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


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


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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 54 ms]
(4) CpxRelTRS
(5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(6) CpxTRS
    (7) CpxTrsMatchBoundsProof [FINISHED, 71 ms]
    (8) BOUNDS(1, n^1)
(9) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(10) TRS for Loop Detection
    (11) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
    (12) BEST
        (13) proven lower bound
            (14) LowerBoundPropagationProof [FINISHED, 0 ms]
            (15) BOUNDS(n^1, INF)
        (16) TRS for Loop Detection


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

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


The TRS R consists of the following rules:

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

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

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

   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(3(x_1)) -> 3(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(5(x_1)) -> 5(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(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 (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1).


The TRS R consists of the following rules:

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

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

   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(3(x_1)) -> 3(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(5(x_1)) -> 5(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(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: INNERMOST
----------------------------------------

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

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


The TRS R consists of the following rules:

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

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

   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(3(x_1)) -> 3(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(5(x_1)) -> 5(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(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: INNERMOST
----------------------------------------

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

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


The TRS R consists of the following rules:

   0(1(2(x1))) -> 0(2(1(0(x1))))
   0(1(2(x1))) -> 1(0(2(3(x1))))
   0(1(2(x1))) -> 0(2(4(1(5(x1)))))
   0(1(2(x1))) -> 0(3(2(1(0(x1)))))
   0(1(2(x1))) -> 1(0(3(2(3(x1)))))
   0(1(2(x1))) -> 0(1(3(4(2(3(x1))))))
   0(5(2(x1))) -> 0(2(4(5(3(x1)))))
   0(5(2(x1))) -> 5(4(2(3(0(4(x1))))))
   2(0(1(x1))) -> 3(0(2(1(x1))))
   2(0(1(x1))) -> 0(2(1(1(4(x1)))))
   2(0(1(x1))) -> 0(3(2(4(1(x1)))))
   2(0(1(x1))) -> 3(0(2(1(4(x1)))))
   2(0(1(x1))) -> 0(2(2(3(4(1(x1))))))
   2(0(1(x1))) -> 0(3(2(3(1(1(x1))))))
   2(0(1(x1))) -> 4(0(4(2(1(4(x1))))))
   2(5(1(x1))) -> 0(2(1(5(1(x1)))))
   2(5(1(x1))) -> 1(4(5(4(2(x1)))))
   2(5(1(x1))) -> 5(0(2(1(4(x1)))))
   2(5(1(x1))) -> 5(2(1(4(1(x1)))))
   2(5(1(x1))) -> 1(5(0(2(4(1(x1))))))
   2(5(1(x1))) -> 5(2(1(1(1(1(x1))))))
   0(1(2(1(x1)))) -> 3(1(4(0(2(1(x1))))))
   0(1(3(1(x1)))) -> 5(0(3(1(1(x1)))))
   0(1(3(1(x1)))) -> 1(0(3(4(2(1(x1))))))
   0(1(5(1(x1)))) -> 5(0(3(1(1(x1)))))
   0(2(1(2(x1)))) -> 0(2(2(1(5(x1)))))
   0(2(5(1(x1)))) -> 1(1(5(0(2(1(x1))))))
   0(5(3(1(x1)))) -> 0(1(4(4(3(5(x1))))))
   0(5(5(2(x1)))) -> 5(4(2(3(5(0(x1))))))
   2(0(1(2(x1)))) -> 0(2(3(2(1(1(x1))))))
   2(0(1(2(x1)))) -> 4(0(2(1(1(2(x1))))))
   2(0(4(1(x1)))) -> 3(0(2(4(1(x1)))))
   2(0(5(1(x1)))) -> 5(4(2(1(0(x1)))))
   2(2(5(1(x1)))) -> 3(2(2(4(5(1(x1))))))
   2(4(0(1(x1)))) -> 1(0(2(4(4(x1)))))
   2(4(0(1(x1)))) -> 3(0(0(2(4(1(x1))))))
   2(4(0(1(x1)))) -> 5(4(0(2(1(1(x1))))))
   2(5(2(1(x1)))) -> 1(5(2(2(3(1(x1))))))
   2(5(4(1(x1)))) -> 4(5(2(1(4(4(x1))))))
   2(5(5(1(x1)))) -> 1(5(4(2(4(5(x1))))))
   2(5(5(2(x1)))) -> 5(5(2(3(2(x1)))))
   0(1(3(0(1(x1))))) -> 0(3(1(0(1(1(x1))))))
   0(2(4(3(1(x1))))) -> 1(3(4(2(3(0(x1))))))
   0(2(4(3(1(x1))))) -> 4(0(3(2(1(0(x1))))))
   0(2(5(3(1(x1))))) -> 5(0(2(3(5(1(x1))))))
   2(0(5(4(1(x1))))) -> 0(4(5(3(2(1(x1))))))
   2(2(0(1(2(x1))))) -> 2(4(0(2(2(1(x1))))))
   2(4(0(5(1(x1))))) -> 1(4(5(0(4(2(x1))))))
   2(4(2(3(1(x1))))) -> 4(2(2(3(3(1(x1))))))
   2(5(2(0(1(x1))))) -> 0(2(4(1(5(2(x1))))))
   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(3(x_1)) -> 3(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(5(x_1)) -> 5(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(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: INNERMOST
----------------------------------------

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

"[50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381]
{(50,51,[0_1|0, 2_1|0, encArg_1|0, encode_0_1|0, encode_1_1|0, encode_2_1|0, encode_3_1|0, encode_4_1|0, encode_5_1|0]), (50,52,[5_1|1]), (50,56,[1_1|1]), (50,61,[0_1|1]), (50,66,[0_1|1]), (50,70,[1_1|1]), (50,74,[5_1|1]), (50,78,[5_1|1]), (50,82,[1_1|1]), (50,87,[5_1|1]), (50,92,[4_1|1]), (50,97,[1_1|1]), (50,102,[1_1|1, 3_1|1, 4_1|1, 5_1|1, 0_1|1, 2_1|1]), (50,103,[0_1|2]), (50,106,[1_1|2]), (50,109,[0_1|2]), (50,113,[0_1|2]), (50,117,[1_1|2]), (50,121,[0_1|2]), (50,126,[3_1|2]), (50,131,[5_1|2]), (50,135,[1_1|2]), (50,140,[0_1|2]), (50,145,[0_1|2]), (50,149,[5_1|2]), (50,154,[0_1|2]), (50,159,[5_1|2]), (50,164,[0_1|2]), (50,168,[1_1|2]), (50,173,[5_1|2]), (50,178,[1_1|2]), (50,183,[4_1|2]), (50,188,[3_1|2]), (50,191,[0_1|2]), (50,195,[0_1|2]), (50,199,[3_1|2]), (50,203,[0_1|2]), (50,208,[0_1|2]), (50,213,[4_1|2]), (50,218,[0_1|2]), (50,223,[4_1|2]), (50,228,[3_1|2]), (50,232,[5_1|2]), (50,236,[0_1|2]), (50,241,[0_1|2]), (50,245,[1_1|2]), (50,249,[5_1|2]), (50,253,[5_1|2]), (50,257,[1_1|2]), (50,262,[5_1|2]), (50,267,[1_1|2]), (50,272,[0_1|2]), (50,277,[4_1|2]), (50,282,[1_1|2]), (50,287,[5_1|2]), (50,291,[3_1|2]), (50,296,[2_1|2]), (50,301,[1_1|2]), (50,305,[3_1|2]), (50,310,[5_1|2]), (50,315,[1_1|2]), (50,320,[4_1|2]), (51,51,[1_1|0, 3_1|0, 4_1|0, 5_1|0, cons_0_1|0, cons_2_1|0]), (52,53,[0_1|1]), (53,54,[3_1|1]), (54,55,[1_1|1]), (55,51,[1_1|1]), (56,57,[0_1|1]), (57,58,[3_1|1]), (58,59,[4_1|1]), (59,60,[2_1|1]), (60,51,[1_1|1]), (61,62,[1_1|1]), (62,63,[4_1|1]), (63,64,[4_1|1]), (64,65,[3_1|1]), (65,51,[5_1|1]), (66,67,[2_1|1]), (67,68,[1_1|1]), (68,69,[5_1|1]), (69,51,[1_1|1]), (70,71,[4_1|1]), (71,72,[5_1|1]), (72,73,[4_1|1]), (73,51,[2_1|1]), (73,66,[0_1|1]), (73,70,[1_1|1]), (73,74,[5_1|1]), (73,78,[5_1|1]), (73,82,[1_1|1]), (73,87,[5_1|1]), (73,92,[4_1|1]), (73,97,[1_1|1]), (74,75,[0_1|1]), (75,76,[2_1|1]), (76,77,[1_1|1]), (77,51,[4_1|1]), (78,79,[2_1|1]), (79,80,[1_1|1]), (80,81,[4_1|1]), (81,51,[1_1|1]), (82,83,[5_1|1]), (83,84,[0_1|1]), (84,85,[2_1|1]), (85,86,[4_1|1]), (86,51,[1_1|1]), (87,88,[2_1|1]), (88,89,[1_1|1]), (89,90,[1_1|1]), (90,91,[1_1|1]), (91,51,[1_1|1]), (92,93,[5_1|1]), (93,94,[2_1|1]), (94,95,[1_1|1]), (95,96,[4_1|1]), (96,51,[4_1|1]), (97,98,[5_1|1]), (98,99,[4_1|1]), (99,100,[2_1|1]), (100,101,[4_1|1]), (101,51,[5_1|1]), (102,51,[encArg_1|1]), (102,102,[1_1|1, 3_1|1, 4_1|1, 5_1|1, 0_1|1, 2_1|1]), (102,103,[0_1|2]), (102,106,[1_1|2]), (102,109,[0_1|2]), (102,113,[0_1|2]), (102,117,[1_1|2]), (102,121,[0_1|2]), (102,126,[3_1|2]), (102,131,[5_1|2]), (102,135,[1_1|2]), (102,140,[0_1|2]), (102,145,[0_1|2]), (102,149,[5_1|2]), (102,154,[0_1|2]), (102,159,[5_1|2]), (102,164,[0_1|2]), (102,168,[1_1|2]), (102,173,[5_1|2]), (102,178,[1_1|2]), (102,183,[4_1|2]), (102,188,[3_1|2]), (102,191,[0_1|2]), (102,195,[0_1|2]), (102,199,[3_1|2]), (102,203,[0_1|2]), (102,208,[0_1|2]), (102,213,[4_1|2]), (102,218,[0_1|2]), (102,223,[4_1|2]), (102,228,[3_1|2]), (102,232,[5_1|2]), (102,236,[0_1|2]), (102,241,[0_1|2]), (102,245,[1_1|2]), (102,249,[5_1|2]), (102,253,[5_1|2]), (102,257,[1_1|2]), (102,262,[5_1|2]), (102,267,[1_1|2]), (102,272,[0_1|2]), (102,277,[4_1|2]), (102,282,[1_1|2]), (102,287,[5_1|2]), (102,291,[3_1|2]), (102,296,[2_1|2]), (102,301,[1_1|2]), (102,305,[3_1|2]), (102,310,[5_1|2]), (102,315,[1_1|2]), (102,320,[4_1|2]), (103,104,[2_1|2]), (104,105,[1_1|2]), (105,102,[0_1|2]), (105,296,[0_1|2]), (105,103,[0_1|2]), (105,106,[1_1|2]), (105,109,[0_1|2]), (105,113,[0_1|2]), (105,117,[1_1|2]), (105,121,[0_1|2]), (105,126,[3_1|2]), (105,131,[5_1|2]), (105,135,[1_1|2]), (105,140,[0_1|2]), (105,145,[0_1|2]), (105,149,[5_1|2]), (105,154,[0_1|2]), (105,159,[5_1|2]), (105,164,[0_1|2]), (105,168,[1_1|2]), (105,173,[5_1|2]), (105,178,[1_1|2]), (105,183,[4_1|2]), (105,325,[0_1|3]), (105,329,[5_1|3]), (105,334,[5_1|3]), (106,107,[0_1|2]), (107,108,[2_1|2]), (108,102,[3_1|2]), (108,296,[3_1|2]), (109,110,[2_1|2]), (110,111,[4_1|2]), (111,112,[1_1|2]), (112,102,[5_1|2]), (112,296,[5_1|2]), (113,114,[3_1|2]), (114,115,[2_1|2]), (115,116,[1_1|2]), (116,102,[0_1|2]), (116,296,[0_1|2]), (116,103,[0_1|2]), (116,106,[1_1|2]), (116,109,[0_1|2]), (116,113,[0_1|2]), (116,117,[1_1|2]), (116,121,[0_1|2]), (116,126,[3_1|2]), (116,131,[5_1|2]), (116,135,[1_1|2]), (116,140,[0_1|2]), (116,145,[0_1|2]), (116,149,[5_1|2]), (116,154,[0_1|2]), (116,159,[5_1|2]), (116,164,[0_1|2]), (116,168,[1_1|2]), (116,173,[5_1|2]), (116,178,[1_1|2]), (116,183,[4_1|2]), (116,325,[0_1|3]), (116,329,[5_1|3]), (116,334,[5_1|3]), (117,118,[0_1|2]), (118,119,[3_1|2]), (119,120,[2_1|2]), (120,102,[3_1|2]), (120,296,[3_1|2]), (121,122,[1_1|2]), (122,123,[3_1|2]), (123,124,[4_1|2]), (124,125,[2_1|2]), (125,102,[3_1|2]), (125,296,[3_1|2]), (126,127,[1_1|2]), (127,128,[4_1|2]), (128,129,[0_1|2]), (128,164,[0_1|2]), (128,339,[0_1|3]), (129,130,[2_1|2]), (130,102,[1_1|2]), (130,106,[1_1|2]), (130,117,[1_1|2]), (130,135,[1_1|2]), (130,168,[1_1|2]), (130,178,[1_1|2]), (130,245,[1_1|2]), (130,257,[1_1|2]), (130,267,[1_1|2]), (130,282,[1_1|2]), (130,301,[1_1|2]), (130,315,[1_1|2]), (131,132,[0_1|2]), (132,133,[3_1|2]), (133,134,[1_1|2]), (134,102,[1_1|2]), (134,106,[1_1|2]), (134,117,[1_1|2]), (134,135,[1_1|2]), (134,168,[1_1|2]), (134,178,[1_1|2]), (134,245,[1_1|2]), (134,257,[1_1|2]), (134,267,[1_1|2]), (134,282,[1_1|2]), (134,301,[1_1|2]), (134,315,[1_1|2]), (134,127,[1_1|2]), (135,136,[0_1|2]), (136,137,[3_1|2]), (137,138,[4_1|2]), (138,139,[2_1|2]), (139,102,[1_1|2]), (139,106,[1_1|2]), (139,117,[1_1|2]), (139,135,[1_1|2]), (139,168,[1_1|2]), (139,178,[1_1|2]), (139,245,[1_1|2]), (139,257,[1_1|2]), (139,267,[1_1|2]), (139,282,[1_1|2]), (139,301,[1_1|2]), (139,315,[1_1|2]), (139,127,[1_1|2]), (140,141,[3_1|2]), (141,142,[1_1|2]), (142,143,[0_1|2]), (143,144,[1_1|2]), (144,102,[1_1|2]), (144,106,[1_1|2]), (144,117,[1_1|2]), (144,135,[1_1|2]), (144,168,[1_1|2]), (144,178,[1_1|2]), (144,245,[1_1|2]), (144,257,[1_1|2]), (144,267,[1_1|2]), (144,282,[1_1|2]), (144,301,[1_1|2]), (144,315,[1_1|2]), (144,122,[1_1|2]), (144,155,[1_1|2]), (145,146,[2_1|2]), (146,147,[4_1|2]), (147,148,[5_1|2]), (148,102,[3_1|2]), (148,296,[3_1|2]), (148,254,[3_1|2]), (148,263,[3_1|2]), (149,150,[4_1|2]), (150,151,[2_1|2]), (151,152,[3_1|2]), (152,153,[0_1|2]), (153,102,[4_1|2]), (153,296,[4_1|2]), (153,254,[4_1|2]), (153,263,[4_1|2]), (154,155,[1_1|2]), (155,156,[4_1|2]), (156,157,[4_1|2]), (157,158,[3_1|2]), (158,102,[5_1|2]), (158,106,[5_1|2]), (158,117,[5_1|2]), (158,135,[5_1|2]), (158,168,[5_1|2]), (158,178,[5_1|2]), (158,245,[5_1|2]), (158,257,[5_1|2]), (158,267,[5_1|2]), (158,282,[5_1|2]), (158,301,[5_1|2]), (158,315,[5_1|2]), (158,127,[5_1|2]), (159,160,[4_1|2]), (160,161,[2_1|2]), (161,162,[3_1|2]), (162,163,[5_1|2]), (163,102,[0_1|2]), (163,296,[0_1|2]), (163,254,[0_1|2]), (163,263,[0_1|2]), (163,289,[0_1|2]), (163,103,[0_1|2]), (163,106,[1_1|2]), (163,109,[0_1|2]), (163,113,[0_1|2]), (163,117,[1_1|2]), (163,121,[0_1|2]), (163,126,[3_1|2]), (163,131,[5_1|2]), (163,135,[1_1|2]), (163,140,[0_1|2]), (163,145,[0_1|2]), (163,149,[5_1|2]), (163,154,[0_1|2]), (163,159,[5_1|2]), (163,164,[0_1|2]), (163,168,[1_1|2]), (163,173,[5_1|2]), (163,178,[1_1|2]), (163,183,[4_1|2]), (163,325,[0_1|3]), (163,329,[5_1|3]), (163,334,[5_1|3]), (164,165,[2_1|2]), (165,166,[2_1|2]), (166,167,[1_1|2]), (167,102,[5_1|2]), (167,296,[5_1|2]), (168,169,[1_1|2]), (169,170,[5_1|2]), (170,171,[0_1|2]), (170,164,[0_1|2]), (170,339,[0_1|3]), (171,172,[2_1|2]), (172,102,[1_1|2]), (172,106,[1_1|2]), (172,117,[1_1|2]), (172,135,[1_1|2]), (172,168,[1_1|2]), (172,178,[1_1|2]), (172,245,[1_1|2]), (172,257,[1_1|2]), (172,267,[1_1|2]), (172,282,[1_1|2]), (172,301,[1_1|2]), (172,315,[1_1|2]), (173,174,[0_1|2]), (174,175,[2_1|2]), (175,176,[3_1|2]), (176,177,[5_1|2]), (177,102,[1_1|2]), (177,106,[1_1|2]), (177,117,[1_1|2]), (177,135,[1_1|2]), (177,168,[1_1|2]), (177,178,[1_1|2]), (177,245,[1_1|2]), (177,257,[1_1|2]), (177,267,[1_1|2]), (177,282,[1_1|2]), (177,301,[1_1|2]), (177,315,[1_1|2]), (177,127,[1_1|2]), (178,179,[3_1|2]), (179,180,[4_1|2]), (180,181,[2_1|2]), (181,182,[3_1|2]), (182,102,[0_1|2]), (182,106,[0_1|2, 1_1|2]), (182,117,[0_1|2, 1_1|2]), (182,135,[0_1|2, 1_1|2]), (182,168,[0_1|2, 1_1|2]), (182,178,[0_1|2, 1_1|2]), (182,245,[0_1|2]), (182,257,[0_1|2]), (182,267,[0_1|2]), (182,282,[0_1|2]), (182,301,[0_1|2]), (182,315,[0_1|2]), (182,127,[0_1|2]), (182,103,[0_1|2]), (182,109,[0_1|2]), (182,113,[0_1|2]), (182,121,[0_1|2]), (182,126,[3_1|2]), (182,131,[5_1|2]), (182,140,[0_1|2]), (182,145,[0_1|2]), (182,149,[5_1|2]), (182,154,[0_1|2]), (182,159,[5_1|2]), (182,164,[0_1|2]), (182,173,[5_1|2]), (182,183,[4_1|2]), (182,325,[0_1|3]), (182,329,[5_1|3]), (182,334,[5_1|3]), (183,184,[0_1|2]), (184,185,[3_1|2]), (185,186,[2_1|2]), (186,187,[1_1|2]), (187,102,[0_1|2]), (187,106,[0_1|2, 1_1|2]), (187,117,[0_1|2, 1_1|2]), (187,135,[0_1|2, 1_1|2]), (187,168,[0_1|2, 1_1|2]), (187,178,[0_1|2, 1_1|2]), (187,245,[0_1|2]), (187,257,[0_1|2]), (187,267,[0_1|2]), (187,282,[0_1|2]), (187,301,[0_1|2]), (187,315,[0_1|2]), (187,127,[0_1|2]), (187,103,[0_1|2]), (187,109,[0_1|2]), (187,113,[0_1|2]), (187,121,[0_1|2]), (187,126,[3_1|2]), (187,131,[5_1|2]), (187,140,[0_1|2]), (187,145,[0_1|2]), (187,149,[5_1|2]), (187,154,[0_1|2]), (187,159,[5_1|2]), (187,164,[0_1|2]), (187,173,[5_1|2]), (187,183,[4_1|2]), (187,325,[0_1|3]), (187,329,[5_1|3]), (187,334,[5_1|3]), (188,189,[0_1|2]), (188,164,[0_1|2]), (188,339,[0_1|3]), (189,190,[2_1|2]), (190,102,[1_1|2]), (190,106,[1_1|2]), (190,117,[1_1|2]), (190,135,[1_1|2]), (190,168,[1_1|2]), (190,178,[1_1|2]), (190,245,[1_1|2]), (190,257,[1_1|2]), (190,267,[1_1|2]), (190,282,[1_1|2]), (190,301,[1_1|2]), (190,315,[1_1|2]), (190,122,[1_1|2]), (190,155,[1_1|2]), (191,192,[2_1|2]), (192,193,[1_1|2]), (193,194,[1_1|2]), (194,102,[4_1|2]), (194,106,[4_1|2]), (194,117,[4_1|2]), (194,135,[4_1|2]), (194,168,[4_1|2]), (194,178,[4_1|2]), (194,245,[4_1|2]), (194,257,[4_1|2]), (194,267,[4_1|2]), (194,282,[4_1|2]), (194,301,[4_1|2]), (194,315,[4_1|2]), (194,122,[4_1|2]), (194,155,[4_1|2]), (195,196,[3_1|2]), (196,197,[2_1|2]), (197,198,[4_1|2]), (198,102,[1_1|2]), (198,106,[1_1|2]), (198,117,[1_1|2]), (198,135,[1_1|2]), (198,168,[1_1|2]), (198,178,[1_1|2]), (198,245,[1_1|2]), (198,257,[1_1|2]), (198,267,[1_1|2]), (198,282,[1_1|2]), (198,301,[1_1|2]), (198,315,[1_1|2]), (198,122,[1_1|2]), (198,155,[1_1|2]), (199,200,[0_1|2]), (200,201,[2_1|2]), (201,202,[1_1|2]), (202,102,[4_1|2]), (202,106,[4_1|2]), (202,117,[4_1|2]), (202,135,[4_1|2]), (202,168,[4_1|2]), (202,178,[4_1|2]), (202,245,[4_1|2]), (202,257,[4_1|2]), (202,267,[4_1|2]), (202,282,[4_1|2]), (202,301,[4_1|2]), (202,315,[4_1|2]), (202,122,[4_1|2]), (202,155,[4_1|2]), (203,204,[2_1|2]), (204,205,[2_1|2]), (205,206,[3_1|2]), (206,207,[4_1|2]), (207,102,[1_1|2]), (207,106,[1_1|2]), (207,117,[1_1|2]), (207,135,[1_1|2]), (207,168,[1_1|2]), (207,178,[1_1|2]), (207,245,[1_1|2]), (207,257,[1_1|2]), (207,267,[1_1|2]), (207,282,[1_1|2]), (207,301,[1_1|2]), (207,315,[1_1|2]), (207,122,[1_1|2]), (207,155,[1_1|2]), (208,209,[3_1|2]), (209,210,[2_1|2]), (210,211,[3_1|2]), (211,212,[1_1|2]), (212,102,[1_1|2]), (212,106,[1_1|2]), (212,117,[1_1|2]), (212,135,[1_1|2]), (212,168,[1_1|2]), (212,178,[1_1|2]), (212,245,[1_1|2]), (212,257,[1_1|2]), (212,267,[1_1|2]), (212,282,[1_1|2]), (212,301,[1_1|2]), (212,315,[1_1|2]), (212,122,[1_1|2]), (212,155,[1_1|2]), (213,214,[0_1|2]), (214,215,[4_1|2]), (215,216,[2_1|2]), (216,217,[1_1|2]), (217,102,[4_1|2]), (217,106,[4_1|2]), (217,117,[4_1|2]), (217,135,[4_1|2]), (217,168,[4_1|2]), (217,178,[4_1|2]), (217,245,[4_1|2]), (217,257,[4_1|2]), (217,267,[4_1|2]), (217,282,[4_1|2]), (217,301,[4_1|2]), (217,315,[4_1|2]), (217,122,[4_1|2]), (217,155,[4_1|2]), (218,219,[2_1|2]), (219,220,[3_1|2]), (220,221,[2_1|2]), (221,222,[1_1|2]), (222,102,[1_1|2]), (222,296,[1_1|2]), (223,224,[0_1|2]), (224,225,[2_1|2]), (225,226,[1_1|2]), (226,227,[1_1|2]), (227,102,[2_1|2]), (227,296,[2_1|2]), (227,188,[3_1|2]), (227,191,[0_1|2]), (227,195,[0_1|2]), (227,199,[3_1|2]), (227,203,[0_1|2]), (227,208,[0_1|2]), (227,213,[4_1|2]), (227,218,[0_1|2]), (227,223,[4_1|2]), (227,228,[3_1|2]), (227,232,[5_1|2]), (227,236,[0_1|2]), (227,241,[0_1|2]), (227,245,[1_1|2]), (227,249,[5_1|2]), (227,253,[5_1|2]), (227,257,[1_1|2]), (227,262,[5_1|2]), (227,267,[1_1|2]), (227,272,[0_1|2]), (227,277,[4_1|2]), (227,282,[1_1|2]), (227,287,[5_1|2]), (227,291,[3_1|2]), (227,301,[1_1|2]), (227,305,[3_1|2]), (227,310,[5_1|2]), (227,315,[1_1|2]), (227,320,[4_1|2]), (227,343,[3_1|3]), (227,346,[0_1|3]), (227,350,[0_1|3]), (227,354,[3_1|3]), (227,358,[0_1|3]), (227,363,[0_1|3]), (227,368,[4_1|3]), (227,373,[1_1|3]), (227,378,[5_1|3]), (228,229,[0_1|2]), (229,230,[2_1|2]), (230,231,[4_1|2]), (231,102,[1_1|2]), (231,106,[1_1|2]), (231,117,[1_1|2]), (231,135,[1_1|2]), (231,168,[1_1|2]), (231,178,[1_1|2]), (231,245,[1_1|2]), (231,257,[1_1|2]), (231,267,[1_1|2]), (231,282,[1_1|2]), (231,301,[1_1|2]), (231,315,[1_1|2]), (232,233,[4_1|2]), (233,234,[2_1|2]), (234,235,[1_1|2]), (235,102,[0_1|2]), (235,106,[0_1|2, 1_1|2]), (235,117,[0_1|2, 1_1|2]), (235,135,[0_1|2, 1_1|2]), (235,168,[0_1|2, 1_1|2]), (235,178,[0_1|2, 1_1|2]), (235,245,[0_1|2]), (235,257,[0_1|2]), (235,267,[0_1|2]), (235,282,[0_1|2]), (235,301,[0_1|2]), (235,315,[0_1|2]), (235,103,[0_1|2]), (235,109,[0_1|2]), (235,113,[0_1|2]), (235,121,[0_1|2]), (235,126,[3_1|2]), (235,131,[5_1|2]), (235,140,[0_1|2]), (235,145,[0_1|2]), (235,149,[5_1|2]), (235,154,[0_1|2]), (235,159,[5_1|2]), (235,164,[0_1|2]), (235,173,[5_1|2]), (235,183,[4_1|2]), (235,325,[0_1|3]), (235,329,[5_1|3]), (235,334,[5_1|3]), (236,237,[4_1|2]), (237,238,[5_1|2]), (238,239,[3_1|2]), (239,240,[2_1|2]), (240,102,[1_1|2]), (240,106,[1_1|2]), (240,117,[1_1|2]), (240,135,[1_1|2]), (240,168,[1_1|2]), (240,178,[1_1|2]), (240,245,[1_1|2]), (240,257,[1_1|2]), (240,267,[1_1|2]), (240,282,[1_1|2]), (240,301,[1_1|2]), (240,315,[1_1|2]), (241,242,[2_1|2]), (242,243,[1_1|2]), (243,244,[5_1|2]), (244,102,[1_1|2]), (244,106,[1_1|2]), (244,117,[1_1|2]), (244,135,[1_1|2]), (244,168,[1_1|2]), (244,178,[1_1|2]), (244,245,[1_1|2]), (244,257,[1_1|2]), (244,267,[1_1|2]), (244,282,[1_1|2]), (244,301,[1_1|2]), (244,315,[1_1|2]), (245,246,[4_1|2]), (246,247,[5_1|2]), (247,248,[4_1|2]), (248,102,[2_1|2]), (248,106,[2_1|2]), (248,117,[2_1|2]), (248,135,[2_1|2]), (248,168,[2_1|2]), (248,178,[2_1|2]), (248,245,[2_1|2, 1_1|2]), (248,257,[2_1|2, 1_1|2]), (248,267,[2_1|2, 1_1|2]), (248,282,[2_1|2, 1_1|2]), (248,301,[2_1|2, 1_1|2]), (248,315,[2_1|2, 1_1|2]), (248,188,[3_1|2]), (248,191,[0_1|2]), (248,195,[0_1|2]), (248,199,[3_1|2]), (248,203,[0_1|2]), (248,208,[0_1|2]), (248,213,[4_1|2]), (248,218,[0_1|2]), (248,223,[4_1|2]), (248,228,[3_1|2]), (248,232,[5_1|2]), (248,236,[0_1|2]), (248,241,[0_1|2]), (248,249,[5_1|2]), (248,253,[5_1|2]), (248,262,[5_1|2]), (248,272,[0_1|2]), (248,277,[4_1|2]), (248,287,[5_1|2]), (248,291,[3_1|2]), (248,296,[2_1|2]), (248,305,[3_1|2]), (248,310,[5_1|2]), (248,320,[4_1|2]), (248,343,[3_1|3]), (248,346,[0_1|3]), (248,350,[0_1|3]), (248,354,[3_1|3]), (248,358,[0_1|3]), (248,363,[0_1|3]), (248,368,[4_1|3]), (248,373,[1_1|3]), (248,378,[5_1|3]), (249,250,[0_1|2]), (250,251,[2_1|2]), (251,252,[1_1|2]), (252,102,[4_1|2]), (252,106,[4_1|2]), (252,117,[4_1|2]), (252,135,[4_1|2]), (252,168,[4_1|2]), (252,178,[4_1|2]), (252,245,[4_1|2]), (252,257,[4_1|2]), (252,267,[4_1|2]), (252,282,[4_1|2]), (252,301,[4_1|2]), (252,315,[4_1|2]), (253,254,[2_1|2]), (254,255,[1_1|2]), (255,256,[4_1|2]), (256,102,[1_1|2]), (256,106,[1_1|2]), (256,117,[1_1|2]), (256,135,[1_1|2]), (256,168,[1_1|2]), (256,178,[1_1|2]), (256,245,[1_1|2]), (256,257,[1_1|2]), (256,267,[1_1|2]), (256,282,[1_1|2]), (256,301,[1_1|2]), (256,315,[1_1|2]), (257,258,[5_1|2]), (258,259,[0_1|2]), (259,260,[2_1|2]), (260,261,[4_1|2]), (261,102,[1_1|2]), (261,106,[1_1|2]), (261,117,[1_1|2]), (261,135,[1_1|2]), (261,168,[1_1|2]), (261,178,[1_1|2]), (261,245,[1_1|2]), (261,257,[1_1|2]), (261,267,[1_1|2]), (261,282,[1_1|2]), (261,301,[1_1|2]), (261,315,[1_1|2]), (262,263,[2_1|2]), (263,264,[1_1|2]), (264,265,[1_1|2]), (265,266,[1_1|2]), (266,102,[1_1|2]), (266,106,[1_1|2]), (266,117,[1_1|2]), (266,135,[1_1|2]), (266,168,[1_1|2]), (266,178,[1_1|2]), (266,245,[1_1|2]), (266,257,[1_1|2]), (266,267,[1_1|2]), (266,282,[1_1|2]), (266,301,[1_1|2]), (266,315,[1_1|2]), (267,268,[5_1|2]), (268,269,[2_1|2]), (269,270,[2_1|2]), (270,271,[3_1|2]), (271,102,[1_1|2]), (271,106,[1_1|2]), (271,117,[1_1|2]), (271,135,[1_1|2]), (271,168,[1_1|2]), (271,178,[1_1|2]), (271,245,[1_1|2]), (271,257,[1_1|2]), (271,267,[1_1|2]), (271,282,[1_1|2]), (271,301,[1_1|2]), (271,315,[1_1|2]), (271,255,[1_1|2]), (271,264,[1_1|2]), (272,273,[2_1|2]), (273,274,[4_1|2]), (274,275,[1_1|2]), (275,276,[5_1|2]), (276,102,[2_1|2]), (276,106,[2_1|2]), (276,117,[2_1|2]), (276,135,[2_1|2]), (276,168,[2_1|2]), (276,178,[2_1|2]), (276,245,[2_1|2, 1_1|2]), (276,257,[2_1|2, 1_1|2]), (276,267,[2_1|2, 1_1|2]), (276,282,[2_1|2, 1_1|2]), (276,301,[2_1|2, 1_1|2]), (276,315,[2_1|2, 1_1|2]), (276,122,[2_1|2]), (276,155,[2_1|2]), (276,188,[3_1|2]), (276,191,[0_1|2]), (276,195,[0_1|2]), (276,199,[3_1|2]), (276,203,[0_1|2]), (276,208,[0_1|2]), (276,213,[4_1|2]), (276,218,[0_1|2]), (276,223,[4_1|2]), (276,228,[3_1|2]), (276,232,[5_1|2]), (276,236,[0_1|2]), (276,241,[0_1|2]), (276,249,[5_1|2]), (276,253,[5_1|2]), (276,262,[5_1|2]), (276,272,[0_1|2]), (276,277,[4_1|2]), (276,287,[5_1|2]), (276,291,[3_1|2]), (276,296,[2_1|2]), (276,305,[3_1|2]), (276,310,[5_1|2]), (276,320,[4_1|2]), (276,343,[3_1|3]), (276,346,[0_1|3]), (276,350,[0_1|3]), (276,354,[3_1|3]), (276,358,[0_1|3]), (276,363,[0_1|3]), (276,368,[4_1|3]), (276,373,[1_1|3]), (276,378,[5_1|3]), (277,278,[5_1|2]), (278,279,[2_1|2]), (279,280,[1_1|2]), (280,281,[4_1|2]), (281,102,[4_1|2]), (281,106,[4_1|2]), (281,117,[4_1|2]), (281,135,[4_1|2]), (281,168,[4_1|2]), (281,178,[4_1|2]), (281,245,[4_1|2]), (281,257,[4_1|2]), (281,267,[4_1|2]), (281,282,[4_1|2]), (281,301,[4_1|2]), (281,315,[4_1|2]), (282,283,[5_1|2]), (283,284,[4_1|2]), (284,285,[2_1|2]), (285,286,[4_1|2]), (286,102,[5_1|2]), (286,106,[5_1|2]), (286,117,[5_1|2]), (286,135,[5_1|2]), (286,168,[5_1|2]), (286,178,[5_1|2]), (286,245,[5_1|2]), (286,257,[5_1|2]), (286,267,[5_1|2]), (286,282,[5_1|2]), (286,301,[5_1|2]), (286,315,[5_1|2]), (287,288,[5_1|2]), (288,289,[2_1|2]), (289,290,[3_1|2]), (290,102,[2_1|2]), (290,296,[2_1|2]), (290,254,[2_1|2]), (290,263,[2_1|2]), (290,289,[2_1|2]), (290,188,[3_1|2]), (290,191,[0_1|2]), (290,195,[0_1|2]), (290,199,[3_1|2]), (290,203,[0_1|2]), (290,208,[0_1|2]), (290,213,[4_1|2]), (290,218,[0_1|2]), (290,223,[4_1|2]), (290,228,[3_1|2]), (290,232,[5_1|2]), (290,236,[0_1|2]), (290,241,[0_1|2]), (290,245,[1_1|2]), (290,249,[5_1|2]), (290,253,[5_1|2]), (290,257,[1_1|2]), (290,262,[5_1|2]), (290,267,[1_1|2]), (290,272,[0_1|2]), (290,277,[4_1|2]), (290,282,[1_1|2]), (290,287,[5_1|2]), (290,291,[3_1|2]), (290,301,[1_1|2]), (290,305,[3_1|2]), (290,310,[5_1|2]), (290,315,[1_1|2]), (290,320,[4_1|2]), (290,343,[3_1|3]), (290,346,[0_1|3]), (290,350,[0_1|3]), (290,354,[3_1|3]), (290,358,[0_1|3]), (290,363,[0_1|3]), (290,368,[4_1|3]), (290,373,[1_1|3]), (290,378,[5_1|3]), (291,292,[2_1|2]), (292,293,[2_1|2]), (293,294,[4_1|2]), (294,295,[5_1|2]), (295,102,[1_1|2]), (295,106,[1_1|2]), (295,117,[1_1|2]), (295,135,[1_1|2]), (295,168,[1_1|2]), (295,178,[1_1|2]), (295,245,[1_1|2]), (295,257,[1_1|2]), (295,267,[1_1|2]), (295,282,[1_1|2]), (295,301,[1_1|2]), (295,315,[1_1|2]), (296,297,[4_1|2]), (297,298,[0_1|2]), (298,299,[2_1|2]), (299,300,[2_1|2]), (300,102,[1_1|2]), (300,296,[1_1|2]), (301,302,[0_1|2]), (302,303,[2_1|2]), (303,304,[4_1|2]), (304,102,[4_1|2]), (304,106,[4_1|2]), (304,117,[4_1|2]), (304,135,[4_1|2]), (304,168,[4_1|2]), (304,178,[4_1|2]), (304,245,[4_1|2]), (304,257,[4_1|2]), (304,267,[4_1|2]), (304,282,[4_1|2]), (304,301,[4_1|2]), (304,315,[4_1|2]), (304,122,[4_1|2]), (304,155,[4_1|2]), (305,306,[0_1|2]), (306,307,[0_1|2]), (307,308,[2_1|2]), (308,309,[4_1|2]), (309,102,[1_1|2]), (309,106,[1_1|2]), (309,117,[1_1|2]), (309,135,[1_1|2]), (309,168,[1_1|2]), (309,178,[1_1|2]), (309,245,[1_1|2]), (309,257,[1_1|2]), (309,267,[1_1|2]), (309,282,[1_1|2]), (309,301,[1_1|2]), (309,315,[1_1|2]), (309,122,[1_1|2]), (309,155,[1_1|2]), (310,311,[4_1|2]), (311,312,[0_1|2]), (312,313,[2_1|2]), (313,314,[1_1|2]), (314,102,[1_1|2]), (314,106,[1_1|2]), (314,117,[1_1|2]), (314,135,[1_1|2]), (314,168,[1_1|2]), (314,178,[1_1|2]), (314,245,[1_1|2]), (314,257,[1_1|2]), (314,267,[1_1|2]), (314,282,[1_1|2]), (314,301,[1_1|2]), (314,315,[1_1|2]), (314,122,[1_1|2]), (314,155,[1_1|2]), (315,316,[4_1|2]), (316,317,[5_1|2]), (317,318,[0_1|2]), (318,319,[4_1|2]), (319,102,[2_1|2]), (319,106,[2_1|2]), (319,117,[2_1|2]), (319,135,[2_1|2]), (319,168,[2_1|2]), (319,178,[2_1|2]), (319,245,[2_1|2, 1_1|2]), (319,257,[2_1|2, 1_1|2]), (319,267,[2_1|2, 1_1|2]), (319,282,[2_1|2, 1_1|2]), (319,301,[2_1|2, 1_1|2]), (319,315,[2_1|2, 1_1|2]), (319,188,[3_1|2]), (319,191,[0_1|2]), (319,195,[0_1|2]), (319,199,[3_1|2]), (319,203,[0_1|2]), (319,208,[0_1|2]), (319,213,[4_1|2]), (319,218,[0_1|2]), (319,223,[4_1|2]), (319,228,[3_1|2]), (319,232,[5_1|2]), (319,236,[0_1|2]), (319,241,[0_1|2]), (319,249,[5_1|2]), (319,253,[5_1|2]), (319,262,[5_1|2]), (319,272,[0_1|2]), (319,277,[4_1|2]), (319,287,[5_1|2]), (319,291,[3_1|2]), (319,296,[2_1|2]), (319,305,[3_1|2]), (319,310,[5_1|2]), (319,320,[4_1|2]), (319,343,[3_1|3]), (319,346,[0_1|3]), (319,350,[0_1|3]), (319,354,[3_1|3]), (319,358,[0_1|3]), (319,363,[0_1|3]), (319,368,[4_1|3]), (319,373,[1_1|3]), (319,378,[5_1|3]), (320,321,[2_1|2]), (321,322,[2_1|2]), (322,323,[3_1|2]), (323,324,[3_1|2]), (324,102,[1_1|2]), (324,106,[1_1|2]), (324,117,[1_1|2]), (324,135,[1_1|2]), (324,168,[1_1|2]), (324,178,[1_1|2]), (324,245,[1_1|2]), (324,257,[1_1|2]), (324,267,[1_1|2]), (324,282,[1_1|2]), (324,301,[1_1|2]), (324,315,[1_1|2]), (324,127,[1_1|2]), (325,326,[2_1|3]), (326,327,[4_1|3]), (327,328,[5_1|3]), (328,254,[3_1|3]), (328,263,[3_1|3]), (328,269,[3_1|3]), (329,330,[4_1|3]), (330,331,[2_1|3]), (331,332,[3_1|3]), (332,333,[0_1|3]), (333,254,[4_1|3]), (333,263,[4_1|3]), (333,269,[4_1|3]), (334,335,[4_1|3]), (335,336,[2_1|3]), (336,337,[3_1|3]), (337,338,[5_1|3]), (338,289,[0_1|3]), (339,340,[2_1|3]), (340,341,[2_1|3]), (341,342,[1_1|3]), (342,296,[5_1|3]), (343,344,[0_1|3]), (344,345,[2_1|3]), (345,122,[1_1|3]), (345,155,[1_1|3]), (346,347,[2_1|3]), (347,348,[1_1|3]), (348,349,[1_1|3]), (349,122,[4_1|3]), (349,155,[4_1|3]), (350,351,[3_1|3]), (351,352,[2_1|3]), (352,353,[4_1|3]), (353,122,[1_1|3]), (353,155,[1_1|3]), (354,355,[0_1|3]), (355,356,[2_1|3]), (356,357,[1_1|3]), (357,122,[4_1|3]), (357,155,[4_1|3]), (358,359,[2_1|3]), (359,360,[2_1|3]), (360,361,[3_1|3]), (361,362,[4_1|3]), (362,122,[1_1|3]), (362,155,[1_1|3]), (363,364,[3_1|3]), (364,365,[2_1|3]), (365,366,[3_1|3]), (366,367,[1_1|3]), (367,122,[1_1|3]), (367,155,[1_1|3]), (368,369,[0_1|3]), (369,370,[4_1|3]), (370,371,[2_1|3]), (371,372,[1_1|3]), (372,122,[4_1|3]), (372,155,[4_1|3]), (373,374,[5_1|3]), (374,375,[2_1|3]), (375,376,[2_1|3]), (376,377,[3_1|3]), (377,255,[1_1|3]), (377,264,[1_1|3]), (378,379,[5_1|3]), (379,380,[2_1|3]), (380,381,[3_1|3]), (381,289,[2_1|3])}"
----------------------------------------

(8)
BOUNDS(1, n^1)

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

(9) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
Transformed a relative TRS into a decreasing-loop problem.
----------------------------------------

(10)
Obligation:
Analyzing the following TRS for decreasing loops:

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


The TRS R consists of the following rules:

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

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

   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(3(x_1)) -> 3(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(5(x_1)) -> 5(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(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: INNERMOST
----------------------------------------

(11) DecreasingLoopProof (LOWER BOUND(ID))
The following loop(s) give(s) rise to the lower bound Omega(n^1):

The rewrite sequence

2(5(1(x1))) ->^+ 1(4(5(4(2(x1)))))

gives rise to a decreasing loop by considering the right hand sides subterm at position [0,0,0,0].

The pumping substitution is [x1 / 5(1(x1))].

The result substitution is [ ].




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

(12)
Complex Obligation (BEST)

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

(13)
Obligation:
Proved the lower bound n^1 for the following obligation:

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


The TRS R consists of the following rules:

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

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

   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(3(x_1)) -> 3(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(5(x_1)) -> 5(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(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: INNERMOST
----------------------------------------

(14) LowerBoundPropagationProof (FINISHED)
Propagated lower bound.
----------------------------------------

(15)
BOUNDS(n^1, INF)

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

(16)
Obligation:
Analyzing the following TRS for decreasing loops:

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


The TRS R consists of the following rules:

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

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

   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(3(x_1)) -> 3(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(5(x_1)) -> 5(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(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: INNERMOST