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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 44 ms]
(4) CpxRelTRS
(5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(6) CpxTRS
    (7) CpxTrsMatchBoundsProof [FINISHED, 58 ms]
    (8) BOUNDS(1, n^1)
(9) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(10) TRS for Loop Detection
    (11) DecreasingLoopProof [LOWER BOUND(ID), 1 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(1(3(2(x1))))
   0(1(2(x1))) -> 0(2(1(0(x1))))
   0(1(2(x1))) -> 0(2(1(3(x1))))
   0(1(2(x1))) -> 0(2(2(1(x1))))
   0(1(2(x1))) -> 0(2(2(1(4(x1)))))
   0(1(2(x1))) -> 5(1(0(5(2(3(x1))))))
   0(2(4(x1))) -> 0(2(1(4(3(x1)))))
   0(4(2(x1))) -> 4(0(2(3(x1))))
   0(4(2(x1))) -> 4(0(5(5(2(x1)))))
   0(0(4(2(x1)))) -> 0(0(2(2(3(4(x1))))))
   0(1(2(2(x1)))) -> 0(2(1(0(2(x1)))))
   0(1(2(2(x1)))) -> 1(3(0(2(2(x1)))))
   0(1(2(4(x1)))) -> 0(1(4(2(3(x1)))))
   0(1(2(4(x1)))) -> 4(0(2(2(1(1(x1))))))
   0(1(2(4(x1)))) -> 4(0(5(5(2(1(x1))))))
   0(1(2(5(x1)))) -> 3(5(5(2(1(0(x1))))))
   0(1(4(2(x1)))) -> 0(5(2(1(4(x1)))))
   0(1(5(2(x1)))) -> 1(5(0(2(3(x1)))))
   0(1(5(2(x1)))) -> 0(2(2(1(0(5(x1))))))
   0(1(5(2(x1)))) -> 5(5(0(2(1(3(x1))))))
   0(2(4(2(x1)))) -> 0(5(4(3(2(2(x1))))))
   0(3(1(2(x1)))) -> 0(2(1(3(2(x1)))))
   0(3(1(2(x1)))) -> 1(0(2(5(3(x1)))))
   0(3(1(2(x1)))) -> 1(5(0(2(3(x1)))))
   0(3(1(2(x1)))) -> 3(0(2(2(1(x1)))))
   0(3(1(2(x1)))) -> 3(2(2(1(0(x1)))))
   0(3(1(2(x1)))) -> 0(3(2(3(1(3(x1))))))
   0(3(4(2(x1)))) -> 0(2(2(3(4(x1)))))
   5(0(1(2(x1)))) -> 1(3(2(5(0(x1)))))
   5(0(1(2(x1)))) -> 5(0(2(1(3(3(x1))))))
   0(1(1(2(5(x1))))) -> 5(0(2(5(1(1(x1))))))
   0(2(3(4(2(x1))))) -> 3(2(2(3(4(0(x1))))))
   0(3(1(2(5(x1))))) -> 2(3(1(3(0(5(x1))))))
   0(3(1(5(2(x1))))) -> 0(3(2(5(1(2(x1))))))
   0(3(4(1(4(x1))))) -> 0(5(3(1(4(4(x1))))))
   0(3(5(1(2(x1))))) -> 5(5(3(2(1(0(x1))))))
   0(4(0(4(2(x1))))) -> 4(4(0(0(2(2(x1))))))
   0(4(1(1(2(x1))))) -> 3(1(4(0(2(1(x1))))))
   0(4(1(2(2(x1))))) -> 4(1(0(2(2(3(x1))))))
   0(4(1(2(5(x1))))) -> 3(4(1(0(2(5(x1))))))
   0(4(2(1(2(x1))))) -> 4(1(3(2(0(2(x1))))))
   0(4(2(1(4(x1))))) -> 0(2(1(4(4(4(x1))))))
   0(4(2(5(2(x1))))) -> 5(4(3(2(2(0(x1))))))
   0(4(5(1(2(x1))))) -> 1(4(2(0(5(5(x1))))))
   0(4(5(1(2(x1))))) -> 4(0(2(5(1(1(x1))))))
   5(0(1(2(2(x1))))) -> 5(0(2(2(1(2(x1))))))
   5(0(2(4(2(x1))))) -> 0(2(2(5(1(4(x1))))))
   5(0(4(4(2(x1))))) -> 0(5(2(5(4(4(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(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_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(2(x1))) -> 0(1(3(2(x1))))
   0(1(2(x1))) -> 0(2(1(0(x1))))
   0(1(2(x1))) -> 0(2(1(3(x1))))
   0(1(2(x1))) -> 0(2(2(1(x1))))
   0(1(2(x1))) -> 0(2(2(1(4(x1)))))
   0(1(2(x1))) -> 5(1(0(5(2(3(x1))))))
   0(2(4(x1))) -> 0(2(1(4(3(x1)))))
   0(4(2(x1))) -> 4(0(2(3(x1))))
   0(4(2(x1))) -> 4(0(5(5(2(x1)))))
   0(0(4(2(x1)))) -> 0(0(2(2(3(4(x1))))))
   0(1(2(2(x1)))) -> 0(2(1(0(2(x1)))))
   0(1(2(2(x1)))) -> 1(3(0(2(2(x1)))))
   0(1(2(4(x1)))) -> 0(1(4(2(3(x1)))))
   0(1(2(4(x1)))) -> 4(0(2(2(1(1(x1))))))
   0(1(2(4(x1)))) -> 4(0(5(5(2(1(x1))))))
   0(1(2(5(x1)))) -> 3(5(5(2(1(0(x1))))))
   0(1(4(2(x1)))) -> 0(5(2(1(4(x1)))))
   0(1(5(2(x1)))) -> 1(5(0(2(3(x1)))))
   0(1(5(2(x1)))) -> 0(2(2(1(0(5(x1))))))
   0(1(5(2(x1)))) -> 5(5(0(2(1(3(x1))))))
   0(2(4(2(x1)))) -> 0(5(4(3(2(2(x1))))))
   0(3(1(2(x1)))) -> 0(2(1(3(2(x1)))))
   0(3(1(2(x1)))) -> 1(0(2(5(3(x1)))))
   0(3(1(2(x1)))) -> 1(5(0(2(3(x1)))))
   0(3(1(2(x1)))) -> 3(0(2(2(1(x1)))))
   0(3(1(2(x1)))) -> 3(2(2(1(0(x1)))))
   0(3(1(2(x1)))) -> 0(3(2(3(1(3(x1))))))
   0(3(4(2(x1)))) -> 0(2(2(3(4(x1)))))
   5(0(1(2(x1)))) -> 1(3(2(5(0(x1)))))
   5(0(1(2(x1)))) -> 5(0(2(1(3(3(x1))))))
   0(1(1(2(5(x1))))) -> 5(0(2(5(1(1(x1))))))
   0(2(3(4(2(x1))))) -> 3(2(2(3(4(0(x1))))))
   0(3(1(2(5(x1))))) -> 2(3(1(3(0(5(x1))))))
   0(3(1(5(2(x1))))) -> 0(3(2(5(1(2(x1))))))
   0(3(4(1(4(x1))))) -> 0(5(3(1(4(4(x1))))))
   0(3(5(1(2(x1))))) -> 5(5(3(2(1(0(x1))))))
   0(4(0(4(2(x1))))) -> 4(4(0(0(2(2(x1))))))
   0(4(1(1(2(x1))))) -> 3(1(4(0(2(1(x1))))))
   0(4(1(2(2(x1))))) -> 4(1(0(2(2(3(x1))))))
   0(4(1(2(5(x1))))) -> 3(4(1(0(2(5(x1))))))
   0(4(2(1(2(x1))))) -> 4(1(3(2(0(2(x1))))))
   0(4(2(1(4(x1))))) -> 0(2(1(4(4(4(x1))))))
   0(4(2(5(2(x1))))) -> 5(4(3(2(2(0(x1))))))
   0(4(5(1(2(x1))))) -> 1(4(2(0(5(5(x1))))))
   0(4(5(1(2(x1))))) -> 4(0(2(5(1(1(x1))))))
   5(0(1(2(2(x1))))) -> 5(0(2(2(1(2(x1))))))
   5(0(2(4(2(x1))))) -> 0(2(2(5(1(4(x1))))))
   5(0(4(4(2(x1))))) -> 0(5(2(5(4(4(x1))))))

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

   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(2(x_1)) -> 2(encArg(x_1))
   encArg(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_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(2(x1))) -> 0(1(3(2(x1))))
   0(1(2(x1))) -> 0(2(1(0(x1))))
   0(1(2(x1))) -> 0(2(1(3(x1))))
   0(1(2(x1))) -> 0(2(2(1(x1))))
   0(1(2(x1))) -> 0(2(2(1(4(x1)))))
   0(1(2(x1))) -> 5(1(0(5(2(3(x1))))))
   0(2(4(x1))) -> 0(2(1(4(3(x1)))))
   0(4(2(x1))) -> 4(0(2(3(x1))))
   0(4(2(x1))) -> 4(0(5(5(2(x1)))))
   0(0(4(2(x1)))) -> 0(0(2(2(3(4(x1))))))
   0(1(2(2(x1)))) -> 0(2(1(0(2(x1)))))
   0(1(2(2(x1)))) -> 1(3(0(2(2(x1)))))
   0(1(2(4(x1)))) -> 0(1(4(2(3(x1)))))
   0(1(2(4(x1)))) -> 4(0(2(2(1(1(x1))))))
   0(1(2(4(x1)))) -> 4(0(5(5(2(1(x1))))))
   0(1(2(5(x1)))) -> 3(5(5(2(1(0(x1))))))
   0(1(4(2(x1)))) -> 0(5(2(1(4(x1)))))
   0(1(5(2(x1)))) -> 1(5(0(2(3(x1)))))
   0(1(5(2(x1)))) -> 0(2(2(1(0(5(x1))))))
   0(1(5(2(x1)))) -> 5(5(0(2(1(3(x1))))))
   0(2(4(2(x1)))) -> 0(5(4(3(2(2(x1))))))
   0(3(1(2(x1)))) -> 0(2(1(3(2(x1)))))
   0(3(1(2(x1)))) -> 1(0(2(5(3(x1)))))
   0(3(1(2(x1)))) -> 1(5(0(2(3(x1)))))
   0(3(1(2(x1)))) -> 3(0(2(2(1(x1)))))
   0(3(1(2(x1)))) -> 3(2(2(1(0(x1)))))
   0(3(1(2(x1)))) -> 0(3(2(3(1(3(x1))))))
   0(3(4(2(x1)))) -> 0(2(2(3(4(x1)))))
   5(0(1(2(x1)))) -> 1(3(2(5(0(x1)))))
   5(0(1(2(x1)))) -> 5(0(2(1(3(3(x1))))))
   0(1(1(2(5(x1))))) -> 5(0(2(5(1(1(x1))))))
   0(2(3(4(2(x1))))) -> 3(2(2(3(4(0(x1))))))
   0(3(1(2(5(x1))))) -> 2(3(1(3(0(5(x1))))))
   0(3(1(5(2(x1))))) -> 0(3(2(5(1(2(x1))))))
   0(3(4(1(4(x1))))) -> 0(5(3(1(4(4(x1))))))
   0(3(5(1(2(x1))))) -> 5(5(3(2(1(0(x1))))))
   0(4(0(4(2(x1))))) -> 4(4(0(0(2(2(x1))))))
   0(4(1(1(2(x1))))) -> 3(1(4(0(2(1(x1))))))
   0(4(1(2(2(x1))))) -> 4(1(0(2(2(3(x1))))))
   0(4(1(2(5(x1))))) -> 3(4(1(0(2(5(x1))))))
   0(4(2(1(2(x1))))) -> 4(1(3(2(0(2(x1))))))
   0(4(2(1(4(x1))))) -> 0(2(1(4(4(4(x1))))))
   0(4(2(5(2(x1))))) -> 5(4(3(2(2(0(x1))))))
   0(4(5(1(2(x1))))) -> 1(4(2(0(5(5(x1))))))
   0(4(5(1(2(x1))))) -> 4(0(2(5(1(1(x1))))))
   5(0(1(2(2(x1))))) -> 5(0(2(2(1(2(x1))))))
   5(0(2(4(2(x1))))) -> 0(2(2(5(1(4(x1))))))
   5(0(4(4(2(x1))))) -> 0(5(2(5(4(4(x1))))))

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

   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(2(x_1)) -> 2(encArg(x_1))
   encArg(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_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(2(x1))) -> 0(1(3(2(x1))))
   0(1(2(x1))) -> 0(2(1(0(x1))))
   0(1(2(x1))) -> 0(2(1(3(x1))))
   0(1(2(x1))) -> 0(2(2(1(x1))))
   0(1(2(x1))) -> 0(2(2(1(4(x1)))))
   0(1(2(x1))) -> 5(1(0(5(2(3(x1))))))
   0(2(4(x1))) -> 0(2(1(4(3(x1)))))
   0(4(2(x1))) -> 4(0(2(3(x1))))
   0(4(2(x1))) -> 4(0(5(5(2(x1)))))
   0(0(4(2(x1)))) -> 0(0(2(2(3(4(x1))))))
   0(1(2(2(x1)))) -> 0(2(1(0(2(x1)))))
   0(1(2(2(x1)))) -> 1(3(0(2(2(x1)))))
   0(1(2(4(x1)))) -> 0(1(4(2(3(x1)))))
   0(1(2(4(x1)))) -> 4(0(2(2(1(1(x1))))))
   0(1(2(4(x1)))) -> 4(0(5(5(2(1(x1))))))
   0(1(2(5(x1)))) -> 3(5(5(2(1(0(x1))))))
   0(1(4(2(x1)))) -> 0(5(2(1(4(x1)))))
   0(1(5(2(x1)))) -> 1(5(0(2(3(x1)))))
   0(1(5(2(x1)))) -> 0(2(2(1(0(5(x1))))))
   0(1(5(2(x1)))) -> 5(5(0(2(1(3(x1))))))
   0(2(4(2(x1)))) -> 0(5(4(3(2(2(x1))))))
   0(3(1(2(x1)))) -> 0(2(1(3(2(x1)))))
   0(3(1(2(x1)))) -> 1(0(2(5(3(x1)))))
   0(3(1(2(x1)))) -> 1(5(0(2(3(x1)))))
   0(3(1(2(x1)))) -> 3(0(2(2(1(x1)))))
   0(3(1(2(x1)))) -> 3(2(2(1(0(x1)))))
   0(3(1(2(x1)))) -> 0(3(2(3(1(3(x1))))))
   0(3(4(2(x1)))) -> 0(2(2(3(4(x1)))))
   5(0(1(2(x1)))) -> 1(3(2(5(0(x1)))))
   5(0(1(2(x1)))) -> 5(0(2(1(3(3(x1))))))
   0(1(1(2(5(x1))))) -> 5(0(2(5(1(1(x1))))))
   0(2(3(4(2(x1))))) -> 3(2(2(3(4(0(x1))))))
   0(3(1(2(5(x1))))) -> 2(3(1(3(0(5(x1))))))
   0(3(1(5(2(x1))))) -> 0(3(2(5(1(2(x1))))))
   0(3(4(1(4(x1))))) -> 0(5(3(1(4(4(x1))))))
   0(3(5(1(2(x1))))) -> 5(5(3(2(1(0(x1))))))
   0(4(0(4(2(x1))))) -> 4(4(0(0(2(2(x1))))))
   0(4(1(1(2(x1))))) -> 3(1(4(0(2(1(x1))))))
   0(4(1(2(2(x1))))) -> 4(1(0(2(2(3(x1))))))
   0(4(1(2(5(x1))))) -> 3(4(1(0(2(5(x1))))))
   0(4(2(1(2(x1))))) -> 4(1(3(2(0(2(x1))))))
   0(4(2(1(4(x1))))) -> 0(2(1(4(4(4(x1))))))
   0(4(2(5(2(x1))))) -> 5(4(3(2(2(0(x1))))))
   0(4(5(1(2(x1))))) -> 1(4(2(0(5(5(x1))))))
   0(4(5(1(2(x1))))) -> 4(0(2(5(1(1(x1))))))
   5(0(1(2(2(x1))))) -> 5(0(2(2(1(2(x1))))))
   5(0(2(4(2(x1))))) -> 0(2(2(5(1(4(x1))))))
   5(0(4(4(2(x1))))) -> 0(5(2(5(4(4(x1))))))
   encArg(1(x_1)) -> 1(encArg(x_1))
   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_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.

"[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]
{(61,62,[0_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]), (61,63,[0_1|1]), (61,66,[0_1|1]), (61,69,[0_1|1]), (61,72,[0_1|1]), (61,75,[0_1|1]), (61,79,[5_1|1]), (61,84,[0_1|1]), (61,88,[1_1|1]), (61,92,[0_1|1]), (61,96,[4_1|1]), (61,101,[4_1|1]), (61,106,[0_1|1]), (61,110,[0_1|1]), (61,114,[0_1|1]), (61,119,[3_1|1]), (61,124,[4_1|1]), (61,127,[4_1|1]), (61,131,[4_1|1]), (61,136,[0_1|1]), (61,141,[3_1|1]), (61,146,[4_1|1]), (61,151,[0_1|1]), (61,155,[1_1|1]), (61,159,[1_1|1]), (61,163,[3_1|1]), (61,167,[3_1|1]), (61,171,[0_1|1]), (61,176,[0_1|1]), (61,180,[0_1|1]), (61,185,[1_1|1, 2_1|1, 3_1|1, 4_1|1, 0_1|1, 5_1|1]), (61,186,[0_1|2]), (61,190,[0_1|2]), (61,193,[0_1|2]), (61,196,[0_1|2]), (61,199,[0_1|2]), (61,202,[0_1|2]), (61,206,[5_1|2]), (61,211,[0_1|2]), (61,215,[1_1|2]), (61,219,[0_1|2]), (61,223,[4_1|2]), (61,228,[4_1|2]), (61,233,[3_1|2]), (61,238,[1_1|2]), (61,242,[0_1|2]), (61,247,[5_1|2]), (61,252,[5_1|2]), (61,257,[0_1|2]), (61,261,[0_1|2]), (61,266,[3_1|2]), (61,271,[4_1|2]), (61,274,[4_1|2]), (61,278,[4_1|2]), (61,283,[0_1|2]), (61,288,[5_1|2]), (61,293,[4_1|2]), (61,298,[3_1|2]), (61,303,[4_1|2]), (61,308,[3_1|2]), (61,313,[1_1|2]), (61,318,[4_1|2]), (61,323,[0_1|2]), (61,328,[0_1|2]), (61,332,[1_1|2]), (61,336,[3_1|2]), (61,340,[3_1|2]), (61,344,[0_1|2]), (61,349,[2_1|2]), (61,354,[0_1|2]), (61,359,[0_1|2]), (61,363,[0_1|2]), (61,368,[5_1|2]), (61,373,[1_1|2]), (61,377,[5_1|2]), (61,382,[5_1|2]), (61,387,[0_1|2]), (61,392,[0_1|2]), (61,397,[0_1|3]), (62,62,[1_1|0, 2_1|0, 3_1|0, 4_1|0, cons_0_1|0, cons_5_1|0]), (63,64,[1_1|1]), (64,65,[3_1|1]), (65,62,[2_1|1]), (66,67,[2_1|1]), (67,68,[1_1|1]), (68,62,[0_1|1]), (68,63,[0_1|1]), (68,66,[0_1|1]), (68,69,[0_1|1]), (68,72,[0_1|1]), (68,75,[0_1|1]), (68,79,[5_1|1]), (68,84,[0_1|1]), (68,88,[1_1|1]), (68,92,[0_1|1]), (68,96,[4_1|1]), (68,101,[4_1|1]), (68,106,[0_1|1]), (68,110,[0_1|1]), (68,114,[0_1|1]), (68,119,[3_1|1]), (68,124,[4_1|1]), (68,127,[4_1|1]), (68,131,[4_1|1]), (68,136,[0_1|1]), (68,141,[3_1|1]), (68,146,[4_1|1]), (68,151,[0_1|1]), (68,155,[1_1|1]), (68,159,[1_1|1]), (68,163,[3_1|1]), (68,167,[3_1|1]), (68,171,[0_1|1]), (68,176,[0_1|1]), (68,180,[0_1|1]), (68,186,[0_1|2]), (69,70,[2_1|1]), (70,71,[1_1|1]), (71,62,[3_1|1]), (72,73,[2_1|1]), (73,74,[2_1|1]), (74,62,[1_1|1]), (75,76,[2_1|1]), (76,77,[2_1|1]), (77,78,[1_1|1]), (78,62,[4_1|1]), (79,80,[1_1|1]), (80,81,[0_1|1]), (81,82,[5_1|1]), (82,83,[2_1|1]), (83,62,[3_1|1]), (84,85,[2_1|1]), (85,86,[1_1|1]), (86,87,[0_1|1]), (86,110,[0_1|1]), (86,114,[0_1|1]), (86,119,[3_1|1]), (87,62,[2_1|1]), (88,89,[3_1|1]), (89,90,[0_1|1]), (90,91,[2_1|1]), (91,62,[2_1|1]), (92,93,[1_1|1]), (93,94,[4_1|1]), (94,95,[2_1|1]), (95,62,[3_1|1]), (96,97,[0_1|1]), (97,98,[2_1|1]), (98,99,[2_1|1]), (99,100,[1_1|1]), (100,62,[1_1|1]), (101,102,[0_1|1]), (102,103,[5_1|1]), (103,104,[5_1|1]), (104,105,[2_1|1]), (105,62,[1_1|1]), (106,107,[5_1|1]), (107,108,[2_1|1]), (108,109,[1_1|1]), (109,62,[4_1|1]), (110,111,[2_1|1]), (111,112,[1_1|1]), (112,113,[4_1|1]), (113,62,[3_1|1]), (114,115,[5_1|1]), (115,116,[4_1|1]), (116,117,[3_1|1]), (117,118,[2_1|1]), (118,62,[2_1|1]), (119,120,[2_1|1]), (120,121,[2_1|1]), (121,122,[3_1|1]), (122,123,[4_1|1]), (123,62,[0_1|1]), (123,63,[0_1|1]), (123,66,[0_1|1]), (123,69,[0_1|1]), (123,72,[0_1|1]), (123,75,[0_1|1]), (123,79,[5_1|1]), (123,84,[0_1|1]), (123,88,[1_1|1]), (123,92,[0_1|1]), (123,96,[4_1|1]), (123,101,[4_1|1]), (123,106,[0_1|1]), (123,110,[0_1|1]), (123,114,[0_1|1]), (123,119,[3_1|1]), (123,124,[4_1|1]), (123,127,[4_1|1]), (123,131,[4_1|1]), (123,136,[0_1|1]), (123,141,[3_1|1]), (123,146,[4_1|1]), (123,151,[0_1|1]), (123,155,[1_1|1]), (123,159,[1_1|1]), (123,163,[3_1|1]), (123,167,[3_1|1]), (123,171,[0_1|1]), (123,176,[0_1|1]), (123,180,[0_1|1]), (123,186,[0_1|2]), (124,125,[0_1|1]), (124,119,[3_1|1]), (125,126,[2_1|1]), (126,62,[3_1|1]), (127,128,[0_1|1]), (128,129,[5_1|1]), (129,130,[5_1|1]), (130,62,[2_1|1]), (131,132,[1_1|1]), (132,133,[3_1|1]), (133,134,[2_1|1]), (134,135,[0_1|1]), (134,110,[0_1|1]), (134,114,[0_1|1]), (134,119,[3_1|1]), (135,62,[2_1|1]), (136,137,[2_1|1]), (137,138,[1_1|1]), (138,139,[4_1|1]), (139,140,[4_1|1]), (140,62,[4_1|1]), (141,142,[1_1|1]), (142,143,[4_1|1]), (143,144,[0_1|1]), (144,145,[2_1|1]), (145,62,[1_1|1]), (146,147,[1_1|1]), (147,148,[0_1|1]), (148,149,[2_1|1]), (149,150,[2_1|1]), (150,62,[3_1|1]), (151,152,[2_1|1]), (152,153,[1_1|1]), (153,154,[3_1|1]), (154,62,[2_1|1]), (155,156,[0_1|1]), (156,157,[2_1|1]), (157,158,[5_1|1]), (158,62,[3_1|1]), (159,160,[5_1|1]), (160,161,[0_1|1]), (160,119,[3_1|1]), (161,162,[2_1|1]), (162,62,[3_1|1]), (163,164,[0_1|1]), (164,165,[2_1|1]), (165,166,[2_1|1]), (166,62,[1_1|1]), (167,168,[2_1|1]), (168,169,[2_1|1]), (169,170,[1_1|1]), (170,62,[0_1|1]), (170,63,[0_1|1]), (170,66,[0_1|1]), (170,69,[0_1|1]), (170,72,[0_1|1]), (170,75,[0_1|1]), (170,79,[5_1|1]), (170,84,[0_1|1]), (170,88,[1_1|1]), (170,92,[0_1|1]), (170,96,[4_1|1]), (170,101,[4_1|1]), (170,106,[0_1|1]), (170,110,[0_1|1]), (170,114,[0_1|1]), (170,119,[3_1|1]), (170,124,[4_1|1]), (170,127,[4_1|1]), (170,131,[4_1|1]), (170,136,[0_1|1]), (170,141,[3_1|1]), (170,146,[4_1|1]), (170,151,[0_1|1]), (170,155,[1_1|1]), (170,159,[1_1|1]), (170,163,[3_1|1]), (170,167,[3_1|1]), (170,171,[0_1|1]), (170,176,[0_1|1]), (170,180,[0_1|1]), (170,186,[0_1|2]), (171,172,[3_1|1]), (172,173,[2_1|1]), (173,174,[3_1|1]), (174,175,[1_1|1]), (175,62,[3_1|1]), (176,177,[2_1|1]), (177,178,[2_1|1]), (178,179,[3_1|1]), (179,62,[4_1|1]), (180,181,[5_1|1]), (181,182,[3_1|1]), (182,183,[1_1|1]), (183,184,[4_1|1]), (184,62,[4_1|1]), (185,62,[encArg_1|1]), (185,185,[1_1|1, 2_1|1, 3_1|1, 4_1|1, 0_1|1, 5_1|1]), (185,190,[0_1|2]), (185,193,[0_1|2]), (185,196,[0_1|2]), (185,199,[0_1|2]), (185,202,[0_1|2]), (185,206,[5_1|2]), (185,211,[0_1|2]), (185,215,[1_1|2]), (185,219,[0_1|2]), (185,223,[4_1|2]), (185,228,[4_1|2]), (185,233,[3_1|2]), (185,186,[0_1|2]), (185,238,[1_1|2]), (185,242,[0_1|2]), (185,247,[5_1|2]), (185,252,[5_1|2]), (185,257,[0_1|2]), (185,261,[0_1|2]), (185,266,[3_1|2]), (185,271,[4_1|2]), (185,274,[4_1|2]), (185,278,[4_1|2]), (185,283,[0_1|2]), (185,288,[5_1|2]), (185,293,[4_1|2]), (185,298,[3_1|2]), (185,303,[4_1|2]), (185,308,[3_1|2]), (185,313,[1_1|2]), (185,318,[4_1|2]), (185,323,[0_1|2]), (185,328,[0_1|2]), (185,332,[1_1|2]), (185,336,[3_1|2]), (185,340,[3_1|2]), (185,344,[0_1|2]), (185,349,[2_1|2]), (185,354,[0_1|2]), (185,359,[0_1|2]), (185,363,[0_1|2]), (185,368,[5_1|2]), (185,373,[1_1|2]), (185,377,[5_1|2]), (185,382,[5_1|2]), (185,387,[0_1|2]), (185,392,[0_1|2]), (185,397,[0_1|3]), (186,187,[5_1|2]), (187,188,[2_1|2]), (188,189,[1_1|2]), (189,95,[4_1|2]), (189,185,[4_1|2]), (189,349,[4_1|2]), (189,315,[4_1|2]), (190,191,[1_1|2]), (191,192,[3_1|2]), (192,185,[2_1|2]), (192,349,[2_1|2]), (193,194,[2_1|2]), (194,195,[1_1|2]), (195,185,[0_1|2]), (195,349,[0_1|2, 2_1|2]), (195,190,[0_1|2]), (195,193,[0_1|2]), (195,196,[0_1|2]), (195,199,[0_1|2]), (195,202,[0_1|2]), (195,206,[5_1|2]), (195,211,[0_1|2]), (195,215,[1_1|2]), (195,219,[0_1|2]), (195,223,[4_1|2]), (195,228,[4_1|2]), (195,233,[3_1|2]), (195,186,[0_1|2]), (195,238,[1_1|2]), (195,242,[0_1|2]), (195,247,[5_1|2]), (195,252,[5_1|2]), (195,257,[0_1|2]), (195,261,[0_1|2]), (195,266,[3_1|2]), (195,271,[4_1|2]), (195,274,[4_1|2]), (195,278,[4_1|2]), (195,283,[0_1|2]), (195,288,[5_1|2]), (195,293,[4_1|2]), (195,298,[3_1|2]), (195,303,[4_1|2]), (195,308,[3_1|2]), (195,313,[1_1|2]), (195,318,[4_1|2]), (195,323,[0_1|2]), (195,328,[0_1|2]), (195,332,[1_1|2]), (195,336,[3_1|2]), (195,340,[3_1|2]), (195,344,[0_1|2]), (195,354,[0_1|2]), (195,359,[0_1|2]), (195,363,[0_1|2]), (195,368,[5_1|2]), (195,401,[0_1|3]), (196,197,[2_1|2]), (197,198,[1_1|2]), (198,185,[3_1|2]), (198,349,[3_1|2]), (199,200,[2_1|2]), (200,201,[2_1|2]), (201,185,[1_1|2]), (201,349,[1_1|2]), (202,203,[2_1|2]), (203,204,[2_1|2]), (204,205,[1_1|2]), (205,185,[4_1|2]), (205,349,[4_1|2]), (206,207,[1_1|2]), (207,208,[0_1|2]), (208,209,[5_1|2]), (209,210,[2_1|2]), (210,185,[3_1|2]), (210,349,[3_1|2]), (211,212,[2_1|2]), (212,213,[1_1|2]), (213,214,[0_1|2]), (213,257,[0_1|2]), (213,261,[0_1|2]), (213,266,[3_1|2]), (213,405,[0_1|3]), (214,185,[2_1|2]), (214,349,[2_1|2]), (215,216,[3_1|2]), (216,217,[0_1|2]), (217,218,[2_1|2]), (218,185,[2_1|2]), (218,349,[2_1|2]), (219,220,[1_1|2]), (220,221,[4_1|2]), (221,222,[2_1|2]), (222,185,[3_1|2]), (222,223,[3_1|2]), (222,228,[3_1|2]), (222,271,[3_1|2]), (222,274,[3_1|2]), (222,278,[3_1|2]), (222,293,[3_1|2]), (222,303,[3_1|2]), (222,318,[3_1|2]), (223,224,[0_1|2]), (224,225,[2_1|2]), (225,226,[2_1|2]), (226,227,[1_1|2]), (227,185,[1_1|2]), (227,223,[1_1|2]), (227,228,[1_1|2]), (227,271,[1_1|2]), (227,274,[1_1|2]), (227,278,[1_1|2]), (227,293,[1_1|2]), (227,303,[1_1|2]), (227,318,[1_1|2]), (228,229,[0_1|2]), (229,230,[5_1|2]), (230,231,[5_1|2]), (231,232,[2_1|2]), (232,185,[1_1|2]), (232,223,[1_1|2]), (232,228,[1_1|2]), (232,271,[1_1|2]), (232,274,[1_1|2]), (232,278,[1_1|2]), (232,293,[1_1|2]), (232,303,[1_1|2]), (232,318,[1_1|2]), (233,234,[5_1|2]), (234,235,[5_1|2]), (235,236,[2_1|2]), (236,237,[1_1|2]), (237,185,[0_1|2]), (237,206,[0_1|2, 5_1|2]), (237,247,[0_1|2, 5_1|2]), (237,252,[0_1|2, 5_1|2]), (237,288,[0_1|2, 5_1|2]), (237,368,[0_1|2, 5_1|2]), (237,377,[0_1|2]), (237,382,[0_1|2]), (237,190,[0_1|2]), (237,193,[0_1|2]), (237,196,[0_1|2]), (237,199,[0_1|2]), (237,202,[0_1|2]), (237,211,[0_1|2]), (237,215,[1_1|2]), (237,219,[0_1|2]), (237,223,[4_1|2]), (237,228,[4_1|2]), (237,233,[3_1|2]), (237,186,[0_1|2]), (237,238,[1_1|2]), (237,242,[0_1|2]), (237,257,[0_1|2]), (237,261,[0_1|2]), (237,266,[3_1|2]), (237,271,[4_1|2]), (237,274,[4_1|2]), (237,278,[4_1|2]), (237,283,[0_1|2]), (237,293,[4_1|2]), (237,298,[3_1|2]), (237,303,[4_1|2]), (237,308,[3_1|2]), (237,313,[1_1|2]), (237,318,[4_1|2]), (237,323,[0_1|2]), (237,328,[0_1|2]), (237,332,[1_1|2]), (237,336,[3_1|2]), (237,340,[3_1|2]), (237,344,[0_1|2]), (237,349,[2_1|2]), (237,354,[0_1|2]), (237,359,[0_1|2]), (237,363,[0_1|2]), (237,401,[0_1|3]), (238,239,[5_1|2]), (239,240,[0_1|2]), (239,266,[3_1|2]), (240,241,[2_1|2]), (241,185,[3_1|2]), (241,349,[3_1|2]), (242,243,[2_1|2]), (243,244,[2_1|2]), (244,245,[1_1|2]), (245,246,[0_1|2]), (246,185,[5_1|2]), (246,349,[5_1|2]), (246,373,[1_1|2]), (246,377,[5_1|2]), (246,382,[5_1|2]), (246,387,[0_1|2]), (246,392,[0_1|2]), (247,248,[5_1|2]), (248,249,[0_1|2]), (249,250,[2_1|2]), (250,251,[1_1|2]), (251,185,[3_1|2]), (251,349,[3_1|2]), (252,253,[0_1|2]), (253,254,[2_1|2]), (254,255,[5_1|2]), (255,256,[1_1|2]), (256,185,[1_1|2]), (256,206,[1_1|2]), (256,247,[1_1|2]), (256,252,[1_1|2]), (256,288,[1_1|2]), (256,368,[1_1|2]), (256,377,[1_1|2]), (256,382,[1_1|2]), (257,258,[2_1|2]), (258,259,[1_1|2]), (259,260,[4_1|2]), (260,185,[3_1|2]), (260,223,[3_1|2]), (260,228,[3_1|2]), (260,271,[3_1|2]), (260,274,[3_1|2]), (260,278,[3_1|2]), (260,293,[3_1|2]), (260,303,[3_1|2]), (260,318,[3_1|2]), (261,262,[5_1|2]), (262,263,[4_1|2]), (263,264,[3_1|2]), (264,265,[2_1|2]), (265,185,[2_1|2]), (265,349,[2_1|2]), (266,267,[2_1|2]), (267,268,[2_1|2]), (268,269,[3_1|2]), (269,270,[4_1|2]), (270,185,[0_1|2]), (270,349,[0_1|2, 2_1|2]), (270,190,[0_1|2]), (270,193,[0_1|2]), (270,196,[0_1|2]), (270,199,[0_1|2]), (270,202,[0_1|2]), (270,206,[5_1|2]), (270,211,[0_1|2]), (270,215,[1_1|2]), (270,219,[0_1|2]), (270,223,[4_1|2]), (270,228,[4_1|2]), (270,233,[3_1|2]), (270,186,[0_1|2]), (270,238,[1_1|2]), (270,242,[0_1|2]), (270,247,[5_1|2]), (270,252,[5_1|2]), (270,257,[0_1|2]), (270,261,[0_1|2]), (270,266,[3_1|2]), (270,271,[4_1|2]), (270,274,[4_1|2]), (270,278,[4_1|2]), (270,283,[0_1|2]), (270,288,[5_1|2]), (270,293,[4_1|2]), (270,298,[3_1|2]), (270,303,[4_1|2]), (270,308,[3_1|2]), (270,313,[1_1|2]), (270,318,[4_1|2]), (270,323,[0_1|2]), (270,328,[0_1|2]), (270,332,[1_1|2]), (270,336,[3_1|2]), (270,340,[3_1|2]), (270,344,[0_1|2]), (270,354,[0_1|2]), (270,359,[0_1|2]), (270,363,[0_1|2]), (270,368,[5_1|2]), (270,401,[0_1|3]), (271,272,[0_1|2]), (271,266,[3_1|2]), (272,273,[2_1|2]), (273,185,[3_1|2]), (273,349,[3_1|2]), (274,275,[0_1|2]), (275,276,[5_1|2]), (276,277,[5_1|2]), (277,185,[2_1|2]), (277,349,[2_1|2]), (278,279,[1_1|2]), (279,280,[3_1|2]), (280,281,[2_1|2]), (281,282,[0_1|2]), (281,257,[0_1|2]), (281,261,[0_1|2]), (281,266,[3_1|2]), (281,405,[0_1|3]), (282,185,[2_1|2]), (282,349,[2_1|2]), (283,284,[2_1|2]), (284,285,[1_1|2]), (285,286,[4_1|2]), (286,287,[4_1|2]), (287,185,[4_1|2]), (287,223,[4_1|2]), (287,228,[4_1|2]), (287,271,[4_1|2]), (287,274,[4_1|2]), (287,278,[4_1|2]), (287,293,[4_1|2]), (287,303,[4_1|2]), (287,318,[4_1|2]), (287,314,[4_1|2]), (288,289,[4_1|2]), (289,290,[3_1|2]), (290,291,[2_1|2]), (291,292,[2_1|2]), (292,185,[0_1|2]), (292,349,[0_1|2, 2_1|2]), (292,190,[0_1|2]), (292,193,[0_1|2]), (292,196,[0_1|2]), (292,199,[0_1|2]), (292,202,[0_1|2]), (292,206,[5_1|2]), (292,211,[0_1|2]), (292,215,[1_1|2]), (292,219,[0_1|2]), (292,223,[4_1|2]), (292,228,[4_1|2]), (292,233,[3_1|2]), (292,186,[0_1|2]), (292,238,[1_1|2]), (292,242,[0_1|2]), (292,247,[5_1|2]), (292,252,[5_1|2]), (292,257,[0_1|2]), (292,261,[0_1|2]), (292,266,[3_1|2]), (292,271,[4_1|2]), (292,274,[4_1|2]), (292,278,[4_1|2]), (292,283,[0_1|2]), (292,288,[5_1|2]), (292,293,[4_1|2]), (292,298,[3_1|2]), (292,303,[4_1|2]), (292,308,[3_1|2]), (292,313,[1_1|2]), (292,318,[4_1|2]), (292,323,[0_1|2]), (292,328,[0_1|2]), (292,332,[1_1|2]), (292,336,[3_1|2]), (292,340,[3_1|2]), (292,344,[0_1|2]), (292,354,[0_1|2]), (292,359,[0_1|2]), (292,363,[0_1|2]), (292,368,[5_1|2]), (292,401,[0_1|3]), (293,294,[4_1|2]), (294,295,[0_1|2]), (295,296,[0_1|2]), (296,297,[2_1|2]), (297,185,[2_1|2]), (297,349,[2_1|2]), (298,299,[1_1|2]), (299,300,[4_1|2]), (300,301,[0_1|2]), (301,302,[2_1|2]), (302,185,[1_1|2]), (302,349,[1_1|2]), (303,304,[1_1|2]), (304,305,[0_1|2]), (305,306,[2_1|2]), (306,307,[2_1|2]), (307,185,[3_1|2]), (307,349,[3_1|2]), (308,309,[4_1|2]), (309,310,[1_1|2]), (310,311,[0_1|2]), (311,312,[2_1|2]), (312,185,[5_1|2]), (312,206,[5_1|2]), (312,247,[5_1|2]), (312,252,[5_1|2]), (312,288,[5_1|2]), (312,368,[5_1|2]), (312,377,[5_1|2]), (312,382,[5_1|2]), (312,373,[1_1|2]), (312,387,[0_1|2]), (312,392,[0_1|2]), (313,314,[4_1|2]), (314,315,[2_1|2]), (315,316,[0_1|2]), (316,317,[5_1|2]), (317,185,[5_1|2]), (317,349,[5_1|2]), (317,373,[1_1|2]), (317,377,[5_1|2]), (317,382,[5_1|2]), (317,387,[0_1|2]), (317,392,[0_1|2]), (318,319,[0_1|2]), (319,320,[2_1|2]), (320,321,[5_1|2]), (321,322,[1_1|2]), (322,185,[1_1|2]), (322,349,[1_1|2]), (323,324,[0_1|2]), (324,325,[2_1|2]), (325,326,[2_1|2]), (326,327,[3_1|2]), (327,185,[4_1|2]), (327,349,[4_1|2]), (328,329,[2_1|2]), (329,330,[1_1|2]), (330,331,[3_1|2]), (331,185,[2_1|2]), (331,349,[2_1|2]), (332,333,[0_1|2]), (333,334,[2_1|2]), (334,335,[5_1|2]), (335,185,[3_1|2]), (335,349,[3_1|2]), (336,337,[0_1|2]), (337,338,[2_1|2]), (338,339,[2_1|2]), (339,185,[1_1|2]), (339,349,[1_1|2]), (340,341,[2_1|2]), (341,342,[2_1|2]), (342,343,[1_1|2]), (343,185,[0_1|2]), (343,349,[0_1|2, 2_1|2]), (343,190,[0_1|2]), (343,193,[0_1|2]), (343,196,[0_1|2]), (343,199,[0_1|2]), (343,202,[0_1|2]), (343,206,[5_1|2]), (343,211,[0_1|2]), (343,215,[1_1|2]), (343,219,[0_1|2]), (343,223,[4_1|2]), (343,228,[4_1|2]), (343,233,[3_1|2]), (343,186,[0_1|2]), (343,238,[1_1|2]), (343,242,[0_1|2]), (343,247,[5_1|2]), (343,252,[5_1|2]), (343,257,[0_1|2]), (343,261,[0_1|2]), (343,266,[3_1|2]), (343,271,[4_1|2]), (343,274,[4_1|2]), (343,278,[4_1|2]), (343,283,[0_1|2]), (343,288,[5_1|2]), (343,293,[4_1|2]), (343,298,[3_1|2]), (343,303,[4_1|2]), (343,308,[3_1|2]), (343,313,[1_1|2]), (343,318,[4_1|2]), (343,323,[0_1|2]), (343,328,[0_1|2]), (343,332,[1_1|2]), (343,336,[3_1|2]), (343,340,[3_1|2]), (343,344,[0_1|2]), (343,354,[0_1|2]), (343,359,[0_1|2]), (343,363,[0_1|2]), (343,368,[5_1|2]), (343,401,[0_1|3]), (344,345,[3_1|2]), (345,346,[2_1|2]), (346,347,[3_1|2]), (347,348,[1_1|2]), (348,185,[3_1|2]), (348,349,[3_1|2]), (349,350,[3_1|2]), (350,351,[1_1|2]), (351,352,[3_1|2]), (352,353,[0_1|2]), (353,185,[5_1|2]), (353,206,[5_1|2]), (353,247,[5_1|2]), (353,252,[5_1|2]), (353,288,[5_1|2]), (353,368,[5_1|2]), (353,377,[5_1|2]), (353,382,[5_1|2]), (353,373,[1_1|2]), (353,387,[0_1|2]), (353,392,[0_1|2]), (354,355,[3_1|2]), (355,356,[2_1|2]), (356,357,[5_1|2]), (357,358,[1_1|2]), (358,185,[2_1|2]), (358,349,[2_1|2]), (359,360,[2_1|2]), (360,361,[2_1|2]), (361,362,[3_1|2]), (362,185,[4_1|2]), (362,349,[4_1|2]), (363,364,[5_1|2]), (364,365,[3_1|2]), (365,366,[1_1|2]), (366,367,[4_1|2]), (367,185,[4_1|2]), (367,223,[4_1|2]), (367,228,[4_1|2]), (367,271,[4_1|2]), (367,274,[4_1|2]), (367,278,[4_1|2]), (367,293,[4_1|2]), (367,303,[4_1|2]), (367,318,[4_1|2]), (367,314,[4_1|2]), (368,369,[5_1|2]), (369,370,[3_1|2]), (370,371,[2_1|2]), (371,372,[1_1|2]), (372,185,[0_1|2]), (372,349,[0_1|2, 2_1|2]), (372,190,[0_1|2]), (372,193,[0_1|2]), (372,196,[0_1|2]), (372,199,[0_1|2]), (372,202,[0_1|2]), (372,206,[5_1|2]), (372,211,[0_1|2]), (372,215,[1_1|2]), (372,219,[0_1|2]), (372,223,[4_1|2]), (372,228,[4_1|2]), (372,233,[3_1|2]), (372,186,[0_1|2]), (372,238,[1_1|2]), (372,242,[0_1|2]), (372,247,[5_1|2]), (372,252,[5_1|2]), (372,257,[0_1|2]), (372,261,[0_1|2]), (372,266,[3_1|2]), (372,271,[4_1|2]), (372,274,[4_1|2]), (372,278,[4_1|2]), (372,283,[0_1|2]), (372,288,[5_1|2]), (372,293,[4_1|2]), (372,298,[3_1|2]), (372,303,[4_1|2]), (372,308,[3_1|2]), (372,313,[1_1|2]), (372,318,[4_1|2]), (372,323,[0_1|2]), (372,328,[0_1|2]), (372,332,[1_1|2]), (372,336,[3_1|2]), (372,340,[3_1|2]), (372,344,[0_1|2]), (372,354,[0_1|2]), (372,359,[0_1|2]), (372,363,[0_1|2]), (372,368,[5_1|2]), (372,401,[0_1|3]), (373,374,[3_1|2]), (374,375,[2_1|2]), (375,376,[5_1|2]), (375,373,[1_1|2]), (375,377,[5_1|2]), (375,382,[5_1|2]), (375,387,[0_1|2]), (375,392,[0_1|2]), (376,185,[0_1|2]), (376,349,[0_1|2, 2_1|2]), (376,190,[0_1|2]), (376,193,[0_1|2]), (376,196,[0_1|2]), (376,199,[0_1|2]), (376,202,[0_1|2]), (376,206,[5_1|2]), (376,211,[0_1|2]), (376,215,[1_1|2]), (376,219,[0_1|2]), (376,223,[4_1|2]), (376,228,[4_1|2]), (376,233,[3_1|2]), (376,186,[0_1|2]), (376,238,[1_1|2]), (376,242,[0_1|2]), (376,247,[5_1|2]), (376,252,[5_1|2]), (376,257,[0_1|2]), (376,261,[0_1|2]), (376,266,[3_1|2]), (376,271,[4_1|2]), (376,274,[4_1|2]), (376,278,[4_1|2]), (376,283,[0_1|2]), (376,288,[5_1|2]), (376,293,[4_1|2]), (376,298,[3_1|2]), (376,303,[4_1|2]), (376,308,[3_1|2]), (376,313,[1_1|2]), (376,318,[4_1|2]), (376,323,[0_1|2]), (376,328,[0_1|2]), (376,332,[1_1|2]), (376,336,[3_1|2]), (376,340,[3_1|2]), (376,344,[0_1|2]), (376,354,[0_1|2]), (376,359,[0_1|2]), (376,363,[0_1|2]), (376,368,[5_1|2]), (376,401,[0_1|3]), (377,378,[0_1|2]), (378,379,[2_1|2]), (379,380,[1_1|2]), (380,381,[3_1|2]), (381,185,[3_1|2]), (381,349,[3_1|2]), (382,383,[0_1|2]), (383,384,[2_1|2]), (384,385,[2_1|2]), (385,386,[1_1|2]), (386,185,[2_1|2]), (386,349,[2_1|2]), (387,388,[2_1|2]), (388,389,[2_1|2]), (389,390,[5_1|2]), (390,391,[1_1|2]), (391,185,[4_1|2]), (391,349,[4_1|2]), (392,393,[5_1|2]), (393,394,[2_1|2]), (394,395,[5_1|2]), (395,396,[4_1|2]), (396,185,[4_1|2]), (396,349,[4_1|2]), (397,398,[5_1|3]), (398,399,[2_1|3]), (399,400,[1_1|3]), (400,222,[4_1|3]), (401,402,[5_1|3]), (402,403,[2_1|3]), (403,404,[1_1|3]), (404,315,[4_1|3]), (404,222,[4_1|3]), (405,406,[2_1|3]), (406,407,[1_1|3]), (407,408,[4_1|3]), (408,223,[3_1|3]), (408,228,[3_1|3]), (408,271,[3_1|3]), (408,274,[3_1|3]), (408,278,[3_1|3]), (408,293,[3_1|3]), (408,303,[3_1|3]), (408,318,[3_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(1(3(2(x1))))
   0(1(2(x1))) -> 0(2(1(0(x1))))
   0(1(2(x1))) -> 0(2(1(3(x1))))
   0(1(2(x1))) -> 0(2(2(1(x1))))
   0(1(2(x1))) -> 0(2(2(1(4(x1)))))
   0(1(2(x1))) -> 5(1(0(5(2(3(x1))))))
   0(2(4(x1))) -> 0(2(1(4(3(x1)))))
   0(4(2(x1))) -> 4(0(2(3(x1))))
   0(4(2(x1))) -> 4(0(5(5(2(x1)))))
   0(0(4(2(x1)))) -> 0(0(2(2(3(4(x1))))))
   0(1(2(2(x1)))) -> 0(2(1(0(2(x1)))))
   0(1(2(2(x1)))) -> 1(3(0(2(2(x1)))))
   0(1(2(4(x1)))) -> 0(1(4(2(3(x1)))))
   0(1(2(4(x1)))) -> 4(0(2(2(1(1(x1))))))
   0(1(2(4(x1)))) -> 4(0(5(5(2(1(x1))))))
   0(1(2(5(x1)))) -> 3(5(5(2(1(0(x1))))))
   0(1(4(2(x1)))) -> 0(5(2(1(4(x1)))))
   0(1(5(2(x1)))) -> 1(5(0(2(3(x1)))))
   0(1(5(2(x1)))) -> 0(2(2(1(0(5(x1))))))
   0(1(5(2(x1)))) -> 5(5(0(2(1(3(x1))))))
   0(2(4(2(x1)))) -> 0(5(4(3(2(2(x1))))))
   0(3(1(2(x1)))) -> 0(2(1(3(2(x1)))))
   0(3(1(2(x1)))) -> 1(0(2(5(3(x1)))))
   0(3(1(2(x1)))) -> 1(5(0(2(3(x1)))))
   0(3(1(2(x1)))) -> 3(0(2(2(1(x1)))))
   0(3(1(2(x1)))) -> 3(2(2(1(0(x1)))))
   0(3(1(2(x1)))) -> 0(3(2(3(1(3(x1))))))
   0(3(4(2(x1)))) -> 0(2(2(3(4(x1)))))
   5(0(1(2(x1)))) -> 1(3(2(5(0(x1)))))
   5(0(1(2(x1)))) -> 5(0(2(1(3(3(x1))))))
   0(1(1(2(5(x1))))) -> 5(0(2(5(1(1(x1))))))
   0(2(3(4(2(x1))))) -> 3(2(2(3(4(0(x1))))))
   0(3(1(2(5(x1))))) -> 2(3(1(3(0(5(x1))))))
   0(3(1(5(2(x1))))) -> 0(3(2(5(1(2(x1))))))
   0(3(4(1(4(x1))))) -> 0(5(3(1(4(4(x1))))))
   0(3(5(1(2(x1))))) -> 5(5(3(2(1(0(x1))))))
   0(4(0(4(2(x1))))) -> 4(4(0(0(2(2(x1))))))
   0(4(1(1(2(x1))))) -> 3(1(4(0(2(1(x1))))))
   0(4(1(2(2(x1))))) -> 4(1(0(2(2(3(x1))))))
   0(4(1(2(5(x1))))) -> 3(4(1(0(2(5(x1))))))
   0(4(2(1(2(x1))))) -> 4(1(3(2(0(2(x1))))))
   0(4(2(1(4(x1))))) -> 0(2(1(4(4(4(x1))))))
   0(4(2(5(2(x1))))) -> 5(4(3(2(2(0(x1))))))
   0(4(5(1(2(x1))))) -> 1(4(2(0(5(5(x1))))))
   0(4(5(1(2(x1))))) -> 4(0(2(5(1(1(x1))))))
   5(0(1(2(2(x1))))) -> 5(0(2(2(1(2(x1))))))
   5(0(2(4(2(x1))))) -> 0(2(2(5(1(4(x1))))))
   5(0(4(4(2(x1))))) -> 0(5(2(5(4(4(x1))))))

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

   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(2(x_1)) -> 2(encArg(x_1))
   encArg(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_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
----------------------------------------

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

The rewrite sequence

0(1(2(x1))) ->^+ 0(2(1(0(x1))))

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

The pumping substitution is [x1 / 1(2(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(1(3(2(x1))))
   0(1(2(x1))) -> 0(2(1(0(x1))))
   0(1(2(x1))) -> 0(2(1(3(x1))))
   0(1(2(x1))) -> 0(2(2(1(x1))))
   0(1(2(x1))) -> 0(2(2(1(4(x1)))))
   0(1(2(x1))) -> 5(1(0(5(2(3(x1))))))
   0(2(4(x1))) -> 0(2(1(4(3(x1)))))
   0(4(2(x1))) -> 4(0(2(3(x1))))
   0(4(2(x1))) -> 4(0(5(5(2(x1)))))
   0(0(4(2(x1)))) -> 0(0(2(2(3(4(x1))))))
   0(1(2(2(x1)))) -> 0(2(1(0(2(x1)))))
   0(1(2(2(x1)))) -> 1(3(0(2(2(x1)))))
   0(1(2(4(x1)))) -> 0(1(4(2(3(x1)))))
   0(1(2(4(x1)))) -> 4(0(2(2(1(1(x1))))))
   0(1(2(4(x1)))) -> 4(0(5(5(2(1(x1))))))
   0(1(2(5(x1)))) -> 3(5(5(2(1(0(x1))))))
   0(1(4(2(x1)))) -> 0(5(2(1(4(x1)))))
   0(1(5(2(x1)))) -> 1(5(0(2(3(x1)))))
   0(1(5(2(x1)))) -> 0(2(2(1(0(5(x1))))))
   0(1(5(2(x1)))) -> 5(5(0(2(1(3(x1))))))
   0(2(4(2(x1)))) -> 0(5(4(3(2(2(x1))))))
   0(3(1(2(x1)))) -> 0(2(1(3(2(x1)))))
   0(3(1(2(x1)))) -> 1(0(2(5(3(x1)))))
   0(3(1(2(x1)))) -> 1(5(0(2(3(x1)))))
   0(3(1(2(x1)))) -> 3(0(2(2(1(x1)))))
   0(3(1(2(x1)))) -> 3(2(2(1(0(x1)))))
   0(3(1(2(x1)))) -> 0(3(2(3(1(3(x1))))))
   0(3(4(2(x1)))) -> 0(2(2(3(4(x1)))))
   5(0(1(2(x1)))) -> 1(3(2(5(0(x1)))))
   5(0(1(2(x1)))) -> 5(0(2(1(3(3(x1))))))
   0(1(1(2(5(x1))))) -> 5(0(2(5(1(1(x1))))))
   0(2(3(4(2(x1))))) -> 3(2(2(3(4(0(x1))))))
   0(3(1(2(5(x1))))) -> 2(3(1(3(0(5(x1))))))
   0(3(1(5(2(x1))))) -> 0(3(2(5(1(2(x1))))))
   0(3(4(1(4(x1))))) -> 0(5(3(1(4(4(x1))))))
   0(3(5(1(2(x1))))) -> 5(5(3(2(1(0(x1))))))
   0(4(0(4(2(x1))))) -> 4(4(0(0(2(2(x1))))))
   0(4(1(1(2(x1))))) -> 3(1(4(0(2(1(x1))))))
   0(4(1(2(2(x1))))) -> 4(1(0(2(2(3(x1))))))
   0(4(1(2(5(x1))))) -> 3(4(1(0(2(5(x1))))))
   0(4(2(1(2(x1))))) -> 4(1(3(2(0(2(x1))))))
   0(4(2(1(4(x1))))) -> 0(2(1(4(4(4(x1))))))
   0(4(2(5(2(x1))))) -> 5(4(3(2(2(0(x1))))))
   0(4(5(1(2(x1))))) -> 1(4(2(0(5(5(x1))))))
   0(4(5(1(2(x1))))) -> 4(0(2(5(1(1(x1))))))
   5(0(1(2(2(x1))))) -> 5(0(2(2(1(2(x1))))))
   5(0(2(4(2(x1))))) -> 0(2(2(5(1(4(x1))))))
   5(0(4(4(2(x1))))) -> 0(5(2(5(4(4(x1))))))

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

   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(2(x_1)) -> 2(encArg(x_1))
   encArg(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_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
----------------------------------------

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

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

   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(2(x_1)) -> 2(encArg(x_1))
   encArg(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_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