WORST_CASE(Omega(n^1), O(n^1))
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 112 ms]
(4) CpxRelTRS
(5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(6) CpxTRS
    (7) CpxTrsMatchBoundsProof [FINISHED, 103 ms]
    (8) BOUNDS(1, n^1)
(9) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 5 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(1(x1))) -> 0(1(2(3(4(1(x1))))))
   0(1(1(x1))) -> 1(3(1(3(4(0(x1))))))
   0(1(1(x1))) -> 5(1(3(0(3(1(x1))))))
   0(1(4(x1))) -> 0(1(3(4(x1))))
   0(1(4(x1))) -> 1(3(4(2(0(x1)))))
   0(1(4(x1))) -> 1(5(3(4(0(x1)))))
   0(1(4(x1))) -> 3(1(3(4(0(x1)))))
   0(1(4(x1))) -> 1(1(5(3(4(0(x1))))))
   0(1(4(x1))) -> 1(2(3(4(3(0(x1))))))
   0(1(4(x1))) -> 1(3(3(4(4(0(x1))))))
   0(1(4(x1))) -> 1(3(4(5(0(5(x1))))))
   0(1(4(x1))) -> 3(4(5(5(0(1(x1))))))
   1(2(4(x1))) -> 1(2(3(4(1(x1)))))
   1(2(4(x1))) -> 5(3(4(1(2(x1)))))
   1(2(4(x1))) -> 1(5(2(3(4(3(x1))))))
   1(2(4(x1))) -> 2(3(3(4(5(1(x1))))))
   5(2(1(x1))) -> 1(2(2(3(5(4(x1))))))
   5(2(1(x1))) -> 1(3(2(5(3(4(x1))))))
   5(2(4(x1))) -> 0(5(2(3(4(x1)))))
   5(2(4(x1))) -> 5(5(3(4(2(x1)))))
   5(2(4(x1))) -> 0(3(4(4(5(2(x1))))))
   5(2(4(x1))) -> 2(2(5(3(4(4(x1))))))
   5(2(4(x1))) -> 2(3(3(4(5(5(x1))))))
   5(2(4(x1))) -> 2(3(4(3(5(3(x1))))))
   5(2(4(x1))) -> 2(5(3(4(0(5(x1))))))
   5(2(4(x1))) -> 3(1(2(5(3(4(x1))))))
   5(2(4(x1))) -> 5(2(3(4(0(3(x1))))))
   0(0(2(4(x1)))) -> 0(4(3(0(2(x1)))))
   0(1(1(5(x1)))) -> 0(1(3(5(1(2(x1))))))
   0(1(2(4(x1)))) -> 0(1(2(3(3(4(x1))))))
   0(1(4(5(x1)))) -> 3(4(0(5(1(x1)))))
   0(1(4(5(x1)))) -> 3(4(5(3(0(1(x1))))))
   0(4(2(1(x1)))) -> 0(4(1(2(3(4(x1))))))
   0(5(1(4(x1)))) -> 0(0(3(5(4(1(x1))))))
   1(0(1(4(x1)))) -> 3(4(0(1(2(1(x1))))))
   1(1(2(4(x1)))) -> 1(3(4(1(2(x1)))))
   1(2(2(4(x1)))) -> 2(2(2(3(4(1(x1))))))
   1(2(4(2(x1)))) -> 1(2(3(4(2(3(x1))))))
   1(5(2(1(x1)))) -> 1(0(3(5(1(2(x1))))))
   1(5(2(4(x1)))) -> 3(2(3(5(1(4(x1))))))
   1(5(2(4(x1)))) -> 5(2(3(3(1(4(x1))))))
   5(0(1(4(x1)))) -> 3(4(0(5(3(1(x1))))))
   5(2(5(1(x1)))) -> 3(5(1(5(2(x1)))))
   0(1(1(5(4(x1))))) -> 0(0(5(4(1(1(x1))))))
   1(0(0(2(4(x1))))) -> 0(2(0(4(4(1(x1))))))
   1(0(4(2(1(x1))))) -> 1(2(3(4(1(0(x1))))))
   1(2(5(0(1(x1))))) -> 2(3(5(1(0(1(x1))))))
   1(5(3(0(4(x1))))) -> 5(1(3(4(0(4(x1))))))
   5(0(5(2(4(x1))))) -> 4(0(0(5(5(2(x1))))))
   5(3(2(4(2(x1))))) -> 2(1(5(3(4(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(2(x_1)) -> 2(encArg(x_1))
   encArg(3(x_1)) -> 3(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_1(x_1)) -> 1(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))
   encode_2(x_1) -> 2(encArg(x_1))
   encode_3(x_1) -> 3(encArg(x_1))
   encode_4(x_1) -> 4(encArg(x_1))
   encode_5(x_1) -> 5(encArg(x_1))


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

(2)
Obligation:
The Runtime Complexity (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(1(x1))) -> 0(1(2(3(4(1(x1))))))
   0(1(1(x1))) -> 1(3(1(3(4(0(x1))))))
   0(1(1(x1))) -> 5(1(3(0(3(1(x1))))))
   0(1(4(x1))) -> 0(1(3(4(x1))))
   0(1(4(x1))) -> 1(3(4(2(0(x1)))))
   0(1(4(x1))) -> 1(5(3(4(0(x1)))))
   0(1(4(x1))) -> 3(1(3(4(0(x1)))))
   0(1(4(x1))) -> 1(1(5(3(4(0(x1))))))
   0(1(4(x1))) -> 1(2(3(4(3(0(x1))))))
   0(1(4(x1))) -> 1(3(3(4(4(0(x1))))))
   0(1(4(x1))) -> 1(3(4(5(0(5(x1))))))
   0(1(4(x1))) -> 3(4(5(5(0(1(x1))))))
   1(2(4(x1))) -> 1(2(3(4(1(x1)))))
   1(2(4(x1))) -> 5(3(4(1(2(x1)))))
   1(2(4(x1))) -> 1(5(2(3(4(3(x1))))))
   1(2(4(x1))) -> 2(3(3(4(5(1(x1))))))
   5(2(1(x1))) -> 1(2(2(3(5(4(x1))))))
   5(2(1(x1))) -> 1(3(2(5(3(4(x1))))))
   5(2(4(x1))) -> 0(5(2(3(4(x1)))))
   5(2(4(x1))) -> 5(5(3(4(2(x1)))))
   5(2(4(x1))) -> 0(3(4(4(5(2(x1))))))
   5(2(4(x1))) -> 2(2(5(3(4(4(x1))))))
   5(2(4(x1))) -> 2(3(3(4(5(5(x1))))))
   5(2(4(x1))) -> 2(3(4(3(5(3(x1))))))
   5(2(4(x1))) -> 2(5(3(4(0(5(x1))))))
   5(2(4(x1))) -> 3(1(2(5(3(4(x1))))))
   5(2(4(x1))) -> 5(2(3(4(0(3(x1))))))
   0(0(2(4(x1)))) -> 0(4(3(0(2(x1)))))
   0(1(1(5(x1)))) -> 0(1(3(5(1(2(x1))))))
   0(1(2(4(x1)))) -> 0(1(2(3(3(4(x1))))))
   0(1(4(5(x1)))) -> 3(4(0(5(1(x1)))))
   0(1(4(5(x1)))) -> 3(4(5(3(0(1(x1))))))
   0(4(2(1(x1)))) -> 0(4(1(2(3(4(x1))))))
   0(5(1(4(x1)))) -> 0(0(3(5(4(1(x1))))))
   1(0(1(4(x1)))) -> 3(4(0(1(2(1(x1))))))
   1(1(2(4(x1)))) -> 1(3(4(1(2(x1)))))
   1(2(2(4(x1)))) -> 2(2(2(3(4(1(x1))))))
   1(2(4(2(x1)))) -> 1(2(3(4(2(3(x1))))))
   1(5(2(1(x1)))) -> 1(0(3(5(1(2(x1))))))
   1(5(2(4(x1)))) -> 3(2(3(5(1(4(x1))))))
   1(5(2(4(x1)))) -> 5(2(3(3(1(4(x1))))))
   5(0(1(4(x1)))) -> 3(4(0(5(3(1(x1))))))
   5(2(5(1(x1)))) -> 3(5(1(5(2(x1)))))
   0(1(1(5(4(x1))))) -> 0(0(5(4(1(1(x1))))))
   1(0(0(2(4(x1))))) -> 0(2(0(4(4(1(x1))))))
   1(0(4(2(1(x1))))) -> 1(2(3(4(1(0(x1))))))
   1(2(5(0(1(x1))))) -> 2(3(5(1(0(1(x1))))))
   1(5(3(0(4(x1))))) -> 5(1(3(4(0(4(x1))))))
   5(0(5(2(4(x1))))) -> 4(0(0(5(5(2(x1))))))
   5(3(2(4(2(x1))))) -> 2(1(5(3(4(2(x1))))))

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

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

Rewrite Strategy: 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(1(x1))) -> 0(1(2(3(4(1(x1))))))
   0(1(1(x1))) -> 1(3(1(3(4(0(x1))))))
   0(1(1(x1))) -> 5(1(3(0(3(1(x1))))))
   0(1(4(x1))) -> 0(1(3(4(x1))))
   0(1(4(x1))) -> 1(3(4(2(0(x1)))))
   0(1(4(x1))) -> 1(5(3(4(0(x1)))))
   0(1(4(x1))) -> 3(1(3(4(0(x1)))))
   0(1(4(x1))) -> 1(1(5(3(4(0(x1))))))
   0(1(4(x1))) -> 1(2(3(4(3(0(x1))))))
   0(1(4(x1))) -> 1(3(3(4(4(0(x1))))))
   0(1(4(x1))) -> 1(3(4(5(0(5(x1))))))
   0(1(4(x1))) -> 3(4(5(5(0(1(x1))))))
   1(2(4(x1))) -> 1(2(3(4(1(x1)))))
   1(2(4(x1))) -> 5(3(4(1(2(x1)))))
   1(2(4(x1))) -> 1(5(2(3(4(3(x1))))))
   1(2(4(x1))) -> 2(3(3(4(5(1(x1))))))
   5(2(1(x1))) -> 1(2(2(3(5(4(x1))))))
   5(2(1(x1))) -> 1(3(2(5(3(4(x1))))))
   5(2(4(x1))) -> 0(5(2(3(4(x1)))))
   5(2(4(x1))) -> 5(5(3(4(2(x1)))))
   5(2(4(x1))) -> 0(3(4(4(5(2(x1))))))
   5(2(4(x1))) -> 2(2(5(3(4(4(x1))))))
   5(2(4(x1))) -> 2(3(3(4(5(5(x1))))))
   5(2(4(x1))) -> 2(3(4(3(5(3(x1))))))
   5(2(4(x1))) -> 2(5(3(4(0(5(x1))))))
   5(2(4(x1))) -> 3(1(2(5(3(4(x1))))))
   5(2(4(x1))) -> 5(2(3(4(0(3(x1))))))
   0(0(2(4(x1)))) -> 0(4(3(0(2(x1)))))
   0(1(1(5(x1)))) -> 0(1(3(5(1(2(x1))))))
   0(1(2(4(x1)))) -> 0(1(2(3(3(4(x1))))))
   0(1(4(5(x1)))) -> 3(4(0(5(1(x1)))))
   0(1(4(5(x1)))) -> 3(4(5(3(0(1(x1))))))
   0(4(2(1(x1)))) -> 0(4(1(2(3(4(x1))))))
   0(5(1(4(x1)))) -> 0(0(3(5(4(1(x1))))))
   1(0(1(4(x1)))) -> 3(4(0(1(2(1(x1))))))
   1(1(2(4(x1)))) -> 1(3(4(1(2(x1)))))
   1(2(2(4(x1)))) -> 2(2(2(3(4(1(x1))))))
   1(2(4(2(x1)))) -> 1(2(3(4(2(3(x1))))))
   1(5(2(1(x1)))) -> 1(0(3(5(1(2(x1))))))
   1(5(2(4(x1)))) -> 3(2(3(5(1(4(x1))))))
   1(5(2(4(x1)))) -> 5(2(3(3(1(4(x1))))))
   5(0(1(4(x1)))) -> 3(4(0(5(3(1(x1))))))
   5(2(5(1(x1)))) -> 3(5(1(5(2(x1)))))
   0(1(1(5(4(x1))))) -> 0(0(5(4(1(1(x1))))))
   1(0(0(2(4(x1))))) -> 0(2(0(4(4(1(x1))))))
   1(0(4(2(1(x1))))) -> 1(2(3(4(1(0(x1))))))
   1(2(5(0(1(x1))))) -> 2(3(5(1(0(1(x1))))))
   1(5(3(0(4(x1))))) -> 5(1(3(4(0(4(x1))))))
   5(0(5(2(4(x1))))) -> 4(0(0(5(5(2(x1))))))
   5(3(2(4(2(x1))))) -> 2(1(5(3(4(2(x1))))))

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

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

Rewrite Strategy: 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(1(x1))) -> 0(1(2(3(4(1(x1))))))
   0(1(1(x1))) -> 1(3(1(3(4(0(x1))))))
   0(1(1(x1))) -> 5(1(3(0(3(1(x1))))))
   0(1(4(x1))) -> 0(1(3(4(x1))))
   0(1(4(x1))) -> 1(3(4(2(0(x1)))))
   0(1(4(x1))) -> 1(5(3(4(0(x1)))))
   0(1(4(x1))) -> 3(1(3(4(0(x1)))))
   0(1(4(x1))) -> 1(1(5(3(4(0(x1))))))
   0(1(4(x1))) -> 1(2(3(4(3(0(x1))))))
   0(1(4(x1))) -> 1(3(3(4(4(0(x1))))))
   0(1(4(x1))) -> 1(3(4(5(0(5(x1))))))
   0(1(4(x1))) -> 3(4(5(5(0(1(x1))))))
   1(2(4(x1))) -> 1(2(3(4(1(x1)))))
   1(2(4(x1))) -> 5(3(4(1(2(x1)))))
   1(2(4(x1))) -> 1(5(2(3(4(3(x1))))))
   1(2(4(x1))) -> 2(3(3(4(5(1(x1))))))
   5(2(1(x1))) -> 1(2(2(3(5(4(x1))))))
   5(2(1(x1))) -> 1(3(2(5(3(4(x1))))))
   5(2(4(x1))) -> 0(5(2(3(4(x1)))))
   5(2(4(x1))) -> 5(5(3(4(2(x1)))))
   5(2(4(x1))) -> 0(3(4(4(5(2(x1))))))
   5(2(4(x1))) -> 2(2(5(3(4(4(x1))))))
   5(2(4(x1))) -> 2(3(3(4(5(5(x1))))))
   5(2(4(x1))) -> 2(3(4(3(5(3(x1))))))
   5(2(4(x1))) -> 2(5(3(4(0(5(x1))))))
   5(2(4(x1))) -> 3(1(2(5(3(4(x1))))))
   5(2(4(x1))) -> 5(2(3(4(0(3(x1))))))
   0(0(2(4(x1)))) -> 0(4(3(0(2(x1)))))
   0(1(1(5(x1)))) -> 0(1(3(5(1(2(x1))))))
   0(1(2(4(x1)))) -> 0(1(2(3(3(4(x1))))))
   0(1(4(5(x1)))) -> 3(4(0(5(1(x1)))))
   0(1(4(5(x1)))) -> 3(4(5(3(0(1(x1))))))
   0(4(2(1(x1)))) -> 0(4(1(2(3(4(x1))))))
   0(5(1(4(x1)))) -> 0(0(3(5(4(1(x1))))))
   1(0(1(4(x1)))) -> 3(4(0(1(2(1(x1))))))
   1(1(2(4(x1)))) -> 1(3(4(1(2(x1)))))
   1(2(2(4(x1)))) -> 2(2(2(3(4(1(x1))))))
   1(2(4(2(x1)))) -> 1(2(3(4(2(3(x1))))))
   1(5(2(1(x1)))) -> 1(0(3(5(1(2(x1))))))
   1(5(2(4(x1)))) -> 3(2(3(5(1(4(x1))))))
   1(5(2(4(x1)))) -> 5(2(3(3(1(4(x1))))))
   5(0(1(4(x1)))) -> 3(4(0(5(3(1(x1))))))
   5(2(5(1(x1)))) -> 3(5(1(5(2(x1)))))
   0(1(1(5(4(x1))))) -> 0(0(5(4(1(1(x1))))))
   1(0(0(2(4(x1))))) -> 0(2(0(4(4(1(x1))))))
   1(0(4(2(1(x1))))) -> 1(2(3(4(1(0(x1))))))
   1(2(5(0(1(x1))))) -> 2(3(5(1(0(1(x1))))))
   1(5(3(0(4(x1))))) -> 5(1(3(4(0(4(x1))))))
   5(0(5(2(4(x1))))) -> 4(0(0(5(5(2(x1))))))
   5(3(2(4(2(x1))))) -> 2(1(5(3(4(2(x1))))))
   encArg(2(x_1)) -> 2(encArg(x_1))
   encArg(3(x_1)) -> 3(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_1(x_1)) -> 1(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))
   encode_2(x_1) -> 2(encArg(x_1))
   encode_3(x_1) -> 3(encArg(x_1))
   encode_4(x_1) -> 4(encArg(x_1))
   encode_5(x_1) -> 5(encArg(x_1))

S is empty.
Rewrite Strategy: 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.

"[59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 580, 581, 582, 583, 584]
{(59,60,[0_1|0, 1_1|0, 5_1|0, encArg_1|0, encode_0_1|0, encode_1_1|0, encode_2_1|0, encode_3_1|0, encode_4_1|0, encode_5_1|0]), (59,61,[1_1|1]), (59,65,[5_1|1]), (59,69,[1_1|1]), (59,74,[2_1|1]), (59,79,[1_1|1]), (59,84,[2_1|1]), (59,89,[0_1|1]), (59,93,[5_1|1]), (59,97,[0_1|1]), (59,102,[2_1|1]), (59,107,[2_1|1]), (59,112,[2_1|1]), (59,117,[2_1|1]), (59,122,[3_1|1]), (59,127,[5_1|1]), (59,132,[2_1|1]), (59,137,[2_1|1, 3_1|1, 4_1|1, 0_1|1, 1_1|1, 5_1|1]), (59,138,[0_1|2]), (59,143,[1_1|2]), (59,148,[5_1|2]), (59,153,[0_1|2]), (59,158,[0_1|2]), (59,163,[0_1|2]), (59,166,[1_1|2]), (59,170,[1_1|2]), (59,174,[3_1|2]), (59,178,[1_1|2]), (59,183,[1_1|2]), (59,188,[1_1|2]), (59,193,[1_1|2]), (59,198,[3_1|2]), (59,203,[3_1|2]), (59,207,[3_1|2]), (59,212,[0_1|2]), (59,217,[0_1|2]), (59,221,[0_1|2]), (59,226,[0_1|2]), (59,231,[1_1|2]), (59,235,[5_1|2]), (59,239,[1_1|2]), (59,244,[2_1|2]), (59,249,[1_1|2]), (59,254,[2_1|2]), (59,259,[2_1|2]), (59,264,[3_1|2]), (59,269,[0_1|2]), (59,274,[1_1|2]), (59,279,[1_1|2]), (59,283,[1_1|2]), (59,288,[3_1|2]), (59,293,[5_1|2]), (59,298,[5_1|2]), (59,303,[1_1|2]), (59,308,[1_1|2]), (59,313,[0_1|2]), (59,317,[5_1|2]), (59,321,[0_1|2]), (59,326,[2_1|2]), (59,331,[2_1|2]), (59,336,[2_1|2]), (59,341,[2_1|2]), (59,346,[3_1|2]), (59,351,[5_1|2]), (59,356,[3_1|2]), (59,360,[3_1|2]), (59,365,[4_1|2]), (59,370,[2_1|2]), (60,60,[2_1|0, 3_1|0, 4_1|0, cons_0_1|0, cons_1_1|0, cons_5_1|0]), (61,62,[2_1|1]), (62,63,[3_1|1]), (63,64,[4_1|1]), (64,60,[1_1|1]), (64,61,[1_1|1]), (64,65,[5_1|1]), (64,69,[1_1|1]), (64,74,[2_1|1]), (64,79,[1_1|1]), (64,84,[2_1|1]), (65,66,[3_1|1]), (66,67,[4_1|1]), (67,68,[1_1|1]), (67,61,[1_1|1]), (67,65,[5_1|1]), (67,69,[1_1|1]), (67,74,[2_1|1]), (67,79,[1_1|1]), (67,84,[2_1|1]), (68,60,[2_1|1]), (69,70,[5_1|1]), (70,71,[2_1|1]), (71,72,[3_1|1]), (72,73,[4_1|1]), (73,60,[3_1|1]), (74,75,[3_1|1]), (75,76,[3_1|1]), (76,77,[4_1|1]), (77,78,[5_1|1]), (78,60,[1_1|1]), (78,61,[1_1|1]), (78,65,[5_1|1]), (78,69,[1_1|1]), (78,74,[2_1|1]), (78,79,[1_1|1]), (78,84,[2_1|1]), (79,80,[2_1|1]), (80,81,[3_1|1]), (81,82,[4_1|1]), (82,83,[2_1|1]), (83,60,[3_1|1]), (84,85,[2_1|1]), (85,86,[2_1|1]), (86,87,[3_1|1]), (87,88,[4_1|1]), (88,60,[1_1|1]), (88,61,[1_1|1]), (88,65,[5_1|1]), (88,69,[1_1|1]), (88,74,[2_1|1]), (88,79,[1_1|1]), (88,84,[2_1|1]), (89,90,[5_1|1]), (90,91,[2_1|1]), (91,92,[3_1|1]), (92,60,[4_1|1]), (93,94,[5_1|1]), (94,95,[3_1|1]), (95,96,[4_1|1]), (96,60,[2_1|1]), (97,98,[3_1|1]), (98,99,[4_1|1]), (99,100,[4_1|1]), (100,101,[5_1|1]), (100,89,[0_1|1]), (100,93,[5_1|1]), (100,97,[0_1|1]), (100,102,[2_1|1]), (100,107,[2_1|1]), (100,112,[2_1|1]), (100,117,[2_1|1]), (100,122,[3_1|1]), (100,127,[5_1|1]), (101,60,[2_1|1]), (102,103,[2_1|1]), (103,104,[5_1|1]), (104,105,[3_1|1]), (105,106,[4_1|1]), (106,60,[4_1|1]), (107,108,[3_1|1]), (108,109,[3_1|1]), (109,110,[4_1|1]), (110,111,[5_1|1]), (110,375,[1_1|2]), (110,380,[1_1|2]), (111,60,[5_1|1]), (111,89,[0_1|1]), (111,93,[5_1|1]), (111,97,[0_1|1]), (111,102,[2_1|1]), (111,107,[2_1|1]), (111,112,[2_1|1]), (111,117,[2_1|1]), (111,122,[3_1|1]), (111,127,[5_1|1]), (111,132,[2_1|1]), (112,113,[3_1|1]), (113,114,[4_1|1]), (114,115,[3_1|1]), (115,116,[5_1|1]), (115,132,[2_1|1]), (116,60,[3_1|1]), (117,118,[5_1|1]), (118,119,[3_1|1]), (119,120,[4_1|1]), (120,121,[0_1|1]), (121,60,[5_1|1]), (121,89,[0_1|1]), (121,93,[5_1|1]), (121,97,[0_1|1]), (121,102,[2_1|1]), (121,107,[2_1|1]), (121,112,[2_1|1]), (121,117,[2_1|1]), (121,122,[3_1|1]), (121,127,[5_1|1]), (121,132,[2_1|1]), (122,123,[1_1|1]), (123,124,[2_1|1]), (124,125,[5_1|1]), (125,126,[3_1|1]), (126,60,[4_1|1]), (127,128,[2_1|1]), (128,129,[3_1|1]), (129,130,[4_1|1]), (130,131,[0_1|1]), (131,60,[3_1|1]), (132,133,[1_1|1]), (133,134,[5_1|1]), (134,135,[3_1|1]), (135,136,[4_1|1]), (136,60,[2_1|1]), (137,60,[encArg_1|1]), (137,137,[2_1|1, 3_1|1, 4_1|1, 0_1|1, 1_1|1, 5_1|1]), (137,138,[0_1|2]), (137,143,[1_1|2]), (137,148,[5_1|2]), (137,153,[0_1|2]), (137,158,[0_1|2]), (137,163,[0_1|2]), (137,166,[1_1|2]), (137,170,[1_1|2]), (137,174,[3_1|2]), (137,178,[1_1|2]), (137,183,[1_1|2]), (137,188,[1_1|2]), (137,193,[1_1|2]), (137,198,[3_1|2]), (137,203,[3_1|2]), (137,207,[3_1|2]), (137,212,[0_1|2]), (137,217,[0_1|2]), (137,221,[0_1|2]), (137,226,[0_1|2]), (137,231,[1_1|2]), (137,235,[5_1|2]), (137,239,[1_1|2]), (137,244,[2_1|2]), (137,249,[1_1|2]), (137,254,[2_1|2]), (137,259,[2_1|2]), (137,264,[3_1|2]), (137,269,[0_1|2]), (137,274,[1_1|2]), (137,279,[1_1|2]), (137,283,[1_1|2]), (137,288,[3_1|2]), (137,293,[5_1|2]), (137,298,[5_1|2]), (137,303,[1_1|2]), (137,308,[1_1|2]), (137,313,[0_1|2]), (137,317,[5_1|2]), (137,321,[0_1|2]), (137,326,[2_1|2]), (137,331,[2_1|2]), (137,336,[2_1|2]), (137,341,[2_1|2]), (137,346,[3_1|2]), (137,351,[5_1|2]), (137,356,[3_1|2]), (137,360,[3_1|2]), (137,365,[4_1|2]), (137,370,[2_1|2]), (138,139,[1_1|2]), (139,140,[2_1|2]), (140,141,[3_1|2]), (141,142,[4_1|2]), (142,137,[1_1|2]), (142,143,[1_1|2]), (142,166,[1_1|2]), (142,170,[1_1|2]), (142,178,[1_1|2]), (142,183,[1_1|2]), (142,188,[1_1|2]), (142,193,[1_1|2]), (142,231,[1_1|2]), (142,239,[1_1|2]), (142,249,[1_1|2]), (142,274,[1_1|2]), (142,279,[1_1|2]), (142,283,[1_1|2]), (142,303,[1_1|2]), (142,308,[1_1|2]), (142,179,[1_1|2]), (142,235,[5_1|2]), (142,244,[2_1|2]), (142,254,[2_1|2]), (142,259,[2_1|2]), (142,264,[3_1|2]), (142,269,[0_1|2]), (142,288,[3_1|2]), (142,293,[5_1|2]), (142,298,[5_1|2]), (143,144,[3_1|2]), (144,145,[1_1|2]), (145,146,[3_1|2]), (146,147,[4_1|2]), (147,137,[0_1|2]), (147,143,[0_1|2, 1_1|2]), (147,166,[0_1|2, 1_1|2]), (147,170,[0_1|2, 1_1|2]), (147,178,[0_1|2, 1_1|2]), (147,183,[0_1|2, 1_1|2]), (147,188,[0_1|2, 1_1|2]), (147,193,[0_1|2, 1_1|2]), (147,231,[0_1|2]), (147,239,[0_1|2]), (147,249,[0_1|2]), (147,274,[0_1|2]), (147,279,[0_1|2]), (147,283,[0_1|2]), (147,303,[0_1|2]), (147,308,[0_1|2]), (147,179,[0_1|2]), (147,138,[0_1|2]), (147,148,[5_1|2]), (147,153,[0_1|2]), (147,158,[0_1|2]), (147,163,[0_1|2]), (147,174,[3_1|2]), (147,198,[3_1|2]), (147,203,[3_1|2]), (147,207,[3_1|2]), (147,212,[0_1|2]), (147,217,[0_1|2]), (147,221,[0_1|2]), (147,226,[0_1|2]), (147,385,[0_1|3]), (147,390,[1_1|3]), (147,395,[5_1|3]), (147,400,[0_1|3]), (148,149,[1_1|2]), (149,150,[3_1|2]), (150,151,[0_1|2]), (151,152,[3_1|2]), (152,137,[1_1|2]), (152,143,[1_1|2]), (152,166,[1_1|2]), (152,170,[1_1|2]), (152,178,[1_1|2]), (152,183,[1_1|2]), (152,188,[1_1|2]), (152,193,[1_1|2]), (152,231,[1_1|2]), (152,239,[1_1|2]), (152,249,[1_1|2]), (152,274,[1_1|2]), (152,279,[1_1|2]), (152,283,[1_1|2]), (152,303,[1_1|2]), (152,308,[1_1|2]), (152,179,[1_1|2]), (152,235,[5_1|2]), (152,244,[2_1|2]), (152,254,[2_1|2]), (152,259,[2_1|2]), (152,264,[3_1|2]), (152,269,[0_1|2]), (152,288,[3_1|2]), (152,293,[5_1|2]), (152,298,[5_1|2]), (153,154,[1_1|2]), (154,155,[3_1|2]), (155,156,[5_1|2]), (156,157,[1_1|2]), (156,231,[1_1|2]), (156,235,[5_1|2]), (156,239,[1_1|2]), (156,244,[2_1|2]), (156,249,[1_1|2]), (156,254,[2_1|2]), (156,259,[2_1|2]), (156,405,[1_1|3]), (156,409,[5_1|3]), (156,413,[1_1|3]), (156,418,[2_1|3]), (157,137,[2_1|2]), (157,148,[2_1|2]), (157,235,[2_1|2]), (157,293,[2_1|2]), (157,298,[2_1|2]), (157,317,[2_1|2]), (157,351,[2_1|2]), (157,171,[2_1|2]), (157,240,[2_1|2]), (157,180,[2_1|2]), (158,159,[0_1|2]), (159,160,[5_1|2]), (160,161,[4_1|2]), (161,162,[1_1|2]), (161,279,[1_1|2]), (162,137,[1_1|2]), (162,365,[1_1|2]), (162,231,[1_1|2]), (162,235,[5_1|2]), (162,239,[1_1|2]), (162,244,[2_1|2]), (162,249,[1_1|2]), (162,254,[2_1|2]), (162,259,[2_1|2]), (162,264,[3_1|2]), (162,269,[0_1|2]), (162,274,[1_1|2]), (162,279,[1_1|2]), (162,283,[1_1|2]), (162,288,[3_1|2]), (162,293,[5_1|2]), (162,298,[5_1|2]), (163,164,[1_1|2]), (164,165,[3_1|2]), (165,137,[4_1|2]), (165,365,[4_1|2]), (166,167,[3_1|2]), (167,168,[4_1|2]), (168,169,[2_1|2]), (169,137,[0_1|2]), (169,365,[0_1|2]), (169,138,[0_1|2]), (169,143,[1_1|2]), (169,148,[5_1|2]), (169,153,[0_1|2]), (169,158,[0_1|2]), (169,163,[0_1|2]), (169,166,[1_1|2]), (169,170,[1_1|2]), (169,174,[3_1|2]), (169,178,[1_1|2]), (169,183,[1_1|2]), (169,188,[1_1|2]), (169,193,[1_1|2]), (169,198,[3_1|2]), (169,203,[3_1|2]), (169,207,[3_1|2]), (169,212,[0_1|2]), (169,217,[0_1|2]), (169,221,[0_1|2]), (169,226,[0_1|2]), (169,385,[0_1|3]), (169,390,[1_1|3]), (169,395,[5_1|3]), (169,400,[0_1|3]), (170,171,[5_1|2]), (171,172,[3_1|2]), (172,173,[4_1|2]), (173,137,[0_1|2]), (173,365,[0_1|2]), (173,138,[0_1|2]), (173,143,[1_1|2]), (173,148,[5_1|2]), (173,153,[0_1|2]), (173,158,[0_1|2]), (173,163,[0_1|2]), (173,166,[1_1|2]), (173,170,[1_1|2]), (173,174,[3_1|2]), (173,178,[1_1|2]), (173,183,[1_1|2]), (173,188,[1_1|2]), (173,193,[1_1|2]), (173,198,[3_1|2]), (173,203,[3_1|2]), (173,207,[3_1|2]), (173,212,[0_1|2]), (173,217,[0_1|2]), (173,221,[0_1|2]), (173,226,[0_1|2]), (173,385,[0_1|3]), (173,390,[1_1|3]), (173,395,[5_1|3]), (173,400,[0_1|3]), (174,175,[1_1|2]), (175,176,[3_1|2]), (176,177,[4_1|2]), (177,137,[0_1|2]), (177,365,[0_1|2]), (177,138,[0_1|2]), (177,143,[1_1|2]), 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(333,334,[4_1|2]), (334,335,[5_1|2]), (334,423,[1_1|3]), (334,428,[1_1|3]), (335,137,[5_1|2]), (335,365,[5_1|2, 4_1|2]), (335,303,[1_1|2]), (335,308,[1_1|2]), (335,313,[0_1|2]), (335,317,[5_1|2]), (335,321,[0_1|2]), (335,326,[2_1|2]), (335,331,[2_1|2]), (335,336,[2_1|2]), (335,341,[2_1|2]), (335,346,[3_1|2]), (335,351,[5_1|2]), (335,356,[3_1|2]), (335,360,[3_1|2]), (335,370,[2_1|2]), (335,423,[1_1|3]), (335,428,[1_1|3]), (336,337,[3_1|2]), (337,338,[4_1|2]), (338,339,[3_1|2]), (339,340,[5_1|2]), (339,370,[2_1|2]), (340,137,[3_1|2]), (340,365,[3_1|2]), (341,342,[5_1|2]), (342,343,[3_1|2]), (343,344,[4_1|2]), (344,345,[0_1|2]), (344,226,[0_1|2]), (345,137,[5_1|2]), (345,365,[5_1|2, 4_1|2]), (345,303,[1_1|2]), (345,308,[1_1|2]), (345,313,[0_1|2]), (345,317,[5_1|2]), (345,321,[0_1|2]), (345,326,[2_1|2]), (345,331,[2_1|2]), (345,336,[2_1|2]), (345,341,[2_1|2]), (345,346,[3_1|2]), (345,351,[5_1|2]), (345,356,[3_1|2]), (345,360,[3_1|2]), (345,370,[2_1|2]), (345,423,[1_1|3]), (345,428,[1_1|3]), (346,347,[1_1|2]), (347,348,[2_1|2]), (348,349,[5_1|2]), (349,350,[3_1|2]), (350,137,[4_1|2]), (350,365,[4_1|2]), (351,352,[2_1|2]), (352,353,[3_1|2]), (353,354,[4_1|2]), (354,355,[0_1|2]), (355,137,[3_1|2]), (355,365,[3_1|2]), (356,357,[5_1|2]), (357,358,[1_1|2]), (357,283,[1_1|2]), (357,288,[3_1|2]), (357,293,[5_1|2]), (357,570,[1_1|3]), (357,575,[3_1|3]), (357,580,[5_1|3]), (358,359,[5_1|2]), (358,303,[1_1|2]), (358,308,[1_1|2]), (358,313,[0_1|2]), (358,317,[5_1|2]), (358,321,[0_1|2]), (358,326,[2_1|2]), (358,331,[2_1|2]), (358,336,[2_1|2]), (358,341,[2_1|2]), (358,346,[3_1|2]), (358,351,[5_1|2]), (358,356,[3_1|2]), (358,513,[1_1|3]), (358,518,[1_1|3]), (358,523,[3_1|3]), (358,527,[0_1|3]), (358,531,[5_1|3]), (358,535,[0_1|3]), (358,540,[2_1|3]), (358,545,[2_1|3]), (358,550,[2_1|3]), (358,555,[2_1|3]), (358,560,[3_1|3]), (358,565,[5_1|3]), (359,137,[2_1|2]), (359,143,[2_1|2]), (359,166,[2_1|2]), (359,170,[2_1|2]), (359,178,[2_1|2]), (359,183,[2_1|2]), (359,188,[2_1|2]), (359,193,[2_1|2]), (359,231,[2_1|2]), (359,239,[2_1|2]), (359,249,[2_1|2]), (359,274,[2_1|2]), (359,279,[2_1|2]), (359,283,[2_1|2]), (359,303,[2_1|2]), (359,308,[2_1|2]), (359,149,[2_1|2]), (359,299,[2_1|2]), (360,361,[4_1|2]), (361,362,[0_1|2]), (362,363,[5_1|2]), (363,364,[3_1|2]), (364,137,[1_1|2]), (364,365,[1_1|2]), (364,231,[1_1|2]), (364,235,[5_1|2]), (364,239,[1_1|2]), (364,244,[2_1|2]), (364,249,[1_1|2]), (364,254,[2_1|2]), (364,259,[2_1|2]), (364,264,[3_1|2]), (364,269,[0_1|2]), (364,274,[1_1|2]), (364,279,[1_1|2]), (364,283,[1_1|2]), (364,288,[3_1|2]), (364,293,[5_1|2]), (364,298,[5_1|2]), (365,366,[0_1|2]), (366,367,[0_1|2]), (367,368,[5_1|2]), (368,369,[5_1|2]), (368,303,[1_1|2]), (368,308,[1_1|2]), (368,313,[0_1|2]), (368,317,[5_1|2]), (368,321,[0_1|2]), (368,326,[2_1|2]), (368,331,[2_1|2]), (368,336,[2_1|2]), (368,341,[2_1|2]), (368,346,[3_1|2]), (368,351,[5_1|2]), (368,356,[3_1|2]), (368,513,[1_1|3]), (368,518,[1_1|3]), (368,523,[3_1|3]), (368,527,[0_1|3]), (368,531,[5_1|3]), (368,535,[0_1|3]), (368,540,[2_1|3]), (368,545,[2_1|3]), (368,550,[2_1|3]), (368,555,[2_1|3]), (368,560,[3_1|3]), (368,565,[5_1|3]), (369,137,[2_1|2]), (369,365,[2_1|2]), (370,371,[1_1|2]), (371,372,[5_1|2]), (372,373,[3_1|2]), (373,374,[4_1|2]), (374,137,[2_1|2]), (374,244,[2_1|2]), (374,254,[2_1|2]), (374,259,[2_1|2]), (374,326,[2_1|2]), (374,331,[2_1|2]), (374,336,[2_1|2]), (374,341,[2_1|2]), (374,370,[2_1|2]), (375,376,[2_1|2]), (376,377,[2_1|2]), (377,378,[3_1|2]), (378,379,[5_1|2]), (379,133,[4_1|2]), (380,381,[3_1|2]), (381,382,[2_1|2]), (382,383,[5_1|2]), (383,384,[3_1|2]), (384,133,[4_1|2]), (385,386,[1_1|3]), (386,387,[2_1|3]), (387,388,[3_1|3]), (388,389,[4_1|3]), (389,179,[1_1|3]), (390,391,[3_1|3]), (391,392,[1_1|3]), (392,393,[3_1|3]), (393,394,[4_1|3]), (394,179,[0_1|3]), (395,396,[1_1|3]), (396,397,[3_1|3]), (397,398,[0_1|3]), (398,399,[3_1|3]), (399,179,[1_1|3]), (400,401,[1_1|3]), (401,402,[3_1|3]), (402,403,[5_1|3]), (403,404,[1_1|3]), (404,180,[2_1|3]), (405,406,[2_1|3]), (406,407,[3_1|3]), (407,408,[4_1|3]), (408,365,[1_1|3]), (409,410,[3_1|3]), (410,411,[4_1|3]), (411,412,[1_1|3]), (412,365,[2_1|3]), (413,414,[5_1|3]), (414,415,[2_1|3]), (415,416,[3_1|3]), (416,417,[4_1|3]), (417,365,[3_1|3]), (418,419,[3_1|3]), (419,420,[3_1|3]), (420,421,[4_1|3]), (421,422,[5_1|3]), (422,365,[1_1|3]), (423,424,[2_1|3]), (424,425,[2_1|3]), (425,426,[3_1|3]), (426,427,[5_1|3]), (427,371,[4_1|3]), (428,429,[3_1|3]), (429,430,[2_1|3]), (430,431,[5_1|3]), (431,432,[3_1|3]), (432,371,[4_1|3]), (433,434,[4_1|3]), (434,435,[0_1|3]), (435,436,[5_1|3]), (436,437,[3_1|3]), (437,365,[1_1|3]), (438,439,[1_1|3]), (439,440,[2_1|3]), (440,441,[3_1|3]), (441,442,[4_1|3]), (442,143,[1_1|3]), (442,166,[1_1|3]), (442,170,[1_1|3]), (442,178,[1_1|3]), (442,183,[1_1|3]), (442,188,[1_1|3]), (442,193,[1_1|3]), (442,231,[1_1|3]), (442,239,[1_1|3]), (442,249,[1_1|3]), (442,274,[1_1|3]), (442,279,[1_1|3]), (442,283,[1_1|3]), (442,303,[1_1|3]), (442,308,[1_1|3]), (442,149,[1_1|3]), (442,299,[1_1|3]), (442,179,[1_1|3]), (443,444,[3_1|3]), (444,445,[1_1|3]), (445,446,[3_1|3]), (446,447,[4_1|3]), (447,143,[0_1|3]), (447,166,[0_1|3]), (447,170,[0_1|3]), (447,178,[0_1|3]), (447,183,[0_1|3]), (447,188,[0_1|3]), (447,193,[0_1|3]), (447,231,[0_1|3]), (447,239,[0_1|3]), (447,249,[0_1|3]), (447,274,[0_1|3]), (447,279,[0_1|3]), (447,283,[0_1|3]), (447,303,[0_1|3]), (447,308,[0_1|3]), (447,149,[0_1|3]), (447,299,[0_1|3]), (447,179,[0_1|3]), (448,449,[1_1|3]), (449,450,[3_1|3]), (450,451,[0_1|3]), (451,452,[3_1|3]), (452,143,[1_1|3]), (452,166,[1_1|3]), (452,170,[1_1|3]), (452,178,[1_1|3]), (452,183,[1_1|3]), (452,188,[1_1|3]), (452,193,[1_1|3]), (452,231,[1_1|3]), (452,239,[1_1|3]), (452,249,[1_1|3]), (452,274,[1_1|3]), (452,279,[1_1|3]), (452,283,[1_1|3]), (452,303,[1_1|3]), (452,308,[1_1|3]), (452,149,[1_1|3]), (452,299,[1_1|3]), (452,179,[1_1|3]), (453,454,[1_1|3]), (454,455,[3_1|3]), (455,456,[5_1|3]), (456,457,[1_1|3]), (457,171,[2_1|3]), (457,240,[2_1|3]), (457,180,[2_1|3]), (458,459,[1_1|3]), (459,460,[3_1|3]), (460,365,[4_1|3]), (461,462,[3_1|3]), (462,463,[4_1|3]), (463,464,[2_1|3]), (464,365,[0_1|3]), (465,466,[5_1|3]), (466,467,[3_1|3]), (467,468,[4_1|3]), (468,365,[0_1|3]), (469,470,[1_1|3]), (470,471,[3_1|3]), (471,472,[4_1|3]), (472,365,[0_1|3]), (473,474,[1_1|3]), (474,475,[5_1|3]), (475,476,[3_1|3]), (476,477,[4_1|3]), (477,365,[0_1|3]), (478,479,[2_1|3]), (479,480,[3_1|3]), (480,481,[4_1|3]), (481,482,[3_1|3]), (482,365,[0_1|3]), (483,484,[3_1|3]), (484,485,[3_1|3]), (485,486,[4_1|3]), (486,487,[4_1|3]), (487,365,[0_1|3]), (488,489,[3_1|3]), (489,490,[4_1|3]), (490,491,[5_1|3]), (491,492,[0_1|3]), (492,365,[5_1|3]), (493,494,[4_1|3]), (494,495,[5_1|3]), (495,496,[5_1|3]), (496,497,[0_1|3]), (497,365,[1_1|3]), (498,499,[0_1|3]), (499,500,[3_1|3]), (500,501,[5_1|3]), (501,502,[4_1|3]), (502,365,[1_1|3]), (503,504,[4_1|3]), (504,505,[0_1|3]), (505,506,[1_1|3]), (506,507,[2_1|3]), (507,365,[1_1|3]), (508,509,[4_1|3]), (509,510,[1_1|3]), (510,511,[2_1|3]), (511,512,[3_1|3]), (512,371,[4_1|3]), (513,514,[2_1|3]), (514,515,[2_1|3]), (515,516,[3_1|3]), (516,517,[5_1|3]), (517,143,[4_1|3]), (517,166,[4_1|3]), (517,170,[4_1|3]), (517,178,[4_1|3]), (517,183,[4_1|3]), (517,188,[4_1|3]), (517,193,[4_1|3]), (517,231,[4_1|3]), (517,239,[4_1|3]), (517,249,[4_1|3]), (517,274,[4_1|3]), (517,279,[4_1|3]), (517,283,[4_1|3]), (517,303,[4_1|3]), (517,308,[4_1|3]), (517,179,[4_1|3]), (518,519,[3_1|3]), (519,520,[2_1|3]), (520,521,[5_1|3]), (521,522,[3_1|3]), (522,143,[4_1|3]), (522,166,[4_1|3]), (522,170,[4_1|3]), (522,178,[4_1|3]), (522,183,[4_1|3]), (522,188,[4_1|3]), (522,193,[4_1|3]), (522,231,[4_1|3]), (522,239,[4_1|3]), (522,249,[4_1|3]), (522,274,[4_1|3]), (522,279,[4_1|3]), (522,283,[4_1|3]), (522,303,[4_1|3]), (522,308,[4_1|3]), (522,179,[4_1|3]), (523,524,[5_1|3]), (524,525,[1_1|3]), (525,526,[5_1|3]), (526,149,[2_1|3]), (526,299,[2_1|3]), (527,528,[5_1|3]), (528,529,[2_1|3]), (529,530,[3_1|3]), (530,365,[4_1|3]), (531,532,[5_1|3]), (532,533,[3_1|3]), (533,534,[4_1|3]), (534,365,[2_1|3]), (535,536,[3_1|3]), (536,537,[4_1|3]), (537,538,[4_1|3]), (538,539,[5_1|3]), (539,365,[2_1|3]), (540,541,[2_1|3]), (541,542,[5_1|3]), (542,543,[3_1|3]), (543,544,[4_1|3]), (544,365,[4_1|3]), (545,546,[3_1|3]), (546,547,[3_1|3]), (547,548,[4_1|3]), (548,549,[5_1|3]), (549,365,[5_1|3]), (550,551,[3_1|3]), (551,552,[4_1|3]), (552,553,[3_1|3]), (553,554,[5_1|3]), (554,365,[3_1|3]), (555,556,[5_1|3]), (556,557,[3_1|3]), (557,558,[4_1|3]), (558,559,[0_1|3]), (559,365,[5_1|3]), (560,561,[1_1|3]), (561,562,[2_1|3]), (562,563,[5_1|3]), (563,564,[3_1|3]), (564,365,[4_1|3]), (565,566,[2_1|3]), (566,567,[3_1|3]), (567,568,[4_1|3]), (568,569,[0_1|3]), (569,365,[3_1|3]), (570,571,[0_1|3]), (571,572,[3_1|3]), (572,573,[5_1|3]), (573,574,[1_1|3]), (574,143,[2_1|3]), (574,166,[2_1|3]), (574,170,[2_1|3]), (574,178,[2_1|3]), (574,183,[2_1|3]), (574,188,[2_1|3]), (574,193,[2_1|3]), (574,231,[2_1|3]), (574,239,[2_1|3]), (574,249,[2_1|3]), (574,274,[2_1|3]), (574,279,[2_1|3]), (574,283,[2_1|3]), (574,303,[2_1|3]), (574,308,[2_1|3]), (574,179,[2_1|3]), (575,576,[2_1|3]), (576,577,[3_1|3]), (577,578,[5_1|3]), (578,579,[1_1|3]), (579,365,[4_1|3]), (580,581,[2_1|3]), (581,582,[3_1|3]), (582,583,[3_1|3]), (583,584,[1_1|3]), (584,365,[4_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(1(x1))) -> 0(1(2(3(4(1(x1))))))
   0(1(1(x1))) -> 1(3(1(3(4(0(x1))))))
   0(1(1(x1))) -> 5(1(3(0(3(1(x1))))))
   0(1(4(x1))) -> 0(1(3(4(x1))))
   0(1(4(x1))) -> 1(3(4(2(0(x1)))))
   0(1(4(x1))) -> 1(5(3(4(0(x1)))))
   0(1(4(x1))) -> 3(1(3(4(0(x1)))))
   0(1(4(x1))) -> 1(1(5(3(4(0(x1))))))
   0(1(4(x1))) -> 1(2(3(4(3(0(x1))))))
   0(1(4(x1))) -> 1(3(3(4(4(0(x1))))))
   0(1(4(x1))) -> 1(3(4(5(0(5(x1))))))
   0(1(4(x1))) -> 3(4(5(5(0(1(x1))))))
   1(2(4(x1))) -> 1(2(3(4(1(x1)))))
   1(2(4(x1))) -> 5(3(4(1(2(x1)))))
   1(2(4(x1))) -> 1(5(2(3(4(3(x1))))))
   1(2(4(x1))) -> 2(3(3(4(5(1(x1))))))
   5(2(1(x1))) -> 1(2(2(3(5(4(x1))))))
   5(2(1(x1))) -> 1(3(2(5(3(4(x1))))))
   5(2(4(x1))) -> 0(5(2(3(4(x1)))))
   5(2(4(x1))) -> 5(5(3(4(2(x1)))))
   5(2(4(x1))) -> 0(3(4(4(5(2(x1))))))
   5(2(4(x1))) -> 2(2(5(3(4(4(x1))))))
   5(2(4(x1))) -> 2(3(3(4(5(5(x1))))))
   5(2(4(x1))) -> 2(3(4(3(5(3(x1))))))
   5(2(4(x1))) -> 2(5(3(4(0(5(x1))))))
   5(2(4(x1))) -> 3(1(2(5(3(4(x1))))))
   5(2(4(x1))) -> 5(2(3(4(0(3(x1))))))
   0(0(2(4(x1)))) -> 0(4(3(0(2(x1)))))
   0(1(1(5(x1)))) -> 0(1(3(5(1(2(x1))))))
   0(1(2(4(x1)))) -> 0(1(2(3(3(4(x1))))))
   0(1(4(5(x1)))) -> 3(4(0(5(1(x1)))))
   0(1(4(5(x1)))) -> 3(4(5(3(0(1(x1))))))
   0(4(2(1(x1)))) -> 0(4(1(2(3(4(x1))))))
   0(5(1(4(x1)))) -> 0(0(3(5(4(1(x1))))))
   1(0(1(4(x1)))) -> 3(4(0(1(2(1(x1))))))
   1(1(2(4(x1)))) -> 1(3(4(1(2(x1)))))
   1(2(2(4(x1)))) -> 2(2(2(3(4(1(x1))))))
   1(2(4(2(x1)))) -> 1(2(3(4(2(3(x1))))))
   1(5(2(1(x1)))) -> 1(0(3(5(1(2(x1))))))
   1(5(2(4(x1)))) -> 3(2(3(5(1(4(x1))))))
   1(5(2(4(x1)))) -> 5(2(3(3(1(4(x1))))))
   5(0(1(4(x1)))) -> 3(4(0(5(3(1(x1))))))
   5(2(5(1(x1)))) -> 3(5(1(5(2(x1)))))
   0(1(1(5(4(x1))))) -> 0(0(5(4(1(1(x1))))))
   1(0(0(2(4(x1))))) -> 0(2(0(4(4(1(x1))))))
   1(0(4(2(1(x1))))) -> 1(2(3(4(1(0(x1))))))
   1(2(5(0(1(x1))))) -> 2(3(5(1(0(1(x1))))))
   1(5(3(0(4(x1))))) -> 5(1(3(4(0(4(x1))))))
   5(0(5(2(4(x1))))) -> 4(0(0(5(5(2(x1))))))
   5(3(2(4(2(x1))))) -> 2(1(5(3(4(2(x1))))))

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

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

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

The rewrite sequence

1(2(4(x1))) ->^+ 2(3(3(4(5(1(x1))))))

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

The pumping substitution is [x1 / 2(4(x1))].

The result substitution is [ ].




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

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

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

Rewrite Strategy: INNERMOST
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(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(1(x1))) -> 0(1(2(3(4(1(x1))))))
   0(1(1(x1))) -> 1(3(1(3(4(0(x1))))))
   0(1(1(x1))) -> 5(1(3(0(3(1(x1))))))
   0(1(4(x1))) -> 0(1(3(4(x1))))
   0(1(4(x1))) -> 1(3(4(2(0(x1)))))
   0(1(4(x1))) -> 1(5(3(4(0(x1)))))
   0(1(4(x1))) -> 3(1(3(4(0(x1)))))
   0(1(4(x1))) -> 1(1(5(3(4(0(x1))))))
   0(1(4(x1))) -> 1(2(3(4(3(0(x1))))))
   0(1(4(x1))) -> 1(3(3(4(4(0(x1))))))
   0(1(4(x1))) -> 1(3(4(5(0(5(x1))))))
   0(1(4(x1))) -> 3(4(5(5(0(1(x1))))))
   1(2(4(x1))) -> 1(2(3(4(1(x1)))))
   1(2(4(x1))) -> 5(3(4(1(2(x1)))))
   1(2(4(x1))) -> 1(5(2(3(4(3(x1))))))
   1(2(4(x1))) -> 2(3(3(4(5(1(x1))))))
   5(2(1(x1))) -> 1(2(2(3(5(4(x1))))))
   5(2(1(x1))) -> 1(3(2(5(3(4(x1))))))
   5(2(4(x1))) -> 0(5(2(3(4(x1)))))
   5(2(4(x1))) -> 5(5(3(4(2(x1)))))
   5(2(4(x1))) -> 0(3(4(4(5(2(x1))))))
   5(2(4(x1))) -> 2(2(5(3(4(4(x1))))))
   5(2(4(x1))) -> 2(3(3(4(5(5(x1))))))
   5(2(4(x1))) -> 2(3(4(3(5(3(x1))))))
   5(2(4(x1))) -> 2(5(3(4(0(5(x1))))))
   5(2(4(x1))) -> 3(1(2(5(3(4(x1))))))
   5(2(4(x1))) -> 5(2(3(4(0(3(x1))))))
   0(0(2(4(x1)))) -> 0(4(3(0(2(x1)))))
   0(1(1(5(x1)))) -> 0(1(3(5(1(2(x1))))))
   0(1(2(4(x1)))) -> 0(1(2(3(3(4(x1))))))
   0(1(4(5(x1)))) -> 3(4(0(5(1(x1)))))
   0(1(4(5(x1)))) -> 3(4(5(3(0(1(x1))))))
   0(4(2(1(x1)))) -> 0(4(1(2(3(4(x1))))))
   0(5(1(4(x1)))) -> 0(0(3(5(4(1(x1))))))
   1(0(1(4(x1)))) -> 3(4(0(1(2(1(x1))))))
   1(1(2(4(x1)))) -> 1(3(4(1(2(x1)))))
   1(2(2(4(x1)))) -> 2(2(2(3(4(1(x1))))))
   1(2(4(2(x1)))) -> 1(2(3(4(2(3(x1))))))
   1(5(2(1(x1)))) -> 1(0(3(5(1(2(x1))))))
   1(5(2(4(x1)))) -> 3(2(3(5(1(4(x1))))))
   1(5(2(4(x1)))) -> 5(2(3(3(1(4(x1))))))
   5(0(1(4(x1)))) -> 3(4(0(5(3(1(x1))))))
   5(2(5(1(x1)))) -> 3(5(1(5(2(x1)))))
   0(1(1(5(4(x1))))) -> 0(0(5(4(1(1(x1))))))
   1(0(0(2(4(x1))))) -> 0(2(0(4(4(1(x1))))))
   1(0(4(2(1(x1))))) -> 1(2(3(4(1(0(x1))))))
   1(2(5(0(1(x1))))) -> 2(3(5(1(0(1(x1))))))
   1(5(3(0(4(x1))))) -> 5(1(3(4(0(4(x1))))))
   5(0(5(2(4(x1))))) -> 4(0(0(5(5(2(x1))))))
   5(3(2(4(2(x1))))) -> 2(1(5(3(4(2(x1))))))

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

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

Rewrite Strategy: INNERMOST