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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 42 ms]
(4) CpxRelTRS
(5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(6) CpxTRS
    (7) CpxTrsMatchBoundsProof [FINISHED, 51 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.

"[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, 382, 383]
{(52,53,[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]), (52,54,[5_1|1]), (52,58,[1_1|1]), (52,63,[0_1|1]), (52,68,[0_1|1]), (52,72,[1_1|1]), (52,76,[5_1|1]), (52,80,[5_1|1]), (52,84,[1_1|1]), (52,89,[5_1|1]), (52,94,[4_1|1]), (52,99,[1_1|1]), (52,104,[1_1|1, 3_1|1, 4_1|1, 5_1|1, 0_1|1, 2_1|1]), (52,105,[0_1|2]), (52,108,[1_1|2]), (52,111,[0_1|2]), (52,115,[0_1|2]), (52,119,[1_1|2]), (52,123,[0_1|2]), (52,128,[3_1|2]), (52,133,[5_1|2]), (52,137,[1_1|2]), (52,142,[0_1|2]), (52,147,[0_1|2]), (52,151,[5_1|2]), (52,156,[0_1|2]), (52,161,[5_1|2]), (52,166,[0_1|2]), (52,170,[1_1|2]), (52,175,[5_1|2]), (52,180,[1_1|2]), (52,185,[4_1|2]), (52,190,[3_1|2]), (52,193,[0_1|2]), (52,197,[0_1|2]), (52,201,[3_1|2]), (52,205,[0_1|2]), (52,210,[0_1|2]), (52,215,[4_1|2]), (52,220,[0_1|2]), (52,225,[4_1|2]), (52,230,[3_1|2]), (52,234,[5_1|2]), (52,238,[0_1|2]), (52,243,[0_1|2]), (52,247,[1_1|2]), (52,251,[5_1|2]), (52,255,[5_1|2]), (52,259,[1_1|2]), (52,264,[5_1|2]), (52,269,[1_1|2]), (52,274,[0_1|2]), (52,279,[4_1|2]), (52,284,[1_1|2]), (52,289,[5_1|2]), (52,293,[3_1|2]), (52,298,[2_1|2]), (52,303,[1_1|2]), (52,307,[3_1|2]), (52,312,[5_1|2]), (52,317,[1_1|2]), (52,322,[4_1|2]), (53,53,[1_1|0, 3_1|0, 4_1|0, 5_1|0, cons_0_1|0, cons_2_1|0]), (54,55,[0_1|1]), (55,56,[3_1|1]), (56,57,[1_1|1]), (57,53,[1_1|1]), (58,59,[0_1|1]), (59,60,[3_1|1]), (60,61,[4_1|1]), (61,62,[2_1|1]), (62,53,[1_1|1]), (63,64,[1_1|1]), (64,65,[4_1|1]), (65,66,[4_1|1]), (66,67,[3_1|1]), (67,53,[5_1|1]), (68,69,[2_1|1]), (69,70,[1_1|1]), (70,71,[5_1|1]), (71,53,[1_1|1]), (72,73,[4_1|1]), (73,74,[5_1|1]), (74,75,[4_1|1]), (75,53,[2_1|1]), (75,68,[0_1|1]), (75,72,[1_1|1]), (75,76,[5_1|1]), (75,80,[5_1|1]), (75,84,[1_1|1]), (75,89,[5_1|1]), (75,94,[4_1|1]), (75,99,[1_1|1]), (76,77,[0_1|1]), (77,78,[2_1|1]), (78,79,[1_1|1]), (79,53,[4_1|1]), (80,81,[2_1|1]), (81,82,[1_1|1]), (82,83,[4_1|1]), (83,53,[1_1|1]), (84,85,[5_1|1]), (85,86,[0_1|1]), (86,87,[2_1|1]), (87,88,[4_1|1]), (88,53,[1_1|1]), (89,90,[2_1|1]), (90,91,[1_1|1]), (91,92,[1_1|1]), (92,93,[1_1|1]), (93,53,[1_1|1]), (94,95,[5_1|1]), (95,96,[2_1|1]), (96,97,[1_1|1]), (97,98,[4_1|1]), (98,53,[4_1|1]), (99,100,[5_1|1]), (100,101,[4_1|1]), (101,102,[2_1|1]), (102,103,[4_1|1]), (103,53,[5_1|1]), (104,53,[encArg_1|1]), (104,104,[1_1|1, 3_1|1, 4_1|1, 5_1|1, 0_1|1, 2_1|1]), (104,105,[0_1|2]), (104,108,[1_1|2]), (104,111,[0_1|2]), (104,115,[0_1|2]), (104,119,[1_1|2]), (104,123,[0_1|2]), (104,128,[3_1|2]), (104,133,[5_1|2]), (104,137,[1_1|2]), (104,142,[0_1|2]), (104,147,[0_1|2]), (104,151,[5_1|2]), (104,156,[0_1|2]), (104,161,[5_1|2]), (104,166,[0_1|2]), (104,170,[1_1|2]), (104,175,[5_1|2]), (104,180,[1_1|2]), (104,185,[4_1|2]), (104,190,[3_1|2]), (104,193,[0_1|2]), (104,197,[0_1|2]), (104,201,[3_1|2]), (104,205,[0_1|2]), (104,210,[0_1|2]), (104,215,[4_1|2]), (104,220,[0_1|2]), (104,225,[4_1|2]), (104,230,[3_1|2]), (104,234,[5_1|2]), (104,238,[0_1|2]), (104,243,[0_1|2]), (104,247,[1_1|2]), (104,251,[5_1|2]), (104,255,[5_1|2]), (104,259,[1_1|2]), (104,264,[5_1|2]), (104,269,[1_1|2]), (104,274,[0_1|2]), (104,279,[4_1|2]), (104,284,[1_1|2]), (104,289,[5_1|2]), (104,293,[3_1|2]), (104,298,[2_1|2]), (104,303,[1_1|2]), (104,307,[3_1|2]), (104,312,[5_1|2]), (104,317,[1_1|2]), (104,322,[4_1|2]), (105,106,[2_1|2]), (106,107,[1_1|2]), (107,104,[0_1|2]), (107,298,[0_1|2]), (107,105,[0_1|2]), (107,108,[1_1|2]), (107,111,[0_1|2]), (107,115,[0_1|2]), (107,119,[1_1|2]), (107,123,[0_1|2]), (107,128,[3_1|2]), (107,133,[5_1|2]), (107,137,[1_1|2]), (107,142,[0_1|2]), (107,147,[0_1|2]), (107,151,[5_1|2]), (107,156,[0_1|2]), (107,161,[5_1|2]), (107,166,[0_1|2]), (107,170,[1_1|2]), (107,175,[5_1|2]), (107,180,[1_1|2]), (107,185,[4_1|2]), (107,327,[0_1|3]), (107,331,[5_1|3]), (107,336,[5_1|3]), (108,109,[0_1|2]), (109,110,[2_1|2]), (110,104,[3_1|2]), (110,298,[3_1|2]), (111,112,[2_1|2]), (112,113,[4_1|2]), (113,114,[1_1|2]), (114,104,[5_1|2]), (114,298,[5_1|2]), (115,116,[3_1|2]), (116,117,[2_1|2]), (117,118,[1_1|2]), (118,104,[0_1|2]), (118,298,[0_1|2]), (118,105,[0_1|2]), (118,108,[1_1|2]), (118,111,[0_1|2]), (118,115,[0_1|2]), (118,119,[1_1|2]), (118,123,[0_1|2]), (118,128,[3_1|2]), (118,133,[5_1|2]), (118,137,[1_1|2]), (118,142,[0_1|2]), (118,147,[0_1|2]), (118,151,[5_1|2]), (118,156,[0_1|2]), (118,161,[5_1|2]), (118,166,[0_1|2]), (118,170,[1_1|2]), (118,175,[5_1|2]), (118,180,[1_1|2]), (118,185,[4_1|2]), (118,327,[0_1|3]), (118,331,[5_1|3]), (118,336,[5_1|3]), (119,120,[0_1|2]), (120,121,[3_1|2]), (121,122,[2_1|2]), (122,104,[3_1|2]), (122,298,[3_1|2]), (123,124,[1_1|2]), (124,125,[3_1|2]), (125,126,[4_1|2]), (126,127,[2_1|2]), (127,104,[3_1|2]), (127,298,[3_1|2]), (128,129,[1_1|2]), (129,130,[4_1|2]), (130,131,[0_1|2]), (130,166,[0_1|2]), (130,341,[0_1|3]), (131,132,[2_1|2]), (132,104,[1_1|2]), (132,108,[1_1|2]), (132,119,[1_1|2]), (132,137,[1_1|2]), (132,170,[1_1|2]), (132,180,[1_1|2]), (132,247,[1_1|2]), (132,259,[1_1|2]), (132,269,[1_1|2]), (132,284,[1_1|2]), (132,303,[1_1|2]), (132,317,[1_1|2]), (133,134,[0_1|2]), (134,135,[3_1|2]), (135,136,[1_1|2]), (136,104,[1_1|2]), (136,108,[1_1|2]), (136,119,[1_1|2]), (136,137,[1_1|2]), (136,170,[1_1|2]), (136,180,[1_1|2]), (136,247,[1_1|2]), (136,259,[1_1|2]), (136,269,[1_1|2]), (136,284,[1_1|2]), (136,303,[1_1|2]), (136,317,[1_1|2]), (136,129,[1_1|2]), (137,138,[0_1|2]), (138,139,[3_1|2]), (139,140,[4_1|2]), (140,141,[2_1|2]), (141,104,[1_1|2]), (141,108,[1_1|2]), (141,119,[1_1|2]), (141,137,[1_1|2]), (141,170,[1_1|2]), (141,180,[1_1|2]), (141,247,[1_1|2]), (141,259,[1_1|2]), (141,269,[1_1|2]), (141,284,[1_1|2]), (141,303,[1_1|2]), (141,317,[1_1|2]), (141,129,[1_1|2]), (142,143,[3_1|2]), (143,144,[1_1|2]), (144,145,[0_1|2]), (145,146,[1_1|2]), (146,104,[1_1|2]), (146,108,[1_1|2]), (146,119,[1_1|2]), (146,137,[1_1|2]), (146,170,[1_1|2]), (146,180,[1_1|2]), (146,247,[1_1|2]), (146,259,[1_1|2]), (146,269,[1_1|2]), (146,284,[1_1|2]), (146,303,[1_1|2]), (146,317,[1_1|2]), (146,124,[1_1|2]), (146,157,[1_1|2]), (147,148,[2_1|2]), (148,149,[4_1|2]), (149,150,[5_1|2]), (150,104,[3_1|2]), (150,298,[3_1|2]), (150,256,[3_1|2]), (150,265,[3_1|2]), (151,152,[4_1|2]), (152,153,[2_1|2]), (153,154,[3_1|2]), (154,155,[0_1|2]), (155,104,[4_1|2]), (155,298,[4_1|2]), (155,256,[4_1|2]), (155,265,[4_1|2]), (156,157,[1_1|2]), (157,158,[4_1|2]), (158,159,[4_1|2]), (159,160,[3_1|2]), (160,104,[5_1|2]), (160,108,[5_1|2]), (160,119,[5_1|2]), (160,137,[5_1|2]), (160,170,[5_1|2]), (160,180,[5_1|2]), (160,247,[5_1|2]), (160,259,[5_1|2]), (160,269,[5_1|2]), (160,284,[5_1|2]), (160,303,[5_1|2]), (160,317,[5_1|2]), (160,129,[5_1|2]), (161,162,[4_1|2]), (162,163,[2_1|2]), (163,164,[3_1|2]), (164,165,[5_1|2]), (165,104,[0_1|2]), (165,298,[0_1|2]), (165,256,[0_1|2]), (165,265,[0_1|2]), (165,291,[0_1|2]), (165,105,[0_1|2]), (165,108,[1_1|2]), (165,111,[0_1|2]), (165,115,[0_1|2]), (165,119,[1_1|2]), (165,123,[0_1|2]), (165,128,[3_1|2]), (165,133,[5_1|2]), (165,137,[1_1|2]), (165,142,[0_1|2]), (165,147,[0_1|2]), (165,151,[5_1|2]), (165,156,[0_1|2]), (165,161,[5_1|2]), (165,166,[0_1|2]), (165,170,[1_1|2]), (165,175,[5_1|2]), (165,180,[1_1|2]), (165,185,[4_1|2]), (165,327,[0_1|3]), (165,331,[5_1|3]), (165,336,[5_1|3]), (166,167,[2_1|2]), (167,168,[2_1|2]), (168,169,[1_1|2]), (169,104,[5_1|2]), (169,298,[5_1|2]), (170,171,[1_1|2]), (171,172,[5_1|2]), (172,173,[0_1|2]), (172,166,[0_1|2]), (172,341,[0_1|3]), (173,174,[2_1|2]), (174,104,[1_1|2]), (174,108,[1_1|2]), (174,119,[1_1|2]), (174,137,[1_1|2]), (174,170,[1_1|2]), (174,180,[1_1|2]), (174,247,[1_1|2]), (174,259,[1_1|2]), (174,269,[1_1|2]), (174,284,[1_1|2]), (174,303,[1_1|2]), (174,317,[1_1|2]), (175,176,[0_1|2]), (176,177,[2_1|2]), (177,178,[3_1|2]), (178,179,[5_1|2]), (179,104,[1_1|2]), (179,108,[1_1|2]), (179,119,[1_1|2]), (179,137,[1_1|2]), (179,170,[1_1|2]), (179,180,[1_1|2]), (179,247,[1_1|2]), (179,259,[1_1|2]), (179,269,[1_1|2]), (179,284,[1_1|2]), (179,303,[1_1|2]), (179,317,[1_1|2]), (179,129,[1_1|2]), (180,181,[3_1|2]), (181,182,[4_1|2]), (182,183,[2_1|2]), (183,184,[3_1|2]), (184,104,[0_1|2]), (184,108,[0_1|2, 1_1|2]), (184,119,[0_1|2, 1_1|2]), (184,137,[0_1|2, 1_1|2]), (184,170,[0_1|2, 1_1|2]), (184,180,[0_1|2, 1_1|2]), (184,247,[0_1|2]), (184,259,[0_1|2]), (184,269,[0_1|2]), (184,284,[0_1|2]), (184,303,[0_1|2]), (184,317,[0_1|2]), (184,129,[0_1|2]), (184,105,[0_1|2]), (184,111,[0_1|2]), (184,115,[0_1|2]), (184,123,[0_1|2]), (184,128,[3_1|2]), (184,133,[5_1|2]), (184,142,[0_1|2]), (184,147,[0_1|2]), (184,151,[5_1|2]), (184,156,[0_1|2]), (184,161,[5_1|2]), (184,166,[0_1|2]), (184,175,[5_1|2]), (184,185,[4_1|2]), (184,327,[0_1|3]), (184,331,[5_1|3]), (184,336,[5_1|3]), (185,186,[0_1|2]), (186,187,[3_1|2]), (187,188,[2_1|2]), (188,189,[1_1|2]), (189,104,[0_1|2]), (189,108,[0_1|2, 1_1|2]), (189,119,[0_1|2, 1_1|2]), (189,137,[0_1|2, 1_1|2]), (189,170,[0_1|2, 1_1|2]), (189,180,[0_1|2, 1_1|2]), (189,247,[0_1|2]), (189,259,[0_1|2]), (189,269,[0_1|2]), (189,284,[0_1|2]), (189,303,[0_1|2]), (189,317,[0_1|2]), (189,129,[0_1|2]), (189,105,[0_1|2]), (189,111,[0_1|2]), (189,115,[0_1|2]), (189,123,[0_1|2]), (189,128,[3_1|2]), (189,133,[5_1|2]), (189,142,[0_1|2]), (189,147,[0_1|2]), (189,151,[5_1|2]), (189,156,[0_1|2]), (189,161,[5_1|2]), (189,166,[0_1|2]), (189,175,[5_1|2]), (189,185,[4_1|2]), (189,327,[0_1|3]), (189,331,[5_1|3]), (189,336,[5_1|3]), (190,191,[0_1|2]), (190,166,[0_1|2]), (190,341,[0_1|3]), (191,192,[2_1|2]), (192,104,[1_1|2]), (192,108,[1_1|2]), (192,119,[1_1|2]), (192,137,[1_1|2]), (192,170,[1_1|2]), (192,180,[1_1|2]), (192,247,[1_1|2]), (192,259,[1_1|2]), (192,269,[1_1|2]), (192,284,[1_1|2]), (192,303,[1_1|2]), (192,317,[1_1|2]), (192,124,[1_1|2]), (192,157,[1_1|2]), (193,194,[2_1|2]), (194,195,[1_1|2]), (195,196,[1_1|2]), (196,104,[4_1|2]), (196,108,[4_1|2]), (196,119,[4_1|2]), (196,137,[4_1|2]), (196,170,[4_1|2]), (196,180,[4_1|2]), (196,247,[4_1|2]), (196,259,[4_1|2]), (196,269,[4_1|2]), (196,284,[4_1|2]), (196,303,[4_1|2]), (196,317,[4_1|2]), (196,124,[4_1|2]), (196,157,[4_1|2]), (197,198,[3_1|2]), (198,199,[2_1|2]), (199,200,[4_1|2]), (200,104,[1_1|2]), (200,108,[1_1|2]), (200,119,[1_1|2]), (200,137,[1_1|2]), (200,170,[1_1|2]), (200,180,[1_1|2]), (200,247,[1_1|2]), (200,259,[1_1|2]), (200,269,[1_1|2]), (200,284,[1_1|2]), (200,303,[1_1|2]), (200,317,[1_1|2]), (200,124,[1_1|2]), (200,157,[1_1|2]), (201,202,[0_1|2]), (202,203,[2_1|2]), (203,204,[1_1|2]), (204,104,[4_1|2]), (204,108,[4_1|2]), (204,119,[4_1|2]), (204,137,[4_1|2]), (204,170,[4_1|2]), (204,180,[4_1|2]), (204,247,[4_1|2]), (204,259,[4_1|2]), (204,269,[4_1|2]), (204,284,[4_1|2]), (204,303,[4_1|2]), (204,317,[4_1|2]), (204,124,[4_1|2]), (204,157,[4_1|2]), (205,206,[2_1|2]), (206,207,[2_1|2]), (207,208,[3_1|2]), (208,209,[4_1|2]), (209,104,[1_1|2]), (209,108,[1_1|2]), (209,119,[1_1|2]), (209,137,[1_1|2]), (209,170,[1_1|2]), (209,180,[1_1|2]), (209,247,[1_1|2]), (209,259,[1_1|2]), (209,269,[1_1|2]), (209,284,[1_1|2]), (209,303,[1_1|2]), (209,317,[1_1|2]), (209,124,[1_1|2]), (209,157,[1_1|2]), (210,211,[3_1|2]), (211,212,[2_1|2]), (212,213,[3_1|2]), (213,214,[1_1|2]), (214,104,[1_1|2]), (214,108,[1_1|2]), (214,119,[1_1|2]), (214,137,[1_1|2]), (214,170,[1_1|2]), (214,180,[1_1|2]), (214,247,[1_1|2]), (214,259,[1_1|2]), (214,269,[1_1|2]), (214,284,[1_1|2]), (214,303,[1_1|2]), (214,317,[1_1|2]), (214,124,[1_1|2]), (214,157,[1_1|2]), (215,216,[0_1|2]), (216,217,[4_1|2]), (217,218,[2_1|2]), (218,219,[1_1|2]), (219,104,[4_1|2]), (219,108,[4_1|2]), (219,119,[4_1|2]), (219,137,[4_1|2]), (219,170,[4_1|2]), (219,180,[4_1|2]), (219,247,[4_1|2]), (219,259,[4_1|2]), (219,269,[4_1|2]), (219,284,[4_1|2]), (219,303,[4_1|2]), (219,317,[4_1|2]), (219,124,[4_1|2]), (219,157,[4_1|2]), (220,221,[2_1|2]), (221,222,[3_1|2]), (222,223,[2_1|2]), (223,224,[1_1|2]), (224,104,[1_1|2]), (224,298,[1_1|2]), (225,226,[0_1|2]), (226,227,[2_1|2]), (227,228,[1_1|2]), (228,229,[1_1|2]), (229,104,[2_1|2]), (229,298,[2_1|2]), (229,190,[3_1|2]), (229,193,[0_1|2]), (229,197,[0_1|2]), (229,201,[3_1|2]), (229,205,[0_1|2]), (229,210,[0_1|2]), (229,215,[4_1|2]), (229,220,[0_1|2]), (229,225,[4_1|2]), (229,230,[3_1|2]), (229,234,[5_1|2]), (229,238,[0_1|2]), (229,243,[0_1|2]), (229,247,[1_1|2]), (229,251,[5_1|2]), (229,255,[5_1|2]), (229,259,[1_1|2]), (229,264,[5_1|2]), (229,269,[1_1|2]), (229,274,[0_1|2]), (229,279,[4_1|2]), (229,284,[1_1|2]), (229,289,[5_1|2]), (229,293,[3_1|2]), (229,303,[1_1|2]), (229,307,[3_1|2]), (229,312,[5_1|2]), (229,317,[1_1|2]), (229,322,[4_1|2]), (229,345,[3_1|3]), (229,348,[0_1|3]), (229,352,[0_1|3]), (229,356,[3_1|3]), (229,360,[0_1|3]), (229,365,[0_1|3]), (229,370,[4_1|3]), (229,375,[1_1|3]), (229,380,[5_1|3]), (230,231,[0_1|2]), (231,232,[2_1|2]), (232,233,[4_1|2]), (233,104,[1_1|2]), (233,108,[1_1|2]), (233,119,[1_1|2]), (233,137,[1_1|2]), (233,170,[1_1|2]), (233,180,[1_1|2]), (233,247,[1_1|2]), (233,259,[1_1|2]), (233,269,[1_1|2]), (233,284,[1_1|2]), (233,303,[1_1|2]), (233,317,[1_1|2]), (234,235,[4_1|2]), (235,236,[2_1|2]), (236,237,[1_1|2]), (237,104,[0_1|2]), (237,108,[0_1|2, 1_1|2]), (237,119,[0_1|2, 1_1|2]), (237,137,[0_1|2, 1_1|2]), (237,170,[0_1|2, 1_1|2]), (237,180,[0_1|2, 1_1|2]), (237,247,[0_1|2]), (237,259,[0_1|2]), (237,269,[0_1|2]), (237,284,[0_1|2]), (237,303,[0_1|2]), (237,317,[0_1|2]), (237,105,[0_1|2]), (237,111,[0_1|2]), (237,115,[0_1|2]), (237,123,[0_1|2]), (237,128,[3_1|2]), (237,133,[5_1|2]), (237,142,[0_1|2]), (237,147,[0_1|2]), (237,151,[5_1|2]), (237,156,[0_1|2]), (237,161,[5_1|2]), (237,166,[0_1|2]), (237,175,[5_1|2]), (237,185,[4_1|2]), (237,327,[0_1|3]), (237,331,[5_1|3]), (237,336,[5_1|3]), (238,239,[4_1|2]), (239,240,[5_1|2]), (240,241,[3_1|2]), (241,242,[2_1|2]), (242,104,[1_1|2]), (242,108,[1_1|2]), (242,119,[1_1|2]), (242,137,[1_1|2]), (242,170,[1_1|2]), (242,180,[1_1|2]), (242,247,[1_1|2]), (242,259,[1_1|2]), (242,269,[1_1|2]), (242,284,[1_1|2]), (242,303,[1_1|2]), (242,317,[1_1|2]), (243,244,[2_1|2]), (244,245,[1_1|2]), (245,246,[5_1|2]), (246,104,[1_1|2]), (246,108,[1_1|2]), (246,119,[1_1|2]), (246,137,[1_1|2]), (246,170,[1_1|2]), (246,180,[1_1|2]), (246,247,[1_1|2]), (246,259,[1_1|2]), (246,269,[1_1|2]), (246,284,[1_1|2]), (246,303,[1_1|2]), (246,317,[1_1|2]), (247,248,[4_1|2]), (248,249,[5_1|2]), (249,250,[4_1|2]), (250,104,[2_1|2]), (250,108,[2_1|2]), (250,119,[2_1|2]), (250,137,[2_1|2]), (250,170,[2_1|2]), (250,180,[2_1|2]), (250,247,[2_1|2, 1_1|2]), (250,259,[2_1|2, 1_1|2]), (250,269,[2_1|2, 1_1|2]), (250,284,[2_1|2, 1_1|2]), (250,303,[2_1|2, 1_1|2]), (250,317,[2_1|2, 1_1|2]), (250,190,[3_1|2]), (250,193,[0_1|2]), (250,197,[0_1|2]), (250,201,[3_1|2]), (250,205,[0_1|2]), (250,210,[0_1|2]), (250,215,[4_1|2]), (250,220,[0_1|2]), (250,225,[4_1|2]), (250,230,[3_1|2]), (250,234,[5_1|2]), (250,238,[0_1|2]), (250,243,[0_1|2]), (250,251,[5_1|2]), (250,255,[5_1|2]), (250,264,[5_1|2]), (250,274,[0_1|2]), (250,279,[4_1|2]), (250,289,[5_1|2]), (250,293,[3_1|2]), (250,298,[2_1|2]), (250,307,[3_1|2]), (250,312,[5_1|2]), (250,322,[4_1|2]), (250,345,[3_1|3]), (250,348,[0_1|3]), (250,352,[0_1|3]), (250,356,[3_1|3]), (250,360,[0_1|3]), (250,365,[0_1|3]), (250,370,[4_1|3]), (250,375,[1_1|3]), (250,380,[5_1|3]), (251,252,[0_1|2]), (252,253,[2_1|2]), (253,254,[1_1|2]), (254,104,[4_1|2]), (254,108,[4_1|2]), (254,119,[4_1|2]), (254,137,[4_1|2]), (254,170,[4_1|2]), (254,180,[4_1|2]), (254,247,[4_1|2]), (254,259,[4_1|2]), (254,269,[4_1|2]), (254,284,[4_1|2]), (254,303,[4_1|2]), (254,317,[4_1|2]), (255,256,[2_1|2]), (256,257,[1_1|2]), (257,258,[4_1|2]), (258,104,[1_1|2]), (258,108,[1_1|2]), (258,119,[1_1|2]), (258,137,[1_1|2]), (258,170,[1_1|2]), (258,180,[1_1|2]), (258,247,[1_1|2]), (258,259,[1_1|2]), (258,269,[1_1|2]), (258,284,[1_1|2]), (258,303,[1_1|2]), (258,317,[1_1|2]), (259,260,[5_1|2]), (260,261,[0_1|2]), (261,262,[2_1|2]), (262,263,[4_1|2]), (263,104,[1_1|2]), (263,108,[1_1|2]), (263,119,[1_1|2]), (263,137,[1_1|2]), (263,170,[1_1|2]), (263,180,[1_1|2]), (263,247,[1_1|2]), (263,259,[1_1|2]), (263,269,[1_1|2]), (263,284,[1_1|2]), (263,303,[1_1|2]), (263,317,[1_1|2]), (264,265,[2_1|2]), (265,266,[1_1|2]), (266,267,[1_1|2]), (267,268,[1_1|2]), (268,104,[1_1|2]), (268,108,[1_1|2]), (268,119,[1_1|2]), (268,137,[1_1|2]), (268,170,[1_1|2]), (268,180,[1_1|2]), (268,247,[1_1|2]), (268,259,[1_1|2]), (268,269,[1_1|2]), (268,284,[1_1|2]), (268,303,[1_1|2]), (268,317,[1_1|2]), (269,270,[5_1|2]), (270,271,[2_1|2]), (271,272,[2_1|2]), (272,273,[3_1|2]), (273,104,[1_1|2]), (273,108,[1_1|2]), (273,119,[1_1|2]), (273,137,[1_1|2]), (273,170,[1_1|2]), (273,180,[1_1|2]), (273,247,[1_1|2]), (273,259,[1_1|2]), (273,269,[1_1|2]), (273,284,[1_1|2]), (273,303,[1_1|2]), (273,317,[1_1|2]), (273,257,[1_1|2]), (273,266,[1_1|2]), (274,275,[2_1|2]), (275,276,[4_1|2]), (276,277,[1_1|2]), (277,278,[5_1|2]), (278,104,[2_1|2]), (278,108,[2_1|2]), (278,119,[2_1|2]), (278,137,[2_1|2]), (278,170,[2_1|2]), (278,180,[2_1|2]), (278,247,[2_1|2, 1_1|2]), (278,259,[2_1|2, 1_1|2]), (278,269,[2_1|2, 1_1|2]), (278,284,[2_1|2, 1_1|2]), (278,303,[2_1|2, 1_1|2]), (278,317,[2_1|2, 1_1|2]), (278,124,[2_1|2]), (278,157,[2_1|2]), (278,190,[3_1|2]), (278,193,[0_1|2]), (278,197,[0_1|2]), (278,201,[3_1|2]), (278,205,[0_1|2]), (278,210,[0_1|2]), (278,215,[4_1|2]), (278,220,[0_1|2]), (278,225,[4_1|2]), (278,230,[3_1|2]), (278,234,[5_1|2]), (278,238,[0_1|2]), (278,243,[0_1|2]), (278,251,[5_1|2]), (278,255,[5_1|2]), (278,264,[5_1|2]), (278,274,[0_1|2]), (278,279,[4_1|2]), (278,289,[5_1|2]), (278,293,[3_1|2]), (278,298,[2_1|2]), (278,307,[3_1|2]), (278,312,[5_1|2]), (278,322,[4_1|2]), (278,345,[3_1|3]), (278,348,[0_1|3]), (278,352,[0_1|3]), (278,356,[3_1|3]), (278,360,[0_1|3]), (278,365,[0_1|3]), (278,370,[4_1|3]), (278,375,[1_1|3]), (278,380,[5_1|3]), (279,280,[5_1|2]), (280,281,[2_1|2]), (281,282,[1_1|2]), (282,283,[4_1|2]), (283,104,[4_1|2]), (283,108,[4_1|2]), (283,119,[4_1|2]), (283,137,[4_1|2]), (283,170,[4_1|2]), (283,180,[4_1|2]), (283,247,[4_1|2]), (283,259,[4_1|2]), (283,269,[4_1|2]), (283,284,[4_1|2]), (283,303,[4_1|2]), (283,317,[4_1|2]), (284,285,[5_1|2]), (285,286,[4_1|2]), (286,287,[2_1|2]), (287,288,[4_1|2]), (288,104,[5_1|2]), (288,108,[5_1|2]), (288,119,[5_1|2]), (288,137,[5_1|2]), (288,170,[5_1|2]), (288,180,[5_1|2]), (288,247,[5_1|2]), (288,259,[5_1|2]), (288,269,[5_1|2]), (288,284,[5_1|2]), (288,303,[5_1|2]), (288,317,[5_1|2]), (289,290,[5_1|2]), (290,291,[2_1|2]), (291,292,[3_1|2]), (292,104,[2_1|2]), (292,298,[2_1|2]), (292,256,[2_1|2]), (292,265,[2_1|2]), (292,291,[2_1|2]), (292,190,[3_1|2]), (292,193,[0_1|2]), (292,197,[0_1|2]), (292,201,[3_1|2]), (292,205,[0_1|2]), (292,210,[0_1|2]), (292,215,[4_1|2]), (292,220,[0_1|2]), (292,225,[4_1|2]), (292,230,[3_1|2]), (292,234,[5_1|2]), (292,238,[0_1|2]), (292,243,[0_1|2]), (292,247,[1_1|2]), (292,251,[5_1|2]), (292,255,[5_1|2]), (292,259,[1_1|2]), (292,264,[5_1|2]), (292,269,[1_1|2]), (292,274,[0_1|2]), (292,279,[4_1|2]), (292,284,[1_1|2]), (292,289,[5_1|2]), (292,293,[3_1|2]), (292,303,[1_1|2]), (292,307,[3_1|2]), (292,312,[5_1|2]), (292,317,[1_1|2]), (292,322,[4_1|2]), (292,345,[3_1|3]), (292,348,[0_1|3]), (292,352,[0_1|3]), (292,356,[3_1|3]), (292,360,[0_1|3]), (292,365,[0_1|3]), (292,370,[4_1|3]), (292,375,[1_1|3]), (292,380,[5_1|3]), (293,294,[2_1|2]), (294,295,[2_1|2]), (295,296,[4_1|2]), (296,297,[5_1|2]), (297,104,[1_1|2]), (297,108,[1_1|2]), (297,119,[1_1|2]), (297,137,[1_1|2]), (297,170,[1_1|2]), (297,180,[1_1|2]), (297,247,[1_1|2]), (297,259,[1_1|2]), (297,269,[1_1|2]), (297,284,[1_1|2]), (297,303,[1_1|2]), (297,317,[1_1|2]), (298,299,[4_1|2]), (299,300,[0_1|2]), (300,301,[2_1|2]), (301,302,[2_1|2]), (302,104,[1_1|2]), (302,298,[1_1|2]), (303,304,[0_1|2]), (304,305,[2_1|2]), (305,306,[4_1|2]), (306,104,[4_1|2]), (306,108,[4_1|2]), (306,119,[4_1|2]), (306,137,[4_1|2]), (306,170,[4_1|2]), (306,180,[4_1|2]), (306,247,[4_1|2]), (306,259,[4_1|2]), (306,269,[4_1|2]), (306,284,[4_1|2]), (306,303,[4_1|2]), (306,317,[4_1|2]), (306,124,[4_1|2]), (306,157,[4_1|2]), (307,308,[0_1|2]), (308,309,[0_1|2]), (309,310,[2_1|2]), (310,311,[4_1|2]), (311,104,[1_1|2]), (311,108,[1_1|2]), (311,119,[1_1|2]), (311,137,[1_1|2]), (311,170,[1_1|2]), (311,180,[1_1|2]), (311,247,[1_1|2]), (311,259,[1_1|2]), (311,269,[1_1|2]), (311,284,[1_1|2]), (311,303,[1_1|2]), (311,317,[1_1|2]), (311,124,[1_1|2]), (311,157,[1_1|2]), (312,313,[4_1|2]), (313,314,[0_1|2]), (314,315,[2_1|2]), (315,316,[1_1|2]), (316,104,[1_1|2]), (316,108,[1_1|2]), (316,119,[1_1|2]), (316,137,[1_1|2]), (316,170,[1_1|2]), (316,180,[1_1|2]), (316,247,[1_1|2]), (316,259,[1_1|2]), (316,269,[1_1|2]), (316,284,[1_1|2]), (316,303,[1_1|2]), (316,317,[1_1|2]), (316,124,[1_1|2]), (316,157,[1_1|2]), (317,318,[4_1|2]), (318,319,[5_1|2]), (319,320,[0_1|2]), (320,321,[4_1|2]), (321,104,[2_1|2]), (321,108,[2_1|2]), (321,119,[2_1|2]), (321,137,[2_1|2]), (321,170,[2_1|2]), (321,180,[2_1|2]), (321,247,[2_1|2, 1_1|2]), (321,259,[2_1|2, 1_1|2]), (321,269,[2_1|2, 1_1|2]), (321,284,[2_1|2, 1_1|2]), (321,303,[2_1|2, 1_1|2]), (321,317,[2_1|2, 1_1|2]), (321,190,[3_1|2]), (321,193,[0_1|2]), (321,197,[0_1|2]), (321,201,[3_1|2]), (321,205,[0_1|2]), (321,210,[0_1|2]), (321,215,[4_1|2]), (321,220,[0_1|2]), (321,225,[4_1|2]), (321,230,[3_1|2]), (321,234,[5_1|2]), (321,238,[0_1|2]), (321,243,[0_1|2]), (321,251,[5_1|2]), (321,255,[5_1|2]), (321,264,[5_1|2]), (321,274,[0_1|2]), (321,279,[4_1|2]), (321,289,[5_1|2]), (321,293,[3_1|2]), (321,298,[2_1|2]), (321,307,[3_1|2]), (321,312,[5_1|2]), (321,322,[4_1|2]), (321,345,[3_1|3]), (321,348,[0_1|3]), (321,352,[0_1|3]), (321,356,[3_1|3]), (321,360,[0_1|3]), (321,365,[0_1|3]), (321,370,[4_1|3]), (321,375,[1_1|3]), (321,380,[5_1|3]), (322,323,[2_1|2]), (323,324,[2_1|2]), (324,325,[3_1|2]), (325,326,[3_1|2]), (326,104,[1_1|2]), (326,108,[1_1|2]), (326,119,[1_1|2]), (326,137,[1_1|2]), (326,170,[1_1|2]), (326,180,[1_1|2]), (326,247,[1_1|2]), (326,259,[1_1|2]), (326,269,[1_1|2]), (326,284,[1_1|2]), (326,303,[1_1|2]), (326,317,[1_1|2]), (326,129,[1_1|2]), (327,328,[2_1|3]), (328,329,[4_1|3]), (329,330,[5_1|3]), (330,256,[3_1|3]), (330,265,[3_1|3]), (330,271,[3_1|3]), (331,332,[4_1|3]), (332,333,[2_1|3]), (333,334,[3_1|3]), (334,335,[0_1|3]), (335,256,[4_1|3]), (335,265,[4_1|3]), (335,271,[4_1|3]), (336,337,[4_1|3]), (337,338,[2_1|3]), (338,339,[3_1|3]), (339,340,[5_1|3]), (340,291,[0_1|3]), (341,342,[2_1|3]), (342,343,[2_1|3]), (343,344,[1_1|3]), (344,298,[5_1|3]), (345,346,[0_1|3]), (346,347,[2_1|3]), (347,124,[1_1|3]), (347,157,[1_1|3]), (348,349,[2_1|3]), (349,350,[1_1|3]), (350,351,[1_1|3]), (351,124,[4_1|3]), (351,157,[4_1|3]), (352,353,[3_1|3]), (353,354,[2_1|3]), (354,355,[4_1|3]), (355,124,[1_1|3]), (355,157,[1_1|3]), (356,357,[0_1|3]), (357,358,[2_1|3]), (358,359,[1_1|3]), (359,124,[4_1|3]), (359,157,[4_1|3]), (360,361,[2_1|3]), (361,362,[2_1|3]), (362,363,[3_1|3]), (363,364,[4_1|3]), (364,124,[1_1|3]), (364,157,[1_1|3]), (365,366,[3_1|3]), (366,367,[2_1|3]), (367,368,[3_1|3]), (368,369,[1_1|3]), (369,124,[1_1|3]), (369,157,[1_1|3]), (370,371,[0_1|3]), (371,372,[4_1|3]), (372,373,[2_1|3]), (373,374,[1_1|3]), (374,124,[4_1|3]), (374,157,[4_1|3]), (375,376,[5_1|3]), (376,377,[2_1|3]), (377,378,[2_1|3]), (378,379,[3_1|3]), (379,257,[1_1|3]), (379,266,[1_1|3]), (380,381,[5_1|3]), (381,382,[2_1|3]), (382,383,[3_1|3]), (383,291,[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