KILLED
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, INF).

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 214 ms]
(4) CpxRelTRS
(5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(6) TRS for Loop Detection
(7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(8) CpxRelTRS
    (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) typed CpxTrs
    (11) OrderProof [LOWER BOUND(ID), 4 ms]
    (12) typed CpxTrs
(13) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(14) CpxTRS
(15) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
(16) CpxRelTRS
    (17) RcToIrcProof [BOTH BOUNDS(ID, ID), 1535 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 22 ms]
        (22) CpxWeightedTrs
        (23) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
        (24) CpxTypedWeightedTrs
        (25) CompletionProof [UPPER BOUND(ID), 0 ms]
        (26) CpxTypedWeightedCompleteTrs
            (27) NarrowingProof [BOTH BOUNDS(ID, ID), 1953 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 116 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 184 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 0 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 918 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 15 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 18 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 6355 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1897 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1870 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1896 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1838 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1918 ms]
        (56) CdtProblem


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

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


The TRS R consists of the following rules:

   0(0(0(1(2(2(3(x1))))))) -> 0(0(0(2(1(2(3(x1)))))))
   4(4(5(5(3(0(1(x1))))))) -> 4(4(3(5(0(5(1(x1)))))))
   0(1(2(4(4(0(1(0(x1)))))))) -> 0(1(4(2(4(1(0(0(x1))))))))
   4(0(4(2(4(0(3(1(x1)))))))) -> 4(0(4(2(0(4(3(1(x1))))))))
   4(4(5(3(2(4(2(5(x1)))))))) -> 4(2(3(5(4(4(2(5(x1))))))))
   3(1(5(3(4(5(1(3(3(x1))))))))) -> 3(1(5(3(5(4(1(3(3(x1)))))))))
   5(1(5(3(5(4(0(0(3(x1))))))))) -> 5(1(5(3(5(0(4(0(3(x1)))))))))
   0(0(0(2(2(3(4(4(3(3(x1)))))))))) -> 0(2(3(0(3(2(1(5(1(3(x1))))))))))
   0(4(5(0(0(4(2(4(5(0(x1)))))))))) -> 3(5(3(5(5(4(0(2(2(3(x1))))))))))
   1(1(5(3(4(3(4(4(2(5(x1)))))))))) -> 1(1(5(3(3(4(4(4(2(5(x1))))))))))
   1(2(0(1(2(4(5(2(4(4(x1)))))))))) -> 1(5(4(2(0(2(2(4(1(4(x1))))))))))
   1(5(2(2(3(3(4(2(4(5(x1)))))))))) -> 1(5(2(3(2(3(4(2(4(5(x1))))))))))
   4(0(5(4(0(2(4(0(4(3(x1)))))))))) -> 2(3(1(3(5(3(1(2(4(5(x1))))))))))
   0(0(5(2(2(4(4(3(3(4(0(x1))))))))))) -> 4(0(4(2(3(1(5(3(5(5(x1))))))))))
   0(2(2(5(5(0(0(4(5(3(4(x1))))))))))) -> 4(0(5(1(3(5(5(4(5(0(x1))))))))))
   0(4(0(4(5(3(3(0(5(5(2(x1))))))))))) -> 4(5(3(5(2(2(1(1(4(3(x1))))))))))
   0(4(3(0(0(0(4(3(2(3(3(x1))))))))))) -> 2(5(1(5(2(4(5(4(3(2(x1))))))))))
   0(4(4(5(4(0(1(3(1(3(4(x1))))))))))) -> 0(4(0(3(4(3(1(4(4(1(5(x1)))))))))))
   0(5(2(0(0(2(1(4(2(4(5(x1))))))))))) -> 5(0(4(3(4(2(5(5(4(1(x1))))))))))
   1(0(1(5(1(5(3(3(1(4(0(x1))))))))))) -> 3(1(2(1(5(2(4(5(1(1(x1))))))))))
   1(1(1(2(2(5(2(1(3(1(0(x1))))))))))) -> 1(5(1(1(3(5(0(0(2(4(x1))))))))))
   2(0(5(0(5(4(4(3(1(3(2(x1))))))))))) -> 2(1(0(3(1(2(1(3(4(0(x1))))))))))
   2(2(0(2(2(5(0(3(2(0(5(x1))))))))))) -> 5(0(3(5(4(2(2(3(1(0(x1))))))))))
   2(5(3(1(0(1(4(4(2(2(4(x1))))))))))) -> 0(5(1(0(0(2(0(5(5(1(x1))))))))))
   3(1(3(2(1(0(5(3(4(0(1(x1))))))))))) -> 1(2(0(4(0(3(2(0(4(0(x1))))))))))
   3(1(3(3(3(0(4(1(1(3(0(x1))))))))))) -> 1(0(2(1(2(1(0(1(1(3(x1))))))))))
   3(2(2(2(1(1(2(0(0(2(0(x1))))))))))) -> 4(4(2(5(4(5(5(0(5(0(x1))))))))))
   3(2(5(3(4(4(0(1(3(5(4(x1))))))))))) -> 5(0(1(3(5(5(1(3(4(2(x1))))))))))
   3(3(3(4(0(2(5(4(5(0(0(x1))))))))))) -> 3(1(5(1(1(5(2(3(1(4(x1))))))))))
   3(4(2(2(2(3(1(3(1(2(1(x1))))))))))) -> 3(4(5(5(4(3(2(1(5(4(x1))))))))))
   3(5(4(4(5(1(1(5(0(2(0(x1))))))))))) -> 3(1(5(1(3(5(0(1(5(1(x1))))))))))
   3(5(5(4(5(3(0(2(5(5(1(x1))))))))))) -> 3(1(1(2(4(2(3(0(2(5(x1))))))))))
   4(0(3(0(0(3(0(5(1(4(3(x1))))))))))) -> 1(2(1(5(5(5(0(4(1(1(x1))))))))))
   4(0(5(2(5(3(0(0(3(5(5(x1))))))))))) -> 0(0(5(2(3(0(3(1(5(5(x1))))))))))
   4(0(5(4(5(5(3(4(3(4(1(x1))))))))))) -> 3(4(1(1(3(1(4(0(1(4(x1))))))))))
   4(0(5(5(2(0(4(0(2(3(5(x1))))))))))) -> 5(5(0(4(3(5(4(1(5(1(x1))))))))))
   4(1(2(0(5(5(4(0(0(0(2(x1))))))))))) -> 3(3(5(4(5(3(2(0(0(2(x1))))))))))
   4(1(3(3(1(5(1(1(2(4(3(x1))))))))))) -> 0(1(2(3(3(2(1(3(3(2(x1))))))))))
   4(1(3(5(2(3(5(5(0(0(3(x1))))))))))) -> 5(2(3(0(3(5(2(3(5(3(x1))))))))))
   4(2(1(2(2(3(3(3(1(3(2(x1))))))))))) -> 5(5(2(3(4(2(5(4(0(3(x1))))))))))
   4(4(3(3(3(2(4(2(5(1(4(x1))))))))))) -> 2(0(3(4(4(1(3(0(2(0(x1))))))))))
   4(5(4(0(2(5(0(2(3(2(5(x1))))))))))) -> 3(3(4(4(5(2(3(5(3(0(x1))))))))))
   5(0(5(0(0(4(0(1(3(4(1(x1))))))))))) -> 2(2(4(2(1(1(3(3(3(0(x1))))))))))
   5(1(0(3(5(0(1(1(3(4(3(x1))))))))))) -> 1(0(3(0(0(4(2(4(5(3(x1))))))))))
   5(5(0(5(3(4(1(2(3(2(2(x1))))))))))) -> 1(2(3(5(5(0(1(3(5(5(x1))))))))))
   5(5(3(3(0(1(4(1(3(3(0(x1))))))))))) -> 2(3(3(4(5(4(2(2(0(1(x1))))))))))
   0(0(0(5(1(5(3(5(1(3(2(3(x1)))))))))))) -> 1(3(3(0(1(4(1(0(5(5(x1))))))))))
   0(5(5(1(1(1(2(5(2(3(5(5(x1)))))))))))) -> 1(3(5(2(3(4(3(3(4(3(x1))))))))))
   2(1(2(0(5(0(3(5(1(2(3(5(x1)))))))))))) -> 1(0(0(4(5(4(1(4(1(0(x1))))))))))
   2(3(2(1(1(1(0(2(1(3(5(1(x1)))))))))))) -> 5(4(3(0(1(2(3(3(2(5(x1))))))))))
   2(3(4(3(5(1(2(4(2(0(2(1(x1)))))))))))) -> 2(4(1(3(2(2(5(5(1(0(x1))))))))))
   4(3(1(3(5(1(5(1(5(0(2(1(x1)))))))))))) -> 0(1(3(1(0(4(0(0(5(3(x1))))))))))
   4(3(3(0(5(2(0(4(4(5(1(2(x1)))))))))))) -> 2(0(1(1(5(1(1(4(0(0(x1))))))))))
   5(1(2(1(0(2(3(1(3(1(0(0(x1)))))))))))) -> 5(2(0(4(2(1(4(1(1(3(x1))))))))))
   5(2(3(3(1(0(1(1(1(4(1(4(x1)))))))))))) -> 0(2(4(0(4(0(4(0(0(1(x1))))))))))
   0(1(1(1(2(0(1(3(0(4(2(3(3(x1))))))))))))) -> 0(4(1(2(4(2(5(0(0(0(x1))))))))))
   0(1(1(4(1(3(2(4(3(5(5(0(1(x1))))))))))))) -> 4(3(2(0(5(0(4(0(4(4(x1))))))))))
   0(1(1(5(1(1(4(4(5(0(4(2(1(x1))))))))))))) -> 0(3(2(0(0(4(3(1(0(4(x1))))))))))
   4(1(1(3(1(3(2(1(2(2(2(0(5(x1))))))))))))) -> 0(3(5(4(0(1(4(0(5(0(x1))))))))))
   4(3(1(1(2(1(2(0(5(2(0(3(2(x1))))))))))))) -> 4(4(4(4(4(0(0(3(4(1(x1))))))))))
   5(1(4(4(3(1(5(4(3(5(1(2(0(x1))))))))))))) -> 2(2(1(3(0(0(4(3(2(5(x1))))))))))
   2(2(4(3(2(2(2(4(2(5(2(0(4(5(x1)))))))))))))) -> 2(2(0(2(2(4(2(5(3(4(4(2(2(5(x1))))))))))))))
   5(4(1(5(1(4(2(5(4(3(0(4(1(0(x1)))))))))))))) -> 5(4(1(1(5(4(2(5(4(3(0(4(1(0(x1))))))))))))))
   1(2(4(0(2(4(0(1(2(4(3(1(0(3(4(x1))))))))))))))) -> 1(2(4(0(2(4(0(1(4(2(3(1(0(3(4(x1)))))))))))))))
   2(0(2(5(4(0(3(3(0(4(2(2(5(5(2(x1))))))))))))))) -> 2(0(2(4(0(5(0(3(4(3(2(2(5(5(2(x1)))))))))))))))
   0(4(0(1(0(2(2(4(3(0(5(0(2(0(4(5(3(x1))))))))))))))))) -> 0(4(0(1(0(2(4(2(3(0(5(0(2(0(4(5(3(x1)))))))))))))))))
   3(2(5(5(2(1(2(2(2(3(2(2(4(0(4(0(3(5(x1)))))))))))))))))) -> 3(5(2(2(5(1(2(2(2(3(2(2(4(0(4(0(3(5(x1))))))))))))))))))
   5(3(1(5(5(3(3(0(2(2(2(2(3(3(4(5(1(1(x1)))))))))))))))))) -> 5(3(1(5(5(3(3(0(2(2(2(3(2(3(4(5(1(1(x1))))))))))))))))))
   5(5(3(4(1(2(0(2(5(3(2(5(4(4(5(5(1(2(x1)))))))))))))))))) -> 5(5(3(4(1(2(0(2(5(3(2(4(5(4(5(5(1(2(x1))))))))))))))))))
   0(0(3(1(5(5(1(5(3(2(0(2(2(4(3(4(0(5(1(x1))))))))))))))))))) -> 0(3(0(5(3(1(1(0(5(2(2(4(5(2(3(4(0(5(1(x1)))))))))))))))))))
   4(5(5(3(5(4(1(1(5(5(3(3(1(5(4(4(5(0(4(x1))))))))))))))))))) -> 4(5(5(3(5(4(1(5(1(5(3(3(1(5(4(4(5(0(4(x1)))))))))))))))))))
   0(5(2(5(4(3(3(2(3(5(0(2(3(2(5(0(5(0(4(1(x1)))))))))))))))))))) -> 0(5(2(5(4(3(3(2(3(5(0(2(3(2(0(5(5(0(4(1(x1))))))))))))))))))))
   2(4(1(4(1(0(4(0(3(1(0(1(1(0(5(4(1(5(1(4(x1)))))))))))))))))))) -> 2(4(1(4(1(0(4(0(3(1(0(1(1(5(0(4(1(5(1(4(x1))))))))))))))))))))
   2(5(2(3(0(0(1(0(5(0(2(5(3(4(0(5(5(5(3(2(x1)))))))))))))))))))) -> 2(5(2(3(0(0(1(0(5(0(2(5(3(4(5(0(5(5(3(2(x1))))))))))))))))))))
   2(4(3(1(4(0(2(5(3(4(1(3(4(0(3(1(0(1(0(1(3(x1))))))))))))))))))))) -> 2(4(3(1(4(0(5(2(3(4(1(3(4(0(3(1(0(1(0(1(3(x1)))))))))))))))))))))
   5(5(2(3(2(0(3(2(5(3(2(5(5(5(5(1(5(5(1(2(2(x1))))))))))))))))))))) -> 5(5(2(3(2(0(3(2(5(3(2(5(5(5(1(5(5(5(1(2(2(x1)))))))))))))))))))))
   2(1(0(5(5(4(1(0(4(2(5(3(1(4(1(3(5(0(0(2(4(5(x1)))))))))))))))))))))) -> 2(1(0(5(5(4(1(0(4(2(5(3(1(4(1(3(0(5(0(2(4(5(x1))))))))))))))))))))))
   2(0(2(4(0(2(4(2(0(0(1(1(0(1(3(5(3(3(4(3(1(2(5(x1))))))))))))))))))))))) -> 2(0(2(2(0(4(4(1(0(1(3(2(0(1(5(0(3(3(1(2(3(4(5(x1)))))))))))))))))))))))
   3(3(2(5(4(4(0(1(3(1(2(1(5(0(0(4(2(1(4(2(2(3(5(x1))))))))))))))))))))))) -> 3(3(2(5(4(4(0(1(3(1(2(1(5(0(4(0(2(1(4(2(2(3(5(x1)))))))))))))))))))))))
   5(1(5(0(3(3(0(1(2(3(3(1(4(5(3(1(2(2(0(3(2(0(5(x1))))))))))))))))))))))) -> 5(1(5(0(3(3(0(1(2(3(3(1(4(5(3(1(2(0(2(3(2(0(5(x1)))))))))))))))))))))))
   3(2(3(3(2(2(5(1(0(5(4(4(5(2(2(4(3(5(2(1(2(1(3(1(x1)))))))))))))))))))))))) -> 3(2(3(3(2(2(5(1(5(0(4(4(5(2(2(4(3(5(2(1(2(1(3(1(x1))))))))))))))))))))))))
   5(0(0(2(4(0(1(5(1(1(3(0(2(2(2(3(5(4(0(4(1(5(2(3(4(x1))))))))))))))))))))))))) -> 5(0(0(2(0(4(1(5(1(1(3(0(2(2(2(3(5(4(0(4(1(5(2(3(4(x1)))))))))))))))))))))))))
   0(4(3(0(3(3(5(3(5(1(4(2(3(3(0(4(0(1(5(0(3(0(2(5(5(0(x1)))))))))))))))))))))))))) -> 0(4(3(0(3(3(5(3(5(1(4(2(3(3(0(4(1(0(5(0(3(0(2(5(5(0(x1))))))))))))))))))))))))))
   1(2(3(2(0(1(0(5(3(0(2(1(1(1(4(4(1(2(4(5(2(2(4(0(3(2(x1)))))))))))))))))))))))))) -> 1(2(3(2(0(1(0(5(3(0(2(1(1(1(4(4(1(4(2(5(2(2(4(0(3(2(x1))))))))))))))))))))))))))
   1(3(3(2(1(2(1(1(0(1(5(0(4(2(5(3(2(3(1(5(3(2(3(4(1(4(2(x1))))))))))))))))))))))))))) -> 1(2(3(3(1(2(1(0(1(1(5(0(4(5(2(3(2(3(1(3(2(5(3(1(4(4(2(x1)))))))))))))))))))))))))))
   4(3(2(1(1(2(4(4(5(1(5(2(2(4(0(2(4(2(4(2(0(4(2(4(4(0(1(x1))))))))))))))))))))))))))) -> 4(3(2(1(2(1(4(4(5(1(5(2(2(4(0(2(4(2(4(2(0(4(2(4(4(0(1(x1)))))))))))))))))))))))))))
   5(5(0(3(2(2(1(3(4(3(5(4(2(5(2(0(4(1(1(2(4(0(5(4(3(2(4(4(x1)))))))))))))))))))))))))))) -> 5(5(0(3(2(2(3(1(4(3(5(4(2(5(2(0(4(1(1(2(4(0(5(4(3(2(4(4(x1))))))))))))))))))))))))))))
   5(5(5(3(5(3(2(5(0(1(5(3(1(2(2(3(3(0(3(1(0(4(1(2(2(5(3(1(3(x1))))))))))))))))))))))))))))) -> 5(5(5(3(5(3(2(5(1(0(5(3(1(2(2(3(3(0(3(1(0(4(1(2(2(5(3(1(3(x1)))))))))))))))))))))))))))))
   0(0(1(4(5(3(1(4(5(1(4(5(1(0(5(2(2(0(1(2(2(3(3(3(0(0(2(1(2(5(x1)))))))))))))))))))))))))))))) -> 0(0(1(4(5(3(1(4(5(1(4(5(1(0(5(2(0(2(1(2(2(3(3(3(0(0(2(1(2(5(x1))))))))))))))))))))))))))))))
   1(5(0(0(1(5(2(1(5(0(5(5(5(0(1(4(0(5(3(4(3(1(2(0(4(0(2(2(1(5(x1)))))))))))))))))))))))))))))) -> 1(5(0(0(1(5(2(5(1(0(5(5(5(0(1(4(0(5(3(4(3(1(2(0(4(0(2(2(1(5(x1))))))))))))))))))))))))))))))
   1(5(0(1(1(4(2(4(3(5(4(5(2(0(3(3(2(0(5(5(4(4(2(5(3(0(2(1(1(0(x1)))))))))))))))))))))))))))))) -> 1(5(0(1(1(4(4(2(3(5(4(5(2(0(3(3(2(0(5(5(4(4(2(5(3(0(2(1(1(0(x1))))))))))))))))))))))))))))))
   2(4(5(5(3(3(1(2(0(5(5(1(0(3(4(4(5(1(3(5(2(4(0(1(1(4(1(4(5(1(x1)))))))))))))))))))))))))))))) -> 2(4(5(5(3(3(1(2(0(5(5(1(0(3(4(4(5(1(3(2(5(4(0(1(1(4(1(4(5(1(x1))))))))))))))))))))))))))))))
   4(2(0(2(1(5(5(4(2(3(2(1(0(4(1(2(0(4(2(3(1(3(0(1(4(2(0(0(2(5(x1)))))))))))))))))))))))))))))) -> 4(2(0(2(1(5(5(4(2(3(2(1(0(1(4(2(0(4(2(3(1(3(0(1(4(2(0(0(2(5(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(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_4(x_1)) -> 4(encArg(x_1))
   encArg(cons_3(x_1)) -> 3(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(encArg(x_1))
   encArg(cons_1(x_1)) -> 1(encArg(x_1))
   encArg(cons_2(x_1)) -> 2(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, INF).


The TRS R consists of the following rules:

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

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

   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_4(x_1)) -> 4(encArg(x_1))
   encArg(cons_3(x_1)) -> 3(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(encArg(x_1))
   encArg(cons_1(x_1)) -> 1(encArg(x_1))
   encArg(cons_2(x_1)) -> 2(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, INF).


The TRS R consists of the following rules:

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

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

   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_4(x_1)) -> 4(encArg(x_1))
   encArg(cons_3(x_1)) -> 3(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(encArg(x_1))
   encArg(cons_1(x_1)) -> 1(encArg(x_1))
   encArg(cons_2(x_1)) -> 2(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) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
Transformed a relative TRS into a decreasing-loop problem.
----------------------------------------

(6)
Obligation:
Analyzing the following TRS for decreasing loops:

The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

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

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

   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_4(x_1)) -> 4(encArg(x_1))
   encArg(cons_3(x_1)) -> 3(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(encArg(x_1))
   encArg(cons_1(x_1)) -> 1(encArg(x_1))
   encArg(cons_2(x_1)) -> 2(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
----------------------------------------

(7) RenamingProof (BOTH BOUNDS(ID, ID))
Renamed function symbols to avoid clashes with predefined symbol.
----------------------------------------

(8)
Obligation:
The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

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

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

   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_4(x_1)) -> 4(encArg(x_1))
   encArg(cons_3(x_1)) -> 3(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(encArg(x_1))
   encArg(cons_1(x_1)) -> 1(encArg(x_1))
   encArg(cons_2(x_1)) -> 2(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
----------------------------------------

(9) TypeInferenceProof (BOTH BOUNDS(ID, ID))
Infered types.
----------------------------------------

(10)
Obligation:
TRS:
Rules:
0(0(0(1(2(2(3(x1))))))) -> 0(0(0(2(1(2(3(x1)))))))
4(4(5(5(3(0(1(x1))))))) -> 4(4(3(5(0(5(1(x1)))))))
0(1(2(4(4(0(1(0(x1)))))))) -> 0(1(4(2(4(1(0(0(x1))))))))
4(0(4(2(4(0(3(1(x1)))))))) -> 4(0(4(2(0(4(3(1(x1))))))))
4(4(5(3(2(4(2(5(x1)))))))) -> 4(2(3(5(4(4(2(5(x1))))))))
3(1(5(3(4(5(1(3(3(x1))))))))) -> 3(1(5(3(5(4(1(3(3(x1)))))))))
5(1(5(3(5(4(0(0(3(x1))))))))) -> 5(1(5(3(5(0(4(0(3(x1)))))))))
0(0(0(2(2(3(4(4(3(3(x1)))))))))) -> 0(2(3(0(3(2(1(5(1(3(x1))))))))))
0(4(5(0(0(4(2(4(5(0(x1)))))))))) -> 3(5(3(5(5(4(0(2(2(3(x1))))))))))
1(1(5(3(4(3(4(4(2(5(x1)))))))))) -> 1(1(5(3(3(4(4(4(2(5(x1))))))))))
1(2(0(1(2(4(5(2(4(4(x1)))))))))) -> 1(5(4(2(0(2(2(4(1(4(x1))))))))))
1(5(2(2(3(3(4(2(4(5(x1)))))))))) -> 1(5(2(3(2(3(4(2(4(5(x1))))))))))
4(0(5(4(0(2(4(0(4(3(x1)))))))))) -> 2(3(1(3(5(3(1(2(4(5(x1))))))))))
0(0(5(2(2(4(4(3(3(4(0(x1))))))))))) -> 4(0(4(2(3(1(5(3(5(5(x1))))))))))
0(2(2(5(5(0(0(4(5(3(4(x1))))))))))) -> 4(0(5(1(3(5(5(4(5(0(x1))))))))))
0(4(0(4(5(3(3(0(5(5(2(x1))))))))))) -> 4(5(3(5(2(2(1(1(4(3(x1))))))))))
0(4(3(0(0(0(4(3(2(3(3(x1))))))))))) -> 2(5(1(5(2(4(5(4(3(2(x1))))))))))
0(4(4(5(4(0(1(3(1(3(4(x1))))))))))) -> 0(4(0(3(4(3(1(4(4(1(5(x1)))))))))))
0(5(2(0(0(2(1(4(2(4(5(x1))))))))))) -> 5(0(4(3(4(2(5(5(4(1(x1))))))))))
1(0(1(5(1(5(3(3(1(4(0(x1))))))))))) -> 3(1(2(1(5(2(4(5(1(1(x1))))))))))
1(1(1(2(2(5(2(1(3(1(0(x1))))))))))) -> 1(5(1(1(3(5(0(0(2(4(x1))))))))))
2(0(5(0(5(4(4(3(1(3(2(x1))))))))))) -> 2(1(0(3(1(2(1(3(4(0(x1))))))))))
2(2(0(2(2(5(0(3(2(0(5(x1))))))))))) -> 5(0(3(5(4(2(2(3(1(0(x1))))))))))
2(5(3(1(0(1(4(4(2(2(4(x1))))))))))) -> 0(5(1(0(0(2(0(5(5(1(x1))))))))))
3(1(3(2(1(0(5(3(4(0(1(x1))))))))))) -> 1(2(0(4(0(3(2(0(4(0(x1))))))))))
3(1(3(3(3(0(4(1(1(3(0(x1))))))))))) -> 1(0(2(1(2(1(0(1(1(3(x1))))))))))
3(2(2(2(1(1(2(0(0(2(0(x1))))))))))) -> 4(4(2(5(4(5(5(0(5(0(x1))))))))))
3(2(5(3(4(4(0(1(3(5(4(x1))))))))))) -> 5(0(1(3(5(5(1(3(4(2(x1))))))))))
3(3(3(4(0(2(5(4(5(0(0(x1))))))))))) -> 3(1(5(1(1(5(2(3(1(4(x1))))))))))
3(4(2(2(2(3(1(3(1(2(1(x1))))))))))) -> 3(4(5(5(4(3(2(1(5(4(x1))))))))))
3(5(4(4(5(1(1(5(0(2(0(x1))))))))))) -> 3(1(5(1(3(5(0(1(5(1(x1))))))))))
3(5(5(4(5(3(0(2(5(5(1(x1))))))))))) -> 3(1(1(2(4(2(3(0(2(5(x1))))))))))
4(0(3(0(0(3(0(5(1(4(3(x1))))))))))) -> 1(2(1(5(5(5(0(4(1(1(x1))))))))))
4(0(5(2(5(3(0(0(3(5(5(x1))))))))))) -> 0(0(5(2(3(0(3(1(5(5(x1))))))))))
4(0(5(4(5(5(3(4(3(4(1(x1))))))))))) -> 3(4(1(1(3(1(4(0(1(4(x1))))))))))
4(0(5(5(2(0(4(0(2(3(5(x1))))))))))) -> 5(5(0(4(3(5(4(1(5(1(x1))))))))))
4(1(2(0(5(5(4(0(0(0(2(x1))))))))))) -> 3(3(5(4(5(3(2(0(0(2(x1))))))))))
4(1(3(3(1(5(1(1(2(4(3(x1))))))))))) -> 0(1(2(3(3(2(1(3(3(2(x1))))))))))
4(1(3(5(2(3(5(5(0(0(3(x1))))))))))) -> 5(2(3(0(3(5(2(3(5(3(x1))))))))))
4(2(1(2(2(3(3(3(1(3(2(x1))))))))))) -> 5(5(2(3(4(2(5(4(0(3(x1))))))))))
4(4(3(3(3(2(4(2(5(1(4(x1))))))))))) -> 2(0(3(4(4(1(3(0(2(0(x1))))))))))
4(5(4(0(2(5(0(2(3(2(5(x1))))))))))) -> 3(3(4(4(5(2(3(5(3(0(x1))))))))))
5(0(5(0(0(4(0(1(3(4(1(x1))))))))))) -> 2(2(4(2(1(1(3(3(3(0(x1))))))))))
5(1(0(3(5(0(1(1(3(4(3(x1))))))))))) -> 1(0(3(0(0(4(2(4(5(3(x1))))))))))
5(5(0(5(3(4(1(2(3(2(2(x1))))))))))) -> 1(2(3(5(5(0(1(3(5(5(x1))))))))))
5(5(3(3(0(1(4(1(3(3(0(x1))))))))))) -> 2(3(3(4(5(4(2(2(0(1(x1))))))))))
0(0(0(5(1(5(3(5(1(3(2(3(x1)))))))))))) -> 1(3(3(0(1(4(1(0(5(5(x1))))))))))
0(5(5(1(1(1(2(5(2(3(5(5(x1)))))))))))) -> 1(3(5(2(3(4(3(3(4(3(x1))))))))))
2(1(2(0(5(0(3(5(1(2(3(5(x1)))))))))))) -> 1(0(0(4(5(4(1(4(1(0(x1))))))))))
2(3(2(1(1(1(0(2(1(3(5(1(x1)))))))))))) -> 5(4(3(0(1(2(3(3(2(5(x1))))))))))
2(3(4(3(5(1(2(4(2(0(2(1(x1)))))))))))) -> 2(4(1(3(2(2(5(5(1(0(x1))))))))))
4(3(1(3(5(1(5(1(5(0(2(1(x1)))))))))))) -> 0(1(3(1(0(4(0(0(5(3(x1))))))))))
4(3(3(0(5(2(0(4(4(5(1(2(x1)))))))))))) -> 2(0(1(1(5(1(1(4(0(0(x1))))))))))
5(1(2(1(0(2(3(1(3(1(0(0(x1)))))))))))) -> 5(2(0(4(2(1(4(1(1(3(x1))))))))))
5(2(3(3(1(0(1(1(1(4(1(4(x1)))))))))))) -> 0(2(4(0(4(0(4(0(0(1(x1))))))))))
0(1(1(1(2(0(1(3(0(4(2(3(3(x1))))))))))))) -> 0(4(1(2(4(2(5(0(0(0(x1))))))))))
0(1(1(4(1(3(2(4(3(5(5(0(1(x1))))))))))))) -> 4(3(2(0(5(0(4(0(4(4(x1))))))))))
0(1(1(5(1(1(4(4(5(0(4(2(1(x1))))))))))))) -> 0(3(2(0(0(4(3(1(0(4(x1))))))))))
4(1(1(3(1(3(2(1(2(2(2(0(5(x1))))))))))))) -> 0(3(5(4(0(1(4(0(5(0(x1))))))))))
4(3(1(1(2(1(2(0(5(2(0(3(2(x1))))))))))))) -> 4(4(4(4(4(0(0(3(4(1(x1))))))))))
5(1(4(4(3(1(5(4(3(5(1(2(0(x1))))))))))))) -> 2(2(1(3(0(0(4(3(2(5(x1))))))))))
2(2(4(3(2(2(2(4(2(5(2(0(4(5(x1)))))))))))))) -> 2(2(0(2(2(4(2(5(3(4(4(2(2(5(x1))))))))))))))
5(4(1(5(1(4(2(5(4(3(0(4(1(0(x1)))))))))))))) -> 5(4(1(1(5(4(2(5(4(3(0(4(1(0(x1))))))))))))))
1(2(4(0(2(4(0(1(2(4(3(1(0(3(4(x1))))))))))))))) -> 1(2(4(0(2(4(0(1(4(2(3(1(0(3(4(x1)))))))))))))))
2(0(2(5(4(0(3(3(0(4(2(2(5(5(2(x1))))))))))))))) -> 2(0(2(4(0(5(0(3(4(3(2(2(5(5(2(x1)))))))))))))))
0(4(0(1(0(2(2(4(3(0(5(0(2(0(4(5(3(x1))))))))))))))))) -> 0(4(0(1(0(2(4(2(3(0(5(0(2(0(4(5(3(x1)))))))))))))))))
3(2(5(5(2(1(2(2(2(3(2(2(4(0(4(0(3(5(x1)))))))))))))))))) -> 3(5(2(2(5(1(2(2(2(3(2(2(4(0(4(0(3(5(x1))))))))))))))))))
5(3(1(5(5(3(3(0(2(2(2(2(3(3(4(5(1(1(x1)))))))))))))))))) -> 5(3(1(5(5(3(3(0(2(2(2(3(2(3(4(5(1(1(x1))))))))))))))))))
5(5(3(4(1(2(0(2(5(3(2(5(4(4(5(5(1(2(x1)))))))))))))))))) -> 5(5(3(4(1(2(0(2(5(3(2(4(5(4(5(5(1(2(x1))))))))))))))))))
0(0(3(1(5(5(1(5(3(2(0(2(2(4(3(4(0(5(1(x1))))))))))))))))))) -> 0(3(0(5(3(1(1(0(5(2(2(4(5(2(3(4(0(5(1(x1)))))))))))))))))))
4(5(5(3(5(4(1(1(5(5(3(3(1(5(4(4(5(0(4(x1))))))))))))))))))) -> 4(5(5(3(5(4(1(5(1(5(3(3(1(5(4(4(5(0(4(x1)))))))))))))))))))
0(5(2(5(4(3(3(2(3(5(0(2(3(2(5(0(5(0(4(1(x1)))))))))))))))))))) -> 0(5(2(5(4(3(3(2(3(5(0(2(3(2(0(5(5(0(4(1(x1))))))))))))))))))))
2(4(1(4(1(0(4(0(3(1(0(1(1(0(5(4(1(5(1(4(x1)))))))))))))))))))) -> 2(4(1(4(1(0(4(0(3(1(0(1(1(5(0(4(1(5(1(4(x1))))))))))))))))))))
2(5(2(3(0(0(1(0(5(0(2(5(3(4(0(5(5(5(3(2(x1)))))))))))))))))))) -> 2(5(2(3(0(0(1(0(5(0(2(5(3(4(5(0(5(5(3(2(x1))))))))))))))))))))
2(4(3(1(4(0(2(5(3(4(1(3(4(0(3(1(0(1(0(1(3(x1))))))))))))))))))))) -> 2(4(3(1(4(0(5(2(3(4(1(3(4(0(3(1(0(1(0(1(3(x1)))))))))))))))))))))
5(5(2(3(2(0(3(2(5(3(2(5(5(5(5(1(5(5(1(2(2(x1))))))))))))))))))))) -> 5(5(2(3(2(0(3(2(5(3(2(5(5(5(1(5(5(5(1(2(2(x1)))))))))))))))))))))
2(1(0(5(5(4(1(0(4(2(5(3(1(4(1(3(5(0(0(2(4(5(x1)))))))))))))))))))))) -> 2(1(0(5(5(4(1(0(4(2(5(3(1(4(1(3(0(5(0(2(4(5(x1))))))))))))))))))))))
2(0(2(4(0(2(4(2(0(0(1(1(0(1(3(5(3(3(4(3(1(2(5(x1))))))))))))))))))))))) -> 2(0(2(2(0(4(4(1(0(1(3(2(0(1(5(0(3(3(1(2(3(4(5(x1)))))))))))))))))))))))
3(3(2(5(4(4(0(1(3(1(2(1(5(0(0(4(2(1(4(2(2(3(5(x1))))))))))))))))))))))) -> 3(3(2(5(4(4(0(1(3(1(2(1(5(0(4(0(2(1(4(2(2(3(5(x1)))))))))))))))))))))))
5(1(5(0(3(3(0(1(2(3(3(1(4(5(3(1(2(2(0(3(2(0(5(x1))))))))))))))))))))))) -> 5(1(5(0(3(3(0(1(2(3(3(1(4(5(3(1(2(0(2(3(2(0(5(x1)))))))))))))))))))))))
3(2(3(3(2(2(5(1(0(5(4(4(5(2(2(4(3(5(2(1(2(1(3(1(x1)))))))))))))))))))))))) -> 3(2(3(3(2(2(5(1(5(0(4(4(5(2(2(4(3(5(2(1(2(1(3(1(x1))))))))))))))))))))))))
5(0(0(2(4(0(1(5(1(1(3(0(2(2(2(3(5(4(0(4(1(5(2(3(4(x1))))))))))))))))))))))))) -> 5(0(0(2(0(4(1(5(1(1(3(0(2(2(2(3(5(4(0(4(1(5(2(3(4(x1)))))))))))))))))))))))))
0(4(3(0(3(3(5(3(5(1(4(2(3(3(0(4(0(1(5(0(3(0(2(5(5(0(x1)))))))))))))))))))))))))) -> 0(4(3(0(3(3(5(3(5(1(4(2(3(3(0(4(1(0(5(0(3(0(2(5(5(0(x1))))))))))))))))))))))))))
1(2(3(2(0(1(0(5(3(0(2(1(1(1(4(4(1(2(4(5(2(2(4(0(3(2(x1)))))))))))))))))))))))))) -> 1(2(3(2(0(1(0(5(3(0(2(1(1(1(4(4(1(4(2(5(2(2(4(0(3(2(x1))))))))))))))))))))))))))
1(3(3(2(1(2(1(1(0(1(5(0(4(2(5(3(2(3(1(5(3(2(3(4(1(4(2(x1))))))))))))))))))))))))))) -> 1(2(3(3(1(2(1(0(1(1(5(0(4(5(2(3(2(3(1(3(2(5(3(1(4(4(2(x1)))))))))))))))))))))))))))
4(3(2(1(1(2(4(4(5(1(5(2(2(4(0(2(4(2(4(2(0(4(2(4(4(0(1(x1))))))))))))))))))))))))))) -> 4(3(2(1(2(1(4(4(5(1(5(2(2(4(0(2(4(2(4(2(0(4(2(4(4(0(1(x1)))))))))))))))))))))))))))
5(5(0(3(2(2(1(3(4(3(5(4(2(5(2(0(4(1(1(2(4(0(5(4(3(2(4(4(x1)))))))))))))))))))))))))))) -> 5(5(0(3(2(2(3(1(4(3(5(4(2(5(2(0(4(1(1(2(4(0(5(4(3(2(4(4(x1))))))))))))))))))))))))))))
5(5(5(3(5(3(2(5(0(1(5(3(1(2(2(3(3(0(3(1(0(4(1(2(2(5(3(1(3(x1))))))))))))))))))))))))))))) -> 5(5(5(3(5(3(2(5(1(0(5(3(1(2(2(3(3(0(3(1(0(4(1(2(2(5(3(1(3(x1)))))))))))))))))))))))))))))
0(0(1(4(5(3(1(4(5(1(4(5(1(0(5(2(2(0(1(2(2(3(3(3(0(0(2(1(2(5(x1)))))))))))))))))))))))))))))) -> 0(0(1(4(5(3(1(4(5(1(4(5(1(0(5(2(0(2(1(2(2(3(3(3(0(0(2(1(2(5(x1))))))))))))))))))))))))))))))
1(5(0(0(1(5(2(1(5(0(5(5(5(0(1(4(0(5(3(4(3(1(2(0(4(0(2(2(1(5(x1)))))))))))))))))))))))))))))) -> 1(5(0(0(1(5(2(5(1(0(5(5(5(0(1(4(0(5(3(4(3(1(2(0(4(0(2(2(1(5(x1))))))))))))))))))))))))))))))
1(5(0(1(1(4(2(4(3(5(4(5(2(0(3(3(2(0(5(5(4(4(2(5(3(0(2(1(1(0(x1)))))))))))))))))))))))))))))) -> 1(5(0(1(1(4(4(2(3(5(4(5(2(0(3(3(2(0(5(5(4(4(2(5(3(0(2(1(1(0(x1))))))))))))))))))))))))))))))
2(4(5(5(3(3(1(2(0(5(5(1(0(3(4(4(5(1(3(5(2(4(0(1(1(4(1(4(5(1(x1)))))))))))))))))))))))))))))) -> 2(4(5(5(3(3(1(2(0(5(5(1(0(3(4(4(5(1(3(2(5(4(0(1(1(4(1(4(5(1(x1))))))))))))))))))))))))))))))
4(2(0(2(1(5(5(4(2(3(2(1(0(4(1(2(0(4(2(3(1(3(0(1(4(2(0(0(2(5(x1)))))))))))))))))))))))))))))) -> 4(2(0(2(1(5(5(4(2(3(2(1(0(1(4(2(0(4(2(3(1(3(0(1(4(2(0(0(2(5(x1))))))))))))))))))))))))))))))
encArg(cons_0(x_1)) -> 0(encArg(x_1))
encArg(cons_4(x_1)) -> 4(encArg(x_1))
encArg(cons_3(x_1)) -> 3(encArg(x_1))
encArg(cons_5(x_1)) -> 5(encArg(x_1))
encArg(cons_1(x_1)) -> 1(encArg(x_1))
encArg(cons_2(x_1)) -> 2(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))

Types:
0 :: 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5 -> 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5
1 :: 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5 -> 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5
2 :: 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5 -> 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5
3 :: 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5 -> 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5
4 :: 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5 -> 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5
5 :: 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5 -> 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5
encArg :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5
cons_0 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> cons_0:cons_4:cons_3:cons_5:cons_1:cons_2
cons_4 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> cons_0:cons_4:cons_3:cons_5:cons_1:cons_2
cons_3 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> cons_0:cons_4:cons_3:cons_5:cons_1:cons_2
cons_5 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> cons_0:cons_4:cons_3:cons_5:cons_1:cons_2
cons_1 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> cons_0:cons_4:cons_3:cons_5:cons_1:cons_2
cons_2 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> cons_0:cons_4:cons_3:cons_5:cons_1:cons_2
encode_0 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5
encode_1 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5
encode_2 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5
encode_3 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5
encode_4 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5
encode_5 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5
hole_3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_51_6 :: 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5
hole_cons_0:cons_4:cons_3:cons_5:cons_1:cons_22_6 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2
gen_cons_0:cons_4:cons_3:cons_5:cons_1:cons_23_6 :: Nat -> cons_0:cons_4:cons_3:cons_5:cons_1:cons_2

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

(11) OrderProof (LOWER BOUND(ID))
Heuristically decided to analyse the following defined symbols:
0, 2, 1, 3, 4, 5, encArg

They will be analysed ascendingly in the following order:
0 = 2
0 = 1
0 = 3
0 = 4
0 = 5
0 < encArg
2 = 1
2 = 3
2 = 4
2 = 5
2 < encArg
1 = 3
1 = 4
1 = 5
1 < encArg
3 = 4
3 = 5
3 < encArg
4 = 5
4 < encArg
5 < encArg

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

(12)
Obligation:
TRS:
Rules:
0(0(0(1(2(2(3(x1))))))) -> 0(0(0(2(1(2(3(x1)))))))
4(4(5(5(3(0(1(x1))))))) -> 4(4(3(5(0(5(1(x1)))))))
0(1(2(4(4(0(1(0(x1)))))))) -> 0(1(4(2(4(1(0(0(x1))))))))
4(0(4(2(4(0(3(1(x1)))))))) -> 4(0(4(2(0(4(3(1(x1))))))))
4(4(5(3(2(4(2(5(x1)))))))) -> 4(2(3(5(4(4(2(5(x1))))))))
3(1(5(3(4(5(1(3(3(x1))))))))) -> 3(1(5(3(5(4(1(3(3(x1)))))))))
5(1(5(3(5(4(0(0(3(x1))))))))) -> 5(1(5(3(5(0(4(0(3(x1)))))))))
0(0(0(2(2(3(4(4(3(3(x1)))))))))) -> 0(2(3(0(3(2(1(5(1(3(x1))))))))))
0(4(5(0(0(4(2(4(5(0(x1)))))))))) -> 3(5(3(5(5(4(0(2(2(3(x1))))))))))
1(1(5(3(4(3(4(4(2(5(x1)))))))))) -> 1(1(5(3(3(4(4(4(2(5(x1))))))))))
1(2(0(1(2(4(5(2(4(4(x1)))))))))) -> 1(5(4(2(0(2(2(4(1(4(x1))))))))))
1(5(2(2(3(3(4(2(4(5(x1)))))))))) -> 1(5(2(3(2(3(4(2(4(5(x1))))))))))
4(0(5(4(0(2(4(0(4(3(x1)))))))))) -> 2(3(1(3(5(3(1(2(4(5(x1))))))))))
0(0(5(2(2(4(4(3(3(4(0(x1))))))))))) -> 4(0(4(2(3(1(5(3(5(5(x1))))))))))
0(2(2(5(5(0(0(4(5(3(4(x1))))))))))) -> 4(0(5(1(3(5(5(4(5(0(x1))))))))))
0(4(0(4(5(3(3(0(5(5(2(x1))))))))))) -> 4(5(3(5(2(2(1(1(4(3(x1))))))))))
0(4(3(0(0(0(4(3(2(3(3(x1))))))))))) -> 2(5(1(5(2(4(5(4(3(2(x1))))))))))
0(4(4(5(4(0(1(3(1(3(4(x1))))))))))) -> 0(4(0(3(4(3(1(4(4(1(5(x1)))))))))))
0(5(2(0(0(2(1(4(2(4(5(x1))))))))))) -> 5(0(4(3(4(2(5(5(4(1(x1))))))))))
1(0(1(5(1(5(3(3(1(4(0(x1))))))))))) -> 3(1(2(1(5(2(4(5(1(1(x1))))))))))
1(1(1(2(2(5(2(1(3(1(0(x1))))))))))) -> 1(5(1(1(3(5(0(0(2(4(x1))))))))))
2(0(5(0(5(4(4(3(1(3(2(x1))))))))))) -> 2(1(0(3(1(2(1(3(4(0(x1))))))))))
2(2(0(2(2(5(0(3(2(0(5(x1))))))))))) -> 5(0(3(5(4(2(2(3(1(0(x1))))))))))
2(5(3(1(0(1(4(4(2(2(4(x1))))))))))) -> 0(5(1(0(0(2(0(5(5(1(x1))))))))))
3(1(3(2(1(0(5(3(4(0(1(x1))))))))))) -> 1(2(0(4(0(3(2(0(4(0(x1))))))))))
3(1(3(3(3(0(4(1(1(3(0(x1))))))))))) -> 1(0(2(1(2(1(0(1(1(3(x1))))))))))
3(2(2(2(1(1(2(0(0(2(0(x1))))))))))) -> 4(4(2(5(4(5(5(0(5(0(x1))))))))))
3(2(5(3(4(4(0(1(3(5(4(x1))))))))))) -> 5(0(1(3(5(5(1(3(4(2(x1))))))))))
3(3(3(4(0(2(5(4(5(0(0(x1))))))))))) -> 3(1(5(1(1(5(2(3(1(4(x1))))))))))
3(4(2(2(2(3(1(3(1(2(1(x1))))))))))) -> 3(4(5(5(4(3(2(1(5(4(x1))))))))))
3(5(4(4(5(1(1(5(0(2(0(x1))))))))))) -> 3(1(5(1(3(5(0(1(5(1(x1))))))))))
3(5(5(4(5(3(0(2(5(5(1(x1))))))))))) -> 3(1(1(2(4(2(3(0(2(5(x1))))))))))
4(0(3(0(0(3(0(5(1(4(3(x1))))))))))) -> 1(2(1(5(5(5(0(4(1(1(x1))))))))))
4(0(5(2(5(3(0(0(3(5(5(x1))))))))))) -> 0(0(5(2(3(0(3(1(5(5(x1))))))))))
4(0(5(4(5(5(3(4(3(4(1(x1))))))))))) -> 3(4(1(1(3(1(4(0(1(4(x1))))))))))
4(0(5(5(2(0(4(0(2(3(5(x1))))))))))) -> 5(5(0(4(3(5(4(1(5(1(x1))))))))))
4(1(2(0(5(5(4(0(0(0(2(x1))))))))))) -> 3(3(5(4(5(3(2(0(0(2(x1))))))))))
4(1(3(3(1(5(1(1(2(4(3(x1))))))))))) -> 0(1(2(3(3(2(1(3(3(2(x1))))))))))
4(1(3(5(2(3(5(5(0(0(3(x1))))))))))) -> 5(2(3(0(3(5(2(3(5(3(x1))))))))))
4(2(1(2(2(3(3(3(1(3(2(x1))))))))))) -> 5(5(2(3(4(2(5(4(0(3(x1))))))))))
4(4(3(3(3(2(4(2(5(1(4(x1))))))))))) -> 2(0(3(4(4(1(3(0(2(0(x1))))))))))
4(5(4(0(2(5(0(2(3(2(5(x1))))))))))) -> 3(3(4(4(5(2(3(5(3(0(x1))))))))))
5(0(5(0(0(4(0(1(3(4(1(x1))))))))))) -> 2(2(4(2(1(1(3(3(3(0(x1))))))))))
5(1(0(3(5(0(1(1(3(4(3(x1))))))))))) -> 1(0(3(0(0(4(2(4(5(3(x1))))))))))
5(5(0(5(3(4(1(2(3(2(2(x1))))))))))) -> 1(2(3(5(5(0(1(3(5(5(x1))))))))))
5(5(3(3(0(1(4(1(3(3(0(x1))))))))))) -> 2(3(3(4(5(4(2(2(0(1(x1))))))))))
0(0(0(5(1(5(3(5(1(3(2(3(x1)))))))))))) -> 1(3(3(0(1(4(1(0(5(5(x1))))))))))
0(5(5(1(1(1(2(5(2(3(5(5(x1)))))))))))) -> 1(3(5(2(3(4(3(3(4(3(x1))))))))))
2(1(2(0(5(0(3(5(1(2(3(5(x1)))))))))))) -> 1(0(0(4(5(4(1(4(1(0(x1))))))))))
2(3(2(1(1(1(0(2(1(3(5(1(x1)))))))))))) -> 5(4(3(0(1(2(3(3(2(5(x1))))))))))
2(3(4(3(5(1(2(4(2(0(2(1(x1)))))))))))) -> 2(4(1(3(2(2(5(5(1(0(x1))))))))))
4(3(1(3(5(1(5(1(5(0(2(1(x1)))))))))))) -> 0(1(3(1(0(4(0(0(5(3(x1))))))))))
4(3(3(0(5(2(0(4(4(5(1(2(x1)))))))))))) -> 2(0(1(1(5(1(1(4(0(0(x1))))))))))
5(1(2(1(0(2(3(1(3(1(0(0(x1)))))))))))) -> 5(2(0(4(2(1(4(1(1(3(x1))))))))))
5(2(3(3(1(0(1(1(1(4(1(4(x1)))))))))))) -> 0(2(4(0(4(0(4(0(0(1(x1))))))))))
0(1(1(1(2(0(1(3(0(4(2(3(3(x1))))))))))))) -> 0(4(1(2(4(2(5(0(0(0(x1))))))))))
0(1(1(4(1(3(2(4(3(5(5(0(1(x1))))))))))))) -> 4(3(2(0(5(0(4(0(4(4(x1))))))))))
0(1(1(5(1(1(4(4(5(0(4(2(1(x1))))))))))))) -> 0(3(2(0(0(4(3(1(0(4(x1))))))))))
4(1(1(3(1(3(2(1(2(2(2(0(5(x1))))))))))))) -> 0(3(5(4(0(1(4(0(5(0(x1))))))))))
4(3(1(1(2(1(2(0(5(2(0(3(2(x1))))))))))))) -> 4(4(4(4(4(0(0(3(4(1(x1))))))))))
5(1(4(4(3(1(5(4(3(5(1(2(0(x1))))))))))))) -> 2(2(1(3(0(0(4(3(2(5(x1))))))))))
2(2(4(3(2(2(2(4(2(5(2(0(4(5(x1)))))))))))))) -> 2(2(0(2(2(4(2(5(3(4(4(2(2(5(x1))))))))))))))
5(4(1(5(1(4(2(5(4(3(0(4(1(0(x1)))))))))))))) -> 5(4(1(1(5(4(2(5(4(3(0(4(1(0(x1))))))))))))))
1(2(4(0(2(4(0(1(2(4(3(1(0(3(4(x1))))))))))))))) -> 1(2(4(0(2(4(0(1(4(2(3(1(0(3(4(x1)))))))))))))))
2(0(2(5(4(0(3(3(0(4(2(2(5(5(2(x1))))))))))))))) -> 2(0(2(4(0(5(0(3(4(3(2(2(5(5(2(x1)))))))))))))))
0(4(0(1(0(2(2(4(3(0(5(0(2(0(4(5(3(x1))))))))))))))))) -> 0(4(0(1(0(2(4(2(3(0(5(0(2(0(4(5(3(x1)))))))))))))))))
3(2(5(5(2(1(2(2(2(3(2(2(4(0(4(0(3(5(x1)))))))))))))))))) -> 3(5(2(2(5(1(2(2(2(3(2(2(4(0(4(0(3(5(x1))))))))))))))))))
5(3(1(5(5(3(3(0(2(2(2(2(3(3(4(5(1(1(x1)))))))))))))))))) -> 5(3(1(5(5(3(3(0(2(2(2(3(2(3(4(5(1(1(x1))))))))))))))))))
5(5(3(4(1(2(0(2(5(3(2(5(4(4(5(5(1(2(x1)))))))))))))))))) -> 5(5(3(4(1(2(0(2(5(3(2(4(5(4(5(5(1(2(x1))))))))))))))))))
0(0(3(1(5(5(1(5(3(2(0(2(2(4(3(4(0(5(1(x1))))))))))))))))))) -> 0(3(0(5(3(1(1(0(5(2(2(4(5(2(3(4(0(5(1(x1)))))))))))))))))))
4(5(5(3(5(4(1(1(5(5(3(3(1(5(4(4(5(0(4(x1))))))))))))))))))) -> 4(5(5(3(5(4(1(5(1(5(3(3(1(5(4(4(5(0(4(x1)))))))))))))))))))
0(5(2(5(4(3(3(2(3(5(0(2(3(2(5(0(5(0(4(1(x1)))))))))))))))))))) -> 0(5(2(5(4(3(3(2(3(5(0(2(3(2(0(5(5(0(4(1(x1))))))))))))))))))))
2(4(1(4(1(0(4(0(3(1(0(1(1(0(5(4(1(5(1(4(x1)))))))))))))))))))) -> 2(4(1(4(1(0(4(0(3(1(0(1(1(5(0(4(1(5(1(4(x1))))))))))))))))))))
2(5(2(3(0(0(1(0(5(0(2(5(3(4(0(5(5(5(3(2(x1)))))))))))))))))))) -> 2(5(2(3(0(0(1(0(5(0(2(5(3(4(5(0(5(5(3(2(x1))))))))))))))))))))
2(4(3(1(4(0(2(5(3(4(1(3(4(0(3(1(0(1(0(1(3(x1))))))))))))))))))))) -> 2(4(3(1(4(0(5(2(3(4(1(3(4(0(3(1(0(1(0(1(3(x1)))))))))))))))))))))
5(5(2(3(2(0(3(2(5(3(2(5(5(5(5(1(5(5(1(2(2(x1))))))))))))))))))))) -> 5(5(2(3(2(0(3(2(5(3(2(5(5(5(1(5(5(5(1(2(2(x1)))))))))))))))))))))
2(1(0(5(5(4(1(0(4(2(5(3(1(4(1(3(5(0(0(2(4(5(x1)))))))))))))))))))))) -> 2(1(0(5(5(4(1(0(4(2(5(3(1(4(1(3(0(5(0(2(4(5(x1))))))))))))))))))))))
2(0(2(4(0(2(4(2(0(0(1(1(0(1(3(5(3(3(4(3(1(2(5(x1))))))))))))))))))))))) -> 2(0(2(2(0(4(4(1(0(1(3(2(0(1(5(0(3(3(1(2(3(4(5(x1)))))))))))))))))))))))
3(3(2(5(4(4(0(1(3(1(2(1(5(0(0(4(2(1(4(2(2(3(5(x1))))))))))))))))))))))) -> 3(3(2(5(4(4(0(1(3(1(2(1(5(0(4(0(2(1(4(2(2(3(5(x1)))))))))))))))))))))))
5(1(5(0(3(3(0(1(2(3(3(1(4(5(3(1(2(2(0(3(2(0(5(x1))))))))))))))))))))))) -> 5(1(5(0(3(3(0(1(2(3(3(1(4(5(3(1(2(0(2(3(2(0(5(x1)))))))))))))))))))))))
3(2(3(3(2(2(5(1(0(5(4(4(5(2(2(4(3(5(2(1(2(1(3(1(x1)))))))))))))))))))))))) -> 3(2(3(3(2(2(5(1(5(0(4(4(5(2(2(4(3(5(2(1(2(1(3(1(x1))))))))))))))))))))))))
5(0(0(2(4(0(1(5(1(1(3(0(2(2(2(3(5(4(0(4(1(5(2(3(4(x1))))))))))))))))))))))))) -> 5(0(0(2(0(4(1(5(1(1(3(0(2(2(2(3(5(4(0(4(1(5(2(3(4(x1)))))))))))))))))))))))))
0(4(3(0(3(3(5(3(5(1(4(2(3(3(0(4(0(1(5(0(3(0(2(5(5(0(x1)))))))))))))))))))))))))) -> 0(4(3(0(3(3(5(3(5(1(4(2(3(3(0(4(1(0(5(0(3(0(2(5(5(0(x1))))))))))))))))))))))))))
1(2(3(2(0(1(0(5(3(0(2(1(1(1(4(4(1(2(4(5(2(2(4(0(3(2(x1)))))))))))))))))))))))))) -> 1(2(3(2(0(1(0(5(3(0(2(1(1(1(4(4(1(4(2(5(2(2(4(0(3(2(x1))))))))))))))))))))))))))
1(3(3(2(1(2(1(1(0(1(5(0(4(2(5(3(2(3(1(5(3(2(3(4(1(4(2(x1))))))))))))))))))))))))))) -> 1(2(3(3(1(2(1(0(1(1(5(0(4(5(2(3(2(3(1(3(2(5(3(1(4(4(2(x1)))))))))))))))))))))))))))
4(3(2(1(1(2(4(4(5(1(5(2(2(4(0(2(4(2(4(2(0(4(2(4(4(0(1(x1))))))))))))))))))))))))))) -> 4(3(2(1(2(1(4(4(5(1(5(2(2(4(0(2(4(2(4(2(0(4(2(4(4(0(1(x1)))))))))))))))))))))))))))
5(5(0(3(2(2(1(3(4(3(5(4(2(5(2(0(4(1(1(2(4(0(5(4(3(2(4(4(x1)))))))))))))))))))))))))))) -> 5(5(0(3(2(2(3(1(4(3(5(4(2(5(2(0(4(1(1(2(4(0(5(4(3(2(4(4(x1))))))))))))))))))))))))))))
5(5(5(3(5(3(2(5(0(1(5(3(1(2(2(3(3(0(3(1(0(4(1(2(2(5(3(1(3(x1))))))))))))))))))))))))))))) -> 5(5(5(3(5(3(2(5(1(0(5(3(1(2(2(3(3(0(3(1(0(4(1(2(2(5(3(1(3(x1)))))))))))))))))))))))))))))
0(0(1(4(5(3(1(4(5(1(4(5(1(0(5(2(2(0(1(2(2(3(3(3(0(0(2(1(2(5(x1)))))))))))))))))))))))))))))) -> 0(0(1(4(5(3(1(4(5(1(4(5(1(0(5(2(0(2(1(2(2(3(3(3(0(0(2(1(2(5(x1))))))))))))))))))))))))))))))
1(5(0(0(1(5(2(1(5(0(5(5(5(0(1(4(0(5(3(4(3(1(2(0(4(0(2(2(1(5(x1)))))))))))))))))))))))))))))) -> 1(5(0(0(1(5(2(5(1(0(5(5(5(0(1(4(0(5(3(4(3(1(2(0(4(0(2(2(1(5(x1))))))))))))))))))))))))))))))
1(5(0(1(1(4(2(4(3(5(4(5(2(0(3(3(2(0(5(5(4(4(2(5(3(0(2(1(1(0(x1)))))))))))))))))))))))))))))) -> 1(5(0(1(1(4(4(2(3(5(4(5(2(0(3(3(2(0(5(5(4(4(2(5(3(0(2(1(1(0(x1))))))))))))))))))))))))))))))
2(4(5(5(3(3(1(2(0(5(5(1(0(3(4(4(5(1(3(5(2(4(0(1(1(4(1(4(5(1(x1)))))))))))))))))))))))))))))) -> 2(4(5(5(3(3(1(2(0(5(5(1(0(3(4(4(5(1(3(2(5(4(0(1(1(4(1(4(5(1(x1))))))))))))))))))))))))))))))
4(2(0(2(1(5(5(4(2(3(2(1(0(4(1(2(0(4(2(3(1(3(0(1(4(2(0(0(2(5(x1)))))))))))))))))))))))))))))) -> 4(2(0(2(1(5(5(4(2(3(2(1(0(1(4(2(0(4(2(3(1(3(0(1(4(2(0(0(2(5(x1))))))))))))))))))))))))))))))
encArg(cons_0(x_1)) -> 0(encArg(x_1))
encArg(cons_4(x_1)) -> 4(encArg(x_1))
encArg(cons_3(x_1)) -> 3(encArg(x_1))
encArg(cons_5(x_1)) -> 5(encArg(x_1))
encArg(cons_1(x_1)) -> 1(encArg(x_1))
encArg(cons_2(x_1)) -> 2(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))

Types:
0 :: 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5 -> 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5
1 :: 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5 -> 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5
2 :: 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5 -> 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5
3 :: 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5 -> 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5
4 :: 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5 -> 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5
5 :: 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5 -> 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5
encArg :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5
cons_0 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> cons_0:cons_4:cons_3:cons_5:cons_1:cons_2
cons_4 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> cons_0:cons_4:cons_3:cons_5:cons_1:cons_2
cons_3 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> cons_0:cons_4:cons_3:cons_5:cons_1:cons_2
cons_5 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> cons_0:cons_4:cons_3:cons_5:cons_1:cons_2
cons_1 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> cons_0:cons_4:cons_3:cons_5:cons_1:cons_2
cons_2 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> cons_0:cons_4:cons_3:cons_5:cons_1:cons_2
encode_0 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5
encode_1 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5
encode_2 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5
encode_3 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5
encode_4 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5
encode_5 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5
hole_3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_51_6 :: 3:2:1:0:5:4:encArg:encode_0:encode_1:encode_2:encode_3:encode_4:encode_5
hole_cons_0:cons_4:cons_3:cons_5:cons_1:cons_22_6 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2
gen_cons_0:cons_4:cons_3:cons_5:cons_1:cons_23_6 :: Nat -> cons_0:cons_4:cons_3:cons_5:cons_1:cons_2


Generator Equations:
gen_cons_0:cons_4:cons_3:cons_5:cons_1:cons_23_6(0) <=> hole_cons_0:cons_4:cons_3:cons_5:cons_1:cons_22_6
gen_cons_0:cons_4:cons_3:cons_5:cons_1:cons_23_6(+(x, 1)) <=> cons_0(gen_cons_0:cons_4:cons_3:cons_5:cons_1:cons_23_6(x))


The following defined symbols remain to be analysed:
2, 0, 1, 3, 4, 5, encArg

They will be analysed ascendingly in the following order:
0 = 2
0 = 1
0 = 3
0 = 4
0 = 5
0 < encArg
2 = 1
2 = 3
2 = 4
2 = 5
2 < encArg
1 = 3
1 = 4
1 = 5
1 < encArg
3 = 4
3 = 5
3 < encArg
4 = 5
4 < encArg
5 < encArg

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

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

(14)
Obligation:
The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   0(0(0(1(2(2(3(x1))))))) -> 0(0(0(2(1(2(3(x1)))))))
   4(4(5(5(3(0(1(x1))))))) -> 4(4(3(5(0(5(1(x1)))))))
   0(1(2(4(4(0(1(0(x1)))))))) -> 0(1(4(2(4(1(0(0(x1))))))))
   4(0(4(2(4(0(3(1(x1)))))))) -> 4(0(4(2(0(4(3(1(x1))))))))
   4(4(5(3(2(4(2(5(x1)))))))) -> 4(2(3(5(4(4(2(5(x1))))))))
   3(1(5(3(4(5(1(3(3(x1))))))))) -> 3(1(5(3(5(4(1(3(3(x1)))))))))
   5(1(5(3(5(4(0(0(3(x1))))))))) -> 5(1(5(3(5(0(4(0(3(x1)))))))))
   0(0(0(2(2(3(4(4(3(3(x1)))))))))) -> 0(2(3(0(3(2(1(5(1(3(x1))))))))))
   0(4(5(0(0(4(2(4(5(0(x1)))))))))) -> 3(5(3(5(5(4(0(2(2(3(x1))))))))))
   1(1(5(3(4(3(4(4(2(5(x1)))))))))) -> 1(1(5(3(3(4(4(4(2(5(x1))))))))))
   1(2(0(1(2(4(5(2(4(4(x1)))))))))) -> 1(5(4(2(0(2(2(4(1(4(x1))))))))))
   1(5(2(2(3(3(4(2(4(5(x1)))))))))) -> 1(5(2(3(2(3(4(2(4(5(x1))))))))))
   4(0(5(4(0(2(4(0(4(3(x1)))))))))) -> 2(3(1(3(5(3(1(2(4(5(x1))))))))))
   0(0(5(2(2(4(4(3(3(4(0(x1))))))))))) -> 4(0(4(2(3(1(5(3(5(5(x1))))))))))
   0(2(2(5(5(0(0(4(5(3(4(x1))))))))))) -> 4(0(5(1(3(5(5(4(5(0(x1))))))))))
   0(4(0(4(5(3(3(0(5(5(2(x1))))))))))) -> 4(5(3(5(2(2(1(1(4(3(x1))))))))))
   0(4(3(0(0(0(4(3(2(3(3(x1))))))))))) -> 2(5(1(5(2(4(5(4(3(2(x1))))))))))
   0(4(4(5(4(0(1(3(1(3(4(x1))))))))))) -> 0(4(0(3(4(3(1(4(4(1(5(x1)))))))))))
   0(5(2(0(0(2(1(4(2(4(5(x1))))))))))) -> 5(0(4(3(4(2(5(5(4(1(x1))))))))))
   1(0(1(5(1(5(3(3(1(4(0(x1))))))))))) -> 3(1(2(1(5(2(4(5(1(1(x1))))))))))
   1(1(1(2(2(5(2(1(3(1(0(x1))))))))))) -> 1(5(1(1(3(5(0(0(2(4(x1))))))))))
   2(0(5(0(5(4(4(3(1(3(2(x1))))))))))) -> 2(1(0(3(1(2(1(3(4(0(x1))))))))))
   2(2(0(2(2(5(0(3(2(0(5(x1))))))))))) -> 5(0(3(5(4(2(2(3(1(0(x1))))))))))
   2(5(3(1(0(1(4(4(2(2(4(x1))))))))))) -> 0(5(1(0(0(2(0(5(5(1(x1))))))))))
   3(1(3(2(1(0(5(3(4(0(1(x1))))))))))) -> 1(2(0(4(0(3(2(0(4(0(x1))))))))))
   3(1(3(3(3(0(4(1(1(3(0(x1))))))))))) -> 1(0(2(1(2(1(0(1(1(3(x1))))))))))
   3(2(2(2(1(1(2(0(0(2(0(x1))))))))))) -> 4(4(2(5(4(5(5(0(5(0(x1))))))))))
   3(2(5(3(4(4(0(1(3(5(4(x1))))))))))) -> 5(0(1(3(5(5(1(3(4(2(x1))))))))))
   3(3(3(4(0(2(5(4(5(0(0(x1))))))))))) -> 3(1(5(1(1(5(2(3(1(4(x1))))))))))
   3(4(2(2(2(3(1(3(1(2(1(x1))))))))))) -> 3(4(5(5(4(3(2(1(5(4(x1))))))))))
   3(5(4(4(5(1(1(5(0(2(0(x1))))))))))) -> 3(1(5(1(3(5(0(1(5(1(x1))))))))))
   3(5(5(4(5(3(0(2(5(5(1(x1))))))))))) -> 3(1(1(2(4(2(3(0(2(5(x1))))))))))
   4(0(3(0(0(3(0(5(1(4(3(x1))))))))))) -> 1(2(1(5(5(5(0(4(1(1(x1))))))))))
   4(0(5(2(5(3(0(0(3(5(5(x1))))))))))) -> 0(0(5(2(3(0(3(1(5(5(x1))))))))))
   4(0(5(4(5(5(3(4(3(4(1(x1))))))))))) -> 3(4(1(1(3(1(4(0(1(4(x1))))))))))
   4(0(5(5(2(0(4(0(2(3(5(x1))))))))))) -> 5(5(0(4(3(5(4(1(5(1(x1))))))))))
   4(1(2(0(5(5(4(0(0(0(2(x1))))))))))) -> 3(3(5(4(5(3(2(0(0(2(x1))))))))))
   4(1(3(3(1(5(1(1(2(4(3(x1))))))))))) -> 0(1(2(3(3(2(1(3(3(2(x1))))))))))
   4(1(3(5(2(3(5(5(0(0(3(x1))))))))))) -> 5(2(3(0(3(5(2(3(5(3(x1))))))))))
   4(2(1(2(2(3(3(3(1(3(2(x1))))))))))) -> 5(5(2(3(4(2(5(4(0(3(x1))))))))))
   4(4(3(3(3(2(4(2(5(1(4(x1))))))))))) -> 2(0(3(4(4(1(3(0(2(0(x1))))))))))
   4(5(4(0(2(5(0(2(3(2(5(x1))))))))))) -> 3(3(4(4(5(2(3(5(3(0(x1))))))))))
   5(0(5(0(0(4(0(1(3(4(1(x1))))))))))) -> 2(2(4(2(1(1(3(3(3(0(x1))))))))))
   5(1(0(3(5(0(1(1(3(4(3(x1))))))))))) -> 1(0(3(0(0(4(2(4(5(3(x1))))))))))
   5(5(0(5(3(4(1(2(3(2(2(x1))))))))))) -> 1(2(3(5(5(0(1(3(5(5(x1))))))))))
   5(5(3(3(0(1(4(1(3(3(0(x1))))))))))) -> 2(3(3(4(5(4(2(2(0(1(x1))))))))))
   0(0(0(5(1(5(3(5(1(3(2(3(x1)))))))))))) -> 1(3(3(0(1(4(1(0(5(5(x1))))))))))
   0(5(5(1(1(1(2(5(2(3(5(5(x1)))))))))))) -> 1(3(5(2(3(4(3(3(4(3(x1))))))))))
   2(1(2(0(5(0(3(5(1(2(3(5(x1)))))))))))) -> 1(0(0(4(5(4(1(4(1(0(x1))))))))))
   2(3(2(1(1(1(0(2(1(3(5(1(x1)))))))))))) -> 5(4(3(0(1(2(3(3(2(5(x1))))))))))
   2(3(4(3(5(1(2(4(2(0(2(1(x1)))))))))))) -> 2(4(1(3(2(2(5(5(1(0(x1))))))))))
   4(3(1(3(5(1(5(1(5(0(2(1(x1)))))))))))) -> 0(1(3(1(0(4(0(0(5(3(x1))))))))))
   4(3(3(0(5(2(0(4(4(5(1(2(x1)))))))))))) -> 2(0(1(1(5(1(1(4(0(0(x1))))))))))
   5(1(2(1(0(2(3(1(3(1(0(0(x1)))))))))))) -> 5(2(0(4(2(1(4(1(1(3(x1))))))))))
   5(2(3(3(1(0(1(1(1(4(1(4(x1)))))))))))) -> 0(2(4(0(4(0(4(0(0(1(x1))))))))))
   0(1(1(1(2(0(1(3(0(4(2(3(3(x1))))))))))))) -> 0(4(1(2(4(2(5(0(0(0(x1))))))))))
   0(1(1(4(1(3(2(4(3(5(5(0(1(x1))))))))))))) -> 4(3(2(0(5(0(4(0(4(4(x1))))))))))
   0(1(1(5(1(1(4(4(5(0(4(2(1(x1))))))))))))) -> 0(3(2(0(0(4(3(1(0(4(x1))))))))))
   4(1(1(3(1(3(2(1(2(2(2(0(5(x1))))))))))))) -> 0(3(5(4(0(1(4(0(5(0(x1))))))))))
   4(3(1(1(2(1(2(0(5(2(0(3(2(x1))))))))))))) -> 4(4(4(4(4(0(0(3(4(1(x1))))))))))
   5(1(4(4(3(1(5(4(3(5(1(2(0(x1))))))))))))) -> 2(2(1(3(0(0(4(3(2(5(x1))))))))))
   2(2(4(3(2(2(2(4(2(5(2(0(4(5(x1)))))))))))))) -> 2(2(0(2(2(4(2(5(3(4(4(2(2(5(x1))))))))))))))
   5(4(1(5(1(4(2(5(4(3(0(4(1(0(x1)))))))))))))) -> 5(4(1(1(5(4(2(5(4(3(0(4(1(0(x1))))))))))))))
   1(2(4(0(2(4(0(1(2(4(3(1(0(3(4(x1))))))))))))))) -> 1(2(4(0(2(4(0(1(4(2(3(1(0(3(4(x1)))))))))))))))
   2(0(2(5(4(0(3(3(0(4(2(2(5(5(2(x1))))))))))))))) -> 2(0(2(4(0(5(0(3(4(3(2(2(5(5(2(x1)))))))))))))))
   0(4(0(1(0(2(2(4(3(0(5(0(2(0(4(5(3(x1))))))))))))))))) -> 0(4(0(1(0(2(4(2(3(0(5(0(2(0(4(5(3(x1)))))))))))))))))
   3(2(5(5(2(1(2(2(2(3(2(2(4(0(4(0(3(5(x1)))))))))))))))))) -> 3(5(2(2(5(1(2(2(2(3(2(2(4(0(4(0(3(5(x1))))))))))))))))))
   5(3(1(5(5(3(3(0(2(2(2(2(3(3(4(5(1(1(x1)))))))))))))))))) -> 5(3(1(5(5(3(3(0(2(2(2(3(2(3(4(5(1(1(x1))))))))))))))))))
   5(5(3(4(1(2(0(2(5(3(2(5(4(4(5(5(1(2(x1)))))))))))))))))) -> 5(5(3(4(1(2(0(2(5(3(2(4(5(4(5(5(1(2(x1))))))))))))))))))
   0(0(3(1(5(5(1(5(3(2(0(2(2(4(3(4(0(5(1(x1))))))))))))))))))) -> 0(3(0(5(3(1(1(0(5(2(2(4(5(2(3(4(0(5(1(x1)))))))))))))))))))
   4(5(5(3(5(4(1(1(5(5(3(3(1(5(4(4(5(0(4(x1))))))))))))))))))) -> 4(5(5(3(5(4(1(5(1(5(3(3(1(5(4(4(5(0(4(x1)))))))))))))))))))
   0(5(2(5(4(3(3(2(3(5(0(2(3(2(5(0(5(0(4(1(x1)))))))))))))))))))) -> 0(5(2(5(4(3(3(2(3(5(0(2(3(2(0(5(5(0(4(1(x1))))))))))))))))))))
   2(4(1(4(1(0(4(0(3(1(0(1(1(0(5(4(1(5(1(4(x1)))))))))))))))))))) -> 2(4(1(4(1(0(4(0(3(1(0(1(1(5(0(4(1(5(1(4(x1))))))))))))))))))))
   2(5(2(3(0(0(1(0(5(0(2(5(3(4(0(5(5(5(3(2(x1)))))))))))))))))))) -> 2(5(2(3(0(0(1(0(5(0(2(5(3(4(5(0(5(5(3(2(x1))))))))))))))))))))
   2(4(3(1(4(0(2(5(3(4(1(3(4(0(3(1(0(1(0(1(3(x1))))))))))))))))))))) -> 2(4(3(1(4(0(5(2(3(4(1(3(4(0(3(1(0(1(0(1(3(x1)))))))))))))))))))))
   5(5(2(3(2(0(3(2(5(3(2(5(5(5(5(1(5(5(1(2(2(x1))))))))))))))))))))) -> 5(5(2(3(2(0(3(2(5(3(2(5(5(5(1(5(5(5(1(2(2(x1)))))))))))))))))))))
   2(1(0(5(5(4(1(0(4(2(5(3(1(4(1(3(5(0(0(2(4(5(x1)))))))))))))))))))))) -> 2(1(0(5(5(4(1(0(4(2(5(3(1(4(1(3(0(5(0(2(4(5(x1))))))))))))))))))))))
   2(0(2(4(0(2(4(2(0(0(1(1(0(1(3(5(3(3(4(3(1(2(5(x1))))))))))))))))))))))) -> 2(0(2(2(0(4(4(1(0(1(3(2(0(1(5(0(3(3(1(2(3(4(5(x1)))))))))))))))))))))))
   3(3(2(5(4(4(0(1(3(1(2(1(5(0(0(4(2(1(4(2(2(3(5(x1))))))))))))))))))))))) -> 3(3(2(5(4(4(0(1(3(1(2(1(5(0(4(0(2(1(4(2(2(3(5(x1)))))))))))))))))))))))
   5(1(5(0(3(3(0(1(2(3(3(1(4(5(3(1(2(2(0(3(2(0(5(x1))))))))))))))))))))))) -> 5(1(5(0(3(3(0(1(2(3(3(1(4(5(3(1(2(0(2(3(2(0(5(x1)))))))))))))))))))))))
   3(2(3(3(2(2(5(1(0(5(4(4(5(2(2(4(3(5(2(1(2(1(3(1(x1)))))))))))))))))))))))) -> 3(2(3(3(2(2(5(1(5(0(4(4(5(2(2(4(3(5(2(1(2(1(3(1(x1))))))))))))))))))))))))
   5(0(0(2(4(0(1(5(1(1(3(0(2(2(2(3(5(4(0(4(1(5(2(3(4(x1))))))))))))))))))))))))) -> 5(0(0(2(0(4(1(5(1(1(3(0(2(2(2(3(5(4(0(4(1(5(2(3(4(x1)))))))))))))))))))))))))
   0(4(3(0(3(3(5(3(5(1(4(2(3(3(0(4(0(1(5(0(3(0(2(5(5(0(x1)))))))))))))))))))))))))) -> 0(4(3(0(3(3(5(3(5(1(4(2(3(3(0(4(1(0(5(0(3(0(2(5(5(0(x1))))))))))))))))))))))))))
   1(2(3(2(0(1(0(5(3(0(2(1(1(1(4(4(1(2(4(5(2(2(4(0(3(2(x1)))))))))))))))))))))))))) -> 1(2(3(2(0(1(0(5(3(0(2(1(1(1(4(4(1(4(2(5(2(2(4(0(3(2(x1))))))))))))))))))))))))))
   1(3(3(2(1(2(1(1(0(1(5(0(4(2(5(3(2(3(1(5(3(2(3(4(1(4(2(x1))))))))))))))))))))))))))) -> 1(2(3(3(1(2(1(0(1(1(5(0(4(5(2(3(2(3(1(3(2(5(3(1(4(4(2(x1)))))))))))))))))))))))))))
   4(3(2(1(1(2(4(4(5(1(5(2(2(4(0(2(4(2(4(2(0(4(2(4(4(0(1(x1))))))))))))))))))))))))))) -> 4(3(2(1(2(1(4(4(5(1(5(2(2(4(0(2(4(2(4(2(0(4(2(4(4(0(1(x1)))))))))))))))))))))))))))
   5(5(0(3(2(2(1(3(4(3(5(4(2(5(2(0(4(1(1(2(4(0(5(4(3(2(4(4(x1)))))))))))))))))))))))))))) -> 5(5(0(3(2(2(3(1(4(3(5(4(2(5(2(0(4(1(1(2(4(0(5(4(3(2(4(4(x1))))))))))))))))))))))))))))
   5(5(5(3(5(3(2(5(0(1(5(3(1(2(2(3(3(0(3(1(0(4(1(2(2(5(3(1(3(x1))))))))))))))))))))))))))))) -> 5(5(5(3(5(3(2(5(1(0(5(3(1(2(2(3(3(0(3(1(0(4(1(2(2(5(3(1(3(x1)))))))))))))))))))))))))))))
   0(0(1(4(5(3(1(4(5(1(4(5(1(0(5(2(2(0(1(2(2(3(3(3(0(0(2(1(2(5(x1)))))))))))))))))))))))))))))) -> 0(0(1(4(5(3(1(4(5(1(4(5(1(0(5(2(0(2(1(2(2(3(3(3(0(0(2(1(2(5(x1))))))))))))))))))))))))))))))
   1(5(0(0(1(5(2(1(5(0(5(5(5(0(1(4(0(5(3(4(3(1(2(0(4(0(2(2(1(5(x1)))))))))))))))))))))))))))))) -> 1(5(0(0(1(5(2(5(1(0(5(5(5(0(1(4(0(5(3(4(3(1(2(0(4(0(2(2(1(5(x1))))))))))))))))))))))))))))))
   1(5(0(1(1(4(2(4(3(5(4(5(2(0(3(3(2(0(5(5(4(4(2(5(3(0(2(1(1(0(x1)))))))))))))))))))))))))))))) -> 1(5(0(1(1(4(4(2(3(5(4(5(2(0(3(3(2(0(5(5(4(4(2(5(3(0(2(1(1(0(x1))))))))))))))))))))))))))))))
   2(4(5(5(3(3(1(2(0(5(5(1(0(3(4(4(5(1(3(5(2(4(0(1(1(4(1(4(5(1(x1)))))))))))))))))))))))))))))) -> 2(4(5(5(3(3(1(2(0(5(5(1(0(3(4(4(5(1(3(2(5(4(0(1(1(4(1(4(5(1(x1))))))))))))))))))))))))))))))
   4(2(0(2(1(5(5(4(2(3(2(1(0(4(1(2(0(4(2(3(1(3(0(1(4(2(0(0(2(5(x1)))))))))))))))))))))))))))))) -> 4(2(0(2(1(5(5(4(2(3(2(1(0(1(4(2(0(4(2(3(1(3(0(1(4(2(0(0(2(5(x1))))))))))))))))))))))))))))))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_4(x_1)) -> 4(encArg(x_1))
   encArg(cons_3(x_1)) -> 3(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(encArg(x_1))
   encArg(cons_1(x_1)) -> 1(encArg(x_1))
   encArg(cons_2(x_1)) -> 2(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
----------------------------------------

(15) NonCtorToCtorProof (UPPER BOUND(ID))
transformed non-ctor to ctor-system
----------------------------------------

(16)
Obligation:
The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   4(c_0(c_5(c_5(c_2(c_0(c_4(c_0(c_2(c_3(c_5(x1))))))))))) -> 5(5(0(4(3(5(4(1(5(1(x1))))))))))
   4(c_5(c_4(c_0(c_2(c_5(c_0(c_2(c_3(c_2(c_5(x1))))))))))) -> 3(3(4(4(5(2(3(5(3(0(x1))))))))))
   5(c_5(c_3(c_4(c_1(c_2(c_0(c_2(c_5(c_3(c_2(c_5(c_4(c_4(c_5(c_5(c_1(c_2(x1)))))))))))))))))) -> 5(5(3(4(1(2(0(2(5(3(2(4(5(4(5(5(1(2(x1))))))))))))))))))
   5(c_1(c_4(c_4(c_3(c_1(c_5(c_4(c_3(c_5(c_1(c_2(c_0(x1))))))))))))) -> 2(2(1(3(0(0(4(3(2(5(x1))))))))))
   0(c_0(c_0(c_2(c_2(c_3(c_4(c_4(c_3(c_3(x1)))))))))) -> 0(2(3(0(3(2(1(5(1(3(x1))))))))))
   4(c_4(c_3(c_3(c_3(c_2(c_4(c_2(c_5(c_1(c_4(x1))))))))))) -> 2(0(3(4(4(1(3(0(2(0(x1))))))))))
   5(c_1(c_2(c_1(c_0(c_2(c_3(c_1(c_3(c_1(c_0(c_0(x1)))))))))))) -> 5(2(0(4(2(1(4(1(1(3(x1))))))))))
   0(c_4(c_3(c_0(c_3(c_3(c_5(c_3(c_5(c_1(c_4(c_2(c_3(c_3(c_0(c_4(c_0(c_1(c_5(c_0(c_3(c_0(c_2(c_5(c_5(c_0(x1)))))))))))))))))))))))))) -> 0(4(3(0(3(3(5(3(5(1(4(2(3(3(0(4(1(0(5(0(3(0(2(5(5(0(x1))))))))))))))))))))))))))
   2(c_1(c_2(c_0(c_5(c_0(c_3(c_5(c_1(c_2(c_3(c_5(x1)))))))))))) -> 1(0(0(4(5(4(1(4(1(0(x1))))))))))
   5(c_0(c_0(c_2(c_4(c_0(c_1(c_5(c_1(c_1(c_3(c_0(c_2(c_2(c_2(c_3(c_5(c_4(c_0(c_4(c_1(c_5(c_2(c_3(c_4(x1))))))))))))))))))))))))) -> 5(0(0(2(0(4(1(5(1(1(3(0(2(2(2(3(5(4(0(4(1(5(2(3(4(x1)))))))))))))))))))))))))
   0(c_5(c_2(c_0(c_0(c_2(c_1(c_4(c_2(c_4(c_5(x1))))))))))) -> 5(0(4(3(4(2(5(5(4(1(x1))))))))))
   4(c_1(c_3(c_3(c_1(c_5(c_1(c_1(c_2(c_4(c_3(x1))))))))))) -> 0(1(2(3(3(2(1(3(3(2(x1))))))))))
   3(c_3(c_3(c_4(c_0(c_2(c_5(c_4(c_5(c_0(c_0(x1))))))))))) -> 3(1(5(1(1(5(2(3(1(4(x1))))))))))
   2(c_5(c_3(c_1(c_0(c_1(c_4(c_4(c_2(c_2(c_4(x1))))))))))) -> 0(5(1(0(0(2(0(5(5(1(x1))))))))))
   3(c_3(c_2(c_5(c_4(c_4(c_0(c_1(c_3(c_1(c_2(c_1(c_5(c_0(c_0(c_4(c_2(c_1(c_4(c_2(c_2(c_3(c_5(x1))))))))))))))))))))))) -> 3(3(2(5(4(4(0(1(3(1(2(1(5(0(4(0(2(1(4(2(2(3(5(x1)))))))))))))))))))))))
   1(c_5(c_0(c_1(c_1(c_4(c_2(c_4(c_3(c_5(c_4(c_5(c_2(c_0(c_3(c_3(c_2(c_0(c_5(c_5(c_4(c_4(c_2(c_5(c_3(c_0(c_2(c_1(c_1(c_0(x1)))))))))))))))))))))))))))))) -> 1(5(0(1(1(4(4(2(3(5(4(5(2(0(3(3(2(0(5(5(4(4(2(5(3(0(2(1(1(0(x1))))))))))))))))))))))))))))))
   4(c_3(c_1(c_3(c_5(c_1(c_5(c_1(c_5(c_0(c_2(c_1(x1)))))))))))) -> 0(1(3(1(0(4(0(0(5(3(x1))))))))))
   2(c_1(c_0(c_5(c_5(c_4(c_1(c_0(c_4(c_2(c_5(c_3(c_1(c_4(c_1(c_3(c_5(c_0(c_0(c_2(c_4(c_5(x1)))))))))))))))))))))) -> 2(1(0(5(5(4(1(0(4(2(5(3(1(4(1(3(0(5(0(2(4(5(x1))))))))))))))))))))))
   4(c_0(c_5(c_4(c_0(c_2(c_4(c_0(c_4(c_3(x1)))))))))) -> 2(3(1(3(5(3(1(2(4(5(x1))))))))))
   0(c_0(c_3(c_1(c_5(c_5(c_1(c_5(c_3(c_2(c_0(c_2(c_2(c_4(c_3(c_4(c_0(c_5(c_1(x1))))))))))))))))))) -> 0(3(0(5(3(1(1(0(5(2(2(4(5(2(3(4(0(5(1(x1)))))))))))))))))))
   1(c_5(c_2(c_2(c_3(c_3(c_4(c_2(c_4(c_5(x1)))))))))) -> 1(5(2(3(2(3(4(2(4(5(x1))))))))))
   5(c_5(c_0(c_5(c_3(c_4(c_1(c_2(c_3(c_2(c_2(x1))))))))))) -> 1(2(3(5(5(0(1(3(5(5(x1))))))))))
   5(c_5(c_0(c_3(c_2(c_2(c_1(c_3(c_4(c_3(c_5(c_4(c_2(c_5(c_2(c_0(c_4(c_1(c_1(c_2(c_4(c_0(c_5(c_4(c_3(c_2(c_4(c_4(x1)))))))))))))))))))))))))))) -> 5(5(0(3(2(2(3(1(4(3(5(4(2(5(2(0(4(1(1(2(4(0(5(4(3(2(4(4(x1))))))))))))))))))))))))))))
   5(c_0(c_5(c_0(c_0(c_4(c_0(c_1(c_3(c_4(c_1(x1))))))))))) -> 2(2(4(2(1(1(3(3(3(0(x1))))))))))
   4(c_0(c_5(c_4(c_5(c_5(c_3(c_4(c_3(c_4(c_1(x1))))))))))) -> 3(4(1(1(3(1(4(0(1(4(x1))))))))))
   1(c_5(c_0(c_0(c_1(c_5(c_2(c_1(c_5(c_0(c_5(c_5(c_5(c_0(c_1(c_4(c_0(c_5(c_3(c_4(c_3(c_1(c_2(c_0(c_4(c_0(c_2(c_2(c_1(c_5(x1)))))))))))))))))))))))))))))) -> 1(5(0(0(1(5(2(5(1(0(5(5(5(0(1(4(0(5(3(4(3(1(2(0(4(0(2(2(1(5(x1))))))))))))))))))))))))))))))
   0(c_1(c_1(c_5(c_1(c_1(c_4(c_4(c_5(c_0(c_4(c_2(c_1(x1))))))))))))) -> 0(3(2(0(0(4(3(1(0(4(x1))))))))))
   1(c_2(c_3(c_2(c_0(c_1(c_0(c_5(c_3(c_0(c_2(c_1(c_1(c_1(c_4(c_4(c_1(c_2(c_4(c_5(c_2(c_2(c_4(c_0(c_3(c_2(x1)))))))))))))))))))))))))) -> 1(2(3(2(0(1(0(5(3(0(2(1(1(1(4(4(1(4(2(5(2(2(4(0(3(2(x1))))))))))))))))))))))))))
   5(c_5(c_5(c_3(c_5(c_3(c_2(c_5(c_0(c_1(c_5(c_3(c_1(c_2(c_2(c_3(c_3(c_0(c_3(c_1(c_0(c_4(c_1(c_2(c_2(c_5(c_3(c_1(c_3(x1))))))))))))))))))))))))))))) -> 5(5(5(3(5(3(2(5(1(0(5(3(1(2(2(3(3(0(3(1(0(4(1(2(2(5(3(1(3(x1)))))))))))))))))))))))))))))
   5(c_2(c_3(c_3(c_1(c_0(c_1(c_1(c_1(c_4(c_1(c_4(x1)))))))))))) -> 0(2(4(0(4(0(4(0(0(1(x1))))))))))
   4(c_3(c_3(c_0(c_5(c_2(c_0(c_4(c_4(c_5(c_1(c_2(x1)))))))))))) -> 2(0(1(1(5(1(1(4(0(0(x1))))))))))
   3(c_4(c_2(c_2(c_2(c_3(c_1(c_3(c_1(c_2(c_1(x1))))))))))) -> 3(4(5(5(4(3(2(1(5(4(x1))))))))))
   0(c_4(c_5(c_0(c_0(c_4(c_2(c_4(c_5(c_0(x1)))))))))) -> 3(5(3(5(5(4(0(2(2(3(x1))))))))))
   2(c_4(c_3(c_1(c_4(c_0(c_2(c_5(c_3(c_4(c_1(c_3(c_4(c_0(c_3(c_1(c_0(c_1(c_0(c_1(c_3(x1))))))))))))))))))))) -> 2(4(3(1(4(0(5(2(3(4(1(3(4(0(3(1(0(1(0(1(3(x1)))))))))))))))))))))
   3(c_1(c_5(c_3(c_4(c_5(c_1(c_3(c_3(x1))))))))) -> 3(1(5(3(5(4(1(3(3(x1)))))))))
   1(c_3(c_3(c_2(c_1(c_2(c_1(c_1(c_0(c_1(c_5(c_0(c_4(c_2(c_5(c_3(c_2(c_3(c_1(c_5(c_3(c_2(c_3(c_4(c_1(c_4(c_2(x1))))))))))))))))))))))))))) -> 1(2(3(3(1(2(1(0(1(1(5(0(4(5(2(3(2(3(1(3(2(5(3(1(4(4(2(x1)))))))))))))))))))))))))))
   4(c_4(c_5(c_5(c_3(c_0(c_1(x1))))))) -> 4(4(3(5(0(5(1(x1)))))))
   3(c_2(c_5(c_5(c_2(c_1(c_2(c_2(c_2(c_3(c_2(c_2(c_4(c_0(c_4(c_0(c_3(c_5(x1)))))))))))))))))) -> 3(5(2(2(5(1(2(2(2(3(2(2(4(0(4(0(3(5(x1))))))))))))))))))
   5(c_1(c_5(c_0(c_3(c_3(c_0(c_1(c_2(c_3(c_3(c_1(c_4(c_5(c_3(c_1(c_2(c_2(c_0(c_3(c_2(c_0(c_5(x1))))))))))))))))))))))) -> 5(1(5(0(3(3(0(1(2(3(3(1(4(5(3(1(2(0(2(3(2(0(5(x1)))))))))))))))))))))))
   2(c_0(c_5(c_0(c_5(c_4(c_4(c_3(c_1(c_3(c_2(x1))))))))))) -> 2(1(0(3(1(2(1(3(4(0(x1))))))))))
   3(c_2(c_5(c_3(c_4(c_4(c_0(c_1(c_3(c_5(c_4(x1))))))))))) -> 5(0(1(3(5(5(1(3(4(2(x1))))))))))
   1(c_0(c_1(c_5(c_1(c_5(c_3(c_3(c_1(c_4(c_0(x1))))))))))) -> 3(1(2(1(5(2(4(5(1(1(x1))))))))))
   3(c_1(c_3(c_3(c_3(c_0(c_4(c_1(c_1(c_3(c_0(x1))))))))))) -> 1(0(2(1(2(1(0(1(1(3(x1))))))))))
   2(c_3(c_4(c_3(c_5(c_1(c_2(c_4(c_2(c_0(c_2(c_1(x1)))))))))))) -> 2(4(1(3(2(2(5(5(1(0(x1))))))))))
   2(c_2(c_4(c_3(c_2(c_2(c_2(c_4(c_2(c_5(c_2(c_0(c_4(c_5(x1)))))))))))))) -> 2(2(0(2(2(4(2(5(3(4(4(2(2(5(x1))))))))))))))
   5(c_1(c_5(c_3(c_5(c_4(c_0(c_0(c_3(x1))))))))) -> 5(1(5(3(5(0(4(0(3(x1)))))))))
   5(c_5(c_2(c_3(c_2(c_0(c_3(c_2(c_5(c_3(c_2(c_5(c_5(c_5(c_5(c_1(c_5(c_5(c_1(c_2(c_2(x1))))))))))))))))))))) -> 5(5(2(3(2(0(3(2(5(3(2(5(5(5(1(5(5(5(1(2(2(x1)))))))))))))))))))))
   0(c_0(c_1(c_4(c_5(c_3(c_1(c_4(c_5(c_1(c_4(c_5(c_1(c_0(c_5(c_2(c_2(c_0(c_1(c_2(c_2(c_3(c_3(c_3(c_0(c_0(c_2(c_1(c_2(c_5(x1)))))))))))))))))))))))))))))) -> 0(0(1(4(5(3(1(4(5(1(4(5(1(0(5(2(0(2(1(2(2(3(3(3(0(0(2(1(2(5(x1))))))))))))))))))))))))))))))
   0(c_5(c_5(c_1(c_1(c_1(c_2(c_5(c_2(c_3(c_5(c_5(x1)))))))))))) -> 1(3(5(2(3(4(3(3(4(3(x1))))))))))
   3(c_2(c_3(c_3(c_2(c_2(c_5(c_1(c_0(c_5(c_4(c_4(c_5(c_2(c_2(c_4(c_3(c_5(c_2(c_1(c_2(c_1(c_3(c_1(x1)))))))))))))))))))))))) -> 3(2(3(3(2(2(5(1(5(0(4(4(5(2(2(4(3(5(2(1(2(1(3(1(x1))))))))))))))))))))))))
   2(c_2(c_0(c_2(c_2(c_5(c_0(c_3(c_2(c_0(c_5(x1))))))))))) -> 5(0(3(5(4(2(2(3(1(0(x1))))))))))
   4(c_1(c_3(c_5(c_2(c_3(c_5(c_5(c_0(c_0(c_3(x1))))))))))) -> 5(2(3(0(3(5(2(3(5(3(x1))))))))))
   4(c_3(c_2(c_1(c_1(c_2(c_4(c_4(c_5(c_1(c_5(c_2(c_2(c_4(c_0(c_2(c_4(c_2(c_4(c_2(c_0(c_4(c_2(c_4(c_4(c_0(c_1(x1))))))))))))))))))))))))))) -> 4(3(2(1(2(1(4(4(5(1(5(2(2(4(0(2(4(2(4(2(0(4(2(4(4(0(1(x1)))))))))))))))))))))))))))
   5(c_1(c_0(c_3(c_5(c_0(c_1(c_1(c_3(c_4(c_3(x1))))))))))) -> 1(0(3(0(0(4(2(4(5(3(x1))))))))))
   4(c_0(c_3(c_0(c_0(c_3(c_0(c_5(c_1(c_4(c_3(x1))))))))))) -> 1(2(1(5(5(5(0(4(1(1(x1))))))))))
   0(c_0(c_5(c_2(c_2(c_4(c_4(c_3(c_3(c_4(c_0(x1))))))))))) -> 4(0(4(2(3(1(5(3(5(5(x1))))))))))
   5(c_4(c_1(c_5(c_1(c_4(c_2(c_5(c_4(c_3(c_0(c_4(c_1(c_0(x1)))))))))))))) -> 5(4(1(1(5(4(2(5(4(3(0(4(1(0(x1))))))))))))))
   1(c_2(c_4(c_0(c_2(c_4(c_0(c_1(c_2(c_4(c_3(c_1(c_0(c_3(c_4(x1))))))))))))))) -> 1(2(4(0(2(4(0(1(4(2(3(1(0(3(4(x1)))))))))))))))
   4(c_1(c_2(c_0(c_5(c_5(c_4(c_0(c_0(c_0(c_2(x1))))))))))) -> 3(3(5(4(5(3(2(0(0(2(x1))))))))))
   5(c_3(c_1(c_5(c_5(c_3(c_3(c_0(c_2(c_2(c_2(c_2(c_3(c_3(c_4(c_5(c_1(c_1(x1)))))))))))))))))) -> 5(3(1(5(5(3(3(0(2(2(2(3(2(3(4(5(1(1(x1))))))))))))))))))
   2(c_0(c_2(c_5(c_4(c_0(c_3(c_3(c_0(c_4(c_2(c_2(c_5(c_5(c_2(x1))))))))))))))) -> 2(0(2(4(0(5(0(3(4(3(2(2(5(5(2(x1)))))))))))))))
   4(c_1(c_1(c_3(c_1(c_3(c_2(c_1(c_2(c_2(c_2(c_0(c_5(x1))))))))))))) -> 0(3(5(4(0(1(4(0(5(0(x1))))))))))
   4(c_4(c_5(c_3(c_2(c_4(c_2(c_5(x1)))))))) -> 4(2(3(5(4(4(2(5(x1))))))))
   3(c_1(c_3(c_2(c_1(c_0(c_5(c_3(c_4(c_0(c_1(x1))))))))))) -> 1(2(0(4(0(3(2(0(4(0(x1))))))))))
   0(c_1(c_1(c_4(c_1(c_3(c_2(c_4(c_3(c_5(c_5(c_0(c_1(x1))))))))))))) -> 4(3(2(0(5(0(4(0(4(4(x1))))))))))
   4(c_5(c_5(c_3(c_5(c_4(c_1(c_1(c_5(c_5(c_3(c_3(c_1(c_5(c_4(c_4(c_5(c_0(c_4(x1))))))))))))))))))) -> 4(5(5(3(5(4(1(5(1(5(3(3(1(5(4(4(5(0(4(x1)))))))))))))))))))
   0(c_2(c_2(c_5(c_5(c_0(c_0(c_4(c_5(c_3(c_4(x1))))))))))) -> 4(0(5(1(3(5(5(4(5(0(x1))))))))))
   0(c_4(c_3(c_0(c_0(c_0(c_4(c_3(c_2(c_3(c_3(x1))))))))))) -> 2(5(1(5(2(4(5(4(3(2(x1))))))))))
   2(c_3(c_2(c_1(c_1(c_1(c_0(c_2(c_1(c_3(c_5(c_1(x1)))))))))))) -> 5(4(3(0(1(2(3(3(2(5(x1))))))))))
   0(c_0(c_0(c_1(c_2(c_2(c_3(x1))))))) -> 0(0(0(2(1(2(3(x1)))))))
   3(c_2(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_2(c_0(x1))))))))))) -> 4(4(2(5(4(5(5(0(5(0(x1))))))))))
   0(c_4(c_0(c_1(c_0(c_2(c_2(c_4(c_3(c_0(c_5(c_0(c_2(c_0(c_4(c_5(c_3(x1))))))))))))))))) -> 0(4(0(1(0(2(4(2(3(0(5(0(2(0(4(5(3(x1)))))))))))))))))
   0(c_5(c_2(c_5(c_4(c_3(c_3(c_2(c_3(c_5(c_0(c_2(c_3(c_2(c_5(c_0(c_5(c_0(c_4(c_1(x1)))))))))))))))))))) -> 0(5(2(5(4(3(3(2(3(5(0(2(3(2(0(5(5(0(4(1(x1))))))))))))))))))))
   4(c_0(c_5(c_2(c_5(c_3(c_0(c_0(c_3(c_5(c_5(x1))))))))))) -> 0(0(5(2(3(0(3(1(5(5(x1))))))))))
   2(c_5(c_2(c_3(c_0(c_0(c_1(c_0(c_5(c_0(c_2(c_5(c_3(c_4(c_0(c_5(c_5(c_5(c_3(c_2(x1)))))))))))))))))))) -> 2(5(2(3(0(0(1(0(5(0(2(5(3(4(5(0(5(5(3(2(x1))))))))))))))))))))
   0(c_4(c_0(c_4(c_5(c_3(c_3(c_0(c_5(c_5(c_2(x1))))))))))) -> 4(5(3(5(2(2(1(1(4(3(x1))))))))))
   0(c_1(c_1(c_1(c_2(c_0(c_1(c_3(c_0(c_4(c_2(c_3(c_3(x1))))))))))))) -> 0(4(1(2(4(2(5(0(0(0(x1))))))))))
   0(c_1(c_2(c_4(c_4(c_0(c_1(c_0(x1)))))))) -> 0(1(4(2(4(1(0(0(x1))))))))
   1(c_2(c_0(c_1(c_2(c_4(c_5(c_2(c_4(c_4(x1)))))))))) -> 1(5(4(2(0(2(2(4(1(4(x1))))))))))
   4(c_2(c_1(c_2(c_2(c_3(c_3(c_3(c_1(c_3(c_2(x1))))))))))) -> 5(5(2(3(4(2(5(4(0(3(x1))))))))))
   3(c_5(c_4(c_4(c_5(c_1(c_1(c_5(c_0(c_2(c_0(x1))))))))))) -> 3(1(5(1(3(5(0(1(5(1(x1))))))))))
   0(c_4(c_4(c_5(c_4(c_0(c_1(c_3(c_1(c_3(c_4(x1))))))))))) -> 0(4(0(3(4(3(1(4(4(1(5(x1)))))))))))
   1(c_1(c_1(c_2(c_2(c_5(c_2(c_1(c_3(c_1(c_0(x1))))))))))) -> 1(5(1(1(3(5(0(0(2(4(x1))))))))))
   3(c_5(c_5(c_4(c_5(c_3(c_0(c_2(c_5(c_5(c_1(x1))))))))))) -> 3(1(1(2(4(2(3(0(2(5(x1))))))))))
   4(c_2(c_0(c_2(c_1(c_5(c_5(c_4(c_2(c_3(c_2(c_1(c_0(c_4(c_1(c_2(c_0(c_4(c_2(c_3(c_1(c_3(c_0(c_1(c_4(c_2(c_0(c_0(c_2(c_5(x1)))))))))))))))))))))))))))))) -> 4(2(0(2(1(5(5(4(2(3(2(1(0(1(4(2(0(4(2(3(1(3(0(1(4(2(0(0(2(5(x1))))))))))))))))))))))))))))))
   4(c_0(c_4(c_2(c_4(c_0(c_3(c_1(x1)))))))) -> 4(0(4(2(0(4(3(1(x1))))))))
   2(c_0(c_2(c_4(c_0(c_2(c_4(c_2(c_0(c_0(c_1(c_1(c_0(c_1(c_3(c_5(c_3(c_3(c_4(c_3(c_1(c_2(c_5(x1))))))))))))))))))))))) -> 2(0(2(2(0(4(4(1(0(1(3(2(0(1(5(0(3(3(1(2(3(4(5(x1)))))))))))))))))))))))
   2(c_4(c_5(c_5(c_3(c_3(c_1(c_2(c_0(c_5(c_5(c_1(c_0(c_3(c_4(c_4(c_5(c_1(c_3(c_5(c_2(c_4(c_0(c_1(c_1(c_4(c_1(c_4(c_5(c_1(x1)))))))))))))))))))))))))))))) -> 2(4(5(5(3(3(1(2(0(5(5(1(0(3(4(4(5(1(3(2(5(4(0(1(1(4(1(4(5(1(x1))))))))))))))))))))))))))))))
   0(c_0(c_0(c_5(c_1(c_5(c_3(c_5(c_1(c_3(c_2(c_3(x1)))))))))))) -> 1(3(3(0(1(4(1(0(5(5(x1))))))))))
   5(c_5(c_3(c_3(c_0(c_1(c_4(c_1(c_3(c_3(c_0(x1))))))))))) -> 2(3(3(4(5(4(2(2(0(1(x1))))))))))
   2(c_4(c_1(c_4(c_1(c_0(c_4(c_0(c_3(c_1(c_0(c_1(c_1(c_0(c_5(c_4(c_1(c_5(c_1(c_4(x1)))))))))))))))))))) -> 2(4(1(4(1(0(4(0(3(1(0(1(1(5(0(4(1(5(1(4(x1))))))))))))))))))))
   1(c_1(c_5(c_3(c_4(c_3(c_4(c_4(c_2(c_5(x1)))))))))) -> 1(1(5(3(3(4(4(4(2(5(x1))))))))))
   4(c_3(c_1(c_1(c_2(c_1(c_2(c_0(c_5(c_2(c_0(c_3(c_2(x1))))))))))))) -> 4(4(4(4(4(0(0(3(4(1(x1))))))))))

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

   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_4(x_1)) -> 4(encArg(x_1))
   encArg(cons_3(x_1)) -> 3(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(encArg(x_1))
   encArg(cons_1(x_1)) -> 1(encArg(x_1))
   encArg(cons_2(x_1)) -> 2(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))
   5(x0) -> c_5(x0)
   0(x0) -> c_0(x0)
   1(x0) -> c_1(x0)
   2(x0) -> c_2(x0)
   3(x0) -> c_3(x0)
   4(x0) -> c_4(x0)

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

(17) RcToIrcProof (BOTH BOUNDS(ID, ID))
Converted rc-obligation to irc-obligation.

As the TRS is a non-duplicating overlay system, we have rc = irc.
----------------------------------------

(18)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   4(c_0(c_5(c_5(c_2(c_0(c_4(c_0(c_2(c_3(c_5(x1))))))))))) -> 5(5(0(4(3(5(4(1(5(1(x1))))))))))
   4(c_5(c_4(c_0(c_2(c_5(c_0(c_2(c_3(c_2(c_5(x1))))))))))) -> 3(3(4(4(5(2(3(5(3(0(x1))))))))))
   5(c_5(c_3(c_4(c_1(c_2(c_0(c_2(c_5(c_3(c_2(c_5(c_4(c_4(c_5(c_5(c_1(c_2(x1)))))))))))))))))) -> 5(5(3(4(1(2(0(2(5(3(2(4(5(4(5(5(1(2(x1))))))))))))))))))
   5(c_1(c_4(c_4(c_3(c_1(c_5(c_4(c_3(c_5(c_1(c_2(c_0(x1))))))))))))) -> 2(2(1(3(0(0(4(3(2(5(x1))))))))))
   0(c_0(c_0(c_2(c_2(c_3(c_4(c_4(c_3(c_3(x1)))))))))) -> 0(2(3(0(3(2(1(5(1(3(x1))))))))))
   4(c_4(c_3(c_3(c_3(c_2(c_4(c_2(c_5(c_1(c_4(x1))))))))))) -> 2(0(3(4(4(1(3(0(2(0(x1))))))))))
   5(c_1(c_2(c_1(c_0(c_2(c_3(c_1(c_3(c_1(c_0(c_0(x1)))))))))))) -> 5(2(0(4(2(1(4(1(1(3(x1))))))))))
   0(c_4(c_3(c_0(c_3(c_3(c_5(c_3(c_5(c_1(c_4(c_2(c_3(c_3(c_0(c_4(c_0(c_1(c_5(c_0(c_3(c_0(c_2(c_5(c_5(c_0(x1)))))))))))))))))))))))))) -> 0(4(3(0(3(3(5(3(5(1(4(2(3(3(0(4(1(0(5(0(3(0(2(5(5(0(x1))))))))))))))))))))))))))
   2(c_1(c_2(c_0(c_5(c_0(c_3(c_5(c_1(c_2(c_3(c_5(x1)))))))))))) -> 1(0(0(4(5(4(1(4(1(0(x1))))))))))
   5(c_0(c_0(c_2(c_4(c_0(c_1(c_5(c_1(c_1(c_3(c_0(c_2(c_2(c_2(c_3(c_5(c_4(c_0(c_4(c_1(c_5(c_2(c_3(c_4(x1))))))))))))))))))))))))) -> 5(0(0(2(0(4(1(5(1(1(3(0(2(2(2(3(5(4(0(4(1(5(2(3(4(x1)))))))))))))))))))))))))
   0(c_5(c_2(c_0(c_0(c_2(c_1(c_4(c_2(c_4(c_5(x1))))))))))) -> 5(0(4(3(4(2(5(5(4(1(x1))))))))))
   4(c_1(c_3(c_3(c_1(c_5(c_1(c_1(c_2(c_4(c_3(x1))))))))))) -> 0(1(2(3(3(2(1(3(3(2(x1))))))))))
   3(c_3(c_3(c_4(c_0(c_2(c_5(c_4(c_5(c_0(c_0(x1))))))))))) -> 3(1(5(1(1(5(2(3(1(4(x1))))))))))
   2(c_5(c_3(c_1(c_0(c_1(c_4(c_4(c_2(c_2(c_4(x1))))))))))) -> 0(5(1(0(0(2(0(5(5(1(x1))))))))))
   3(c_3(c_2(c_5(c_4(c_4(c_0(c_1(c_3(c_1(c_2(c_1(c_5(c_0(c_0(c_4(c_2(c_1(c_4(c_2(c_2(c_3(c_5(x1))))))))))))))))))))))) -> 3(3(2(5(4(4(0(1(3(1(2(1(5(0(4(0(2(1(4(2(2(3(5(x1)))))))))))))))))))))))
   1(c_5(c_0(c_1(c_1(c_4(c_2(c_4(c_3(c_5(c_4(c_5(c_2(c_0(c_3(c_3(c_2(c_0(c_5(c_5(c_4(c_4(c_2(c_5(c_3(c_0(c_2(c_1(c_1(c_0(x1)))))))))))))))))))))))))))))) -> 1(5(0(1(1(4(4(2(3(5(4(5(2(0(3(3(2(0(5(5(4(4(2(5(3(0(2(1(1(0(x1))))))))))))))))))))))))))))))
   4(c_3(c_1(c_3(c_5(c_1(c_5(c_1(c_5(c_0(c_2(c_1(x1)))))))))))) -> 0(1(3(1(0(4(0(0(5(3(x1))))))))))
   2(c_1(c_0(c_5(c_5(c_4(c_1(c_0(c_4(c_2(c_5(c_3(c_1(c_4(c_1(c_3(c_5(c_0(c_0(c_2(c_4(c_5(x1)))))))))))))))))))))) -> 2(1(0(5(5(4(1(0(4(2(5(3(1(4(1(3(0(5(0(2(4(5(x1))))))))))))))))))))))
   4(c_0(c_5(c_4(c_0(c_2(c_4(c_0(c_4(c_3(x1)))))))))) -> 2(3(1(3(5(3(1(2(4(5(x1))))))))))
   0(c_0(c_3(c_1(c_5(c_5(c_1(c_5(c_3(c_2(c_0(c_2(c_2(c_4(c_3(c_4(c_0(c_5(c_1(x1))))))))))))))))))) -> 0(3(0(5(3(1(1(0(5(2(2(4(5(2(3(4(0(5(1(x1)))))))))))))))))))
   1(c_5(c_2(c_2(c_3(c_3(c_4(c_2(c_4(c_5(x1)))))))))) -> 1(5(2(3(2(3(4(2(4(5(x1))))))))))
   5(c_5(c_0(c_5(c_3(c_4(c_1(c_2(c_3(c_2(c_2(x1))))))))))) -> 1(2(3(5(5(0(1(3(5(5(x1))))))))))
   5(c_5(c_0(c_3(c_2(c_2(c_1(c_3(c_4(c_3(c_5(c_4(c_2(c_5(c_2(c_0(c_4(c_1(c_1(c_2(c_4(c_0(c_5(c_4(c_3(c_2(c_4(c_4(x1)))))))))))))))))))))))))))) -> 5(5(0(3(2(2(3(1(4(3(5(4(2(5(2(0(4(1(1(2(4(0(5(4(3(2(4(4(x1))))))))))))))))))))))))))))
   5(c_0(c_5(c_0(c_0(c_4(c_0(c_1(c_3(c_4(c_1(x1))))))))))) -> 2(2(4(2(1(1(3(3(3(0(x1))))))))))
   4(c_0(c_5(c_4(c_5(c_5(c_3(c_4(c_3(c_4(c_1(x1))))))))))) -> 3(4(1(1(3(1(4(0(1(4(x1))))))))))
   1(c_5(c_0(c_0(c_1(c_5(c_2(c_1(c_5(c_0(c_5(c_5(c_5(c_0(c_1(c_4(c_0(c_5(c_3(c_4(c_3(c_1(c_2(c_0(c_4(c_0(c_2(c_2(c_1(c_5(x1)))))))))))))))))))))))))))))) -> 1(5(0(0(1(5(2(5(1(0(5(5(5(0(1(4(0(5(3(4(3(1(2(0(4(0(2(2(1(5(x1))))))))))))))))))))))))))))))
   0(c_1(c_1(c_5(c_1(c_1(c_4(c_4(c_5(c_0(c_4(c_2(c_1(x1))))))))))))) -> 0(3(2(0(0(4(3(1(0(4(x1))))))))))
   1(c_2(c_3(c_2(c_0(c_1(c_0(c_5(c_3(c_0(c_2(c_1(c_1(c_1(c_4(c_4(c_1(c_2(c_4(c_5(c_2(c_2(c_4(c_0(c_3(c_2(x1)))))))))))))))))))))))))) -> 1(2(3(2(0(1(0(5(3(0(2(1(1(1(4(4(1(4(2(5(2(2(4(0(3(2(x1))))))))))))))))))))))))))
   5(c_5(c_5(c_3(c_5(c_3(c_2(c_5(c_0(c_1(c_5(c_3(c_1(c_2(c_2(c_3(c_3(c_0(c_3(c_1(c_0(c_4(c_1(c_2(c_2(c_5(c_3(c_1(c_3(x1))))))))))))))))))))))))))))) -> 5(5(5(3(5(3(2(5(1(0(5(3(1(2(2(3(3(0(3(1(0(4(1(2(2(5(3(1(3(x1)))))))))))))))))))))))))))))
   5(c_2(c_3(c_3(c_1(c_0(c_1(c_1(c_1(c_4(c_1(c_4(x1)))))))))))) -> 0(2(4(0(4(0(4(0(0(1(x1))))))))))
   4(c_3(c_3(c_0(c_5(c_2(c_0(c_4(c_4(c_5(c_1(c_2(x1)))))))))))) -> 2(0(1(1(5(1(1(4(0(0(x1))))))))))
   3(c_4(c_2(c_2(c_2(c_3(c_1(c_3(c_1(c_2(c_1(x1))))))))))) -> 3(4(5(5(4(3(2(1(5(4(x1))))))))))
   0(c_4(c_5(c_0(c_0(c_4(c_2(c_4(c_5(c_0(x1)))))))))) -> 3(5(3(5(5(4(0(2(2(3(x1))))))))))
   2(c_4(c_3(c_1(c_4(c_0(c_2(c_5(c_3(c_4(c_1(c_3(c_4(c_0(c_3(c_1(c_0(c_1(c_0(c_1(c_3(x1))))))))))))))))))))) -> 2(4(3(1(4(0(5(2(3(4(1(3(4(0(3(1(0(1(0(1(3(x1)))))))))))))))))))))
   3(c_1(c_5(c_3(c_4(c_5(c_1(c_3(c_3(x1))))))))) -> 3(1(5(3(5(4(1(3(3(x1)))))))))
   1(c_3(c_3(c_2(c_1(c_2(c_1(c_1(c_0(c_1(c_5(c_0(c_4(c_2(c_5(c_3(c_2(c_3(c_1(c_5(c_3(c_2(c_3(c_4(c_1(c_4(c_2(x1))))))))))))))))))))))))))) -> 1(2(3(3(1(2(1(0(1(1(5(0(4(5(2(3(2(3(1(3(2(5(3(1(4(4(2(x1)))))))))))))))))))))))))))
   4(c_4(c_5(c_5(c_3(c_0(c_1(x1))))))) -> 4(4(3(5(0(5(1(x1)))))))
   3(c_2(c_5(c_5(c_2(c_1(c_2(c_2(c_2(c_3(c_2(c_2(c_4(c_0(c_4(c_0(c_3(c_5(x1)))))))))))))))))) -> 3(5(2(2(5(1(2(2(2(3(2(2(4(0(4(0(3(5(x1))))))))))))))))))
   5(c_1(c_5(c_0(c_3(c_3(c_0(c_1(c_2(c_3(c_3(c_1(c_4(c_5(c_3(c_1(c_2(c_2(c_0(c_3(c_2(c_0(c_5(x1))))))))))))))))))))))) -> 5(1(5(0(3(3(0(1(2(3(3(1(4(5(3(1(2(0(2(3(2(0(5(x1)))))))))))))))))))))))
   2(c_0(c_5(c_0(c_5(c_4(c_4(c_3(c_1(c_3(c_2(x1))))))))))) -> 2(1(0(3(1(2(1(3(4(0(x1))))))))))
   3(c_2(c_5(c_3(c_4(c_4(c_0(c_1(c_3(c_5(c_4(x1))))))))))) -> 5(0(1(3(5(5(1(3(4(2(x1))))))))))
   1(c_0(c_1(c_5(c_1(c_5(c_3(c_3(c_1(c_4(c_0(x1))))))))))) -> 3(1(2(1(5(2(4(5(1(1(x1))))))))))
   3(c_1(c_3(c_3(c_3(c_0(c_4(c_1(c_1(c_3(c_0(x1))))))))))) -> 1(0(2(1(2(1(0(1(1(3(x1))))))))))
   2(c_3(c_4(c_3(c_5(c_1(c_2(c_4(c_2(c_0(c_2(c_1(x1)))))))))))) -> 2(4(1(3(2(2(5(5(1(0(x1))))))))))
   2(c_2(c_4(c_3(c_2(c_2(c_2(c_4(c_2(c_5(c_2(c_0(c_4(c_5(x1)))))))))))))) -> 2(2(0(2(2(4(2(5(3(4(4(2(2(5(x1))))))))))))))
   5(c_1(c_5(c_3(c_5(c_4(c_0(c_0(c_3(x1))))))))) -> 5(1(5(3(5(0(4(0(3(x1)))))))))
   5(c_5(c_2(c_3(c_2(c_0(c_3(c_2(c_5(c_3(c_2(c_5(c_5(c_5(c_5(c_1(c_5(c_5(c_1(c_2(c_2(x1))))))))))))))))))))) -> 5(5(2(3(2(0(3(2(5(3(2(5(5(5(1(5(5(5(1(2(2(x1)))))))))))))))))))))
   0(c_0(c_1(c_4(c_5(c_3(c_1(c_4(c_5(c_1(c_4(c_5(c_1(c_0(c_5(c_2(c_2(c_0(c_1(c_2(c_2(c_3(c_3(c_3(c_0(c_0(c_2(c_1(c_2(c_5(x1)))))))))))))))))))))))))))))) -> 0(0(1(4(5(3(1(4(5(1(4(5(1(0(5(2(0(2(1(2(2(3(3(3(0(0(2(1(2(5(x1))))))))))))))))))))))))))))))
   0(c_5(c_5(c_1(c_1(c_1(c_2(c_5(c_2(c_3(c_5(c_5(x1)))))))))))) -> 1(3(5(2(3(4(3(3(4(3(x1))))))))))
   3(c_2(c_3(c_3(c_2(c_2(c_5(c_1(c_0(c_5(c_4(c_4(c_5(c_2(c_2(c_4(c_3(c_5(c_2(c_1(c_2(c_1(c_3(c_1(x1)))))))))))))))))))))))) -> 3(2(3(3(2(2(5(1(5(0(4(4(5(2(2(4(3(5(2(1(2(1(3(1(x1))))))))))))))))))))))))
   2(c_2(c_0(c_2(c_2(c_5(c_0(c_3(c_2(c_0(c_5(x1))))))))))) -> 5(0(3(5(4(2(2(3(1(0(x1))))))))))
   4(c_1(c_3(c_5(c_2(c_3(c_5(c_5(c_0(c_0(c_3(x1))))))))))) -> 5(2(3(0(3(5(2(3(5(3(x1))))))))))
   4(c_3(c_2(c_1(c_1(c_2(c_4(c_4(c_5(c_1(c_5(c_2(c_2(c_4(c_0(c_2(c_4(c_2(c_4(c_2(c_0(c_4(c_2(c_4(c_4(c_0(c_1(x1))))))))))))))))))))))))))) -> 4(3(2(1(2(1(4(4(5(1(5(2(2(4(0(2(4(2(4(2(0(4(2(4(4(0(1(x1)))))))))))))))))))))))))))
   5(c_1(c_0(c_3(c_5(c_0(c_1(c_1(c_3(c_4(c_3(x1))))))))))) -> 1(0(3(0(0(4(2(4(5(3(x1))))))))))
   4(c_0(c_3(c_0(c_0(c_3(c_0(c_5(c_1(c_4(c_3(x1))))))))))) -> 1(2(1(5(5(5(0(4(1(1(x1))))))))))
   0(c_0(c_5(c_2(c_2(c_4(c_4(c_3(c_3(c_4(c_0(x1))))))))))) -> 4(0(4(2(3(1(5(3(5(5(x1))))))))))
   5(c_4(c_1(c_5(c_1(c_4(c_2(c_5(c_4(c_3(c_0(c_4(c_1(c_0(x1)))))))))))))) -> 5(4(1(1(5(4(2(5(4(3(0(4(1(0(x1))))))))))))))
   1(c_2(c_4(c_0(c_2(c_4(c_0(c_1(c_2(c_4(c_3(c_1(c_0(c_3(c_4(x1))))))))))))))) -> 1(2(4(0(2(4(0(1(4(2(3(1(0(3(4(x1)))))))))))))))
   4(c_1(c_2(c_0(c_5(c_5(c_4(c_0(c_0(c_0(c_2(x1))))))))))) -> 3(3(5(4(5(3(2(0(0(2(x1))))))))))
   5(c_3(c_1(c_5(c_5(c_3(c_3(c_0(c_2(c_2(c_2(c_2(c_3(c_3(c_4(c_5(c_1(c_1(x1)))))))))))))))))) -> 5(3(1(5(5(3(3(0(2(2(2(3(2(3(4(5(1(1(x1))))))))))))))))))
   2(c_0(c_2(c_5(c_4(c_0(c_3(c_3(c_0(c_4(c_2(c_2(c_5(c_5(c_2(x1))))))))))))))) -> 2(0(2(4(0(5(0(3(4(3(2(2(5(5(2(x1)))))))))))))))
   4(c_1(c_1(c_3(c_1(c_3(c_2(c_1(c_2(c_2(c_2(c_0(c_5(x1))))))))))))) -> 0(3(5(4(0(1(4(0(5(0(x1))))))))))
   4(c_4(c_5(c_3(c_2(c_4(c_2(c_5(x1)))))))) -> 4(2(3(5(4(4(2(5(x1))))))))
   3(c_1(c_3(c_2(c_1(c_0(c_5(c_3(c_4(c_0(c_1(x1))))))))))) -> 1(2(0(4(0(3(2(0(4(0(x1))))))))))
   0(c_1(c_1(c_4(c_1(c_3(c_2(c_4(c_3(c_5(c_5(c_0(c_1(x1))))))))))))) -> 4(3(2(0(5(0(4(0(4(4(x1))))))))))
   4(c_5(c_5(c_3(c_5(c_4(c_1(c_1(c_5(c_5(c_3(c_3(c_1(c_5(c_4(c_4(c_5(c_0(c_4(x1))))))))))))))))))) -> 4(5(5(3(5(4(1(5(1(5(3(3(1(5(4(4(5(0(4(x1)))))))))))))))))))
   0(c_2(c_2(c_5(c_5(c_0(c_0(c_4(c_5(c_3(c_4(x1))))))))))) -> 4(0(5(1(3(5(5(4(5(0(x1))))))))))
   0(c_4(c_3(c_0(c_0(c_0(c_4(c_3(c_2(c_3(c_3(x1))))))))))) -> 2(5(1(5(2(4(5(4(3(2(x1))))))))))
   2(c_3(c_2(c_1(c_1(c_1(c_0(c_2(c_1(c_3(c_5(c_1(x1)))))))))))) -> 5(4(3(0(1(2(3(3(2(5(x1))))))))))
   0(c_0(c_0(c_1(c_2(c_2(c_3(x1))))))) -> 0(0(0(2(1(2(3(x1)))))))
   3(c_2(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_2(c_0(x1))))))))))) -> 4(4(2(5(4(5(5(0(5(0(x1))))))))))
   0(c_4(c_0(c_1(c_0(c_2(c_2(c_4(c_3(c_0(c_5(c_0(c_2(c_0(c_4(c_5(c_3(x1))))))))))))))))) -> 0(4(0(1(0(2(4(2(3(0(5(0(2(0(4(5(3(x1)))))))))))))))))
   0(c_5(c_2(c_5(c_4(c_3(c_3(c_2(c_3(c_5(c_0(c_2(c_3(c_2(c_5(c_0(c_5(c_0(c_4(c_1(x1)))))))))))))))))))) -> 0(5(2(5(4(3(3(2(3(5(0(2(3(2(0(5(5(0(4(1(x1))))))))))))))))))))
   4(c_0(c_5(c_2(c_5(c_3(c_0(c_0(c_3(c_5(c_5(x1))))))))))) -> 0(0(5(2(3(0(3(1(5(5(x1))))))))))
   2(c_5(c_2(c_3(c_0(c_0(c_1(c_0(c_5(c_0(c_2(c_5(c_3(c_4(c_0(c_5(c_5(c_5(c_3(c_2(x1)))))))))))))))))))) -> 2(5(2(3(0(0(1(0(5(0(2(5(3(4(5(0(5(5(3(2(x1))))))))))))))))))))
   0(c_4(c_0(c_4(c_5(c_3(c_3(c_0(c_5(c_5(c_2(x1))))))))))) -> 4(5(3(5(2(2(1(1(4(3(x1))))))))))
   0(c_1(c_1(c_1(c_2(c_0(c_1(c_3(c_0(c_4(c_2(c_3(c_3(x1))))))))))))) -> 0(4(1(2(4(2(5(0(0(0(x1))))))))))
   0(c_1(c_2(c_4(c_4(c_0(c_1(c_0(x1)))))))) -> 0(1(4(2(4(1(0(0(x1))))))))
   1(c_2(c_0(c_1(c_2(c_4(c_5(c_2(c_4(c_4(x1)))))))))) -> 1(5(4(2(0(2(2(4(1(4(x1))))))))))
   4(c_2(c_1(c_2(c_2(c_3(c_3(c_3(c_1(c_3(c_2(x1))))))))))) -> 5(5(2(3(4(2(5(4(0(3(x1))))))))))
   3(c_5(c_4(c_4(c_5(c_1(c_1(c_5(c_0(c_2(c_0(x1))))))))))) -> 3(1(5(1(3(5(0(1(5(1(x1))))))))))
   0(c_4(c_4(c_5(c_4(c_0(c_1(c_3(c_1(c_3(c_4(x1))))))))))) -> 0(4(0(3(4(3(1(4(4(1(5(x1)))))))))))
   1(c_1(c_1(c_2(c_2(c_5(c_2(c_1(c_3(c_1(c_0(x1))))))))))) -> 1(5(1(1(3(5(0(0(2(4(x1))))))))))
   3(c_5(c_5(c_4(c_5(c_3(c_0(c_2(c_5(c_5(c_1(x1))))))))))) -> 3(1(1(2(4(2(3(0(2(5(x1))))))))))
   4(c_2(c_0(c_2(c_1(c_5(c_5(c_4(c_2(c_3(c_2(c_1(c_0(c_4(c_1(c_2(c_0(c_4(c_2(c_3(c_1(c_3(c_0(c_1(c_4(c_2(c_0(c_0(c_2(c_5(x1)))))))))))))))))))))))))))))) -> 4(2(0(2(1(5(5(4(2(3(2(1(0(1(4(2(0(4(2(3(1(3(0(1(4(2(0(0(2(5(x1))))))))))))))))))))))))))))))
   4(c_0(c_4(c_2(c_4(c_0(c_3(c_1(x1)))))))) -> 4(0(4(2(0(4(3(1(x1))))))))
   2(c_0(c_2(c_4(c_0(c_2(c_4(c_2(c_0(c_0(c_1(c_1(c_0(c_1(c_3(c_5(c_3(c_3(c_4(c_3(c_1(c_2(c_5(x1))))))))))))))))))))))) -> 2(0(2(2(0(4(4(1(0(1(3(2(0(1(5(0(3(3(1(2(3(4(5(x1)))))))))))))))))))))))
   2(c_4(c_5(c_5(c_3(c_3(c_1(c_2(c_0(c_5(c_5(c_1(c_0(c_3(c_4(c_4(c_5(c_1(c_3(c_5(c_2(c_4(c_0(c_1(c_1(c_4(c_1(c_4(c_5(c_1(x1)))))))))))))))))))))))))))))) -> 2(4(5(5(3(3(1(2(0(5(5(1(0(3(4(4(5(1(3(2(5(4(0(1(1(4(1(4(5(1(x1))))))))))))))))))))))))))))))
   0(c_0(c_0(c_5(c_1(c_5(c_3(c_5(c_1(c_3(c_2(c_3(x1)))))))))))) -> 1(3(3(0(1(4(1(0(5(5(x1))))))))))
   5(c_5(c_3(c_3(c_0(c_1(c_4(c_1(c_3(c_3(c_0(x1))))))))))) -> 2(3(3(4(5(4(2(2(0(1(x1))))))))))
   2(c_4(c_1(c_4(c_1(c_0(c_4(c_0(c_3(c_1(c_0(c_1(c_1(c_0(c_5(c_4(c_1(c_5(c_1(c_4(x1)))))))))))))))))))) -> 2(4(1(4(1(0(4(0(3(1(0(1(1(5(0(4(1(5(1(4(x1))))))))))))))))))))
   1(c_1(c_5(c_3(c_4(c_3(c_4(c_4(c_2(c_5(x1)))))))))) -> 1(1(5(3(3(4(4(4(2(5(x1))))))))))
   4(c_3(c_1(c_1(c_2(c_1(c_2(c_0(c_5(c_2(c_0(c_3(c_2(x1))))))))))))) -> 4(4(4(4(4(0(0(3(4(1(x1))))))))))

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

   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_4(x_1)) -> 4(encArg(x_1))
   encArg(cons_3(x_1)) -> 3(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(encArg(x_1))
   encArg(cons_1(x_1)) -> 1(encArg(x_1))
   encArg(cons_2(x_1)) -> 2(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))
   5(x0) -> c_5(x0)
   0(x0) -> c_0(x0)
   1(x0) -> c_1(x0)
   2(x0) -> c_2(x0)
   3(x0) -> c_3(x0)
   4(x0) -> c_4(x0)

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

(19) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
Transformed relative TRS to weighted TRS
----------------------------------------

(20)
Obligation:
The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   4(c_0(c_5(c_5(c_2(c_0(c_4(c_0(c_2(c_3(c_5(x1))))))))))) -> 5(5(0(4(3(5(4(1(5(1(x1)))))))))) [1]
   4(c_5(c_4(c_0(c_2(c_5(c_0(c_2(c_3(c_2(c_5(x1))))))))))) -> 3(3(4(4(5(2(3(5(3(0(x1)))))))))) [1]
   5(c_5(c_3(c_4(c_1(c_2(c_0(c_2(c_5(c_3(c_2(c_5(c_4(c_4(c_5(c_5(c_1(c_2(x1)))))))))))))))))) -> 5(5(3(4(1(2(0(2(5(3(2(4(5(4(5(5(1(2(x1)))))))))))))))))) [1]
   5(c_1(c_4(c_4(c_3(c_1(c_5(c_4(c_3(c_5(c_1(c_2(c_0(x1))))))))))))) -> 2(2(1(3(0(0(4(3(2(5(x1)))))))))) [1]
   0(c_0(c_0(c_2(c_2(c_3(c_4(c_4(c_3(c_3(x1)))))))))) -> 0(2(3(0(3(2(1(5(1(3(x1)))))))))) [1]
   4(c_4(c_3(c_3(c_3(c_2(c_4(c_2(c_5(c_1(c_4(x1))))))))))) -> 2(0(3(4(4(1(3(0(2(0(x1)))))))))) [1]
   5(c_1(c_2(c_1(c_0(c_2(c_3(c_1(c_3(c_1(c_0(c_0(x1)))))))))))) -> 5(2(0(4(2(1(4(1(1(3(x1)))))))))) [1]
   0(c_4(c_3(c_0(c_3(c_3(c_5(c_3(c_5(c_1(c_4(c_2(c_3(c_3(c_0(c_4(c_0(c_1(c_5(c_0(c_3(c_0(c_2(c_5(c_5(c_0(x1)))))))))))))))))))))))))) -> 0(4(3(0(3(3(5(3(5(1(4(2(3(3(0(4(1(0(5(0(3(0(2(5(5(0(x1)))))))))))))))))))))))))) [1]
   2(c_1(c_2(c_0(c_5(c_0(c_3(c_5(c_1(c_2(c_3(c_5(x1)))))))))))) -> 1(0(0(4(5(4(1(4(1(0(x1)))))))))) [1]
   5(c_0(c_0(c_2(c_4(c_0(c_1(c_5(c_1(c_1(c_3(c_0(c_2(c_2(c_2(c_3(c_5(c_4(c_0(c_4(c_1(c_5(c_2(c_3(c_4(x1))))))))))))))))))))))))) -> 5(0(0(2(0(4(1(5(1(1(3(0(2(2(2(3(5(4(0(4(1(5(2(3(4(x1))))))))))))))))))))))))) [1]
   0(c_5(c_2(c_0(c_0(c_2(c_1(c_4(c_2(c_4(c_5(x1))))))))))) -> 5(0(4(3(4(2(5(5(4(1(x1)))))))))) [1]
   4(c_1(c_3(c_3(c_1(c_5(c_1(c_1(c_2(c_4(c_3(x1))))))))))) -> 0(1(2(3(3(2(1(3(3(2(x1)))))))))) [1]
   3(c_3(c_3(c_4(c_0(c_2(c_5(c_4(c_5(c_0(c_0(x1))))))))))) -> 3(1(5(1(1(5(2(3(1(4(x1)))))))))) [1]
   2(c_5(c_3(c_1(c_0(c_1(c_4(c_4(c_2(c_2(c_4(x1))))))))))) -> 0(5(1(0(0(2(0(5(5(1(x1)))))))))) [1]
   3(c_3(c_2(c_5(c_4(c_4(c_0(c_1(c_3(c_1(c_2(c_1(c_5(c_0(c_0(c_4(c_2(c_1(c_4(c_2(c_2(c_3(c_5(x1))))))))))))))))))))))) -> 3(3(2(5(4(4(0(1(3(1(2(1(5(0(4(0(2(1(4(2(2(3(5(x1))))))))))))))))))))))) [1]
   1(c_5(c_0(c_1(c_1(c_4(c_2(c_4(c_3(c_5(c_4(c_5(c_2(c_0(c_3(c_3(c_2(c_0(c_5(c_5(c_4(c_4(c_2(c_5(c_3(c_0(c_2(c_1(c_1(c_0(x1)))))))))))))))))))))))))))))) -> 1(5(0(1(1(4(4(2(3(5(4(5(2(0(3(3(2(0(5(5(4(4(2(5(3(0(2(1(1(0(x1)))))))))))))))))))))))))))))) [1]
   4(c_3(c_1(c_3(c_5(c_1(c_5(c_1(c_5(c_0(c_2(c_1(x1)))))))))))) -> 0(1(3(1(0(4(0(0(5(3(x1)))))))))) [1]
   2(c_1(c_0(c_5(c_5(c_4(c_1(c_0(c_4(c_2(c_5(c_3(c_1(c_4(c_1(c_3(c_5(c_0(c_0(c_2(c_4(c_5(x1)))))))))))))))))))))) -> 2(1(0(5(5(4(1(0(4(2(5(3(1(4(1(3(0(5(0(2(4(5(x1)))))))))))))))))))))) [1]
   4(c_0(c_5(c_4(c_0(c_2(c_4(c_0(c_4(c_3(x1)))))))))) -> 2(3(1(3(5(3(1(2(4(5(x1)))))))))) [1]
   0(c_0(c_3(c_1(c_5(c_5(c_1(c_5(c_3(c_2(c_0(c_2(c_2(c_4(c_3(c_4(c_0(c_5(c_1(x1))))))))))))))))))) -> 0(3(0(5(3(1(1(0(5(2(2(4(5(2(3(4(0(5(1(x1))))))))))))))))))) [1]
   1(c_5(c_2(c_2(c_3(c_3(c_4(c_2(c_4(c_5(x1)))))))))) -> 1(5(2(3(2(3(4(2(4(5(x1)))))))))) [1]
   5(c_5(c_0(c_5(c_3(c_4(c_1(c_2(c_3(c_2(c_2(x1))))))))))) -> 1(2(3(5(5(0(1(3(5(5(x1)))))))))) [1]
   5(c_5(c_0(c_3(c_2(c_2(c_1(c_3(c_4(c_3(c_5(c_4(c_2(c_5(c_2(c_0(c_4(c_1(c_1(c_2(c_4(c_0(c_5(c_4(c_3(c_2(c_4(c_4(x1)))))))))))))))))))))))))))) -> 5(5(0(3(2(2(3(1(4(3(5(4(2(5(2(0(4(1(1(2(4(0(5(4(3(2(4(4(x1)))))))))))))))))))))))))))) [1]
   5(c_0(c_5(c_0(c_0(c_4(c_0(c_1(c_3(c_4(c_1(x1))))))))))) -> 2(2(4(2(1(1(3(3(3(0(x1)))))))))) [1]
   4(c_0(c_5(c_4(c_5(c_5(c_3(c_4(c_3(c_4(c_1(x1))))))))))) -> 3(4(1(1(3(1(4(0(1(4(x1)))))))))) [1]
   1(c_5(c_0(c_0(c_1(c_5(c_2(c_1(c_5(c_0(c_5(c_5(c_5(c_0(c_1(c_4(c_0(c_5(c_3(c_4(c_3(c_1(c_2(c_0(c_4(c_0(c_2(c_2(c_1(c_5(x1)))))))))))))))))))))))))))))) -> 1(5(0(0(1(5(2(5(1(0(5(5(5(0(1(4(0(5(3(4(3(1(2(0(4(0(2(2(1(5(x1)))))))))))))))))))))))))))))) [1]
   0(c_1(c_1(c_5(c_1(c_1(c_4(c_4(c_5(c_0(c_4(c_2(c_1(x1))))))))))))) -> 0(3(2(0(0(4(3(1(0(4(x1)))))))))) [1]
   1(c_2(c_3(c_2(c_0(c_1(c_0(c_5(c_3(c_0(c_2(c_1(c_1(c_1(c_4(c_4(c_1(c_2(c_4(c_5(c_2(c_2(c_4(c_0(c_3(c_2(x1)))))))))))))))))))))))))) -> 1(2(3(2(0(1(0(5(3(0(2(1(1(1(4(4(1(4(2(5(2(2(4(0(3(2(x1)))))))))))))))))))))))))) [1]
   5(c_5(c_5(c_3(c_5(c_3(c_2(c_5(c_0(c_1(c_5(c_3(c_1(c_2(c_2(c_3(c_3(c_0(c_3(c_1(c_0(c_4(c_1(c_2(c_2(c_5(c_3(c_1(c_3(x1))))))))))))))))))))))))))))) -> 5(5(5(3(5(3(2(5(1(0(5(3(1(2(2(3(3(0(3(1(0(4(1(2(2(5(3(1(3(x1))))))))))))))))))))))))))))) [1]
   5(c_2(c_3(c_3(c_1(c_0(c_1(c_1(c_1(c_4(c_1(c_4(x1)))))))))))) -> 0(2(4(0(4(0(4(0(0(1(x1)))))))))) [1]
   4(c_3(c_3(c_0(c_5(c_2(c_0(c_4(c_4(c_5(c_1(c_2(x1)))))))))))) -> 2(0(1(1(5(1(1(4(0(0(x1)))))))))) [1]
   3(c_4(c_2(c_2(c_2(c_3(c_1(c_3(c_1(c_2(c_1(x1))))))))))) -> 3(4(5(5(4(3(2(1(5(4(x1)))))))))) [1]
   0(c_4(c_5(c_0(c_0(c_4(c_2(c_4(c_5(c_0(x1)))))))))) -> 3(5(3(5(5(4(0(2(2(3(x1)))))))))) [1]
   2(c_4(c_3(c_1(c_4(c_0(c_2(c_5(c_3(c_4(c_1(c_3(c_4(c_0(c_3(c_1(c_0(c_1(c_0(c_1(c_3(x1))))))))))))))))))))) -> 2(4(3(1(4(0(5(2(3(4(1(3(4(0(3(1(0(1(0(1(3(x1))))))))))))))))))))) [1]
   3(c_1(c_5(c_3(c_4(c_5(c_1(c_3(c_3(x1))))))))) -> 3(1(5(3(5(4(1(3(3(x1))))))))) [1]
   1(c_3(c_3(c_2(c_1(c_2(c_1(c_1(c_0(c_1(c_5(c_0(c_4(c_2(c_5(c_3(c_2(c_3(c_1(c_5(c_3(c_2(c_3(c_4(c_1(c_4(c_2(x1))))))))))))))))))))))))))) -> 1(2(3(3(1(2(1(0(1(1(5(0(4(5(2(3(2(3(1(3(2(5(3(1(4(4(2(x1))))))))))))))))))))))))))) [1]
   4(c_4(c_5(c_5(c_3(c_0(c_1(x1))))))) -> 4(4(3(5(0(5(1(x1))))))) [1]
   3(c_2(c_5(c_5(c_2(c_1(c_2(c_2(c_2(c_3(c_2(c_2(c_4(c_0(c_4(c_0(c_3(c_5(x1)))))))))))))))))) -> 3(5(2(2(5(1(2(2(2(3(2(2(4(0(4(0(3(5(x1)))))))))))))))))) [1]
   5(c_1(c_5(c_0(c_3(c_3(c_0(c_1(c_2(c_3(c_3(c_1(c_4(c_5(c_3(c_1(c_2(c_2(c_0(c_3(c_2(c_0(c_5(x1))))))))))))))))))))))) -> 5(1(5(0(3(3(0(1(2(3(3(1(4(5(3(1(2(0(2(3(2(0(5(x1))))))))))))))))))))))) [1]
   2(c_0(c_5(c_0(c_5(c_4(c_4(c_3(c_1(c_3(c_2(x1))))))))))) -> 2(1(0(3(1(2(1(3(4(0(x1)))))))))) [1]
   3(c_2(c_5(c_3(c_4(c_4(c_0(c_1(c_3(c_5(c_4(x1))))))))))) -> 5(0(1(3(5(5(1(3(4(2(x1)))))))))) [1]
   1(c_0(c_1(c_5(c_1(c_5(c_3(c_3(c_1(c_4(c_0(x1))))))))))) -> 3(1(2(1(5(2(4(5(1(1(x1)))))))))) [1]
   3(c_1(c_3(c_3(c_3(c_0(c_4(c_1(c_1(c_3(c_0(x1))))))))))) -> 1(0(2(1(2(1(0(1(1(3(x1)))))))))) [1]
   2(c_3(c_4(c_3(c_5(c_1(c_2(c_4(c_2(c_0(c_2(c_1(x1)))))))))))) -> 2(4(1(3(2(2(5(5(1(0(x1)))))))))) [1]
   2(c_2(c_4(c_3(c_2(c_2(c_2(c_4(c_2(c_5(c_2(c_0(c_4(c_5(x1)))))))))))))) -> 2(2(0(2(2(4(2(5(3(4(4(2(2(5(x1)))))))))))))) [1]
   5(c_1(c_5(c_3(c_5(c_4(c_0(c_0(c_3(x1))))))))) -> 5(1(5(3(5(0(4(0(3(x1))))))))) [1]
   5(c_5(c_2(c_3(c_2(c_0(c_3(c_2(c_5(c_3(c_2(c_5(c_5(c_5(c_5(c_1(c_5(c_5(c_1(c_2(c_2(x1))))))))))))))))))))) -> 5(5(2(3(2(0(3(2(5(3(2(5(5(5(1(5(5(5(1(2(2(x1))))))))))))))))))))) [1]
   0(c_0(c_1(c_4(c_5(c_3(c_1(c_4(c_5(c_1(c_4(c_5(c_1(c_0(c_5(c_2(c_2(c_0(c_1(c_2(c_2(c_3(c_3(c_3(c_0(c_0(c_2(c_1(c_2(c_5(x1)))))))))))))))))))))))))))))) -> 0(0(1(4(5(3(1(4(5(1(4(5(1(0(5(2(0(2(1(2(2(3(3(3(0(0(2(1(2(5(x1)))))))))))))))))))))))))))))) [1]
   0(c_5(c_5(c_1(c_1(c_1(c_2(c_5(c_2(c_3(c_5(c_5(x1)))))))))))) -> 1(3(5(2(3(4(3(3(4(3(x1)))))))))) [1]
   3(c_2(c_3(c_3(c_2(c_2(c_5(c_1(c_0(c_5(c_4(c_4(c_5(c_2(c_2(c_4(c_3(c_5(c_2(c_1(c_2(c_1(c_3(c_1(x1)))))))))))))))))))))))) -> 3(2(3(3(2(2(5(1(5(0(4(4(5(2(2(4(3(5(2(1(2(1(3(1(x1)))))))))))))))))))))))) [1]
   2(c_2(c_0(c_2(c_2(c_5(c_0(c_3(c_2(c_0(c_5(x1))))))))))) -> 5(0(3(5(4(2(2(3(1(0(x1)))))))))) [1]
   4(c_1(c_3(c_5(c_2(c_3(c_5(c_5(c_0(c_0(c_3(x1))))))))))) -> 5(2(3(0(3(5(2(3(5(3(x1)))))))))) [1]
   4(c_3(c_2(c_1(c_1(c_2(c_4(c_4(c_5(c_1(c_5(c_2(c_2(c_4(c_0(c_2(c_4(c_2(c_4(c_2(c_0(c_4(c_2(c_4(c_4(c_0(c_1(x1))))))))))))))))))))))))))) -> 4(3(2(1(2(1(4(4(5(1(5(2(2(4(0(2(4(2(4(2(0(4(2(4(4(0(1(x1))))))))))))))))))))))))))) [1]
   5(c_1(c_0(c_3(c_5(c_0(c_1(c_1(c_3(c_4(c_3(x1))))))))))) -> 1(0(3(0(0(4(2(4(5(3(x1)))))))))) [1]
   4(c_0(c_3(c_0(c_0(c_3(c_0(c_5(c_1(c_4(c_3(x1))))))))))) -> 1(2(1(5(5(5(0(4(1(1(x1)))))))))) [1]
   0(c_0(c_5(c_2(c_2(c_4(c_4(c_3(c_3(c_4(c_0(x1))))))))))) -> 4(0(4(2(3(1(5(3(5(5(x1)))))))))) [1]
   5(c_4(c_1(c_5(c_1(c_4(c_2(c_5(c_4(c_3(c_0(c_4(c_1(c_0(x1)))))))))))))) -> 5(4(1(1(5(4(2(5(4(3(0(4(1(0(x1)))))))))))))) [1]
   1(c_2(c_4(c_0(c_2(c_4(c_0(c_1(c_2(c_4(c_3(c_1(c_0(c_3(c_4(x1))))))))))))))) -> 1(2(4(0(2(4(0(1(4(2(3(1(0(3(4(x1))))))))))))))) [1]
   4(c_1(c_2(c_0(c_5(c_5(c_4(c_0(c_0(c_0(c_2(x1))))))))))) -> 3(3(5(4(5(3(2(0(0(2(x1)))))))))) [1]
   5(c_3(c_1(c_5(c_5(c_3(c_3(c_0(c_2(c_2(c_2(c_2(c_3(c_3(c_4(c_5(c_1(c_1(x1)))))))))))))))))) -> 5(3(1(5(5(3(3(0(2(2(2(3(2(3(4(5(1(1(x1)))))))))))))))))) [1]
   2(c_0(c_2(c_5(c_4(c_0(c_3(c_3(c_0(c_4(c_2(c_2(c_5(c_5(c_2(x1))))))))))))))) -> 2(0(2(4(0(5(0(3(4(3(2(2(5(5(2(x1))))))))))))))) [1]
   4(c_1(c_1(c_3(c_1(c_3(c_2(c_1(c_2(c_2(c_2(c_0(c_5(x1))))))))))))) -> 0(3(5(4(0(1(4(0(5(0(x1)))))))))) [1]
   4(c_4(c_5(c_3(c_2(c_4(c_2(c_5(x1)))))))) -> 4(2(3(5(4(4(2(5(x1)))))))) [1]
   3(c_1(c_3(c_2(c_1(c_0(c_5(c_3(c_4(c_0(c_1(x1))))))))))) -> 1(2(0(4(0(3(2(0(4(0(x1)))))))))) [1]
   0(c_1(c_1(c_4(c_1(c_3(c_2(c_4(c_3(c_5(c_5(c_0(c_1(x1))))))))))))) -> 4(3(2(0(5(0(4(0(4(4(x1)))))))))) [1]
   4(c_5(c_5(c_3(c_5(c_4(c_1(c_1(c_5(c_5(c_3(c_3(c_1(c_5(c_4(c_4(c_5(c_0(c_4(x1))))))))))))))))))) -> 4(5(5(3(5(4(1(5(1(5(3(3(1(5(4(4(5(0(4(x1))))))))))))))))))) [1]
   0(c_2(c_2(c_5(c_5(c_0(c_0(c_4(c_5(c_3(c_4(x1))))))))))) -> 4(0(5(1(3(5(5(4(5(0(x1)))))))))) [1]
   0(c_4(c_3(c_0(c_0(c_0(c_4(c_3(c_2(c_3(c_3(x1))))))))))) -> 2(5(1(5(2(4(5(4(3(2(x1)))))))))) [1]
   2(c_3(c_2(c_1(c_1(c_1(c_0(c_2(c_1(c_3(c_5(c_1(x1)))))))))))) -> 5(4(3(0(1(2(3(3(2(5(x1)))))))))) [1]
   0(c_0(c_0(c_1(c_2(c_2(c_3(x1))))))) -> 0(0(0(2(1(2(3(x1))))))) [1]
   3(c_2(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_2(c_0(x1))))))))))) -> 4(4(2(5(4(5(5(0(5(0(x1)))))))))) [1]
   0(c_4(c_0(c_1(c_0(c_2(c_2(c_4(c_3(c_0(c_5(c_0(c_2(c_0(c_4(c_5(c_3(x1))))))))))))))))) -> 0(4(0(1(0(2(4(2(3(0(5(0(2(0(4(5(3(x1))))))))))))))))) [1]
   0(c_5(c_2(c_5(c_4(c_3(c_3(c_2(c_3(c_5(c_0(c_2(c_3(c_2(c_5(c_0(c_5(c_0(c_4(c_1(x1)))))))))))))))))))) -> 0(5(2(5(4(3(3(2(3(5(0(2(3(2(0(5(5(0(4(1(x1)))))))))))))))))))) [1]
   4(c_0(c_5(c_2(c_5(c_3(c_0(c_0(c_3(c_5(c_5(x1))))))))))) -> 0(0(5(2(3(0(3(1(5(5(x1)))))))))) [1]
   2(c_5(c_2(c_3(c_0(c_0(c_1(c_0(c_5(c_0(c_2(c_5(c_3(c_4(c_0(c_5(c_5(c_5(c_3(c_2(x1)))))))))))))))))))) -> 2(5(2(3(0(0(1(0(5(0(2(5(3(4(5(0(5(5(3(2(x1)))))))))))))))))))) [1]
   0(c_4(c_0(c_4(c_5(c_3(c_3(c_0(c_5(c_5(c_2(x1))))))))))) -> 4(5(3(5(2(2(1(1(4(3(x1)))))))))) [1]
   0(c_1(c_1(c_1(c_2(c_0(c_1(c_3(c_0(c_4(c_2(c_3(c_3(x1))))))))))))) -> 0(4(1(2(4(2(5(0(0(0(x1)))))))))) [1]
   0(c_1(c_2(c_4(c_4(c_0(c_1(c_0(x1)))))))) -> 0(1(4(2(4(1(0(0(x1)))))))) [1]
   1(c_2(c_0(c_1(c_2(c_4(c_5(c_2(c_4(c_4(x1)))))))))) -> 1(5(4(2(0(2(2(4(1(4(x1)))))))))) [1]
   4(c_2(c_1(c_2(c_2(c_3(c_3(c_3(c_1(c_3(c_2(x1))))))))))) -> 5(5(2(3(4(2(5(4(0(3(x1)))))))))) [1]
   3(c_5(c_4(c_4(c_5(c_1(c_1(c_5(c_0(c_2(c_0(x1))))))))))) -> 3(1(5(1(3(5(0(1(5(1(x1)))))))))) [1]
   0(c_4(c_4(c_5(c_4(c_0(c_1(c_3(c_1(c_3(c_4(x1))))))))))) -> 0(4(0(3(4(3(1(4(4(1(5(x1))))))))))) [1]
   1(c_1(c_1(c_2(c_2(c_5(c_2(c_1(c_3(c_1(c_0(x1))))))))))) -> 1(5(1(1(3(5(0(0(2(4(x1)))))))))) [1]
   3(c_5(c_5(c_4(c_5(c_3(c_0(c_2(c_5(c_5(c_1(x1))))))))))) -> 3(1(1(2(4(2(3(0(2(5(x1)))))))))) [1]
   4(c_2(c_0(c_2(c_1(c_5(c_5(c_4(c_2(c_3(c_2(c_1(c_0(c_4(c_1(c_2(c_0(c_4(c_2(c_3(c_1(c_3(c_0(c_1(c_4(c_2(c_0(c_0(c_2(c_5(x1)))))))))))))))))))))))))))))) -> 4(2(0(2(1(5(5(4(2(3(2(1(0(1(4(2(0(4(2(3(1(3(0(1(4(2(0(0(2(5(x1)))))))))))))))))))))))))))))) [1]
   4(c_0(c_4(c_2(c_4(c_0(c_3(c_1(x1)))))))) -> 4(0(4(2(0(4(3(1(x1)))))))) [1]
   2(c_0(c_2(c_4(c_0(c_2(c_4(c_2(c_0(c_0(c_1(c_1(c_0(c_1(c_3(c_5(c_3(c_3(c_4(c_3(c_1(c_2(c_5(x1))))))))))))))))))))))) -> 2(0(2(2(0(4(4(1(0(1(3(2(0(1(5(0(3(3(1(2(3(4(5(x1))))))))))))))))))))))) [1]
   2(c_4(c_5(c_5(c_3(c_3(c_1(c_2(c_0(c_5(c_5(c_1(c_0(c_3(c_4(c_4(c_5(c_1(c_3(c_5(c_2(c_4(c_0(c_1(c_1(c_4(c_1(c_4(c_5(c_1(x1)))))))))))))))))))))))))))))) -> 2(4(5(5(3(3(1(2(0(5(5(1(0(3(4(4(5(1(3(2(5(4(0(1(1(4(1(4(5(1(x1)))))))))))))))))))))))))))))) [1]
   0(c_0(c_0(c_5(c_1(c_5(c_3(c_5(c_1(c_3(c_2(c_3(x1)))))))))))) -> 1(3(3(0(1(4(1(0(5(5(x1)))))))))) [1]
   5(c_5(c_3(c_3(c_0(c_1(c_4(c_1(c_3(c_3(c_0(x1))))))))))) -> 2(3(3(4(5(4(2(2(0(1(x1)))))))))) [1]
   2(c_4(c_1(c_4(c_1(c_0(c_4(c_0(c_3(c_1(c_0(c_1(c_1(c_0(c_5(c_4(c_1(c_5(c_1(c_4(x1)))))))))))))))))))) -> 2(4(1(4(1(0(4(0(3(1(0(1(1(5(0(4(1(5(1(4(x1)))))))))))))))))))) [1]
   1(c_1(c_5(c_3(c_4(c_3(c_4(c_4(c_2(c_5(x1)))))))))) -> 1(1(5(3(3(4(4(4(2(5(x1)))))))))) [1]
   4(c_3(c_1(c_1(c_2(c_1(c_2(c_0(c_5(c_2(c_0(c_3(c_2(x1))))))))))))) -> 4(4(4(4(4(0(0(3(4(1(x1)))))))))) [1]
   encArg(cons_0(x_1)) -> 0(encArg(x_1)) [0]
   encArg(cons_4(x_1)) -> 4(encArg(x_1)) [0]
   encArg(cons_3(x_1)) -> 3(encArg(x_1)) [0]
   encArg(cons_5(x_1)) -> 5(encArg(x_1)) [0]
   encArg(cons_1(x_1)) -> 1(encArg(x_1)) [0]
   encArg(cons_2(x_1)) -> 2(encArg(x_1)) [0]
   encode_0(x_1) -> 0(encArg(x_1)) [0]
   encode_1(x_1) -> 1(encArg(x_1)) [0]
   encode_2(x_1) -> 2(encArg(x_1)) [0]
   encode_3(x_1) -> 3(encArg(x_1)) [0]
   encode_4(x_1) -> 4(encArg(x_1)) [0]
   encode_5(x_1) -> 5(encArg(x_1)) [0]
   5(x0) -> c_5(x0) [0]
   0(x0) -> c_0(x0) [0]
   1(x0) -> c_1(x0) [0]
   2(x0) -> c_2(x0) [0]
   3(x0) -> c_3(x0) [0]
   4(x0) -> c_4(x0) [0]

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

(21) CpxWeightedTrsRenamingProof (BOTH BOUNDS(ID, ID))
Renamed defined symbols to avoid conflicts with arithmetic symbols:

4 => 4'
1 => 1'
5 => 5'
3 => 3'
0 => 0'
2 => 2'

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

(22)
Obligation:
The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   4'(c_0(c_5(c_5(c_2(c_0(c_4(c_0(c_2(c_3(c_5(x1))))))))))) -> 5'(5'(0'(4'(3'(5'(4'(1'(5'(1'(x1)))))))))) [1]
   4'(c_5(c_4(c_0(c_2(c_5(c_0(c_2(c_3(c_2(c_5(x1))))))))))) -> 3'(3'(4'(4'(5'(2'(3'(5'(3'(0'(x1)))))))))) [1]
   5'(c_5(c_3(c_4(c_1(c_2(c_0(c_2(c_5(c_3(c_2(c_5(c_4(c_4(c_5(c_5(c_1(c_2(x1)))))))))))))))))) -> 5'(5'(3'(4'(1'(2'(0'(2'(5'(3'(2'(4'(5'(4'(5'(5'(1'(2'(x1)))))))))))))))))) [1]
   5'(c_1(c_4(c_4(c_3(c_1(c_5(c_4(c_3(c_5(c_1(c_2(c_0(x1))))))))))))) -> 2'(2'(1'(3'(0'(0'(4'(3'(2'(5'(x1)))))))))) [1]
   0'(c_0(c_0(c_2(c_2(c_3(c_4(c_4(c_3(c_3(x1)))))))))) -> 0'(2'(3'(0'(3'(2'(1'(5'(1'(3'(x1)))))))))) [1]
   4'(c_4(c_3(c_3(c_3(c_2(c_4(c_2(c_5(c_1(c_4(x1))))))))))) -> 2'(0'(3'(4'(4'(1'(3'(0'(2'(0'(x1)))))))))) [1]
   5'(c_1(c_2(c_1(c_0(c_2(c_3(c_1(c_3(c_1(c_0(c_0(x1)))))))))))) -> 5'(2'(0'(4'(2'(1'(4'(1'(1'(3'(x1)))))))))) [1]
   0'(c_4(c_3(c_0(c_3(c_3(c_5(c_3(c_5(c_1(c_4(c_2(c_3(c_3(c_0(c_4(c_0(c_1(c_5(c_0(c_3(c_0(c_2(c_5(c_5(c_0(x1)))))))))))))))))))))))))) -> 0'(4'(3'(0'(3'(3'(5'(3'(5'(1'(4'(2'(3'(3'(0'(4'(1'(0'(5'(0'(3'(0'(2'(5'(5'(0'(x1)))))))))))))))))))))))))) [1]
   2'(c_1(c_2(c_0(c_5(c_0(c_3(c_5(c_1(c_2(c_3(c_5(x1)))))))))))) -> 1'(0'(0'(4'(5'(4'(1'(4'(1'(0'(x1)))))))))) [1]
   5'(c_0(c_0(c_2(c_4(c_0(c_1(c_5(c_1(c_1(c_3(c_0(c_2(c_2(c_2(c_3(c_5(c_4(c_0(c_4(c_1(c_5(c_2(c_3(c_4(x1))))))))))))))))))))))))) -> 5'(0'(0'(2'(0'(4'(1'(5'(1'(1'(3'(0'(2'(2'(2'(3'(5'(4'(0'(4'(1'(5'(2'(3'(4'(x1))))))))))))))))))))))))) [1]
   0'(c_5(c_2(c_0(c_0(c_2(c_1(c_4(c_2(c_4(c_5(x1))))))))))) -> 5'(0'(4'(3'(4'(2'(5'(5'(4'(1'(x1)))))))))) [1]
   4'(c_1(c_3(c_3(c_1(c_5(c_1(c_1(c_2(c_4(c_3(x1))))))))))) -> 0'(1'(2'(3'(3'(2'(1'(3'(3'(2'(x1)))))))))) [1]
   3'(c_3(c_3(c_4(c_0(c_2(c_5(c_4(c_5(c_0(c_0(x1))))))))))) -> 3'(1'(5'(1'(1'(5'(2'(3'(1'(4'(x1)))))))))) [1]
   2'(c_5(c_3(c_1(c_0(c_1(c_4(c_4(c_2(c_2(c_4(x1))))))))))) -> 0'(5'(1'(0'(0'(2'(0'(5'(5'(1'(x1)))))))))) [1]
   3'(c_3(c_2(c_5(c_4(c_4(c_0(c_1(c_3(c_1(c_2(c_1(c_5(c_0(c_0(c_4(c_2(c_1(c_4(c_2(c_2(c_3(c_5(x1))))))))))))))))))))))) -> 3'(3'(2'(5'(4'(4'(0'(1'(3'(1'(2'(1'(5'(0'(4'(0'(2'(1'(4'(2'(2'(3'(5'(x1))))))))))))))))))))))) [1]
   1'(c_5(c_0(c_1(c_1(c_4(c_2(c_4(c_3(c_5(c_4(c_5(c_2(c_0(c_3(c_3(c_2(c_0(c_5(c_5(c_4(c_4(c_2(c_5(c_3(c_0(c_2(c_1(c_1(c_0(x1)))))))))))))))))))))))))))))) -> 1'(5'(0'(1'(1'(4'(4'(2'(3'(5'(4'(5'(2'(0'(3'(3'(2'(0'(5'(5'(4'(4'(2'(5'(3'(0'(2'(1'(1'(0'(x1)))))))))))))))))))))))))))))) [1]
   4'(c_3(c_1(c_3(c_5(c_1(c_5(c_1(c_5(c_0(c_2(c_1(x1)))))))))))) -> 0'(1'(3'(1'(0'(4'(0'(0'(5'(3'(x1)))))))))) [1]
   2'(c_1(c_0(c_5(c_5(c_4(c_1(c_0(c_4(c_2(c_5(c_3(c_1(c_4(c_1(c_3(c_5(c_0(c_0(c_2(c_4(c_5(x1)))))))))))))))))))))) -> 2'(1'(0'(5'(5'(4'(1'(0'(4'(2'(5'(3'(1'(4'(1'(3'(0'(5'(0'(2'(4'(5'(x1)))))))))))))))))))))) [1]
   4'(c_0(c_5(c_4(c_0(c_2(c_4(c_0(c_4(c_3(x1)))))))))) -> 2'(3'(1'(3'(5'(3'(1'(2'(4'(5'(x1)))))))))) [1]
   0'(c_0(c_3(c_1(c_5(c_5(c_1(c_5(c_3(c_2(c_0(c_2(c_2(c_4(c_3(c_4(c_0(c_5(c_1(x1))))))))))))))))))) -> 0'(3'(0'(5'(3'(1'(1'(0'(5'(2'(2'(4'(5'(2'(3'(4'(0'(5'(1'(x1))))))))))))))))))) [1]
   1'(c_5(c_2(c_2(c_3(c_3(c_4(c_2(c_4(c_5(x1)))))))))) -> 1'(5'(2'(3'(2'(3'(4'(2'(4'(5'(x1)))))))))) [1]
   5'(c_5(c_0(c_5(c_3(c_4(c_1(c_2(c_3(c_2(c_2(x1))))))))))) -> 1'(2'(3'(5'(5'(0'(1'(3'(5'(5'(x1)))))))))) [1]
   5'(c_5(c_0(c_3(c_2(c_2(c_1(c_3(c_4(c_3(c_5(c_4(c_2(c_5(c_2(c_0(c_4(c_1(c_1(c_2(c_4(c_0(c_5(c_4(c_3(c_2(c_4(c_4(x1)))))))))))))))))))))))))))) -> 5'(5'(0'(3'(2'(2'(3'(1'(4'(3'(5'(4'(2'(5'(2'(0'(4'(1'(1'(2'(4'(0'(5'(4'(3'(2'(4'(4'(x1)))))))))))))))))))))))))))) [1]
   5'(c_0(c_5(c_0(c_0(c_4(c_0(c_1(c_3(c_4(c_1(x1))))))))))) -> 2'(2'(4'(2'(1'(1'(3'(3'(3'(0'(x1)))))))))) [1]
   4'(c_0(c_5(c_4(c_5(c_5(c_3(c_4(c_3(c_4(c_1(x1))))))))))) -> 3'(4'(1'(1'(3'(1'(4'(0'(1'(4'(x1)))))))))) [1]
   1'(c_5(c_0(c_0(c_1(c_5(c_2(c_1(c_5(c_0(c_5(c_5(c_5(c_0(c_1(c_4(c_0(c_5(c_3(c_4(c_3(c_1(c_2(c_0(c_4(c_0(c_2(c_2(c_1(c_5(x1)))))))))))))))))))))))))))))) -> 1'(5'(0'(0'(1'(5'(2'(5'(1'(0'(5'(5'(5'(0'(1'(4'(0'(5'(3'(4'(3'(1'(2'(0'(4'(0'(2'(2'(1'(5'(x1)))))))))))))))))))))))))))))) [1]
   0'(c_1(c_1(c_5(c_1(c_1(c_4(c_4(c_5(c_0(c_4(c_2(c_1(x1))))))))))))) -> 0'(3'(2'(0'(0'(4'(3'(1'(0'(4'(x1)))))))))) [1]
   1'(c_2(c_3(c_2(c_0(c_1(c_0(c_5(c_3(c_0(c_2(c_1(c_1(c_1(c_4(c_4(c_1(c_2(c_4(c_5(c_2(c_2(c_4(c_0(c_3(c_2(x1)))))))))))))))))))))))))) -> 1'(2'(3'(2'(0'(1'(0'(5'(3'(0'(2'(1'(1'(1'(4'(4'(1'(4'(2'(5'(2'(2'(4'(0'(3'(2'(x1)))))))))))))))))))))))))) [1]
   5'(c_5(c_5(c_3(c_5(c_3(c_2(c_5(c_0(c_1(c_5(c_3(c_1(c_2(c_2(c_3(c_3(c_0(c_3(c_1(c_0(c_4(c_1(c_2(c_2(c_5(c_3(c_1(c_3(x1))))))))))))))))))))))))))))) -> 5'(5'(5'(3'(5'(3'(2'(5'(1'(0'(5'(3'(1'(2'(2'(3'(3'(0'(3'(1'(0'(4'(1'(2'(2'(5'(3'(1'(3'(x1))))))))))))))))))))))))))))) [1]
   5'(c_2(c_3(c_3(c_1(c_0(c_1(c_1(c_1(c_4(c_1(c_4(x1)))))))))))) -> 0'(2'(4'(0'(4'(0'(4'(0'(0'(1'(x1)))))))))) [1]
   4'(c_3(c_3(c_0(c_5(c_2(c_0(c_4(c_4(c_5(c_1(c_2(x1)))))))))))) -> 2'(0'(1'(1'(5'(1'(1'(4'(0'(0'(x1)))))))))) [1]
   3'(c_4(c_2(c_2(c_2(c_3(c_1(c_3(c_1(c_2(c_1(x1))))))))))) -> 3'(4'(5'(5'(4'(3'(2'(1'(5'(4'(x1)))))))))) [1]
   0'(c_4(c_5(c_0(c_0(c_4(c_2(c_4(c_5(c_0(x1)))))))))) -> 3'(5'(3'(5'(5'(4'(0'(2'(2'(3'(x1)))))))))) [1]
   2'(c_4(c_3(c_1(c_4(c_0(c_2(c_5(c_3(c_4(c_1(c_3(c_4(c_0(c_3(c_1(c_0(c_1(c_0(c_1(c_3(x1))))))))))))))))))))) -> 2'(4'(3'(1'(4'(0'(5'(2'(3'(4'(1'(3'(4'(0'(3'(1'(0'(1'(0'(1'(3'(x1))))))))))))))))))))) [1]
   3'(c_1(c_5(c_3(c_4(c_5(c_1(c_3(c_3(x1))))))))) -> 3'(1'(5'(3'(5'(4'(1'(3'(3'(x1))))))))) [1]
   1'(c_3(c_3(c_2(c_1(c_2(c_1(c_1(c_0(c_1(c_5(c_0(c_4(c_2(c_5(c_3(c_2(c_3(c_1(c_5(c_3(c_2(c_3(c_4(c_1(c_4(c_2(x1))))))))))))))))))))))))))) -> 1'(2'(3'(3'(1'(2'(1'(0'(1'(1'(5'(0'(4'(5'(2'(3'(2'(3'(1'(3'(2'(5'(3'(1'(4'(4'(2'(x1))))))))))))))))))))))))))) [1]
   4'(c_4(c_5(c_5(c_3(c_0(c_1(x1))))))) -> 4'(4'(3'(5'(0'(5'(1'(x1))))))) [1]
   3'(c_2(c_5(c_5(c_2(c_1(c_2(c_2(c_2(c_3(c_2(c_2(c_4(c_0(c_4(c_0(c_3(c_5(x1)))))))))))))))))) -> 3'(5'(2'(2'(5'(1'(2'(2'(2'(3'(2'(2'(4'(0'(4'(0'(3'(5'(x1)))))))))))))))))) [1]
   5'(c_1(c_5(c_0(c_3(c_3(c_0(c_1(c_2(c_3(c_3(c_1(c_4(c_5(c_3(c_1(c_2(c_2(c_0(c_3(c_2(c_0(c_5(x1))))))))))))))))))))))) -> 5'(1'(5'(0'(3'(3'(0'(1'(2'(3'(3'(1'(4'(5'(3'(1'(2'(0'(2'(3'(2'(0'(5'(x1))))))))))))))))))))))) [1]
   2'(c_0(c_5(c_0(c_5(c_4(c_4(c_3(c_1(c_3(c_2(x1))))))))))) -> 2'(1'(0'(3'(1'(2'(1'(3'(4'(0'(x1)))))))))) [1]
   3'(c_2(c_5(c_3(c_4(c_4(c_0(c_1(c_3(c_5(c_4(x1))))))))))) -> 5'(0'(1'(3'(5'(5'(1'(3'(4'(2'(x1)))))))))) [1]
   1'(c_0(c_1(c_5(c_1(c_5(c_3(c_3(c_1(c_4(c_0(x1))))))))))) -> 3'(1'(2'(1'(5'(2'(4'(5'(1'(1'(x1)))))))))) [1]
   3'(c_1(c_3(c_3(c_3(c_0(c_4(c_1(c_1(c_3(c_0(x1))))))))))) -> 1'(0'(2'(1'(2'(1'(0'(1'(1'(3'(x1)))))))))) [1]
   2'(c_3(c_4(c_3(c_5(c_1(c_2(c_4(c_2(c_0(c_2(c_1(x1)))))))))))) -> 2'(4'(1'(3'(2'(2'(5'(5'(1'(0'(x1)))))))))) [1]
   2'(c_2(c_4(c_3(c_2(c_2(c_2(c_4(c_2(c_5(c_2(c_0(c_4(c_5(x1)))))))))))))) -> 2'(2'(0'(2'(2'(4'(2'(5'(3'(4'(4'(2'(2'(5'(x1)))))))))))))) [1]
   5'(c_1(c_5(c_3(c_5(c_4(c_0(c_0(c_3(x1))))))))) -> 5'(1'(5'(3'(5'(0'(4'(0'(3'(x1))))))))) [1]
   5'(c_5(c_2(c_3(c_2(c_0(c_3(c_2(c_5(c_3(c_2(c_5(c_5(c_5(c_5(c_1(c_5(c_5(c_1(c_2(c_2(x1))))))))))))))))))))) -> 5'(5'(2'(3'(2'(0'(3'(2'(5'(3'(2'(5'(5'(5'(1'(5'(5'(5'(1'(2'(2'(x1))))))))))))))))))))) [1]
   0'(c_0(c_1(c_4(c_5(c_3(c_1(c_4(c_5(c_1(c_4(c_5(c_1(c_0(c_5(c_2(c_2(c_0(c_1(c_2(c_2(c_3(c_3(c_3(c_0(c_0(c_2(c_1(c_2(c_5(x1)))))))))))))))))))))))))))))) -> 0'(0'(1'(4'(5'(3'(1'(4'(5'(1'(4'(5'(1'(0'(5'(2'(0'(2'(1'(2'(2'(3'(3'(3'(0'(0'(2'(1'(2'(5'(x1)))))))))))))))))))))))))))))) [1]
   0'(c_5(c_5(c_1(c_1(c_1(c_2(c_5(c_2(c_3(c_5(c_5(x1)))))))))))) -> 1'(3'(5'(2'(3'(4'(3'(3'(4'(3'(x1)))))))))) [1]
   3'(c_2(c_3(c_3(c_2(c_2(c_5(c_1(c_0(c_5(c_4(c_4(c_5(c_2(c_2(c_4(c_3(c_5(c_2(c_1(c_2(c_1(c_3(c_1(x1)))))))))))))))))))))))) -> 3'(2'(3'(3'(2'(2'(5'(1'(5'(0'(4'(4'(5'(2'(2'(4'(3'(5'(2'(1'(2'(1'(3'(1'(x1)))))))))))))))))))))))) [1]
   2'(c_2(c_0(c_2(c_2(c_5(c_0(c_3(c_2(c_0(c_5(x1))))))))))) -> 5'(0'(3'(5'(4'(2'(2'(3'(1'(0'(x1)))))))))) [1]
   4'(c_1(c_3(c_5(c_2(c_3(c_5(c_5(c_0(c_0(c_3(x1))))))))))) -> 5'(2'(3'(0'(3'(5'(2'(3'(5'(3'(x1)))))))))) [1]
   4'(c_3(c_2(c_1(c_1(c_2(c_4(c_4(c_5(c_1(c_5(c_2(c_2(c_4(c_0(c_2(c_4(c_2(c_4(c_2(c_0(c_4(c_2(c_4(c_4(c_0(c_1(x1))))))))))))))))))))))))))) -> 4'(3'(2'(1'(2'(1'(4'(4'(5'(1'(5'(2'(2'(4'(0'(2'(4'(2'(4'(2'(0'(4'(2'(4'(4'(0'(1'(x1))))))))))))))))))))))))))) [1]
   5'(c_1(c_0(c_3(c_5(c_0(c_1(c_1(c_3(c_4(c_3(x1))))))))))) -> 1'(0'(3'(0'(0'(4'(2'(4'(5'(3'(x1)))))))))) [1]
   4'(c_0(c_3(c_0(c_0(c_3(c_0(c_5(c_1(c_4(c_3(x1))))))))))) -> 1'(2'(1'(5'(5'(5'(0'(4'(1'(1'(x1)))))))))) [1]
   0'(c_0(c_5(c_2(c_2(c_4(c_4(c_3(c_3(c_4(c_0(x1))))))))))) -> 4'(0'(4'(2'(3'(1'(5'(3'(5'(5'(x1)))))))))) [1]
   5'(c_4(c_1(c_5(c_1(c_4(c_2(c_5(c_4(c_3(c_0(c_4(c_1(c_0(x1)))))))))))))) -> 5'(4'(1'(1'(5'(4'(2'(5'(4'(3'(0'(4'(1'(0'(x1)))))))))))))) [1]
   1'(c_2(c_4(c_0(c_2(c_4(c_0(c_1(c_2(c_4(c_3(c_1(c_0(c_3(c_4(x1))))))))))))))) -> 1'(2'(4'(0'(2'(4'(0'(1'(4'(2'(3'(1'(0'(3'(4'(x1))))))))))))))) [1]
   4'(c_1(c_2(c_0(c_5(c_5(c_4(c_0(c_0(c_0(c_2(x1))))))))))) -> 3'(3'(5'(4'(5'(3'(2'(0'(0'(2'(x1)))))))))) [1]
   5'(c_3(c_1(c_5(c_5(c_3(c_3(c_0(c_2(c_2(c_2(c_2(c_3(c_3(c_4(c_5(c_1(c_1(x1)))))))))))))))))) -> 5'(3'(1'(5'(5'(3'(3'(0'(2'(2'(2'(3'(2'(3'(4'(5'(1'(1'(x1)))))))))))))))))) [1]
   2'(c_0(c_2(c_5(c_4(c_0(c_3(c_3(c_0(c_4(c_2(c_2(c_5(c_5(c_2(x1))))))))))))))) -> 2'(0'(2'(4'(0'(5'(0'(3'(4'(3'(2'(2'(5'(5'(2'(x1))))))))))))))) [1]
   4'(c_1(c_1(c_3(c_1(c_3(c_2(c_1(c_2(c_2(c_2(c_0(c_5(x1))))))))))))) -> 0'(3'(5'(4'(0'(1'(4'(0'(5'(0'(x1)))))))))) [1]
   4'(c_4(c_5(c_3(c_2(c_4(c_2(c_5(x1)))))))) -> 4'(2'(3'(5'(4'(4'(2'(5'(x1)))))))) [1]
   3'(c_1(c_3(c_2(c_1(c_0(c_5(c_3(c_4(c_0(c_1(x1))))))))))) -> 1'(2'(0'(4'(0'(3'(2'(0'(4'(0'(x1)))))))))) [1]
   0'(c_1(c_1(c_4(c_1(c_3(c_2(c_4(c_3(c_5(c_5(c_0(c_1(x1))))))))))))) -> 4'(3'(2'(0'(5'(0'(4'(0'(4'(4'(x1)))))))))) [1]
   4'(c_5(c_5(c_3(c_5(c_4(c_1(c_1(c_5(c_5(c_3(c_3(c_1(c_5(c_4(c_4(c_5(c_0(c_4(x1))))))))))))))))))) -> 4'(5'(5'(3'(5'(4'(1'(5'(1'(5'(3'(3'(1'(5'(4'(4'(5'(0'(4'(x1))))))))))))))))))) [1]
   0'(c_2(c_2(c_5(c_5(c_0(c_0(c_4(c_5(c_3(c_4(x1))))))))))) -> 4'(0'(5'(1'(3'(5'(5'(4'(5'(0'(x1)))))))))) [1]
   0'(c_4(c_3(c_0(c_0(c_0(c_4(c_3(c_2(c_3(c_3(x1))))))))))) -> 2'(5'(1'(5'(2'(4'(5'(4'(3'(2'(x1)))))))))) [1]
   2'(c_3(c_2(c_1(c_1(c_1(c_0(c_2(c_1(c_3(c_5(c_1(x1)))))))))))) -> 5'(4'(3'(0'(1'(2'(3'(3'(2'(5'(x1)))))))))) [1]
   0'(c_0(c_0(c_1(c_2(c_2(c_3(x1))))))) -> 0'(0'(0'(2'(1'(2'(3'(x1))))))) [1]
   3'(c_2(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_2(c_0(x1))))))))))) -> 4'(4'(2'(5'(4'(5'(5'(0'(5'(0'(x1)))))))))) [1]
   0'(c_4(c_0(c_1(c_0(c_2(c_2(c_4(c_3(c_0(c_5(c_0(c_2(c_0(c_4(c_5(c_3(x1))))))))))))))))) -> 0'(4'(0'(1'(0'(2'(4'(2'(3'(0'(5'(0'(2'(0'(4'(5'(3'(x1))))))))))))))))) [1]
   0'(c_5(c_2(c_5(c_4(c_3(c_3(c_2(c_3(c_5(c_0(c_2(c_3(c_2(c_5(c_0(c_5(c_0(c_4(c_1(x1)))))))))))))))))))) -> 0'(5'(2'(5'(4'(3'(3'(2'(3'(5'(0'(2'(3'(2'(0'(5'(5'(0'(4'(1'(x1)))))))))))))))))))) [1]
   4'(c_0(c_5(c_2(c_5(c_3(c_0(c_0(c_3(c_5(c_5(x1))))))))))) -> 0'(0'(5'(2'(3'(0'(3'(1'(5'(5'(x1)))))))))) [1]
   2'(c_5(c_2(c_3(c_0(c_0(c_1(c_0(c_5(c_0(c_2(c_5(c_3(c_4(c_0(c_5(c_5(c_5(c_3(c_2(x1)))))))))))))))))))) -> 2'(5'(2'(3'(0'(0'(1'(0'(5'(0'(2'(5'(3'(4'(5'(0'(5'(5'(3'(2'(x1)))))))))))))))))))) [1]
   0'(c_4(c_0(c_4(c_5(c_3(c_3(c_0(c_5(c_5(c_2(x1))))))))))) -> 4'(5'(3'(5'(2'(2'(1'(1'(4'(3'(x1)))))))))) [1]
   0'(c_1(c_1(c_1(c_2(c_0(c_1(c_3(c_0(c_4(c_2(c_3(c_3(x1))))))))))))) -> 0'(4'(1'(2'(4'(2'(5'(0'(0'(0'(x1)))))))))) [1]
   0'(c_1(c_2(c_4(c_4(c_0(c_1(c_0(x1)))))))) -> 0'(1'(4'(2'(4'(1'(0'(0'(x1)))))))) [1]
   1'(c_2(c_0(c_1(c_2(c_4(c_5(c_2(c_4(c_4(x1)))))))))) -> 1'(5'(4'(2'(0'(2'(2'(4'(1'(4'(x1)))))))))) [1]
   4'(c_2(c_1(c_2(c_2(c_3(c_3(c_3(c_1(c_3(c_2(x1))))))))))) -> 5'(5'(2'(3'(4'(2'(5'(4'(0'(3'(x1)))))))))) [1]
   3'(c_5(c_4(c_4(c_5(c_1(c_1(c_5(c_0(c_2(c_0(x1))))))))))) -> 3'(1'(5'(1'(3'(5'(0'(1'(5'(1'(x1)))))))))) [1]
   0'(c_4(c_4(c_5(c_4(c_0(c_1(c_3(c_1(c_3(c_4(x1))))))))))) -> 0'(4'(0'(3'(4'(3'(1'(4'(4'(1'(5'(x1))))))))))) [1]
   1'(c_1(c_1(c_2(c_2(c_5(c_2(c_1(c_3(c_1(c_0(x1))))))))))) -> 1'(5'(1'(1'(3'(5'(0'(0'(2'(4'(x1)))))))))) [1]
   3'(c_5(c_5(c_4(c_5(c_3(c_0(c_2(c_5(c_5(c_1(x1))))))))))) -> 3'(1'(1'(2'(4'(2'(3'(0'(2'(5'(x1)))))))))) [1]
   4'(c_2(c_0(c_2(c_1(c_5(c_5(c_4(c_2(c_3(c_2(c_1(c_0(c_4(c_1(c_2(c_0(c_4(c_2(c_3(c_1(c_3(c_0(c_1(c_4(c_2(c_0(c_0(c_2(c_5(x1)))))))))))))))))))))))))))))) -> 4'(2'(0'(2'(1'(5'(5'(4'(2'(3'(2'(1'(0'(1'(4'(2'(0'(4'(2'(3'(1'(3'(0'(1'(4'(2'(0'(0'(2'(5'(x1)))))))))))))))))))))))))))))) [1]
   4'(c_0(c_4(c_2(c_4(c_0(c_3(c_1(x1)))))))) -> 4'(0'(4'(2'(0'(4'(3'(1'(x1)))))))) [1]
   2'(c_0(c_2(c_4(c_0(c_2(c_4(c_2(c_0(c_0(c_1(c_1(c_0(c_1(c_3(c_5(c_3(c_3(c_4(c_3(c_1(c_2(c_5(x1))))))))))))))))))))))) -> 2'(0'(2'(2'(0'(4'(4'(1'(0'(1'(3'(2'(0'(1'(5'(0'(3'(3'(1'(2'(3'(4'(5'(x1))))))))))))))))))))))) [1]
   2'(c_4(c_5(c_5(c_3(c_3(c_1(c_2(c_0(c_5(c_5(c_1(c_0(c_3(c_4(c_4(c_5(c_1(c_3(c_5(c_2(c_4(c_0(c_1(c_1(c_4(c_1(c_4(c_5(c_1(x1)))))))))))))))))))))))))))))) -> 2'(4'(5'(5'(3'(3'(1'(2'(0'(5'(5'(1'(0'(3'(4'(4'(5'(1'(3'(2'(5'(4'(0'(1'(1'(4'(1'(4'(5'(1'(x1)))))))))))))))))))))))))))))) [1]
   0'(c_0(c_0(c_5(c_1(c_5(c_3(c_5(c_1(c_3(c_2(c_3(x1)))))))))))) -> 1'(3'(3'(0'(1'(4'(1'(0'(5'(5'(x1)))))))))) [1]
   5'(c_5(c_3(c_3(c_0(c_1(c_4(c_1(c_3(c_3(c_0(x1))))))))))) -> 2'(3'(3'(4'(5'(4'(2'(2'(0'(1'(x1)))))))))) [1]
   2'(c_4(c_1(c_4(c_1(c_0(c_4(c_0(c_3(c_1(c_0(c_1(c_1(c_0(c_5(c_4(c_1(c_5(c_1(c_4(x1)))))))))))))))))))) -> 2'(4'(1'(4'(1'(0'(4'(0'(3'(1'(0'(1'(1'(5'(0'(4'(1'(5'(1'(4'(x1)))))))))))))))))))) [1]
   1'(c_1(c_5(c_3(c_4(c_3(c_4(c_4(c_2(c_5(x1)))))))))) -> 1'(1'(5'(3'(3'(4'(4'(4'(2'(5'(x1)))))))))) [1]
   4'(c_3(c_1(c_1(c_2(c_1(c_2(c_0(c_5(c_2(c_0(c_3(c_2(x1))))))))))))) -> 4'(4'(4'(4'(4'(0'(0'(3'(4'(1'(x1)))))))))) [1]
   encArg(cons_0(x_1)) -> 0'(encArg(x_1)) [0]
   encArg(cons_4(x_1)) -> 4'(encArg(x_1)) [0]
   encArg(cons_3(x_1)) -> 3'(encArg(x_1)) [0]
   encArg(cons_5(x_1)) -> 5'(encArg(x_1)) [0]
   encArg(cons_1(x_1)) -> 1'(encArg(x_1)) [0]
   encArg(cons_2(x_1)) -> 2'(encArg(x_1)) [0]
   encode_0(x_1) -> 0'(encArg(x_1)) [0]
   encode_1(x_1) -> 1'(encArg(x_1)) [0]
   encode_2(x_1) -> 2'(encArg(x_1)) [0]
   encode_3(x_1) -> 3'(encArg(x_1)) [0]
   encode_4(x_1) -> 4'(encArg(x_1)) [0]
   encode_5(x_1) -> 5'(encArg(x_1)) [0]
   5'(x0) -> c_5(x0) [0]
   0'(x0) -> c_0(x0) [0]
   1'(x0) -> c_1(x0) [0]
   2'(x0) -> c_2(x0) [0]
   3'(x0) -> c_3(x0) [0]
   4'(x0) -> c_4(x0) [0]

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

(23) TypeInferenceProof (BOTH BOUNDS(ID, ID))
Infered types.
----------------------------------------

(24)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   4'(c_0(c_5(c_5(c_2(c_0(c_4(c_0(c_2(c_3(c_5(x1))))))))))) -> 5'(5'(0'(4'(3'(5'(4'(1'(5'(1'(x1)))))))))) [1]
   4'(c_5(c_4(c_0(c_2(c_5(c_0(c_2(c_3(c_2(c_5(x1))))))))))) -> 3'(3'(4'(4'(5'(2'(3'(5'(3'(0'(x1)))))))))) [1]
   5'(c_5(c_3(c_4(c_1(c_2(c_0(c_2(c_5(c_3(c_2(c_5(c_4(c_4(c_5(c_5(c_1(c_2(x1)))))))))))))))))) -> 5'(5'(3'(4'(1'(2'(0'(2'(5'(3'(2'(4'(5'(4'(5'(5'(1'(2'(x1)))))))))))))))))) [1]
   5'(c_1(c_4(c_4(c_3(c_1(c_5(c_4(c_3(c_5(c_1(c_2(c_0(x1))))))))))))) -> 2'(2'(1'(3'(0'(0'(4'(3'(2'(5'(x1)))))))))) [1]
   0'(c_0(c_0(c_2(c_2(c_3(c_4(c_4(c_3(c_3(x1)))))))))) -> 0'(2'(3'(0'(3'(2'(1'(5'(1'(3'(x1)))))))))) [1]
   4'(c_4(c_3(c_3(c_3(c_2(c_4(c_2(c_5(c_1(c_4(x1))))))))))) -> 2'(0'(3'(4'(4'(1'(3'(0'(2'(0'(x1)))))))))) [1]
   5'(c_1(c_2(c_1(c_0(c_2(c_3(c_1(c_3(c_1(c_0(c_0(x1)))))))))))) -> 5'(2'(0'(4'(2'(1'(4'(1'(1'(3'(x1)))))))))) [1]
   0'(c_4(c_3(c_0(c_3(c_3(c_5(c_3(c_5(c_1(c_4(c_2(c_3(c_3(c_0(c_4(c_0(c_1(c_5(c_0(c_3(c_0(c_2(c_5(c_5(c_0(x1)))))))))))))))))))))))))) -> 0'(4'(3'(0'(3'(3'(5'(3'(5'(1'(4'(2'(3'(3'(0'(4'(1'(0'(5'(0'(3'(0'(2'(5'(5'(0'(x1)))))))))))))))))))))))))) [1]
   2'(c_1(c_2(c_0(c_5(c_0(c_3(c_5(c_1(c_2(c_3(c_5(x1)))))))))))) -> 1'(0'(0'(4'(5'(4'(1'(4'(1'(0'(x1)))))))))) [1]
   5'(c_0(c_0(c_2(c_4(c_0(c_1(c_5(c_1(c_1(c_3(c_0(c_2(c_2(c_2(c_3(c_5(c_4(c_0(c_4(c_1(c_5(c_2(c_3(c_4(x1))))))))))))))))))))))))) -> 5'(0'(0'(2'(0'(4'(1'(5'(1'(1'(3'(0'(2'(2'(2'(3'(5'(4'(0'(4'(1'(5'(2'(3'(4'(x1))))))))))))))))))))))))) [1]
   0'(c_5(c_2(c_0(c_0(c_2(c_1(c_4(c_2(c_4(c_5(x1))))))))))) -> 5'(0'(4'(3'(4'(2'(5'(5'(4'(1'(x1)))))))))) [1]
   4'(c_1(c_3(c_3(c_1(c_5(c_1(c_1(c_2(c_4(c_3(x1))))))))))) -> 0'(1'(2'(3'(3'(2'(1'(3'(3'(2'(x1)))))))))) [1]
   3'(c_3(c_3(c_4(c_0(c_2(c_5(c_4(c_5(c_0(c_0(x1))))))))))) -> 3'(1'(5'(1'(1'(5'(2'(3'(1'(4'(x1)))))))))) [1]
   2'(c_5(c_3(c_1(c_0(c_1(c_4(c_4(c_2(c_2(c_4(x1))))))))))) -> 0'(5'(1'(0'(0'(2'(0'(5'(5'(1'(x1)))))))))) [1]
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   2'(c_4(c_5(c_5(c_3(c_3(c_1(c_2(c_0(c_5(c_5(c_1(c_0(c_3(c_4(c_4(c_5(c_1(c_3(c_5(c_2(c_4(c_0(c_1(c_1(c_4(c_1(c_4(c_5(c_1(x1)))))))))))))))))))))))))))))) -> 2'(4'(5'(5'(3'(3'(1'(2'(0'(5'(5'(1'(0'(3'(4'(4'(5'(1'(3'(2'(5'(4'(0'(1'(1'(4'(1'(4'(5'(1'(x1)))))))))))))))))))))))))))))) [1]
   0'(c_0(c_0(c_5(c_1(c_5(c_3(c_5(c_1(c_3(c_2(c_3(x1)))))))))))) -> 1'(3'(3'(0'(1'(4'(1'(0'(5'(5'(x1)))))))))) [1]
   5'(c_5(c_3(c_3(c_0(c_1(c_4(c_1(c_3(c_3(c_0(x1))))))))))) -> 2'(3'(3'(4'(5'(4'(2'(2'(0'(1'(x1)))))))))) [1]
   2'(c_4(c_1(c_4(c_1(c_0(c_4(c_0(c_3(c_1(c_0(c_1(c_1(c_0(c_5(c_4(c_1(c_5(c_1(c_4(x1)))))))))))))))))))) -> 2'(4'(1'(4'(1'(0'(4'(0'(3'(1'(0'(1'(1'(5'(0'(4'(1'(5'(1'(4'(x1)))))))))))))))))))) [1]
   1'(c_1(c_5(c_3(c_4(c_3(c_4(c_4(c_2(c_5(x1)))))))))) -> 1'(1'(5'(3'(3'(4'(4'(4'(2'(5'(x1)))))))))) [1]
   4'(c_3(c_1(c_1(c_2(c_1(c_2(c_0(c_5(c_2(c_0(c_3(c_2(x1))))))))))))) -> 4'(4'(4'(4'(4'(0'(0'(3'(4'(1'(x1)))))))))) [1]
   encArg(cons_0(x_1)) -> 0'(encArg(x_1)) [0]
   encArg(cons_4(x_1)) -> 4'(encArg(x_1)) [0]
   encArg(cons_3(x_1)) -> 3'(encArg(x_1)) [0]
   encArg(cons_5(x_1)) -> 5'(encArg(x_1)) [0]
   encArg(cons_1(x_1)) -> 1'(encArg(x_1)) [0]
   encArg(cons_2(x_1)) -> 2'(encArg(x_1)) [0]
   encode_0(x_1) -> 0'(encArg(x_1)) [0]
   encode_1(x_1) -> 1'(encArg(x_1)) [0]
   encode_2(x_1) -> 2'(encArg(x_1)) [0]
   encode_3(x_1) -> 3'(encArg(x_1)) [0]
   encode_4(x_1) -> 4'(encArg(x_1)) [0]
   encode_5(x_1) -> 5'(encArg(x_1)) [0]
   5'(x0) -> c_5(x0) [0]
   0'(x0) -> c_0(x0) [0]
   1'(x0) -> c_1(x0) [0]
   2'(x0) -> c_2(x0) [0]
   3'(x0) -> c_3(x0) [0]
   4'(x0) -> c_4(x0) [0]

The TRS has the following type information:
4' :: c_5:c_3:c_2:c_0:c_4:c_1 -> c_5:c_3:c_2:c_0:c_4:c_1
c_0 :: c_5:c_3:c_2:c_0:c_4:c_1 -> c_5:c_3:c_2:c_0:c_4:c_1
c_5 :: c_5:c_3:c_2:c_0:c_4:c_1 -> c_5:c_3:c_2:c_0:c_4:c_1
c_2 :: c_5:c_3:c_2:c_0:c_4:c_1 -> c_5:c_3:c_2:c_0:c_4:c_1
c_4 :: c_5:c_3:c_2:c_0:c_4:c_1 -> c_5:c_3:c_2:c_0:c_4:c_1
c_3 :: c_5:c_3:c_2:c_0:c_4:c_1 -> c_5:c_3:c_2:c_0:c_4:c_1
5' :: c_5:c_3:c_2:c_0:c_4:c_1 -> c_5:c_3:c_2:c_0:c_4:c_1
0' :: c_5:c_3:c_2:c_0:c_4:c_1 -> c_5:c_3:c_2:c_0:c_4:c_1
3' :: c_5:c_3:c_2:c_0:c_4:c_1 -> c_5:c_3:c_2:c_0:c_4:c_1
1' :: c_5:c_3:c_2:c_0:c_4:c_1 -> c_5:c_3:c_2:c_0:c_4:c_1
2' :: c_5:c_3:c_2:c_0:c_4:c_1 -> c_5:c_3:c_2:c_0:c_4:c_1
c_1 :: c_5:c_3:c_2:c_0:c_4:c_1 -> c_5:c_3:c_2:c_0:c_4:c_1
encArg :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> c_5:c_3:c_2:c_0:c_4:c_1
cons_0 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> cons_0:cons_4:cons_3:cons_5:cons_1:cons_2
cons_4 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> cons_0:cons_4:cons_3:cons_5:cons_1:cons_2
cons_3 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> cons_0:cons_4:cons_3:cons_5:cons_1:cons_2
cons_5 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> cons_0:cons_4:cons_3:cons_5:cons_1:cons_2
cons_1 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> cons_0:cons_4:cons_3:cons_5:cons_1:cons_2
cons_2 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> cons_0:cons_4:cons_3:cons_5:cons_1:cons_2
encode_0 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> c_5:c_3:c_2:c_0:c_4:c_1
encode_1 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> c_5:c_3:c_2:c_0:c_4:c_1
encode_2 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> c_5:c_3:c_2:c_0:c_4:c_1
encode_3 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> c_5:c_3:c_2:c_0:c_4:c_1
encode_4 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> c_5:c_3:c_2:c_0:c_4:c_1
encode_5 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> c_5:c_3:c_2:c_0:c_4:c_1

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

(25) CompletionProof (UPPER BOUND(ID))
The transformation into a RNTS is sound, since:

(a) The obligation is a constructor system where every type has a constant constructor,

(b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols:
none

(c) The following functions are completely defined:

   encArg_1
   encode_0_1
   encode_1_1
   encode_2_1
   encode_3_1
   encode_4_1
   encode_5_1
   5'_1
   0'_1
   1'_1
   2'_1
   3'_1
   4'_1

Due to the following rules being added:

   encArg(v0) -> const [0]
   encode_0(v0) -> const [0]
   encode_1(v0) -> const [0]
   encode_2(v0) -> const [0]
   encode_3(v0) -> const [0]
   encode_4(v0) -> const [0]
   encode_5(v0) -> const [0]
   5'(v0) -> const [0]
   0'(v0) -> const [0]
   1'(v0) -> const [0]
   2'(v0) -> const [0]
   3'(v0) -> const [0]
   4'(v0) -> const [0]

And the following fresh constants:    const, const1

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

(26)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   4'(c_0(c_5(c_5(c_2(c_0(c_4(c_0(c_2(c_3(c_5(x1))))))))))) -> 5'(5'(0'(4'(3'(5'(4'(1'(5'(1'(x1)))))))))) [1]
   4'(c_5(c_4(c_0(c_2(c_5(c_0(c_2(c_3(c_2(c_5(x1))))))))))) -> 3'(3'(4'(4'(5'(2'(3'(5'(3'(0'(x1)))))))))) [1]
   5'(c_5(c_3(c_4(c_1(c_2(c_0(c_2(c_5(c_3(c_2(c_5(c_4(c_4(c_5(c_5(c_1(c_2(x1)))))))))))))))))) -> 5'(5'(3'(4'(1'(2'(0'(2'(5'(3'(2'(4'(5'(4'(5'(5'(1'(2'(x1)))))))))))))))))) [1]
   5'(c_1(c_4(c_4(c_3(c_1(c_5(c_4(c_3(c_5(c_1(c_2(c_0(x1))))))))))))) -> 2'(2'(1'(3'(0'(0'(4'(3'(2'(5'(x1)))))))))) [1]
   0'(c_0(c_0(c_2(c_2(c_3(c_4(c_4(c_3(c_3(x1)))))))))) -> 0'(2'(3'(0'(3'(2'(1'(5'(1'(3'(x1)))))))))) [1]
   4'(c_4(c_3(c_3(c_3(c_2(c_4(c_2(c_5(c_1(c_4(x1))))))))))) -> 2'(0'(3'(4'(4'(1'(3'(0'(2'(0'(x1)))))))))) [1]
   5'(c_1(c_2(c_1(c_0(c_2(c_3(c_1(c_3(c_1(c_0(c_0(x1)))))))))))) -> 5'(2'(0'(4'(2'(1'(4'(1'(1'(3'(x1)))))))))) [1]
   0'(c_4(c_3(c_0(c_3(c_3(c_5(c_3(c_5(c_1(c_4(c_2(c_3(c_3(c_0(c_4(c_0(c_1(c_5(c_0(c_3(c_0(c_2(c_5(c_5(c_0(x1)))))))))))))))))))))))))) -> 0'(4'(3'(0'(3'(3'(5'(3'(5'(1'(4'(2'(3'(3'(0'(4'(1'(0'(5'(0'(3'(0'(2'(5'(5'(0'(x1)))))))))))))))))))))))))) [1]
   2'(c_1(c_2(c_0(c_5(c_0(c_3(c_5(c_1(c_2(c_3(c_5(x1)))))))))))) -> 1'(0'(0'(4'(5'(4'(1'(4'(1'(0'(x1)))))))))) [1]
   5'(c_0(c_0(c_2(c_4(c_0(c_1(c_5(c_1(c_1(c_3(c_0(c_2(c_2(c_2(c_3(c_5(c_4(c_0(c_4(c_1(c_5(c_2(c_3(c_4(x1))))))))))))))))))))))))) -> 5'(0'(0'(2'(0'(4'(1'(5'(1'(1'(3'(0'(2'(2'(2'(3'(5'(4'(0'(4'(1'(5'(2'(3'(4'(x1))))))))))))))))))))))))) [1]
   0'(c_5(c_2(c_0(c_0(c_2(c_1(c_4(c_2(c_4(c_5(x1))))))))))) -> 5'(0'(4'(3'(4'(2'(5'(5'(4'(1'(x1)))))))))) [1]
   4'(c_1(c_3(c_3(c_1(c_5(c_1(c_1(c_2(c_4(c_3(x1))))))))))) -> 0'(1'(2'(3'(3'(2'(1'(3'(3'(2'(x1)))))))))) [1]
   3'(c_3(c_3(c_4(c_0(c_2(c_5(c_4(c_5(c_0(c_0(x1))))))))))) -> 3'(1'(5'(1'(1'(5'(2'(3'(1'(4'(x1)))))))))) [1]
   2'(c_5(c_3(c_1(c_0(c_1(c_4(c_4(c_2(c_2(c_4(x1))))))))))) -> 0'(5'(1'(0'(0'(2'(0'(5'(5'(1'(x1)))))))))) [1]
   3'(c_3(c_2(c_5(c_4(c_4(c_0(c_1(c_3(c_1(c_2(c_1(c_5(c_0(c_0(c_4(c_2(c_1(c_4(c_2(c_2(c_3(c_5(x1))))))))))))))))))))))) -> 3'(3'(2'(5'(4'(4'(0'(1'(3'(1'(2'(1'(5'(0'(4'(0'(2'(1'(4'(2'(2'(3'(5'(x1))))))))))))))))))))))) [1]
   1'(c_5(c_0(c_1(c_1(c_4(c_2(c_4(c_3(c_5(c_4(c_5(c_2(c_0(c_3(c_3(c_2(c_0(c_5(c_5(c_4(c_4(c_2(c_5(c_3(c_0(c_2(c_1(c_1(c_0(x1)))))))))))))))))))))))))))))) -> 1'(5'(0'(1'(1'(4'(4'(2'(3'(5'(4'(5'(2'(0'(3'(3'(2'(0'(5'(5'(4'(4'(2'(5'(3'(0'(2'(1'(1'(0'(x1)))))))))))))))))))))))))))))) [1]
   4'(c_3(c_1(c_3(c_5(c_1(c_5(c_1(c_5(c_0(c_2(c_1(x1)))))))))))) -> 0'(1'(3'(1'(0'(4'(0'(0'(5'(3'(x1)))))))))) [1]
   2'(c_1(c_0(c_5(c_5(c_4(c_1(c_0(c_4(c_2(c_5(c_3(c_1(c_4(c_1(c_3(c_5(c_0(c_0(c_2(c_4(c_5(x1)))))))))))))))))))))) -> 2'(1'(0'(5'(5'(4'(1'(0'(4'(2'(5'(3'(1'(4'(1'(3'(0'(5'(0'(2'(4'(5'(x1)))))))))))))))))))))) [1]
   4'(c_0(c_5(c_4(c_0(c_2(c_4(c_0(c_4(c_3(x1)))))))))) -> 2'(3'(1'(3'(5'(3'(1'(2'(4'(5'(x1)))))))))) [1]
   0'(c_0(c_3(c_1(c_5(c_5(c_1(c_5(c_3(c_2(c_0(c_2(c_2(c_4(c_3(c_4(c_0(c_5(c_1(x1))))))))))))))))))) -> 0'(3'(0'(5'(3'(1'(1'(0'(5'(2'(2'(4'(5'(2'(3'(4'(0'(5'(1'(x1))))))))))))))))))) [1]
   1'(c_5(c_2(c_2(c_3(c_3(c_4(c_2(c_4(c_5(x1)))))))))) -> 1'(5'(2'(3'(2'(3'(4'(2'(4'(5'(x1)))))))))) [1]
   5'(c_5(c_0(c_5(c_3(c_4(c_1(c_2(c_3(c_2(c_2(x1))))))))))) -> 1'(2'(3'(5'(5'(0'(1'(3'(5'(5'(x1)))))))))) [1]
   5'(c_5(c_0(c_3(c_2(c_2(c_1(c_3(c_4(c_3(c_5(c_4(c_2(c_5(c_2(c_0(c_4(c_1(c_1(c_2(c_4(c_0(c_5(c_4(c_3(c_2(c_4(c_4(x1)))))))))))))))))))))))))))) -> 5'(5'(0'(3'(2'(2'(3'(1'(4'(3'(5'(4'(2'(5'(2'(0'(4'(1'(1'(2'(4'(0'(5'(4'(3'(2'(4'(4'(x1)))))))))))))))))))))))))))) [1]
   5'(c_0(c_5(c_0(c_0(c_4(c_0(c_1(c_3(c_4(c_1(x1))))))))))) -> 2'(2'(4'(2'(1'(1'(3'(3'(3'(0'(x1)))))))))) [1]
   4'(c_0(c_5(c_4(c_5(c_5(c_3(c_4(c_3(c_4(c_1(x1))))))))))) -> 3'(4'(1'(1'(3'(1'(4'(0'(1'(4'(x1)))))))))) [1]
   1'(c_5(c_0(c_0(c_1(c_5(c_2(c_1(c_5(c_0(c_5(c_5(c_5(c_0(c_1(c_4(c_0(c_5(c_3(c_4(c_3(c_1(c_2(c_0(c_4(c_0(c_2(c_2(c_1(c_5(x1)))))))))))))))))))))))))))))) -> 1'(5'(0'(0'(1'(5'(2'(5'(1'(0'(5'(5'(5'(0'(1'(4'(0'(5'(3'(4'(3'(1'(2'(0'(4'(0'(2'(2'(1'(5'(x1)))))))))))))))))))))))))))))) [1]
   0'(c_1(c_1(c_5(c_1(c_1(c_4(c_4(c_5(c_0(c_4(c_2(c_1(x1))))))))))))) -> 0'(3'(2'(0'(0'(4'(3'(1'(0'(4'(x1)))))))))) [1]
   1'(c_2(c_3(c_2(c_0(c_1(c_0(c_5(c_3(c_0(c_2(c_1(c_1(c_1(c_4(c_4(c_1(c_2(c_4(c_5(c_2(c_2(c_4(c_0(c_3(c_2(x1)))))))))))))))))))))))))) -> 1'(2'(3'(2'(0'(1'(0'(5'(3'(0'(2'(1'(1'(1'(4'(4'(1'(4'(2'(5'(2'(2'(4'(0'(3'(2'(x1)))))))))))))))))))))))))) [1]
   5'(c_5(c_5(c_3(c_5(c_3(c_2(c_5(c_0(c_1(c_5(c_3(c_1(c_2(c_2(c_3(c_3(c_0(c_3(c_1(c_0(c_4(c_1(c_2(c_2(c_5(c_3(c_1(c_3(x1))))))))))))))))))))))))))))) -> 5'(5'(5'(3'(5'(3'(2'(5'(1'(0'(5'(3'(1'(2'(2'(3'(3'(0'(3'(1'(0'(4'(1'(2'(2'(5'(3'(1'(3'(x1))))))))))))))))))))))))))))) [1]
   5'(c_2(c_3(c_3(c_1(c_0(c_1(c_1(c_1(c_4(c_1(c_4(x1)))))))))))) -> 0'(2'(4'(0'(4'(0'(4'(0'(0'(1'(x1)))))))))) [1]
   4'(c_3(c_3(c_0(c_5(c_2(c_0(c_4(c_4(c_5(c_1(c_2(x1)))))))))))) -> 2'(0'(1'(1'(5'(1'(1'(4'(0'(0'(x1)))))))))) [1]
   3'(c_4(c_2(c_2(c_2(c_3(c_1(c_3(c_1(c_2(c_1(x1))))))))))) -> 3'(4'(5'(5'(4'(3'(2'(1'(5'(4'(x1)))))))))) [1]
   0'(c_4(c_5(c_0(c_0(c_4(c_2(c_4(c_5(c_0(x1)))))))))) -> 3'(5'(3'(5'(5'(4'(0'(2'(2'(3'(x1)))))))))) [1]
   2'(c_4(c_3(c_1(c_4(c_0(c_2(c_5(c_3(c_4(c_1(c_3(c_4(c_0(c_3(c_1(c_0(c_1(c_0(c_1(c_3(x1))))))))))))))))))))) -> 2'(4'(3'(1'(4'(0'(5'(2'(3'(4'(1'(3'(4'(0'(3'(1'(0'(1'(0'(1'(3'(x1))))))))))))))))))))) [1]
   3'(c_1(c_5(c_3(c_4(c_5(c_1(c_3(c_3(x1))))))))) -> 3'(1'(5'(3'(5'(4'(1'(3'(3'(x1))))))))) [1]
   1'(c_3(c_3(c_2(c_1(c_2(c_1(c_1(c_0(c_1(c_5(c_0(c_4(c_2(c_5(c_3(c_2(c_3(c_1(c_5(c_3(c_2(c_3(c_4(c_1(c_4(c_2(x1))))))))))))))))))))))))))) -> 1'(2'(3'(3'(1'(2'(1'(0'(1'(1'(5'(0'(4'(5'(2'(3'(2'(3'(1'(3'(2'(5'(3'(1'(4'(4'(2'(x1))))))))))))))))))))))))))) [1]
   4'(c_4(c_5(c_5(c_3(c_0(c_1(x1))))))) -> 4'(4'(3'(5'(0'(5'(1'(x1))))))) [1]
   3'(c_2(c_5(c_5(c_2(c_1(c_2(c_2(c_2(c_3(c_2(c_2(c_4(c_0(c_4(c_0(c_3(c_5(x1)))))))))))))))))) -> 3'(5'(2'(2'(5'(1'(2'(2'(2'(3'(2'(2'(4'(0'(4'(0'(3'(5'(x1)))))))))))))))))) [1]
   5'(c_1(c_5(c_0(c_3(c_3(c_0(c_1(c_2(c_3(c_3(c_1(c_4(c_5(c_3(c_1(c_2(c_2(c_0(c_3(c_2(c_0(c_5(x1))))))))))))))))))))))) -> 5'(1'(5'(0'(3'(3'(0'(1'(2'(3'(3'(1'(4'(5'(3'(1'(2'(0'(2'(3'(2'(0'(5'(x1))))))))))))))))))))))) [1]
   2'(c_0(c_5(c_0(c_5(c_4(c_4(c_3(c_1(c_3(c_2(x1))))))))))) -> 2'(1'(0'(3'(1'(2'(1'(3'(4'(0'(x1)))))))))) [1]
   3'(c_2(c_5(c_3(c_4(c_4(c_0(c_1(c_3(c_5(c_4(x1))))))))))) -> 5'(0'(1'(3'(5'(5'(1'(3'(4'(2'(x1)))))))))) [1]
   1'(c_0(c_1(c_5(c_1(c_5(c_3(c_3(c_1(c_4(c_0(x1))))))))))) -> 3'(1'(2'(1'(5'(2'(4'(5'(1'(1'(x1)))))))))) [1]
   3'(c_1(c_3(c_3(c_3(c_0(c_4(c_1(c_1(c_3(c_0(x1))))))))))) -> 1'(0'(2'(1'(2'(1'(0'(1'(1'(3'(x1)))))))))) [1]
   2'(c_3(c_4(c_3(c_5(c_1(c_2(c_4(c_2(c_0(c_2(c_1(x1)))))))))))) -> 2'(4'(1'(3'(2'(2'(5'(5'(1'(0'(x1)))))))))) [1]
   2'(c_2(c_4(c_3(c_2(c_2(c_2(c_4(c_2(c_5(c_2(c_0(c_4(c_5(x1)))))))))))))) -> 2'(2'(0'(2'(2'(4'(2'(5'(3'(4'(4'(2'(2'(5'(x1)))))))))))))) [1]
   5'(c_1(c_5(c_3(c_5(c_4(c_0(c_0(c_3(x1))))))))) -> 5'(1'(5'(3'(5'(0'(4'(0'(3'(x1))))))))) [1]
   5'(c_5(c_2(c_3(c_2(c_0(c_3(c_2(c_5(c_3(c_2(c_5(c_5(c_5(c_5(c_1(c_5(c_5(c_1(c_2(c_2(x1))))))))))))))))))))) -> 5'(5'(2'(3'(2'(0'(3'(2'(5'(3'(2'(5'(5'(5'(1'(5'(5'(5'(1'(2'(2'(x1))))))))))))))))))))) [1]
   0'(c_0(c_1(c_4(c_5(c_3(c_1(c_4(c_5(c_1(c_4(c_5(c_1(c_0(c_5(c_2(c_2(c_0(c_1(c_2(c_2(c_3(c_3(c_3(c_0(c_0(c_2(c_1(c_2(c_5(x1)))))))))))))))))))))))))))))) -> 0'(0'(1'(4'(5'(3'(1'(4'(5'(1'(4'(5'(1'(0'(5'(2'(0'(2'(1'(2'(2'(3'(3'(3'(0'(0'(2'(1'(2'(5'(x1)))))))))))))))))))))))))))))) [1]
   0'(c_5(c_5(c_1(c_1(c_1(c_2(c_5(c_2(c_3(c_5(c_5(x1)))))))))))) -> 1'(3'(5'(2'(3'(4'(3'(3'(4'(3'(x1)))))))))) [1]
   3'(c_2(c_3(c_3(c_2(c_2(c_5(c_1(c_0(c_5(c_4(c_4(c_5(c_2(c_2(c_4(c_3(c_5(c_2(c_1(c_2(c_1(c_3(c_1(x1)))))))))))))))))))))))) -> 3'(2'(3'(3'(2'(2'(5'(1'(5'(0'(4'(4'(5'(2'(2'(4'(3'(5'(2'(1'(2'(1'(3'(1'(x1)))))))))))))))))))))))) [1]
   2'(c_2(c_0(c_2(c_2(c_5(c_0(c_3(c_2(c_0(c_5(x1))))))))))) -> 5'(0'(3'(5'(4'(2'(2'(3'(1'(0'(x1)))))))))) [1]
   4'(c_1(c_3(c_5(c_2(c_3(c_5(c_5(c_0(c_0(c_3(x1))))))))))) -> 5'(2'(3'(0'(3'(5'(2'(3'(5'(3'(x1)))))))))) [1]
   4'(c_3(c_2(c_1(c_1(c_2(c_4(c_4(c_5(c_1(c_5(c_2(c_2(c_4(c_0(c_2(c_4(c_2(c_4(c_2(c_0(c_4(c_2(c_4(c_4(c_0(c_1(x1))))))))))))))))))))))))))) -> 4'(3'(2'(1'(2'(1'(4'(4'(5'(1'(5'(2'(2'(4'(0'(2'(4'(2'(4'(2'(0'(4'(2'(4'(4'(0'(1'(x1))))))))))))))))))))))))))) [1]
   5'(c_1(c_0(c_3(c_5(c_0(c_1(c_1(c_3(c_4(c_3(x1))))))))))) -> 1'(0'(3'(0'(0'(4'(2'(4'(5'(3'(x1)))))))))) [1]
   4'(c_0(c_3(c_0(c_0(c_3(c_0(c_5(c_1(c_4(c_3(x1))))))))))) -> 1'(2'(1'(5'(5'(5'(0'(4'(1'(1'(x1)))))))))) [1]
   0'(c_0(c_5(c_2(c_2(c_4(c_4(c_3(c_3(c_4(c_0(x1))))))))))) -> 4'(0'(4'(2'(3'(1'(5'(3'(5'(5'(x1)))))))))) [1]
   5'(c_4(c_1(c_5(c_1(c_4(c_2(c_5(c_4(c_3(c_0(c_4(c_1(c_0(x1)))))))))))))) -> 5'(4'(1'(1'(5'(4'(2'(5'(4'(3'(0'(4'(1'(0'(x1)))))))))))))) [1]
   1'(c_2(c_4(c_0(c_2(c_4(c_0(c_1(c_2(c_4(c_3(c_1(c_0(c_3(c_4(x1))))))))))))))) -> 1'(2'(4'(0'(2'(4'(0'(1'(4'(2'(3'(1'(0'(3'(4'(x1))))))))))))))) [1]
   4'(c_1(c_2(c_0(c_5(c_5(c_4(c_0(c_0(c_0(c_2(x1))))))))))) -> 3'(3'(5'(4'(5'(3'(2'(0'(0'(2'(x1)))))))))) [1]
   5'(c_3(c_1(c_5(c_5(c_3(c_3(c_0(c_2(c_2(c_2(c_2(c_3(c_3(c_4(c_5(c_1(c_1(x1)))))))))))))))))) -> 5'(3'(1'(5'(5'(3'(3'(0'(2'(2'(2'(3'(2'(3'(4'(5'(1'(1'(x1)))))))))))))))))) [1]
   2'(c_0(c_2(c_5(c_4(c_0(c_3(c_3(c_0(c_4(c_2(c_2(c_5(c_5(c_2(x1))))))))))))))) -> 2'(0'(2'(4'(0'(5'(0'(3'(4'(3'(2'(2'(5'(5'(2'(x1))))))))))))))) [1]
   4'(c_1(c_1(c_3(c_1(c_3(c_2(c_1(c_2(c_2(c_2(c_0(c_5(x1))))))))))))) -> 0'(3'(5'(4'(0'(1'(4'(0'(5'(0'(x1)))))))))) [1]
   4'(c_4(c_5(c_3(c_2(c_4(c_2(c_5(x1)))))))) -> 4'(2'(3'(5'(4'(4'(2'(5'(x1)))))))) [1]
   3'(c_1(c_3(c_2(c_1(c_0(c_5(c_3(c_4(c_0(c_1(x1))))))))))) -> 1'(2'(0'(4'(0'(3'(2'(0'(4'(0'(x1)))))))))) [1]
   0'(c_1(c_1(c_4(c_1(c_3(c_2(c_4(c_3(c_5(c_5(c_0(c_1(x1))))))))))))) -> 4'(3'(2'(0'(5'(0'(4'(0'(4'(4'(x1)))))))))) [1]
   4'(c_5(c_5(c_3(c_5(c_4(c_1(c_1(c_5(c_5(c_3(c_3(c_1(c_5(c_4(c_4(c_5(c_0(c_4(x1))))))))))))))))))) -> 4'(5'(5'(3'(5'(4'(1'(5'(1'(5'(3'(3'(1'(5'(4'(4'(5'(0'(4'(x1))))))))))))))))))) [1]
   0'(c_2(c_2(c_5(c_5(c_0(c_0(c_4(c_5(c_3(c_4(x1))))))))))) -> 4'(0'(5'(1'(3'(5'(5'(4'(5'(0'(x1)))))))))) [1]
   0'(c_4(c_3(c_0(c_0(c_0(c_4(c_3(c_2(c_3(c_3(x1))))))))))) -> 2'(5'(1'(5'(2'(4'(5'(4'(3'(2'(x1)))))))))) [1]
   2'(c_3(c_2(c_1(c_1(c_1(c_0(c_2(c_1(c_3(c_5(c_1(x1)))))))))))) -> 5'(4'(3'(0'(1'(2'(3'(3'(2'(5'(x1)))))))))) [1]
   0'(c_0(c_0(c_1(c_2(c_2(c_3(x1))))))) -> 0'(0'(0'(2'(1'(2'(3'(x1))))))) [1]
   3'(c_2(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_2(c_0(x1))))))))))) -> 4'(4'(2'(5'(4'(5'(5'(0'(5'(0'(x1)))))))))) [1]
   0'(c_4(c_0(c_1(c_0(c_2(c_2(c_4(c_3(c_0(c_5(c_0(c_2(c_0(c_4(c_5(c_3(x1))))))))))))))))) -> 0'(4'(0'(1'(0'(2'(4'(2'(3'(0'(5'(0'(2'(0'(4'(5'(3'(x1))))))))))))))))) [1]
   0'(c_5(c_2(c_5(c_4(c_3(c_3(c_2(c_3(c_5(c_0(c_2(c_3(c_2(c_5(c_0(c_5(c_0(c_4(c_1(x1)))))))))))))))))))) -> 0'(5'(2'(5'(4'(3'(3'(2'(3'(5'(0'(2'(3'(2'(0'(5'(5'(0'(4'(1'(x1)))))))))))))))))))) [1]
   4'(c_0(c_5(c_2(c_5(c_3(c_0(c_0(c_3(c_5(c_5(x1))))))))))) -> 0'(0'(5'(2'(3'(0'(3'(1'(5'(5'(x1)))))))))) [1]
   2'(c_5(c_2(c_3(c_0(c_0(c_1(c_0(c_5(c_0(c_2(c_5(c_3(c_4(c_0(c_5(c_5(c_5(c_3(c_2(x1)))))))))))))))))))) -> 2'(5'(2'(3'(0'(0'(1'(0'(5'(0'(2'(5'(3'(4'(5'(0'(5'(5'(3'(2'(x1)))))))))))))))))))) [1]
   0'(c_4(c_0(c_4(c_5(c_3(c_3(c_0(c_5(c_5(c_2(x1))))))))))) -> 4'(5'(3'(5'(2'(2'(1'(1'(4'(3'(x1)))))))))) [1]
   0'(c_1(c_1(c_1(c_2(c_0(c_1(c_3(c_0(c_4(c_2(c_3(c_3(x1))))))))))))) -> 0'(4'(1'(2'(4'(2'(5'(0'(0'(0'(x1)))))))))) [1]
   0'(c_1(c_2(c_4(c_4(c_0(c_1(c_0(x1)))))))) -> 0'(1'(4'(2'(4'(1'(0'(0'(x1)))))))) [1]
   1'(c_2(c_0(c_1(c_2(c_4(c_5(c_2(c_4(c_4(x1)))))))))) -> 1'(5'(4'(2'(0'(2'(2'(4'(1'(4'(x1)))))))))) [1]
   4'(c_2(c_1(c_2(c_2(c_3(c_3(c_3(c_1(c_3(c_2(x1))))))))))) -> 5'(5'(2'(3'(4'(2'(5'(4'(0'(3'(x1)))))))))) [1]
   3'(c_5(c_4(c_4(c_5(c_1(c_1(c_5(c_0(c_2(c_0(x1))))))))))) -> 3'(1'(5'(1'(3'(5'(0'(1'(5'(1'(x1)))))))))) [1]
   0'(c_4(c_4(c_5(c_4(c_0(c_1(c_3(c_1(c_3(c_4(x1))))))))))) -> 0'(4'(0'(3'(4'(3'(1'(4'(4'(1'(5'(x1))))))))))) [1]
   1'(c_1(c_1(c_2(c_2(c_5(c_2(c_1(c_3(c_1(c_0(x1))))))))))) -> 1'(5'(1'(1'(3'(5'(0'(0'(2'(4'(x1)))))))))) [1]
   3'(c_5(c_5(c_4(c_5(c_3(c_0(c_2(c_5(c_5(c_1(x1))))))))))) -> 3'(1'(1'(2'(4'(2'(3'(0'(2'(5'(x1)))))))))) [1]
   4'(c_2(c_0(c_2(c_1(c_5(c_5(c_4(c_2(c_3(c_2(c_1(c_0(c_4(c_1(c_2(c_0(c_4(c_2(c_3(c_1(c_3(c_0(c_1(c_4(c_2(c_0(c_0(c_2(c_5(x1)))))))))))))))))))))))))))))) -> 4'(2'(0'(2'(1'(5'(5'(4'(2'(3'(2'(1'(0'(1'(4'(2'(0'(4'(2'(3'(1'(3'(0'(1'(4'(2'(0'(0'(2'(5'(x1)))))))))))))))))))))))))))))) [1]
   4'(c_0(c_4(c_2(c_4(c_0(c_3(c_1(x1)))))))) -> 4'(0'(4'(2'(0'(4'(3'(1'(x1)))))))) [1]
   2'(c_0(c_2(c_4(c_0(c_2(c_4(c_2(c_0(c_0(c_1(c_1(c_0(c_1(c_3(c_5(c_3(c_3(c_4(c_3(c_1(c_2(c_5(x1))))))))))))))))))))))) -> 2'(0'(2'(2'(0'(4'(4'(1'(0'(1'(3'(2'(0'(1'(5'(0'(3'(3'(1'(2'(3'(4'(5'(x1))))))))))))))))))))))) [1]
   2'(c_4(c_5(c_5(c_3(c_3(c_1(c_2(c_0(c_5(c_5(c_1(c_0(c_3(c_4(c_4(c_5(c_1(c_3(c_5(c_2(c_4(c_0(c_1(c_1(c_4(c_1(c_4(c_5(c_1(x1)))))))))))))))))))))))))))))) -> 2'(4'(5'(5'(3'(3'(1'(2'(0'(5'(5'(1'(0'(3'(4'(4'(5'(1'(3'(2'(5'(4'(0'(1'(1'(4'(1'(4'(5'(1'(x1)))))))))))))))))))))))))))))) [1]
   0'(c_0(c_0(c_5(c_1(c_5(c_3(c_5(c_1(c_3(c_2(c_3(x1)))))))))))) -> 1'(3'(3'(0'(1'(4'(1'(0'(5'(5'(x1)))))))))) [1]
   5'(c_5(c_3(c_3(c_0(c_1(c_4(c_1(c_3(c_3(c_0(x1))))))))))) -> 2'(3'(3'(4'(5'(4'(2'(2'(0'(1'(x1)))))))))) [1]
   2'(c_4(c_1(c_4(c_1(c_0(c_4(c_0(c_3(c_1(c_0(c_1(c_1(c_0(c_5(c_4(c_1(c_5(c_1(c_4(x1)))))))))))))))))))) -> 2'(4'(1'(4'(1'(0'(4'(0'(3'(1'(0'(1'(1'(5'(0'(4'(1'(5'(1'(4'(x1)))))))))))))))))))) [1]
   1'(c_1(c_5(c_3(c_4(c_3(c_4(c_4(c_2(c_5(x1)))))))))) -> 1'(1'(5'(3'(3'(4'(4'(4'(2'(5'(x1)))))))))) [1]
   4'(c_3(c_1(c_1(c_2(c_1(c_2(c_0(c_5(c_2(c_0(c_3(c_2(x1))))))))))))) -> 4'(4'(4'(4'(4'(0'(0'(3'(4'(1'(x1)))))))))) [1]
   encArg(cons_0(x_1)) -> 0'(encArg(x_1)) [0]
   encArg(cons_4(x_1)) -> 4'(encArg(x_1)) [0]
   encArg(cons_3(x_1)) -> 3'(encArg(x_1)) [0]
   encArg(cons_5(x_1)) -> 5'(encArg(x_1)) [0]
   encArg(cons_1(x_1)) -> 1'(encArg(x_1)) [0]
   encArg(cons_2(x_1)) -> 2'(encArg(x_1)) [0]
   encode_0(x_1) -> 0'(encArg(x_1)) [0]
   encode_1(x_1) -> 1'(encArg(x_1)) [0]
   encode_2(x_1) -> 2'(encArg(x_1)) [0]
   encode_3(x_1) -> 3'(encArg(x_1)) [0]
   encode_4(x_1) -> 4'(encArg(x_1)) [0]
   encode_5(x_1) -> 5'(encArg(x_1)) [0]
   5'(x0) -> c_5(x0) [0]
   0'(x0) -> c_0(x0) [0]
   1'(x0) -> c_1(x0) [0]
   2'(x0) -> c_2(x0) [0]
   3'(x0) -> c_3(x0) [0]
   4'(x0) -> c_4(x0) [0]
   encArg(v0) -> const [0]
   encode_0(v0) -> const [0]
   encode_1(v0) -> const [0]
   encode_2(v0) -> const [0]
   encode_3(v0) -> const [0]
   encode_4(v0) -> const [0]
   encode_5(v0) -> const [0]
   5'(v0) -> const [0]
   0'(v0) -> const [0]
   1'(v0) -> const [0]
   2'(v0) -> const [0]
   3'(v0) -> const [0]
   4'(v0) -> const [0]

The TRS has the following type information:
4' :: c_5:c_3:c_2:c_0:c_4:c_1:const -> c_5:c_3:c_2:c_0:c_4:c_1:const
c_0 :: c_5:c_3:c_2:c_0:c_4:c_1:const -> c_5:c_3:c_2:c_0:c_4:c_1:const
c_5 :: c_5:c_3:c_2:c_0:c_4:c_1:const -> c_5:c_3:c_2:c_0:c_4:c_1:const
c_2 :: c_5:c_3:c_2:c_0:c_4:c_1:const -> c_5:c_3:c_2:c_0:c_4:c_1:const
c_4 :: c_5:c_3:c_2:c_0:c_4:c_1:const -> c_5:c_3:c_2:c_0:c_4:c_1:const
c_3 :: c_5:c_3:c_2:c_0:c_4:c_1:const -> c_5:c_3:c_2:c_0:c_4:c_1:const
5' :: c_5:c_3:c_2:c_0:c_4:c_1:const -> c_5:c_3:c_2:c_0:c_4:c_1:const
0' :: c_5:c_3:c_2:c_0:c_4:c_1:const -> c_5:c_3:c_2:c_0:c_4:c_1:const
3' :: c_5:c_3:c_2:c_0:c_4:c_1:const -> c_5:c_3:c_2:c_0:c_4:c_1:const
1' :: c_5:c_3:c_2:c_0:c_4:c_1:const -> c_5:c_3:c_2:c_0:c_4:c_1:const
2' :: c_5:c_3:c_2:c_0:c_4:c_1:const -> c_5:c_3:c_2:c_0:c_4:c_1:const
c_1 :: c_5:c_3:c_2:c_0:c_4:c_1:const -> c_5:c_3:c_2:c_0:c_4:c_1:const
encArg :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> c_5:c_3:c_2:c_0:c_4:c_1:const
cons_0 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> cons_0:cons_4:cons_3:cons_5:cons_1:cons_2
cons_4 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> cons_0:cons_4:cons_3:cons_5:cons_1:cons_2
cons_3 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> cons_0:cons_4:cons_3:cons_5:cons_1:cons_2
cons_5 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> cons_0:cons_4:cons_3:cons_5:cons_1:cons_2
cons_1 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> cons_0:cons_4:cons_3:cons_5:cons_1:cons_2
cons_2 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> cons_0:cons_4:cons_3:cons_5:cons_1:cons_2
encode_0 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> c_5:c_3:c_2:c_0:c_4:c_1:const
encode_1 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> c_5:c_3:c_2:c_0:c_4:c_1:const
encode_2 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> c_5:c_3:c_2:c_0:c_4:c_1:const
encode_3 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> c_5:c_3:c_2:c_0:c_4:c_1:const
encode_4 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> c_5:c_3:c_2:c_0:c_4:c_1:const
encode_5 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2 -> c_5:c_3:c_2:c_0:c_4:c_1:const
const :: c_5:c_3:c_2:c_0:c_4:c_1:const
const1 :: cons_0:cons_4:cons_3:cons_5:cons_1:cons_2

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

(27) NarrowingProof (BOTH BOUNDS(ID, ID))
Narrowed the inner basic terms of all right-hand sides by a single narrowing step.
----------------------------------------

(28)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   4'(c_0(c_5(c_5(c_2(c_0(c_4(c_0(c_2(c_3(c_5(c_5(c_0(c_1(c_1(c_4(c_2(c_4(c_3(c_5(c_4(c_5(c_2(c_0(c_3(c_3(c_2(c_0(c_5(c_5(c_4(c_4(c_2(c_5(c_3(c_0(c_2(c_1(c_1(c_0(x1')))))))))))))))))))))))))))))))))))))))) -> 5'(5'(0'(4'(3'(5'(4'(1'(5'(1'(5'(0'(1'(1'(4'(4'(2'(3'(5'(4'(5'(2'(0'(3'(3'(2'(0'(5'(5'(4'(4'(2'(5'(3'(0'(2'(1'(1'(0'(x1'))))))))))))))))))))))))))))))))))))))) [2]
   4'(c_0(c_5(c_5(c_2(c_0(c_4(c_0(c_2(c_3(c_5(c_5(c_2(c_2(c_3(c_3(c_4(c_2(c_4(c_5(x1'')))))))))))))))))))) -> 5'(5'(0'(4'(3'(5'(4'(1'(5'(1'(5'(2'(3'(2'(3'(4'(2'(4'(5'(x1''))))))))))))))))))) [2]
   4'(c_0(c_5(c_5(c_2(c_0(c_4(c_0(c_2(c_3(c_5(c_5(c_0(c_0(c_1(c_5(c_2(c_1(c_5(c_0(c_5(c_5(c_5(c_0(c_1(c_4(c_0(c_5(c_3(c_4(c_3(c_1(c_2(c_0(c_4(c_0(c_2(c_2(c_1(c_5(x11)))))))))))))))))))))))))))))))))))))))) -> 5'(5'(0'(4'(3'(5'(4'(1'(5'(1'(5'(0'(0'(1'(5'(2'(5'(1'(0'(5'(5'(5'(0'(1'(4'(0'(5'(3'(4'(3'(1'(2'(0'(4'(0'(2'(2'(1'(5'(x11))))))))))))))))))))))))))))))))))))))) [2]
   4'(c_0(c_5(c_5(c_2(c_0(c_4(c_0(c_2(c_3(c_5(c_2(c_3(c_2(c_0(c_1(c_0(c_5(c_3(c_0(c_2(c_1(c_1(c_1(c_4(c_4(c_1(c_2(c_4(c_5(c_2(c_2(c_4(c_0(c_3(c_2(x12)))))))))))))))))))))))))))))))))))) -> 5'(5'(0'(4'(3'(5'(4'(1'(5'(1'(2'(3'(2'(0'(1'(0'(5'(3'(0'(2'(1'(1'(1'(4'(4'(1'(4'(2'(5'(2'(2'(4'(0'(3'(2'(x12))))))))))))))))))))))))))))))))))) [2]
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   2'(c_5(c_3(c_1(c_0(c_1(c_4(c_4(c_2(c_2(c_4(c_2(c_0(c_1(c_2(c_4(c_5(c_2(c_4(c_4(x1216)))))))))))))))))))) -> 0'(5'(1'(0'(0'(2'(0'(5'(5'(1'(5'(4'(2'(0'(2'(2'(4'(1'(4'(x1216))))))))))))))))))) [2]
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   2'(c_5(c_3(c_1(c_0(c_1(c_4(c_4(c_2(c_2(c_4(x1))))))))))) -> 0'(5'(1'(0'(0'(2'(0'(5'(5'(c_1(x1)))))))))) [1]
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   5'(c_5(c_5(c_3(c_5(c_3(c_2(c_5(c_0(c_1(c_5(c_3(c_1(c_2(c_2(c_3(c_3(c_0(c_3(c_1(c_0(c_4(c_1(c_2(c_2(c_5(c_3(c_1(c_3(c_3(c_3(c_4(c_0(c_2(c_5(c_4(c_5(c_0(c_0(x1454))))))))))))))))))))))))))))))))))))))) -> 5'(5'(5'(3'(5'(3'(2'(5'(1'(0'(5'(3'(1'(2'(2'(3'(3'(0'(3'(1'(0'(4'(1'(2'(2'(5'(3'(1'(3'(1'(5'(1'(1'(5'(2'(3'(1'(4'(x1454)))))))))))))))))))))))))))))))))))))) [2]
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   5'(c_2(c_3(c_3(c_1(c_0(c_1(c_1(c_1(c_4(c_1(c_4(c_2(c_0(c_1(c_2(c_4(c_5(c_2(c_4(c_4(x1473))))))))))))))))))))) -> 0'(2'(4'(0'(4'(0'(4'(0'(0'(1'(5'(4'(2'(0'(2'(2'(4'(1'(4'(x1473))))))))))))))))))) [2]
   5'(c_2(c_3(c_3(c_1(c_0(c_1(c_1(c_1(c_4(c_1(c_4(c_1(c_1(c_2(c_2(c_5(c_2(c_1(c_3(c_1(c_0(x1474)))))))))))))))))))))) -> 0'(2'(4'(0'(4'(0'(4'(0'(0'(1'(5'(1'(1'(3'(5'(0'(0'(2'(4'(x1474))))))))))))))))))) [2]
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   5'(c_2(c_3(c_3(c_1(c_0(c_1(c_1(c_1(c_4(c_1(c_4(x1)))))))))))) -> 0'(2'(4'(0'(4'(0'(4'(0'(0'(c_1(x1)))))))))) [1]
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   0'(c_4(c_5(c_0(c_0(c_4(c_2(c_4(c_5(c_0(c_1(c_5(c_3(c_4(c_5(c_1(c_3(c_3(x1520)))))))))))))))))) -> 3'(5'(3'(5'(5'(4'(0'(2'(2'(3'(1'(5'(3'(5'(4'(1'(3'(3'(x1520)))))))))))))))))) [2]
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   0'(c_4(c_5(c_0(c_0(c_4(c_2(c_4(c_5(c_0(c_1(c_3(c_3(c_3(c_0(c_4(c_1(c_1(c_3(c_0(x1523)))))))))))))))))))) -> 3'(5'(3'(5'(5'(4'(0'(2'(2'(1'(0'(2'(1'(2'(1'(0'(1'(1'(3'(x1523))))))))))))))))))) [2]
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   4'(c_4(c_5(c_5(c_3(c_0(c_1(c_5(c_0(c_0(c_1(c_5(c_2(c_1(c_5(c_0(c_5(c_5(c_5(c_0(c_1(c_4(c_0(c_5(c_3(c_4(c_3(c_1(c_2(c_0(c_4(c_0(c_2(c_2(c_1(c_5(x1569)))))))))))))))))))))))))))))))))))) -> 4'(4'(3'(5'(0'(5'(1'(5'(0'(0'(1'(5'(2'(5'(1'(0'(5'(5'(5'(0'(1'(4'(0'(5'(3'(4'(3'(1'(2'(0'(4'(0'(2'(2'(1'(5'(x1569)))))))))))))))))))))))))))))))))))) [2]
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   4'(c_4(c_5(c_5(c_3(c_0(c_1(c_2(c_4(c_0(c_2(c_4(c_0(c_1(c_2(c_4(c_3(c_1(c_0(c_3(c_4(x1573))))))))))))))))))))) -> 4'(4'(3'(5'(0'(5'(1'(2'(4'(0'(2'(4'(0'(1'(4'(2'(3'(1'(0'(3'(4'(x1573))))))))))))))))))))) [2]
   4'(c_4(c_5(c_5(c_3(c_0(c_1(c_2(c_0(c_1(c_2(c_4(c_5(c_2(c_4(c_4(x1574)))))))))))))))) -> 4'(4'(3'(5'(0'(5'(1'(5'(4'(2'(0'(2'(2'(4'(1'(4'(x1574)))))))))))))))) [2]
   4'(c_4(c_5(c_5(c_3(c_0(c_1(c_1(c_1(c_2(c_2(c_5(c_2(c_1(c_3(c_1(c_0(x1575))))))))))))))))) -> 4'(4'(3'(5'(0'(5'(1'(5'(1'(1'(3'(5'(0'(0'(2'(4'(x1575)))))))))))))))) [2]
   4'(c_4(c_5(c_5(c_3(c_0(c_1(c_1(c_5(c_3(c_4(c_3(c_4(c_4(c_2(c_5(x1576)))))))))))))))) -> 4'(4'(3'(5'(0'(5'(1'(1'(5'(3'(3'(4'(4'(4'(2'(5'(x1576)))))))))))))))) [2]
   4'(c_4(c_5(c_5(c_3(c_0(c_1(x1))))))) -> 4'(4'(3'(5'(0'(5'(c_1(x1))))))) [1]
   4'(c_4(c_5(c_5(c_3(c_0(c_1(x1))))))) -> 4'(4'(3'(5'(0'(5'(const)))))) [1]
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   3'(c_2(c_5(c_5(c_2(c_1(c_2(c_2(c_2(c_3(c_2(c_2(c_4(c_0(c_4(c_0(c_3(c_5(c_1(c_2(c_1(c_0(c_2(c_3(c_1(c_3(c_1(c_0(c_0(x1579))))))))))))))))))))))))))))) -> 3'(5'(2'(2'(5'(1'(2'(2'(2'(3'(2'(2'(4'(0'(4'(0'(3'(5'(2'(0'(4'(2'(1'(4'(1'(1'(3'(x1579))))))))))))))))))))))))))) [2]
   3'(c_2(c_5(c_5(c_2(c_1(c_2(c_2(c_2(c_3(c_2(c_2(c_4(c_0(c_4(c_0(c_3(c_5(c_0(c_0(c_2(c_4(c_0(c_1(c_5(c_1(c_1(c_3(c_0(c_2(c_2(c_2(c_3(c_5(c_4(c_0(c_4(c_1(c_5(c_2(c_3(c_4(x1580)))))))))))))))))))))))))))))))))))))))))) -> 3'(5'(2'(2'(5'(1'(2'(2'(2'(3'(2'(2'(4'(0'(4'(0'(3'(5'(0'(0'(2'(0'(4'(1'(5'(1'(1'(3'(0'(2'(2'(2'(3'(5'(4'(0'(4'(1'(5'(2'(3'(4'(x1580)))))))))))))))))))))))))))))))))))))))))) [2]
   3'(c_2(c_5(c_5(c_2(c_1(c_2(c_2(c_2(c_3(c_2(c_2(c_4(c_0(c_4(c_0(c_3(c_5(c_5(c_0(c_5(c_3(c_4(c_1(c_2(c_3(c_2(c_2(x1581)))))))))))))))))))))))))))) -> 3'(5'(2'(2'(5'(1'(2'(2'(2'(3'(2'(2'(4'(0'(4'(0'(3'(1'(2'(3'(5'(5'(0'(1'(3'(5'(5'(x1581))))))))))))))))))))))))))) [2]
   3'(c_2(c_5(c_5(c_2(c_1(c_2(c_2(c_2(c_3(c_2(c_2(c_4(c_0(c_4(c_0(c_3(c_5(c_5(c_0(c_3(c_2(c_2(c_1(c_3(c_4(c_3(c_5(c_4(c_2(c_5(c_2(c_0(c_4(c_1(c_1(c_2(c_4(c_0(c_5(c_4(c_3(c_2(c_4(c_4(x1582))))))))))))))))))))))))))))))))))))))))))))) -> 3'(5'(2'(2'(5'(1'(2'(2'(2'(3'(2'(2'(4'(0'(4'(0'(3'(5'(5'(0'(3'(2'(2'(3'(1'(4'(3'(5'(4'(2'(5'(2'(0'(4'(1'(1'(2'(4'(0'(5'(4'(3'(2'(4'(4'(x1582))))))))))))))))))))))))))))))))))))))))))))) [2]
   3'(c_2(c_5(c_5(c_2(c_1(c_2(c_2(c_2(c_3(c_2(c_2(c_4(c_0(c_4(c_0(c_3(c_5(c_0(c_5(c_0(c_0(c_4(c_0(c_1(c_3(c_4(c_1(x1583)))))))))))))))))))))))))))) -> 3'(5'(2'(2'(5'(1'(2'(2'(2'(3'(2'(2'(4'(0'(4'(0'(3'(2'(2'(4'(2'(1'(1'(3'(3'(3'(0'(x1583))))))))))))))))))))))))))) [2]
   3'(c_2(c_5(c_5(c_2(c_1(c_2(c_2(c_2(c_3(c_2(c_2(c_4(c_0(c_4(c_0(c_3(c_5(c_5(c_5(c_3(c_5(c_3(c_2(c_5(c_0(c_1(c_5(c_3(c_1(c_2(c_2(c_3(c_3(c_0(c_3(c_1(c_0(c_4(c_1(c_2(c_2(c_5(c_3(c_1(c_3(x1584)))))))))))))))))))))))))))))))))))))))))))))) -> 3'(5'(2'(2'(5'(1'(2'(2'(2'(3'(2'(2'(4'(0'(4'(0'(3'(5'(5'(5'(3'(5'(3'(2'(5'(1'(0'(5'(3'(1'(2'(2'(3'(3'(0'(3'(1'(0'(4'(1'(2'(2'(5'(3'(1'(3'(x1584)))))))))))))))))))))))))))))))))))))))))))))) [2]
   3'(c_2(c_5(c_5(c_2(c_1(c_2(c_2(c_2(c_3(c_2(c_2(c_4(c_0(c_4(c_0(c_3(c_5(c_2(c_3(c_3(c_1(c_0(c_1(c_1(c_1(c_4(c_1(c_4(x1585))))))))))))))))))))))))))))) -> 3'(5'(2'(2'(5'(1'(2'(2'(2'(3'(2'(2'(4'(0'(4'(0'(3'(0'(2'(4'(0'(4'(0'(4'(0'(0'(1'(x1585))))))))))))))))))))))))))) [2]
   3'(c_2(c_5(c_5(c_2(c_1(c_2(c_2(c_2(c_3(c_2(c_2(c_4(c_0(c_4(c_0(c_3(c_5(c_1(c_5(c_0(c_3(c_3(c_0(c_1(c_2(c_3(c_3(c_1(c_4(c_5(c_3(c_1(c_2(c_2(c_0(c_3(c_2(c_0(c_5(x1586)))))))))))))))))))))))))))))))))))))))) -> 3'(5'(2'(2'(5'(1'(2'(2'(2'(3'(2'(2'(4'(0'(4'(0'(3'(5'(1'(5'(0'(3'(3'(0'(1'(2'(3'(3'(1'(4'(5'(3'(1'(2'(0'(2'(3'(2'(0'(5'(x1586)))))))))))))))))))))))))))))))))))))))) [2]
   3'(c_2(c_5(c_5(c_2(c_1(c_2(c_2(c_2(c_3(c_2(c_2(c_4(c_0(c_4(c_0(c_3(c_5(c_1(c_5(c_3(c_5(c_4(c_0(c_0(c_3(x1587)))))))))))))))))))))))))) -> 3'(5'(2'(2'(5'(1'(2'(2'(2'(3'(2'(2'(4'(0'(4'(0'(3'(5'(1'(5'(3'(5'(0'(4'(0'(3'(x1587)))))))))))))))))))))))))) [2]
   3'(c_2(c_5(c_5(c_2(c_1(c_2(c_2(c_2(c_3(c_2(c_2(c_4(c_0(c_4(c_0(c_3(c_5(c_5(c_2(c_3(c_2(c_0(c_3(c_2(c_5(c_3(c_2(c_5(c_5(c_5(c_5(c_1(c_5(c_5(c_1(c_2(c_2(x1588)))))))))))))))))))))))))))))))))))))) -> 3'(5'(2'(2'(5'(1'(2'(2'(2'(3'(2'(2'(4'(0'(4'(0'(3'(5'(5'(2'(3'(2'(0'(3'(2'(5'(3'(2'(5'(5'(5'(1'(5'(5'(5'(1'(2'(2'(x1588)))))))))))))))))))))))))))))))))))))) [2]
   3'(c_2(c_5(c_5(c_2(c_1(c_2(c_2(c_2(c_3(c_2(c_2(c_4(c_0(c_4(c_0(c_3(c_5(c_1(c_0(c_3(c_5(c_0(c_1(c_1(c_3(c_4(c_3(x1589)))))))))))))))))))))))))))) -> 3'(5'(2'(2'(5'(1'(2'(2'(2'(3'(2'(2'(4'(0'(4'(0'(3'(1'(0'(3'(0'(0'(4'(2'(4'(5'(3'(x1589))))))))))))))))))))))))))) [2]
   3'(c_2(c_5(c_5(c_2(c_1(c_2(c_2(c_2(c_3(c_2(c_2(c_4(c_0(c_4(c_0(c_3(c_5(c_4(c_1(c_5(c_1(c_4(c_2(c_5(c_4(c_3(c_0(c_4(c_1(c_0(x1590))))))))))))))))))))))))))))))) -> 3'(5'(2'(2'(5'(1'(2'(2'(2'(3'(2'(2'(4'(0'(4'(0'(3'(5'(4'(1'(1'(5'(4'(2'(5'(4'(3'(0'(4'(1'(0'(x1590))))))))))))))))))))))))))))))) [2]
   3'(c_2(c_5(c_5(c_2(c_1(c_2(c_2(c_2(c_3(c_2(c_2(c_4(c_0(c_4(c_0(c_3(c_5(c_3(c_1(c_5(c_5(c_3(c_3(c_0(c_2(c_2(c_2(c_2(c_3(c_3(c_4(c_5(c_1(c_1(x1591))))))))))))))))))))))))))))))))))) -> 3'(5'(2'(2'(5'(1'(2'(2'(2'(3'(2'(2'(4'(0'(4'(0'(3'(5'(3'(1'(5'(5'(3'(3'(0'(2'(2'(2'(3'(2'(3'(4'(5'(1'(1'(x1591))))))))))))))))))))))))))))))))))) [2]
   3'(c_2(c_5(c_5(c_2(c_1(c_2(c_2(c_2(c_3(c_2(c_2(c_4(c_0(c_4(c_0(c_3(c_5(c_5(c_3(c_3(c_0(c_1(c_4(c_1(c_3(c_3(c_0(x1592)))))))))))))))))))))))))))) -> 3'(5'(2'(2'(5'(1'(2'(2'(2'(3'(2'(2'(4'(0'(4'(0'(3'(2'(3'(3'(4'(5'(4'(2'(2'(0'(1'(x1592))))))))))))))))))))))))))) [2]
   3'(c_2(c_5(c_5(c_2(c_1(c_2(c_2(c_2(c_3(c_2(c_2(c_4(c_0(c_4(c_0(c_3(c_5(x1)))))))))))))))))) -> 3'(5'(2'(2'(5'(1'(2'(2'(2'(3'(2'(2'(4'(0'(4'(0'(3'(c_5(x1)))))))))))))))))) [1]
   3'(c_2(c_5(c_5(c_2(c_1(c_2(c_2(c_2(c_3(c_2(c_2(c_4(c_0(c_4(c_0(c_3(c_5(x1)))))))))))))))))) -> 3'(5'(2'(2'(5'(1'(2'(2'(2'(3'(2'(2'(4'(0'(4'(0'(3'(const))))))))))))))))) [1]
   5'(c_1(c_5(c_0(c_3(c_3(c_0(c_1(c_2(c_3(c_3(c_1(c_4(c_5(c_3(c_1(c_2(c_2(c_0(c_3(c_2(c_0(c_5(c_5(c_3(c_4(c_1(c_2(c_0(c_2(c_5(c_3(c_2(c_5(c_4(c_4(c_5(c_5(c_1(c_2(x1593)))))))))))))))))))))))))))))))))))))))) -> 5'(1'(5'(0'(3'(3'(0'(1'(2'(3'(3'(1'(4'(5'(3'(1'(2'(0'(2'(3'(2'(0'(5'(5'(3'(4'(1'(2'(0'(2'(5'(3'(2'(4'(5'(4'(5'(5'(1'(2'(x1593)))))))))))))))))))))))))))))))))))))))) [2]
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   2'(c_0(c_5(c_0(c_5(c_4(c_4(c_3(c_1(c_3(c_2(x1))))))))))) -> 2'(1'(0'(3'(1'(2'(1'(3'(4'(0'(x1)))))))))) [1]
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   3'(c_2(c_5(c_3(c_4(c_4(c_0(c_1(c_3(c_5(c_4(c_5(c_3(c_1(c_0(c_1(c_4(c_4(c_2(c_2(c_4(x1630))))))))))))))))))))) -> 5'(0'(1'(3'(5'(5'(1'(3'(4'(0'(5'(1'(0'(0'(2'(0'(5'(5'(1'(x1630))))))))))))))))))) [2]
   3'(c_2(c_5(c_3(c_4(c_4(c_0(c_1(c_3(c_5(c_4(c_1(c_0(c_5(c_5(c_4(c_1(c_0(c_4(c_2(c_5(c_3(c_1(c_4(c_1(c_3(c_5(c_0(c_0(c_2(c_4(c_5(x1631)))))))))))))))))))))))))))))))) -> 5'(0'(1'(3'(5'(5'(1'(3'(4'(2'(1'(0'(5'(5'(4'(1'(0'(4'(2'(5'(3'(1'(4'(1'(3'(0'(5'(0'(2'(4'(5'(x1631))))))))))))))))))))))))))))))) [2]
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   3'(c_2(c_5(c_3(c_4(c_4(c_0(c_1(c_3(c_5(c_4(c_3(c_4(c_3(c_5(c_1(c_2(c_4(c_2(c_0(c_2(c_1(x1634)))))))))))))))))))))) -> 5'(0'(1'(3'(5'(5'(1'(3'(4'(2'(4'(1'(3'(2'(2'(5'(5'(1'(0'(x1634))))))))))))))))))) [2]
   3'(c_2(c_5(c_3(c_4(c_4(c_0(c_1(c_3(c_5(c_4(c_2(c_4(c_3(c_2(c_2(c_2(c_4(c_2(c_5(c_2(c_0(c_4(c_5(x1635)))))))))))))))))))))))) -> 5'(0'(1'(3'(5'(5'(1'(3'(4'(2'(2'(0'(2'(2'(4'(2'(5'(3'(4'(4'(2'(2'(5'(x1635))))))))))))))))))))))) [2]
   3'(c_2(c_5(c_3(c_4(c_4(c_0(c_1(c_3(c_5(c_4(c_2(c_0(c_2(c_2(c_5(c_0(c_3(c_2(c_0(c_5(x1636))))))))))))))))))))) -> 5'(0'(1'(3'(5'(5'(1'(3'(4'(5'(0'(3'(5'(4'(2'(2'(3'(1'(0'(x1636))))))))))))))))))) [2]
   3'(c_2(c_5(c_3(c_4(c_4(c_0(c_1(c_3(c_5(c_4(c_0(c_2(c_5(c_4(c_0(c_3(c_3(c_0(c_4(c_2(c_2(c_5(c_5(c_2(x1637))))))))))))))))))))))))) -> 5'(0'(1'(3'(5'(5'(1'(3'(4'(2'(0'(2'(4'(0'(5'(0'(3'(4'(3'(2'(2'(5'(5'(2'(x1637)))))))))))))))))))))))) [2]
   3'(c_2(c_5(c_3(c_4(c_4(c_0(c_1(c_3(c_5(c_4(c_3(c_2(c_1(c_1(c_1(c_0(c_2(c_1(c_3(c_5(c_1(x1638)))))))))))))))))))))) -> 5'(0'(1'(3'(5'(5'(1'(3'(4'(5'(4'(3'(0'(1'(2'(3'(3'(2'(5'(x1638))))))))))))))))))) [2]
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   1'(c_0(c_1(c_5(c_1(c_5(c_3(c_3(c_1(c_4(c_0(c_5(c_0(c_0(c_1(c_5(c_2(c_1(c_5(c_0(c_5(c_5(c_5(c_0(c_1(c_4(c_0(c_5(c_3(c_4(c_3(c_1(c_2(c_0(c_4(c_0(c_2(c_2(c_1(c_5(x1645)))))))))))))))))))))))))))))))))))))))) -> 3'(1'(2'(1'(5'(2'(4'(5'(1'(1'(5'(0'(0'(1'(5'(2'(5'(1'(0'(5'(5'(5'(0'(1'(4'(0'(5'(3'(4'(3'(1'(2'(0'(4'(0'(2'(2'(1'(5'(x1645))))))))))))))))))))))))))))))))))))))) [2]
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   2'(c_2(c_0(c_2(c_2(c_5(c_0(c_3(c_2(c_0(c_5(x1))))))))))) -> 5'(0'(3'(5'(4'(2'(2'(3'(1'(0'(x1)))))))))) [1]
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   4'(c_1(c_3(c_5(c_2(c_3(c_5(c_5(c_0(c_0(c_3(c_1(c_5(c_3(c_4(c_5(c_1(c_3(c_3(x1788))))))))))))))))))) -> 5'(2'(3'(0'(3'(5'(2'(3'(5'(3'(1'(5'(3'(5'(4'(1'(3'(3'(x1788)))))))))))))))))) [2]
   4'(c_1(c_3(c_5(c_2(c_3(c_5(c_5(c_0(c_0(c_3(c_2(c_5(c_5(c_2(c_1(c_2(c_2(c_2(c_3(c_2(c_2(c_4(c_0(c_4(c_0(c_3(c_5(x1789)))))))))))))))))))))))))))) -> 5'(2'(3'(0'(3'(5'(2'(3'(5'(3'(5'(2'(2'(5'(1'(2'(2'(2'(3'(2'(2'(4'(0'(4'(0'(3'(5'(x1789))))))))))))))))))))))))))) [2]
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   4'(c_1(c_3(c_5(c_2(c_3(c_5(c_5(c_0(c_0(c_3(c_1(c_3(c_3(c_3(c_0(c_4(c_1(c_1(c_3(c_0(x1791))))))))))))))))))))) -> 5'(2'(3'(0'(3'(5'(2'(3'(5'(1'(0'(2'(1'(2'(1'(0'(1'(1'(3'(x1791))))))))))))))))))) [2]
   4'(c_1(c_3(c_5(c_2(c_3(c_5(c_5(c_0(c_0(c_3(c_2(c_3(c_3(c_2(c_2(c_5(c_1(c_0(c_5(c_4(c_4(c_5(c_2(c_2(c_4(c_3(c_5(c_2(c_1(c_2(c_1(c_3(c_1(x1792)))))))))))))))))))))))))))))))))) -> 5'(2'(3'(0'(3'(5'(2'(3'(5'(3'(2'(3'(3'(2'(2'(5'(1'(5'(0'(4'(4'(5'(2'(2'(4'(3'(5'(2'(1'(2'(1'(3'(1'(x1792))))))))))))))))))))))))))))))))) [2]
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   4'(c_1(c_3(c_5(c_2(c_3(c_5(c_5(c_0(c_0(c_3(c_2(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_2(c_0(x1794))))))))))))))))))))) -> 5'(2'(3'(0'(3'(5'(2'(3'(5'(4'(4'(2'(5'(4'(5'(5'(0'(5'(0'(x1794))))))))))))))))))) [2]
   4'(c_1(c_3(c_5(c_2(c_3(c_5(c_5(c_0(c_0(c_3(c_5(c_4(c_4(c_5(c_1(c_1(c_5(c_0(c_2(c_0(x1795))))))))))))))))))))) -> 5'(2'(3'(0'(3'(5'(2'(3'(5'(3'(1'(5'(1'(3'(5'(0'(1'(5'(1'(x1795))))))))))))))))))) [2]
   4'(c_1(c_3(c_5(c_2(c_3(c_5(c_5(c_0(c_0(c_3(c_5(c_5(c_4(c_5(c_3(c_0(c_2(c_5(c_5(c_1(x1796))))))))))))))))))))) -> 5'(2'(3'(0'(3'(5'(2'(3'(5'(3'(1'(1'(2'(4'(2'(3'(0'(2'(5'(x1796))))))))))))))))))) [2]
   4'(c_1(c_3(c_5(c_2(c_3(c_5(c_5(c_0(c_0(c_3(x1))))))))))) -> 5'(2'(3'(0'(3'(5'(2'(3'(5'(c_3(x1)))))))))) [1]
   4'(c_1(c_3(c_5(c_2(c_3(c_5(c_5(c_0(c_0(c_3(x1))))))))))) -> 5'(2'(3'(0'(3'(5'(2'(3'(5'(const))))))))) [1]
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   4'(c_3(c_2(c_1(c_1(c_2(c_4(c_4(c_5(c_1(c_5(c_2(c_2(c_4(c_0(c_2(c_4(c_2(c_4(c_2(c_0(c_4(c_2(c_4(c_4(c_0(c_1(c_3(c_3(c_2(c_1(c_2(c_1(c_1(c_0(c_1(c_5(c_0(c_4(c_2(c_5(c_3(c_2(c_3(c_1(c_5(c_3(c_2(c_3(c_4(c_1(c_4(c_2(x1801))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 4'(3'(2'(1'(2'(1'(4'(4'(5'(1'(5'(2'(2'(4'(0'(2'(4'(2'(4'(2'(0'(4'(2'(4'(4'(0'(1'(2'(3'(3'(1'(2'(1'(0'(1'(1'(5'(0'(4'(5'(2'(3'(2'(3'(1'(3'(2'(5'(3'(1'(4'(4'(2'(x1801))))))))))))))))))))))))))))))))))))))))))))))))))))) [2]
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   5'(c_1(c_0(c_3(c_5(c_0(c_1(c_1(c_3(c_4(c_3(c_3(c_2(c_5(c_4(c_4(c_0(c_1(c_3(c_1(c_2(c_1(c_5(c_0(c_0(c_4(c_2(c_1(c_4(c_2(c_2(c_3(c_5(x1808))))))))))))))))))))))))))))))))) -> 1'(0'(3'(0'(0'(4'(2'(4'(5'(3'(3'(2'(5'(4'(4'(0'(1'(3'(1'(2'(1'(5'(0'(4'(0'(2'(1'(4'(2'(2'(3'(5'(x1808)))))))))))))))))))))))))))))))) [2]
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   5'(c_1(c_0(c_3(c_5(c_0(c_1(c_1(c_3(c_4(c_3(c_1(c_5(c_3(c_4(c_5(c_1(c_3(c_3(x1810))))))))))))))))))) -> 1'(0'(3'(0'(0'(4'(2'(4'(5'(3'(1'(5'(3'(5'(4'(1'(3'(3'(x1810)))))))))))))))))) [2]
   5'(c_1(c_0(c_3(c_5(c_0(c_1(c_1(c_3(c_4(c_3(c_2(c_5(c_5(c_2(c_1(c_2(c_2(c_2(c_3(c_2(c_2(c_4(c_0(c_4(c_0(c_3(c_5(x1811)))))))))))))))))))))))))))) -> 1'(0'(3'(0'(0'(4'(2'(4'(5'(3'(5'(2'(2'(5'(1'(2'(2'(2'(3'(2'(2'(4'(0'(4'(0'(3'(5'(x1811))))))))))))))))))))))))))) [2]
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   5'(c_1(c_0(c_3(c_5(c_0(c_1(c_1(c_3(c_4(c_3(c_1(c_3(c_3(c_3(c_0(c_4(c_1(c_1(c_3(c_0(x1813))))))))))))))))))))) -> 1'(0'(3'(0'(0'(4'(2'(4'(5'(1'(0'(2'(1'(2'(1'(0'(1'(1'(3'(x1813))))))))))))))))))) [2]
   5'(c_1(c_0(c_3(c_5(c_0(c_1(c_1(c_3(c_4(c_3(c_2(c_3(c_3(c_2(c_2(c_5(c_1(c_0(c_5(c_4(c_4(c_5(c_2(c_2(c_4(c_3(c_5(c_2(c_1(c_2(c_1(c_3(c_1(x1814)))))))))))))))))))))))))))))))))) -> 1'(0'(3'(0'(0'(4'(2'(4'(5'(3'(2'(3'(3'(2'(2'(5'(1'(5'(0'(4'(4'(5'(2'(2'(4'(3'(5'(2'(1'(2'(1'(3'(1'(x1814))))))))))))))))))))))))))))))))) [2]
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   5'(c_1(c_0(c_3(c_5(c_0(c_1(c_1(c_3(c_4(c_3(c_2(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_2(c_0(x1816))))))))))))))))))))) -> 1'(0'(3'(0'(0'(4'(2'(4'(5'(4'(4'(2'(5'(4'(5'(5'(0'(5'(0'(x1816))))))))))))))))))) [2]
   5'(c_1(c_0(c_3(c_5(c_0(c_1(c_1(c_3(c_4(c_3(c_5(c_4(c_4(c_5(c_1(c_1(c_5(c_0(c_2(c_0(x1817))))))))))))))))))))) -> 1'(0'(3'(0'(0'(4'(2'(4'(5'(3'(1'(5'(1'(3'(5'(0'(1'(5'(1'(x1817))))))))))))))))))) [2]
   5'(c_1(c_0(c_3(c_5(c_0(c_1(c_1(c_3(c_4(c_3(c_5(c_5(c_4(c_5(c_3(c_0(c_2(c_5(c_5(c_1(x1818))))))))))))))))))))) -> 1'(0'(3'(0'(0'(4'(2'(4'(5'(3'(1'(1'(2'(4'(2'(3'(0'(2'(5'(x1818))))))))))))))))))) [2]
   5'(c_1(c_0(c_3(c_5(c_0(c_1(c_1(c_3(c_4(c_3(x1))))))))))) -> 1'(0'(3'(0'(0'(4'(2'(4'(5'(c_3(x1)))))))))) [1]
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   3'(c_5(c_5(c_4(c_5(c_3(c_0(c_2(c_5(c_5(c_1(c_5(c_0(c_5(c_3(c_4(c_1(c_2(c_3(c_2(c_2(x11292))))))))))))))))))))) -> 3'(1'(1'(2'(4'(2'(3'(0'(2'(1'(2'(3'(5'(5'(0'(1'(3'(5'(5'(x11292))))))))))))))))))) [2]
   3'(c_5(c_5(c_4(c_5(c_3(c_0(c_2(c_5(c_5(c_1(c_5(c_0(c_3(c_2(c_2(c_1(c_3(c_4(c_3(c_5(c_4(c_2(c_5(c_2(c_0(c_4(c_1(c_1(c_2(c_4(c_0(c_5(c_4(c_3(c_2(c_4(c_4(x11293)))))))))))))))))))))))))))))))))))))) -> 3'(1'(1'(2'(4'(2'(3'(0'(2'(5'(5'(0'(3'(2'(2'(3'(1'(4'(3'(5'(4'(2'(5'(2'(0'(4'(1'(1'(2'(4'(0'(5'(4'(3'(2'(4'(4'(x11293))))))))))))))))))))))))))))))))))))) [2]
   3'(c_5(c_5(c_4(c_5(c_3(c_0(c_2(c_5(c_5(c_1(c_0(c_5(c_0(c_0(c_4(c_0(c_1(c_3(c_4(c_1(x11294))))))))))))))))))))) -> 3'(1'(1'(2'(4'(2'(3'(0'(2'(2'(2'(4'(2'(1'(1'(3'(3'(3'(0'(x11294))))))))))))))))))) [2]
   3'(c_5(c_5(c_4(c_5(c_3(c_0(c_2(c_5(c_5(c_1(c_5(c_5(c_3(c_5(c_3(c_2(c_5(c_0(c_1(c_5(c_3(c_1(c_2(c_2(c_3(c_3(c_0(c_3(c_1(c_0(c_4(c_1(c_2(c_2(c_5(c_3(c_1(c_3(x11295))))))))))))))))))))))))))))))))))))))) -> 3'(1'(1'(2'(4'(2'(3'(0'(2'(5'(5'(5'(3'(5'(3'(2'(5'(1'(0'(5'(3'(1'(2'(2'(3'(3'(0'(3'(1'(0'(4'(1'(2'(2'(5'(3'(1'(3'(x11295)))))))))))))))))))))))))))))))))))))) [2]
   3'(c_5(c_5(c_4(c_5(c_3(c_0(c_2(c_5(c_5(c_1(c_2(c_3(c_3(c_1(c_0(c_1(c_1(c_1(c_4(c_1(c_4(x11296)))))))))))))))))))))) -> 3'(1'(1'(2'(4'(2'(3'(0'(2'(0'(2'(4'(0'(4'(0'(4'(0'(0'(1'(x11296))))))))))))))))))) [2]
   3'(c_5(c_5(c_4(c_5(c_3(c_0(c_2(c_5(c_5(c_1(c_1(c_5(c_0(c_3(c_3(c_0(c_1(c_2(c_3(c_3(c_1(c_4(c_5(c_3(c_1(c_2(c_2(c_0(c_3(c_2(c_0(c_5(x11297))))))))))))))))))))))))))))))))) -> 3'(1'(1'(2'(4'(2'(3'(0'(2'(5'(1'(5'(0'(3'(3'(0'(1'(2'(3'(3'(1'(4'(5'(3'(1'(2'(0'(2'(3'(2'(0'(5'(x11297)))))))))))))))))))))))))))))))) [2]
   3'(c_5(c_5(c_4(c_5(c_3(c_0(c_2(c_5(c_5(c_1(c_1(c_5(c_3(c_5(c_4(c_0(c_0(c_3(x11298))))))))))))))))))) -> 3'(1'(1'(2'(4'(2'(3'(0'(2'(5'(1'(5'(3'(5'(0'(4'(0'(3'(x11298)))))))))))))))))) [2]
   3'(c_5(c_5(c_4(c_5(c_3(c_0(c_2(c_5(c_5(c_1(c_5(c_2(c_3(c_2(c_0(c_3(c_2(c_5(c_3(c_2(c_5(c_5(c_5(c_5(c_1(c_5(c_5(c_1(c_2(c_2(x11299))))))))))))))))))))))))))))))) -> 3'(1'(1'(2'(4'(2'(3'(0'(2'(5'(5'(2'(3'(2'(0'(3'(2'(5'(3'(2'(5'(5'(5'(1'(5'(5'(5'(1'(2'(2'(x11299)))))))))))))))))))))))))))))) [2]
   3'(c_5(c_5(c_4(c_5(c_3(c_0(c_2(c_5(c_5(c_1(c_1(c_0(c_3(c_5(c_0(c_1(c_1(c_3(c_4(c_3(x11300))))))))))))))))))))) -> 3'(1'(1'(2'(4'(2'(3'(0'(2'(1'(0'(3'(0'(0'(4'(2'(4'(5'(3'(x11300))))))))))))))))))) [2]
   3'(c_5(c_5(c_4(c_5(c_3(c_0(c_2(c_5(c_5(c_1(c_4(c_1(c_5(c_1(c_4(c_2(c_5(c_4(c_3(c_0(c_4(c_1(c_0(x11301)))))))))))))))))))))))) -> 3'(1'(1'(2'(4'(2'(3'(0'(2'(5'(4'(1'(1'(5'(4'(2'(5'(4'(3'(0'(4'(1'(0'(x11301))))))))))))))))))))))) [2]
   3'(c_5(c_5(c_4(c_5(c_3(c_0(c_2(c_5(c_5(c_1(c_3(c_1(c_5(c_5(c_3(c_3(c_0(c_2(c_2(c_2(c_2(c_3(c_3(c_4(c_5(c_1(c_1(x11302)))))))))))))))))))))))))))) -> 3'(1'(1'(2'(4'(2'(3'(0'(2'(5'(3'(1'(5'(5'(3'(3'(0'(2'(2'(2'(3'(2'(3'(4'(5'(1'(1'(x11302))))))))))))))))))))))))))) [2]
   3'(c_5(c_5(c_4(c_5(c_3(c_0(c_2(c_5(c_5(c_1(c_5(c_3(c_3(c_0(c_1(c_4(c_1(c_3(c_3(c_0(x11303))))))))))))))))))))) -> 3'(1'(1'(2'(4'(2'(3'(0'(2'(2'(3'(3'(4'(5'(4'(2'(2'(0'(1'(x11303))))))))))))))))))) [2]
   3'(c_5(c_5(c_4(c_5(c_3(c_0(c_2(c_5(c_5(c_1(x1))))))))))) -> 3'(1'(1'(2'(4'(2'(3'(0'(2'(c_5(x1)))))))))) [1]
   3'(c_5(c_5(c_4(c_5(c_3(c_0(c_2(c_5(c_5(c_1(x1))))))))))) -> 3'(1'(1'(2'(4'(2'(3'(0'(2'(const))))))))) [1]
   4'(c_2(c_0(c_2(c_1(c_5(c_5(c_4(c_2(c_3(c_2(c_1(c_0(c_4(c_1(c_2(c_0(c_4(c_2(c_3(c_1(c_3(c_0(c_1(c_4(c_2(c_0(c_0(c_2(c_5(c_5(c_3(c_4(c_1(c_2(c_0(c_2(c_5(c_3(c_2(c_5(c_4(c_4(c_5(c_5(c_1(c_2(x11304))))))))))))))))))))))))))))))))))))))))))))))) -> 4'(2'(0'(2'(1'(5'(5'(4'(2'(3'(2'(1'(0'(1'(4'(2'(0'(4'(2'(3'(1'(3'(0'(1'(4'(2'(0'(0'(2'(5'(5'(3'(4'(1'(2'(0'(2'(5'(3'(2'(4'(5'(4'(5'(5'(1'(2'(x11304))))))))))))))))))))))))))))))))))))))))))))))) [2]
   4'(c_2(c_0(c_2(c_1(c_5(c_5(c_4(c_2(c_3(c_2(c_1(c_0(c_4(c_1(c_2(c_0(c_4(c_2(c_3(c_1(c_3(c_0(c_1(c_4(c_2(c_0(c_0(c_2(c_5(c_1(c_4(c_4(c_3(c_1(c_5(c_4(c_3(c_5(c_1(c_2(c_0(x11305)))))))))))))))))))))))))))))))))))))))))) -> 4'(2'(0'(2'(1'(5'(5'(4'(2'(3'(2'(1'(0'(1'(4'(2'(0'(4'(2'(3'(1'(3'(0'(1'(4'(2'(0'(0'(2'(2'(2'(1'(3'(0'(0'(4'(3'(2'(5'(x11305))))))))))))))))))))))))))))))))))))))) [2]
   4'(c_2(c_0(c_2(c_1(c_5(c_5(c_4(c_2(c_3(c_2(c_1(c_0(c_4(c_1(c_2(c_0(c_4(c_2(c_3(c_1(c_3(c_0(c_1(c_4(c_2(c_0(c_0(c_2(c_5(c_1(c_2(c_1(c_0(c_2(c_3(c_1(c_3(c_1(c_0(c_0(x11306))))))))))))))))))))))))))))))))))))))))) -> 4'(2'(0'(2'(1'(5'(5'(4'(2'(3'(2'(1'(0'(1'(4'(2'(0'(4'(2'(3'(1'(3'(0'(1'(4'(2'(0'(0'(2'(5'(2'(0'(4'(2'(1'(4'(1'(1'(3'(x11306))))))))))))))))))))))))))))))))))))))) [2]
   4'(c_2(c_0(c_2(c_1(c_5(c_5(c_4(c_2(c_3(c_2(c_1(c_0(c_4(c_1(c_2(c_0(c_4(c_2(c_3(c_1(c_3(c_0(c_1(c_4(c_2(c_0(c_0(c_2(c_5(c_0(c_0(c_2(c_4(c_0(c_1(c_5(c_1(c_1(c_3(c_0(c_2(c_2(c_2(c_3(c_5(c_4(c_0(c_4(c_1(c_5(c_2(c_3(c_4(x11307)))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 4'(2'(0'(2'(1'(5'(5'(4'(2'(3'(2'(1'(0'(1'(4'(2'(0'(4'(2'(3'(1'(3'(0'(1'(4'(2'(0'(0'(2'(5'(0'(0'(2'(0'(4'(1'(5'(1'(1'(3'(0'(2'(2'(2'(3'(5'(4'(0'(4'(1'(5'(2'(3'(4'(x11307)))))))))))))))))))))))))))))))))))))))))))))))))))))) [2]
   4'(c_2(c_0(c_2(c_1(c_5(c_5(c_4(c_2(c_3(c_2(c_1(c_0(c_4(c_1(c_2(c_0(c_4(c_2(c_3(c_1(c_3(c_0(c_1(c_4(c_2(c_0(c_0(c_2(c_5(c_5(c_0(c_5(c_3(c_4(c_1(c_2(c_3(c_2(c_2(x11308)))))))))))))))))))))))))))))))))))))))) -> 4'(2'(0'(2'(1'(5'(5'(4'(2'(3'(2'(1'(0'(1'(4'(2'(0'(4'(2'(3'(1'(3'(0'(1'(4'(2'(0'(0'(2'(1'(2'(3'(5'(5'(0'(1'(3'(5'(5'(x11308))))))))))))))))))))))))))))))))))))))) [2]
   4'(c_2(c_0(c_2(c_1(c_5(c_5(c_4(c_2(c_3(c_2(c_1(c_0(c_4(c_1(c_2(c_0(c_4(c_2(c_3(c_1(c_3(c_0(c_1(c_4(c_2(c_0(c_0(c_2(c_5(c_5(c_0(c_3(c_2(c_2(c_1(c_3(c_4(c_3(c_5(c_4(c_2(c_5(c_2(c_0(c_4(c_1(c_1(c_2(c_4(c_0(c_5(c_4(c_3(c_2(c_4(c_4(x11309))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 4'(2'(0'(2'(1'(5'(5'(4'(2'(3'(2'(1'(0'(1'(4'(2'(0'(4'(2'(3'(1'(3'(0'(1'(4'(2'(0'(0'(2'(5'(5'(0'(3'(2'(2'(3'(1'(4'(3'(5'(4'(2'(5'(2'(0'(4'(1'(1'(2'(4'(0'(5'(4'(3'(2'(4'(4'(x11309))))))))))))))))))))))))))))))))))))))))))))))))))))))))) [2]
   4'(c_2(c_0(c_2(c_1(c_5(c_5(c_4(c_2(c_3(c_2(c_1(c_0(c_4(c_1(c_2(c_0(c_4(c_2(c_3(c_1(c_3(c_0(c_1(c_4(c_2(c_0(c_0(c_2(c_5(c_0(c_5(c_0(c_0(c_4(c_0(c_1(c_3(c_4(c_1(x11310)))))))))))))))))))))))))))))))))))))))) -> 4'(2'(0'(2'(1'(5'(5'(4'(2'(3'(2'(1'(0'(1'(4'(2'(0'(4'(2'(3'(1'(3'(0'(1'(4'(2'(0'(0'(2'(2'(2'(4'(2'(1'(1'(3'(3'(3'(0'(x11310))))))))))))))))))))))))))))))))))))))) [2]
   4'(c_2(c_0(c_2(c_1(c_5(c_5(c_4(c_2(c_3(c_2(c_1(c_0(c_4(c_1(c_2(c_0(c_4(c_2(c_3(c_1(c_3(c_0(c_1(c_4(c_2(c_0(c_0(c_2(c_5(c_5(c_5(c_3(c_5(c_3(c_2(c_5(c_0(c_1(c_5(c_3(c_1(c_2(c_2(c_3(c_3(c_0(c_3(c_1(c_0(c_4(c_1(c_2(c_2(c_5(c_3(c_1(c_3(x11311)))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 4'(2'(0'(2'(1'(5'(5'(4'(2'(3'(2'(1'(0'(1'(4'(2'(0'(4'(2'(3'(1'(3'(0'(1'(4'(2'(0'(0'(2'(5'(5'(5'(3'(5'(3'(2'(5'(1'(0'(5'(3'(1'(2'(2'(3'(3'(0'(3'(1'(0'(4'(1'(2'(2'(5'(3'(1'(3'(x11311)))))))))))))))))))))))))))))))))))))))))))))))))))))))))) [2]
   4'(c_2(c_0(c_2(c_1(c_5(c_5(c_4(c_2(c_3(c_2(c_1(c_0(c_4(c_1(c_2(c_0(c_4(c_2(c_3(c_1(c_3(c_0(c_1(c_4(c_2(c_0(c_0(c_2(c_5(c_2(c_3(c_3(c_1(c_0(c_1(c_1(c_1(c_4(c_1(c_4(x11312))))))))))))))))))))))))))))))))))))))))) -> 4'(2'(0'(2'(1'(5'(5'(4'(2'(3'(2'(1'(0'(1'(4'(2'(0'(4'(2'(3'(1'(3'(0'(1'(4'(2'(0'(0'(2'(0'(2'(4'(0'(4'(0'(4'(0'(0'(1'(x11312))))))))))))))))))))))))))))))))))))))) [2]
   4'(c_2(c_0(c_2(c_1(c_5(c_5(c_4(c_2(c_3(c_2(c_1(c_0(c_4(c_1(c_2(c_0(c_4(c_2(c_3(c_1(c_3(c_0(c_1(c_4(c_2(c_0(c_0(c_2(c_5(c_1(c_5(c_0(c_3(c_3(c_0(c_1(c_2(c_3(c_3(c_1(c_4(c_5(c_3(c_1(c_2(c_2(c_0(c_3(c_2(c_0(c_5(x11313)))))))))))))))))))))))))))))))))))))))))))))))))))) -> 4'(2'(0'(2'(1'(5'(5'(4'(2'(3'(2'(1'(0'(1'(4'(2'(0'(4'(2'(3'(1'(3'(0'(1'(4'(2'(0'(0'(2'(5'(1'(5'(0'(3'(3'(0'(1'(2'(3'(3'(1'(4'(5'(3'(1'(2'(0'(2'(3'(2'(0'(5'(x11313)))))))))))))))))))))))))))))))))))))))))))))))))))) [2]
   4'(c_2(c_0(c_2(c_1(c_5(c_5(c_4(c_2(c_3(c_2(c_1(c_0(c_4(c_1(c_2(c_0(c_4(c_2(c_3(c_1(c_3(c_0(c_1(c_4(c_2(c_0(c_0(c_2(c_5(c_1(c_5(c_3(c_5(c_4(c_0(c_0(c_3(x11314)))))))))))))))))))))))))))))))))))))) -> 4'(2'(0'(2'(1'(5'(5'(4'(2'(3'(2'(1'(0'(1'(4'(2'(0'(4'(2'(3'(1'(3'(0'(1'(4'(2'(0'(0'(2'(5'(1'(5'(3'(5'(0'(4'(0'(3'(x11314)))))))))))))))))))))))))))))))))))))) [2]
   4'(c_2(c_0(c_2(c_1(c_5(c_5(c_4(c_2(c_3(c_2(c_1(c_0(c_4(c_1(c_2(c_0(c_4(c_2(c_3(c_1(c_3(c_0(c_1(c_4(c_2(c_0(c_0(c_2(c_5(c_5(c_2(c_3(c_2(c_0(c_3(c_2(c_5(c_3(c_2(c_5(c_5(c_5(c_5(c_1(c_5(c_5(c_1(c_2(c_2(x11315)))))))))))))))))))))))))))))))))))))))))))))))))) -> 4'(2'(0'(2'(1'(5'(5'(4'(2'(3'(2'(1'(0'(1'(4'(2'(0'(4'(2'(3'(1'(3'(0'(1'(4'(2'(0'(0'(2'(5'(5'(2'(3'(2'(0'(3'(2'(5'(3'(2'(5'(5'(5'(1'(5'(5'(5'(1'(2'(2'(x11315)))))))))))))))))))))))))))))))))))))))))))))))))) [2]
   4'(c_2(c_0(c_2(c_1(c_5(c_5(c_4(c_2(c_3(c_2(c_1(c_0(c_4(c_1(c_2(c_0(c_4(c_2(c_3(c_1(c_3(c_0(c_1(c_4(c_2(c_0(c_0(c_2(c_5(c_1(c_0(c_3(c_5(c_0(c_1(c_1(c_3(c_4(c_3(x11316)))))))))))))))))))))))))))))))))))))))) -> 4'(2'(0'(2'(1'(5'(5'(4'(2'(3'(2'(1'(0'(1'(4'(2'(0'(4'(2'(3'(1'(3'(0'(1'(4'(2'(0'(0'(2'(1'(0'(3'(0'(0'(4'(2'(4'(5'(3'(x11316))))))))))))))))))))))))))))))))))))))) [2]
   4'(c_2(c_0(c_2(c_1(c_5(c_5(c_4(c_2(c_3(c_2(c_1(c_0(c_4(c_1(c_2(c_0(c_4(c_2(c_3(c_1(c_3(c_0(c_1(c_4(c_2(c_0(c_0(c_2(c_5(c_4(c_1(c_5(c_1(c_4(c_2(c_5(c_4(c_3(c_0(c_4(c_1(c_0(x11317))))))))))))))))))))))))))))))))))))))))))) -> 4'(2'(0'(2'(1'(5'(5'(4'(2'(3'(2'(1'(0'(1'(4'(2'(0'(4'(2'(3'(1'(3'(0'(1'(4'(2'(0'(0'(2'(5'(4'(1'(1'(5'(4'(2'(5'(4'(3'(0'(4'(1'(0'(x11317))))))))))))))))))))))))))))))))))))))))))) [2]
   4'(c_2(c_0(c_2(c_1(c_5(c_5(c_4(c_2(c_3(c_2(c_1(c_0(c_4(c_1(c_2(c_0(c_4(c_2(c_3(c_1(c_3(c_0(c_1(c_4(c_2(c_0(c_0(c_2(c_5(c_3(c_1(c_5(c_5(c_3(c_3(c_0(c_2(c_2(c_2(c_2(c_3(c_3(c_4(c_5(c_1(c_1(x11318))))))))))))))))))))))))))))))))))))))))))))))) -> 4'(2'(0'(2'(1'(5'(5'(4'(2'(3'(2'(1'(0'(1'(4'(2'(0'(4'(2'(3'(1'(3'(0'(1'(4'(2'(0'(0'(2'(5'(3'(1'(5'(5'(3'(3'(0'(2'(2'(2'(3'(2'(3'(4'(5'(1'(1'(x11318))))))))))))))))))))))))))))))))))))))))))))))) [2]
   4'(c_2(c_0(c_2(c_1(c_5(c_5(c_4(c_2(c_3(c_2(c_1(c_0(c_4(c_1(c_2(c_0(c_4(c_2(c_3(c_1(c_3(c_0(c_1(c_4(c_2(c_0(c_0(c_2(c_5(c_5(c_3(c_3(c_0(c_1(c_4(c_1(c_3(c_3(c_0(x11319)))))))))))))))))))))))))))))))))))))))) -> 4'(2'(0'(2'(1'(5'(5'(4'(2'(3'(2'(1'(0'(1'(4'(2'(0'(4'(2'(3'(1'(3'(0'(1'(4'(2'(0'(0'(2'(2'(3'(3'(4'(5'(4'(2'(2'(0'(1'(x11319))))))))))))))))))))))))))))))))))))))) [2]
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   4'(c_0(c_4(c_2(c_4(c_0(c_3(c_1(x1)))))))) -> 4'(0'(4'(2'(0'(4'(3'(c_1(x1)))))))) [1]
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