x1)))))))))))))))
   0(5(2(1(2(5(0(5(5(3(2(1(x1)))))))))))) -> 2(1(4(5(4(2(3(4(0(2(1(4(4(0(x1))))))))))))))
   1(0(3(5(1(5(1(2(3(0(3(1(x1)))))))))))) -> 1(4(1(1(1(1(4(3(1(1(0(1(3(4(3(4(4(x1)))))))))))))))))
   1(0(5(1(1(5(3(5(2(3(5(3(x1)))))))))))) -> 0(0(4(5(1(2(4(2(4(5(1(4(1(1(x1))))))))))))))
   1(0(5(1(3(3(5(5(0(0(2(3(x1)))))))))))) -> 1(0(3(5(3(4(4(4(4(1(4(1(2(4(0(x1)))))))))))))))
   1(1(0(5(0(5(2(4(2(3(5(2(x1)))))))))))) -> 1(1(3(4(4(4(4(4(4(5(4(3(1(4(3(1(4(3(x1))))))))))))))))))
   1(1(2(1(3(0(3(2(5(3(3(5(x1)))))))))))) -> 3(3(5(3(4(4(5(1(4(4(4(1(3(4(4(1(4(3(x1))))))))))))))))))
   1(1(2(1(3(5(4(4(0(0(3(2(x1)))))))))))) -> 4(0(1(1(0(4(3(4(3(1(0(0(4(5(x1))))))))))))))
   1(1(2(3(3(4(0(5(0(0(0(1(x1)))))))))))) -> 2(2(4(4(5(2(1(1(3(4(3(4(4(1(3(x1)))))))))))))))
   1(2(0(0(5(5(0(5(0(0(0(3(x1)))))))))))) -> 0(2(3(0(4(4(4(0(1(3(3(5(3(3(3(1(4(x1)))))))))))))))))
   1(2(0(5(0(4(1(1(2(5(1(1(x1)))))))))))) -> 2(2(4(3(3(0(3(4(0(1(5(4(4(4(4(x1)))))))))))))))
   1(2(0(5(4(1(5(5(1(3(5(2(x1)))))))))))) -> 0(4(1(3(4(4(1(4(4(0(4(4(3(2(4(4(5(x1)))))))))))))))))
   1(2(0(5(5(5(5(3(2(3(2(1(x1)))))))))))) -> 5(1(5(5(0(4(0(0(4(1(4(4(4(1(1(3(3(3(x1))))))))))))))))))
   1(2(1(3(5(2(2(2(2(1(3(4(x1)))))))))))) -> 4(4(1(0(5(4(3(1(5(5(4(0(4(4(x1))))))))))))))
   1(2(3(2(0(5(5(2(0(0(1(2(x1)))))))))))) -> 5(1(4(1(4(2(2(2(1(4(0(4(4(5(x1))))))))))))))
   1(2(3(5(2(0(0(1(2(0(2(2(x1)))))))))))) -> 2(1(4(4(1(4(4(1(1(2(0(3(3(0(0(4(1(4(x1))))))))))))))))))
   1(5(0(2(4(3(2(5(5(3(1(3(x1)))))))))))) -> 4(3(2(0(2(2(2(4(1(4(4(1(2(3(x1))))))))))))))
   1(5(2(1(1(5(4(0(0(2(2(2(x1)))))))))))) -> 1(2(4(1(1(4(1(1(3(4(5(1(4(1(x1))))))))))))))
   1(5(2(3(2(0(5(2(2(5(1(3(x1)))))))))))) -> 0(1(4(1(1(5(1(3(5(4(0(3(1(4(2(x1)))))))))))))))
   1(5(2(5(5(5(3(5(0(2(3(0(x1)))))))))))) -> 1(3(3(4(3(1(4(3(0(1(0(2(2(4(4(0(1(x1)))))))))))))))))
   1(5(3(5(5(5(2(2(3(5(5(3(x1)))))))))))) -> 4(4(5(3(3(0(2(4(3(3(4(2(2(4(0(1(x1))))))))))))))))
   1(5(4(0(5(2(5(4(3(5(2(1(x1)))))))))))) -> 4(1(4(3(1(4(4(4(0(5(3(3(4(4(2(1(x1))))))))))))))))
   1(5(4(3(2(3(4(0(0(3(1(3(x1)))))))))))) -> 1(4(3(2(4(2(4(4(5(3(3(5(1(0(x1))))))))))))))
   1(5(5(5(0(4(3(4(3(2(5(3(x1)))))))))))) -> 4(4(3(4(5(3(1(0(4(2(0(0(4(0(1(4(x1))))))))))))))))
   2(0(3(0(5(0(5(0(5(3(2(2(x1)))))))))))) -> 4(5(4(5(4(4(4(2(4(3(1(0(2(3(4(3(x1))))))))))))))))
   2(1(2(5(2(5(0(5(1(2(0(1(x1)))))))))))) -> 2(4(1(4(1(4(1(1(1(4(4(4(4(1(4(0(3(2(x1))))))))))))))))))
   2(1(5(2(0(5(0(3(4(5(2(5(x1)))))))))))) -> 1(3(2(1(2(5(4(4(3(0(4(4(4(4(4(1(1(x1)))))))))))))))))
   2(1(5(5(5(2(1(5(1(4(4(1(x1)))))))))))) -> 4(3(0(4(1(0(4(0(4(4(1(2(5(4(4(x1)))))))))))))))
   2(2(5(5(3(0(1(2(3(0(2(5(x1)))))))))))) -> 2(0(1(4(4(5(0(1(3(0(2(2(4(3(x1))))))))))))))
   2(3(2(5(1(0(0(4(3(3(5(3(x1)))))))))))) -> 4(1(1(4(1(4(4(4(0(4(4(3(4(3(4(1(4(3(x1))))))))))))))))))
   2(3(2(5(1(0(3(5(0(5(2(3(x1)))))))))))) -> 2(1(3(3(2(4(2(4(0(4(4(1(2(4(4(0(x1))))))))))))))))
   2(3(5(5(4(0(2(0(0(0(2(0(x1)))))))))))) -> 4(3(1(3(4(1(5(4(4(0(1(4(5(4(4(2(x1))))))))))))))))
   2(5(0(5(1(2(2(3(3(2(0(3(x1)))))))))))) -> 2(4(1(3(2(0(1(5(4(4(5(3(0(4(4(4(x1))))))))))))))))
   2(5(1(2(5(4(4(3(0(0(5(5(x1)))))))))))) -> 4(4(4(2(4(5(5(4(1(2(1(4(0(3(4(x1)))))))))))))))
   2(5(2(2(0(0(0(1(1(3(2(2(x1)))))))))))) -> 0(4(5(4(2(4(4(4(4(4(4(3(1(4(1(1(4(2(x1))))))))))))))))))
   3(0(2(5(3(1(2(5(0(2(3(1(x1)))))))))))) -> 3(4(4(4(1(5(0(1(4(1(5(0(1(4(5(4(x1))))))))))))))))
   3(0(3(5(5(2(1(4(0(1(3(5(x1)))))))))))) -> 1(4(4(1(3(2(4(4(1(0(0(1(5(3(x1))))))))))))))
   3(1(3(3(0(5(5(1(3(0(1(3(x1)))))))))))) -> 1(5(3(2(4(4(4(4(0(2(2(1(4(4(x1))))))))))))))
   3(2(0(0(5(0(5(5(5(3(5(2(x1)))))))))))) -> 4(0(1(4(2(4(4(0(5(0(4(4(3(1(0(1(0(0(x1))))))))))))))))))
   3(2(0(2(1(0(5(0(0(0(1(2(x1)))))))))))) -> 4(5(4(4(1(3(1(5(4(2(4(0(1(4(4(1(x1))))))))))))))))
   3(2(2(1(3(5(5(5(5(3(3(1(x1)))))))))))) -> 1(1(1(3(4(1(2(4(5(2(2(0(4(1(x1))))))))))))))
   3(2(2(5(2(5(5(1(5(5(1(5(x1)))))))))))) -> 4(4(5(3(3(3(5(3(1(4(4(1(4(3(1(1(0(1(x1))))))))))))))))))
   3(2(5(2(2(1(2(5(5(5(0(0(x1)))))))))))) -> 1(3(0(2(0(5(1(4(4(1(3(1(4(5(4(0(4(x1)))))))))))))))))
   3(3(2(1(5(2(0(4(5(1(0(5(x1)))))))))))) -> 3(1(4(3(4(1(0(5(0(4(0(4(3(1(4(4(x1))))))))))))))))
   3(3(5(1(1(5(0(3(5(1(1(1(x1)))))))))))) -> 4(4(3(3(1(4(4(1(1(3(4(4(1(0(1(5(4(4(x1))))))))))))))))))
   3(3(5(2(0(2(3(1(1(1(0(5(x1)))))))))))) -> 1(1(4(0(1(2(4(5(4(0(1(4(1(3(4(4(x1))))))))))))))))
   3(3(5(3(3(0(1(2(2(1(1(5(x1)))))))))))) -> 4(2(3(4(1(1(3(1(5(2(4(4(1(1(1(x1)))))))))))))))
   3(3(5(4(3(5(0(0(3(5(2(1(x1)))))))))))) -> 0(2(4(4(0(4(4(4(5(2(1(1(3(3(5(1(4(x1)))))))))))))))))
   3(4(0(3(0(3(5(0(2(3(2(1(x1)))))))))))) -> 3(1(3(4(1(4(4(4(4(0(1(1(3(2(0(x1)))))))))))))))
   3(5(0(2(5(3(3(2(0(2(2(4(x1)))))))))))) -> 4(3(3(3(1(3(4(1(3(4(4(4(5(4(1(3(1(4(x1))))))))))))))))))
   3(5(1(0(3(5(2(1(1(3(5(0(x1)))))))))))) -> 1(1(1(5(4(4(4(3(4(0(5(1(4(4(0(0(x1))))))))))))))))
   3(5(5(0(0(5(2(2(2(5(5(4(x1)))))))))))) -> 4(3(4(2(4(1(4(4(3(3(2(2(4(3(4(3(x1))))))))))))))))
   3(5(5(2(3(0(0(1(3(2(5(3(x1)))))))))))) -> 0(1(4(0(0(1(1(3(3(1(1(0(0(2(4(x1)))))))))))))))
   3(5(5(5(2(0(1(2(2(4(2(3(x1)))))))))))) -> 0(2(0(4(4(1(0(4(5(4(1(4(4(4(4(1(4(2(x1))))))))))))))))))
   4(0(5(0(5(4(3(5(2(2(5(0(x1)))))))))))) -> 0(4(5(2(4(4(0(4(2(0(4(4(5(1(0(x1)))))))))))))))
   4(1(2(0(0(0(0(0(1(5(3(1(x1)))))))))))) -> 4(1(4(4(2(5(1(4(3(1(1(5(5(3(x1))))))))))))))
   4(3(0(0(1(5(3(2(1(0(1(0(x1)))))))))))) -> 0(1(2(4(5(4(4(4(2(4(3(0(1(4(x1))))))))))))))
   4(3(0(3(3(0(2(3(0(5(1(3(x1)))))))))))) -> 0(1(2(2(3(4(5(4(4(3(3(4(4(1(x1))))))))))))))
   4(3(5(2(2(1(2(0(2(5(0(0(x1)))))))))))) -> 1(4(4(3(5(5(0(4(4(4(4(3(4(0(x1))))))))))))))
   4(5(3(5(2(1(2(3(3(3(2(5(x1)))))))))))) -> 4(4(5(4(5(4(5(1(4(4(3(4(4(4(1(5(x1))))))))))))))))
   4(5(5(2(3(1(1(5(5(2(0(5(x1)))))))))))) -> 4(0(4(1(4(4(0(1(4(4(5(1(2(3(2(4(x1))))))))))))))))
   4(5(5(3(3(5(2(3(2(2(0(5(x1)))))))))))) -> 0(1(4(2(4(4(5(4(4(4(5(5(4(5(4(4(5(x1)))))))))))))))))
   5(0(3(4(4(3(0(3(2(5(0(0(x1)))))))))))) -> 3(3(4(3(4(4(0(2(1(4(1(1(4(4(4(x1)))))))))))))))
   5(0(5(3(0(1(1(3(4(0(2(5(x1)))))))))))) -> 3(2(4(3(2(4(4(4(4(1(4(4(0(3(x1))))))))))))))
   5(1(3(0(5(2(2(1(4(5(3(1(x1)))))))))))) -> 4(4(1(4(1(4(1(3(4(3(1(0(3(4(x1))))))))))))))
   5(1(5(5(2(3(1(3(1(1(0(3(x1)))))))))))) -> 0(0(1(5(4(3(1(5(4(4(1(1(4(0(x1))))))))))))))
   5(2(1(0(3(5(5(1(0(5(0(2(x1)))))))))))) -> 4(4(2(3(1(3(3(4(5(4(1(3(1(4(4(3(4(x1)))))))))))))))))
   5(2(1(2(3(2(1(5(0(3(3(4(x1)))))))))))) -> 1(4(4(0(1(2(1(4(3(0(4(5(2(5(x1))))))))))))))
   5(2(3(2(3(0(5(2(4(0(5(5(x1)))))))))))) -> 4(4(2(4(2(4(1(4(4(4(5(4(4(1(x1))))))))))))))
   5(2(5(0(5(4(2(5(2(2(3(5(x1)))))))))))) -> 1(4(4(1(1(4(1(2(1(0(3(3(3(4(0(2(4(2(x1))))))))))))))))))
   5(2(5(3(4(0(2(3(3(2(0(3(x1)))))))))))) -> 4(0(5(4(0(3(5(0(1(4(4(1(3(4(1(x1)))))))))))))))
   5(3(0(2(3(3(2(5(1(1(4(5(x1)))))))))))) -> 4(3(4(1(0(1(3(3(5(4(1(2(1(4(4(x1)))))))))))))))
   5(3(0(5(5(2(5(3(4(5(2(2(x1)))))))))))) -> 1(1(3(3(2(4(2(4(4(2(2(1(0(1(3(4(x1))))))))))))))))
   5(3(1(5(1(2(2(2(2(5(2(5(x1)))))))))))) -> 1(1(4(4(4(4(5(3(4(1(2(0(1(0(0(x1)))))))))))))))
   5(3(2(5(1(5(2(5(0(0(0(5(x1)))))))))))) -> 5(3(2(2(0(4(2(5(4(1(5(2(0(4(x1))))))))))))))
   5(3(3(2(3(1(2(2(1(5(5(0(x1)))))))))))) -> 5(5(4(4(1(1(1(4(1(3(0(1(4(2(1(4(4(x1)))))))))))))))))
   5(4(0(2(5(5(3(1(2(3(1(0(x1)))))))))))) -> 1(4(4(2(4(1(4(1(3(3(1(3(1(3(1(4(4(3(x1))))))))))))))))))
   5(5(0(2(3(5(2(1(5(0(5(5(x1)))))))))))) -> 1(1(0(2(4(4(4(2(0(4(5(0(2(4(1(5(4(4(x1))))))))))))))))))
   5(5(1(2(3(2(5(3(5(5(0(4(x1)))))))))))) -> 0(1(1(0(3(4(0(3(3(4(4(1(0(5(1(1(4(x1)))))))))))))))))
   5(5(1(5(5(4(1(5(2(5(1(1(x1)))))))))))) -> 4(0(4(1(1(0(0(4(4(1(1(5(4(4(5(4(4(4(x1))))))))))))))))))
   5(5(3(5(1(2(3(4(2(5(5(3(x1)))))))))))) -> 4(1(3(1(5(4(1(3(1(4(3(2(2(4(4(0(4(4(x1))))))))))))))))))
   5(5(4(5(3(3(5(2(5(5(2(2(x1)))))))))))) -> 1(3(2(1(2(5(2(4(1(1(0(4(1(4(x1))))))))))))))
   5(5(5(1(1(1(2(0(5(0(2(5(x1)))))))))))) -> 1(4(1(4(3(4(0(4(3(3(4(4(0(4(0(4(4(0(x1))))))))))))))))))
   5(5(5(2(2(3(0(1(0(0(5(3(x1)))))))))))) -> 3(5(4(0(1(1(4(1(1(1(3(5(1(3(x1))))))))))))))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_1(x_1)) -> 1(encArg(x_1))
   encArg(cons_2(x_1)) -> 2(encArg(x_1))
   encArg(cons_3(x_1)) -> 3(encArg(x_1))
   encArg(cons_4(x_1)) -> 4(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_3(x_1) -> 3(encArg(x_1))
   encode_5(x_1) -> 5(encArg(x_1))
   encode_2(x_1) -> 2(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))
   encode_4(x_1) -> 4(encArg(x_1))

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

(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 2. 
The certificate found is represented by the following graph.

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{(70,71,[0_1|0, 1_1|0, 2_1|0, 3_1|0, 4_1|0, 5_1|0, encArg_1|0, encode_0_1|0, encode_3_1|0, encode_5_1|0, encode_2_1|0, encode_1_1|0, encode_4_1|0]), (70,72,[0_1|1, 1_1|1, 2_1|1, 3_1|1, 4_1|1, 5_1|1]), (70,73,[1_1|2]), (70,89,[3_1|2]), (70,106,[0_1|2]), (70,119,[4_1|2]), (70,132,[4_1|2]), (70,146,[3_1|2]), (70,162,[4_1|2]), (70,175,[2_1|2]), (70,188,[1_1|2]), (70,204,[0_1|2]), (70,221,[4_1|2]), (70,237,[3_1|2]), (70,251,[4_1|2]), (70,265,[2_1|2]), (70,278,[1_1|2]), (70,294,[0_1|2]), (70,307,[1_1|2]), (70,321,[1_1|2]), (70,338,[3_1|2]), (70,355,[4_1|2]), (70,368,[2_1|2]), (70,382,[0_1|2]), (70,398,[2_1|2]), (70,412,[0_1|2]), (70,428,[5_1|2]), (70,445,[4_1|2]), (70,458,[5_1|2]), (70,471,[2_1|2]), (70,488,[4_1|2]), (70,501,[1_1|2]), (70,514,[0_1|2]), (70,528,[1_1|2]), (70,544,[4_1|2]), (70,559,[4_1|2]), (70,574,[1_1|2]), (70,587,[4_1|2]), (70,602,[4_1|2]), (70,617,[2_1|2]), (70,634,[1_1|2]), (70,650,[4_1|2]), (70,664,[2_1|2]), (70,677,[4_1|2]), (70,694,[2_1|2]), (70,709,[4_1|2]), (70,724,[2_1|2]), (70,739,[4_1|2]), (70,753,[0_1|2]), (70,770,[3_1|2]), (70,785,[1_1|2]), (70,798,[1_1|2]), (70,811,[4_1|2]), (70,828,[4_1|2]), (70,843,[1_1|2]), (70,856,[4_1|2]), (70,873,[1_1|2]), (70,889,[3_1|2]), (70,904,[4_1|2]), (70,921,[1_1|2]), (70,936,[4_1|2]), (70,950,[0_1|2]), (70,966,[3_1|2]), (70,980,[4_1|2]), (70,997,[1_1|2]), (70,1012,[4_1|2]), (70,1027,[0_1|2]), (70,1041,[0_1|2]), (70,1058,[0_1|2]), (70,1072,[4_1|2]), (70,1085,[0_1|2]), (70,1098,[0_1|2]), (70,1111,[1_1|2]), (70,1124,[4_1|2]), (70,1139,[4_1|2]), (70,1154,[0_1|2]), (70,1170,[3_1|2]), (70,1184,[3_1|2]), (70,1197,[4_1|2]), (70,1210,[0_1|2]), (70,1223,[4_1|2]), (70,1239,[1_1|2]), (70,1252,[4_1|2]), (70,1265,[1_1|2]), (70,1282,[4_1|2]), (70,1296,[4_1|2]), (70,1310,[1_1|2]), (70,1325,[1_1|2]), (70,1339,[5_1|2]), (70,1352,[5_1|2]), (70,1368,[1_1|2]), (70,1385,[1_1|2]), (70,1402,[0_1|2]), (70,1418,[4_1|2]), (70,1435,[4_1|2]), (70,1452,[1_1|2]), (70,1465,[1_1|2]), (70,1482,[3_1|2]), (71,71,[cons_0_1|0, cons_1_1|0, cons_2_1|0, cons_3_1|0, cons_4_1|0, cons_5_1|0]), (72,71,[encArg_1|1]), (72,72,[0_1|1, 1_1|1, 2_1|1, 3_1|1, 4_1|1, 5_1|1]), (72,73,[1_1|2]), (72,89,[3_1|2]), (72,106,[0_1|2]), (72,119,[4_1|2]), (72,132,[4_1|2]), (72,146,[3_1|2]), (72,162,[4_1|2]), (72,175,[2_1|2]), (72,188,[1_1|2]), (72,204,[0_1|2]), (72,221,[4_1|2]), (72,237,[3_1|2]), (72,251,[4_1|2]), (72,265,[2_1|2]), (72,278,[1_1|2]), (72,294,[0_1|2]), (72,307,[1_1|2]), (72,321,[1_1|2]), (72,338,[3_1|2]), (72,355,[4_1|2]), (72,368,[2_1|2]), (72,382,[0_1|2]), (72,398,[2_1|2]), (72,412,[0_1|2]), (72,428,[5_1|2]), (72,445,[4_1|2]), (72,458,[5_1|2]), (72,471,[2_1|2]), (72,488,[4_1|2]), (72,501,[1_1|2]), (72,514,[0_1|2]), (72,528,[1_1|2]), (72,544,[4_1|2]), (72,559,[4_1|2]), (72,574,[1_1|2]), (72,587,[4_1|2]), (72,602,[4_1|2]), (72,617,[2_1|2]), (72,634,[1_1|2]), (72,650,[4_1|2]), (72,664,[2_1|2]), (72,677,[4_1|2]), (72,694,[2_1|2]), (72,709,[4_1|2]), (72,724,[2_1|2]), (72,739,[4_1|2]), (72,753,[0_1|2]), (72,770,[3_1|2]), (72,785,[1_1|2]), (72,798,[1_1|2]), (72,811,[4_1|2]), (72,828,[4_1|2]), (72,843,[1_1|2]), (72,856,[4_1|2]), (72,873,[1_1|2]), (72,889,[3_1|2]), (72,904,[4_1|2]), (72,921,[1_1|2]), (72,936,[4_1|2]), (72,950,[0_1|2]), (72,966,[3_1|2]), (72,980,[4_1|2]), (72,997,[1_1|2]), (72,1012,[4_1|2]), (72,1027,[0_1|2]), (72,1041,[0_1|2]), (72,1058,[0_1|2]), (72,1072,[4_1|2]), (72,1085,[0_1|2]), (72,1098,[0_1|2]), (72,1111,[1_1|2]), (72,1124,[4_1|2]), (72,1139,[4_1|2]), (72,1154,[0_1|2]), (72,1170,[3_1|2]), (72,1184,[3_1|2]), (72,1197,[4_1|2]), (72,1210,[0_1|2]), (72,1223,[4_1|2]), (72,1239,[1_1|2]), (72,1252,[4_1|2]), (72,1265,[1_1|2]), (72,1282,[4_1|2]), (72,1296,[4_1|2]), (72,1310,[1_1|2]), (72,1325,[1_1|2]), (72,1339,[5_1|2]), (72,1352,[5_1|2]), (72,1368,[1_1|2]), (72,1385,[1_1|2]), (72,1402,[0_1|2]), (72,1418,[4_1|2]), (72,1435,[4_1|2]), (72,1452,[1_1|2]), (72,1465,[1_1|2]), (72,1482,[3_1|2]), (73,74,[4_1|2]), (74,75,[4_1|2]), (75,76,[1_1|2]), (76,77,[4_1|2]), (77,78,[4_1|2]), (78,79,[0_1|2]), (79,80,[1_1|2]), (80,81,[1_1|2]), (81,82,[3_1|2]), (82,83,[3_1|2]), (83,84,[1_1|2]), (84,85,[4_1|2]), (85,86,[4_1|2]), (86,87,[1_1|2]), (86,321,[1_1|2]), (87,88,[1_1|2]), (87,278,[1_1|2]), (87,294,[0_1|2]), (87,307,[1_1|2]), (88,72,[0_1|2]), (88,175,[0_1|2, 2_1|2]), (88,265,[0_1|2, 2_1|2]), (88,368,[0_1|2]), (88,398,[0_1|2]), (88,471,[0_1|2]), (88,617,[0_1|2]), (88,664,[0_1|2]), (88,694,[0_1|2]), (88,724,[0_1|2]), (88,383,[0_1|2]), (88,951,[0_1|2]), (88,1042,[0_1|2]), (88,73,[1_1|2]), (88,89,[3_1|2]), (88,106,[0_1|2]), (88,119,[4_1|2]), (88,132,[4_1|2]), (88,146,[3_1|2]), (88,162,[4_1|2]), (88,188,[1_1|2]), (88,204,[0_1|2]), (88,221,[4_1|2]), (88,237,[3_1|2]), (88,251,[4_1|2]), (89,90,[4_1|2]), (90,91,[1_1|2]), (91,92,[4_1|2]), (92,93,[4_1|2]), (93,94,[4_1|2]), (94,95,[4_1|2]), (95,96,[1_1|2]), (96,97,[0_1|2]), (97,98,[0_1|2]), (98,99,[4_1|2]), (99,100,[5_1|2]), (100,101,[4_1|2]), (101,102,[4_1|2]), (102,103,[3_1|2]), (103,104,[0_1|2]), (104,105,[4_1|2]), (104,1085,[0_1|2]), (104,1098,[0_1|2]), (104,1111,[1_1|2]), (105,72,[3_1|2]), (105,73,[3_1|2]), (105,188,[3_1|2]), (105,278,[3_1|2]), (105,307,[3_1|2]), (105,321,[3_1|2]), (105,501,[3_1|2]), (105,528,[3_1|2]), (105,574,[3_1|2]), (105,634,[3_1|2]), (105,785,[3_1|2, 1_1|2]), (105,798,[3_1|2, 1_1|2]), (105,843,[3_1|2, 1_1|2]), (105,873,[3_1|2, 1_1|2]), (105,921,[3_1|2, 1_1|2]), (105,997,[3_1|2, 1_1|2]), (105,1111,[3_1|2]), (105,1239,[3_1|2]), (105,1265,[3_1|2]), (105,1310,[3_1|2]), (105,1325,[3_1|2]), (105,1368,[3_1|2]), (105,1385,[3_1|2]), (105,1452,[3_1|2]), (105,1465,[3_1|2]), (105,120,[3_1|2]), (105,252,[3_1|2]), (105,560,[3_1|2]), (105,678,[3_1|2]), (105,1073,[3_1|2]), (105,1436,[3_1|2]), (105,619,[3_1|2]), (105,726,[3_1|2]), (105,770,[3_1|2]), (105,811,[4_1|2]), (105,828,[4_1|2]), (105,856,[4_1|2]), (105,889,[3_1|2]), (105,904,[4_1|2]), (105,936,[4_1|2]), (105,950,[0_1|2]), (105,966,[3_1|2]), (105,980,[4_1|2]), (105,1012,[4_1|2]), (105,1027,[0_1|2]), (105,1041,[0_1|2]), (106,107,[1_1|2]), (107,108,[0_1|2]), (108,109,[5_1|2]), (109,110,[4_1|2]), (110,111,[2_1|2]), (111,112,[3_1|2]), (112,113,[3_1|2]), (113,114,[5_1|2]), (114,115,[4_1|2]), (115,116,[5_1|2]), (116,117,[4_1|2]), (117,118,[4_1|2]), (117,1058,[0_1|2]), (118,72,[0_1|2]), (118,428,[0_1|2]), (118,458,[0_1|2]), (118,1339,[0_1|2]), (118,1352,[0_1|2]), (118,73,[1_1|2]), (118,89,[3_1|2]), (118,106,[0_1|2]), (118,119,[4_1|2]), (118,132,[4_1|2]), (118,146,[3_1|2]), (118,162,[4_1|2]), (118,175,[2_1|2]), (118,188,[1_1|2]), (118,204,[0_1|2]), (118,221,[4_1|2]), (118,237,[3_1|2]), (118,251,[4_1|2]), (118,265,[2_1|2]), (119,120,[1_1|2]), (120,121,[5_1|2]), (121,122,[5_1|2]), (122,123,[0_1|2]), (123,124,[0_1|2]), (124,125,[1_1|2]), (125,126,[4_1|2]), (126,127,[4_1|2]), (127,128,[4_1|2]), (128,129,[1_1|2]), (129,130,[1_1|2]), (130,131,[3_1|2]), (130,770,[3_1|2]), (130,785,[1_1|2]), (131,72,[0_1|2]), (131,428,[0_1|2]), (131,458,[0_1|2]), (131,1339,[0_1|2]), (131,1352,[0_1|2]), (131,73,[1_1|2]), (131,89,[3_1|2]), (131,106,[0_1|2]), (131,119,[4_1|2]), (131,132,[4_1|2]), (131,146,[3_1|2]), (131,162,[4_1|2]), (131,175,[2_1|2]), (131,188,[1_1|2]), (131,204,[0_1|2]), (131,221,[4_1|2]), (131,237,[3_1|2]), (131,251,[4_1|2]), (131,265,[2_1|2]), (132,133,[4_1|2]), (133,134,[2_1|2]), (134,135,[4_1|2]), (135,136,[0_1|2]), (136,137,[1_1|2]), (137,138,[1_1|2]), (138,139,[0_1|2]), (139,140,[4_1|2]), (140,141,[0_1|2]), (141,142,[2_1|2]), (142,143,[0_1|2]), (143,144,[5_1|2]), (143,1452,[1_1|2]), (144,145,[5_1|2]), (144,1368,[1_1|2]), (145,72,[4_1|2]), (145,89,[4_1|2]), (145,146,[4_1|2]), (145,237,[4_1|2]), (145,338,[4_1|2]), (145,770,[4_1|2]), (145,889,[4_1|2]), (145,966,[4_1|2]), (145,1170,[4_1|2]), (145,1184,[4_1|2]), (145,1482,[4_1|2]), (145,1058,[0_1|2]), (145,1072,[4_1|2]), (145,1085,[0_1|2]), (145,1098,[0_1|2]), (145,1111,[1_1|2]), (145,1124,[4_1|2]), (145,1139,[4_1|2]), (145,1154,[0_1|2]), (146,147,[4_1|2]), (147,148,[0_1|2]), (148,149,[1_1|2]), (149,150,[4_1|2]), (150,151,[4_1|2]), (151,152,[4_1|2]), 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(1451,1072,[4_1|2]), (1451,1085,[0_1|2]), (1451,1098,[0_1|2]), (1451,1111,[1_1|2]), (1451,1124,[4_1|2]), (1451,1139,[4_1|2]), (1451,1154,[0_1|2]), (1452,1453,[3_1|2]), (1453,1454,[2_1|2]), (1454,1455,[1_1|2]), (1455,1456,[2_1|2]), (1456,1457,[5_1|2]), (1457,1458,[2_1|2]), (1458,1459,[4_1|2]), (1459,1460,[1_1|2]), (1460,1461,[1_1|2]), (1461,1462,[0_1|2]), (1462,1463,[4_1|2]), (1463,1464,[1_1|2]), (1464,72,[4_1|2]), (1464,175,[4_1|2]), (1464,265,[4_1|2]), (1464,368,[4_1|2]), (1464,398,[4_1|2]), (1464,471,[4_1|2]), (1464,617,[4_1|2]), (1464,664,[4_1|2]), (1464,694,[4_1|2]), (1464,724,[4_1|2]), (1464,176,[4_1|2]), (1464,369,[4_1|2]), (1464,399,[4_1|2]), (1464,1058,[0_1|2]), (1464,1072,[4_1|2]), (1464,1085,[0_1|2]), (1464,1098,[0_1|2]), (1464,1111,[1_1|2]), (1464,1124,[4_1|2]), (1464,1139,[4_1|2]), (1464,1154,[0_1|2]), (1465,1466,[4_1|2]), (1466,1467,[1_1|2]), (1467,1468,[4_1|2]), (1468,1469,[3_1|2]), (1469,1470,[4_1|2]), (1470,1471,[0_1|2]), (1471,1472,[4_1|2]), (1472,1473,[3_1|2]), (1473,1474,[3_1|2]), (1474,1475,[4_1|2]), (1475,1476,[4_1|2]), (1476,1477,[0_1|2]), (1477,1478,[4_1|2]), (1478,1479,[0_1|2]), (1479,1480,[4_1|2]), (1480,1481,[4_1|2]), (1480,1058,[0_1|2]), (1481,72,[0_1|2]), (1481,428,[0_1|2]), (1481,458,[0_1|2]), (1481,1339,[0_1|2]), (1481,1352,[0_1|2]), (1481,73,[1_1|2]), (1481,89,[3_1|2]), (1481,106,[0_1|2]), (1481,119,[4_1|2]), (1481,132,[4_1|2]), (1481,146,[3_1|2]), (1481,162,[4_1|2]), (1481,175,[2_1|2]), (1481,188,[1_1|2]), (1481,204,[0_1|2]), (1481,221,[4_1|2]), (1481,237,[3_1|2]), (1481,251,[4_1|2]), (1481,265,[2_1|2]), (1482,1483,[5_1|2]), (1483,1484,[4_1|2]), (1484,1485,[0_1|2]), (1485,1486,[1_1|2]), (1486,1487,[1_1|2]), (1487,1488,[4_1|2]), (1488,1489,[1_1|2]), (1489,1490,[1_1|2]), (1490,1491,[1_1|2]), (1491,1492,[3_1|2]), (1492,1493,[5_1|2]), (1492,1197,[4_1|2]), (1493,1494,[1_1|2]), (1494,72,[3_1|2]), (1494,89,[3_1|2]), (1494,146,[3_1|2]), (1494,237,[3_1|2]), (1494,338,[3_1|2]), (1494,770,[3_1|2]), (1494,889,[3_1|2]), (1494,966,[3_1|2]), (1494,1170,[3_1|2]), (1494,1184,[3_1|2]), (1494,1482,[3_1|2]), (1494,1340,[3_1|2]), (1494,785,[1_1|2]), (1494,798,[1_1|2]), (1494,811,[4_1|2]), (1494,828,[4_1|2]), (1494,843,[1_1|2]), (1494,856,[4_1|2]), (1494,873,[1_1|2]), (1494,904,[4_1|2]), (1494,921,[1_1|2]), (1494,936,[4_1|2]), (1494,950,[0_1|2]), (1494,980,[4_1|2]), (1494,997,[1_1|2]), (1494,1012,[4_1|2]), (1494,1027,[0_1|2]), (1494,1041,[0_1|2])}"
----------------------------------------

(8)
BOUNDS(1, n^1)