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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 197 ms]
(4) CpxRelTRS
(5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(6) CpxTRS
    (7) CpxTrsMatchBoundsProof [FINISHED, 71 ms]
    (8) BOUNDS(1, n^1)
(9) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(10) TRS for Loop Detection
    (11) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
    (12) BEST
        (13) proven lower bound
            (14) LowerBoundPropagationProof [FINISHED, 0 ms]
            (15) BOUNDS(n^1, INF)
        (16) TRS for Loop Detection


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

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


The TRS R consists of the following rules:

   0(1(2(x1))) -> 0(0(2(1(x1))))
   0(1(2(x1))) -> 0(2(1(3(x1))))
   0(1(2(x1))) -> 0(0(2(1(4(4(x1))))))
   0(3(1(x1))) -> 0(1(3(4(0(x1)))))
   0(3(1(x1))) -> 0(1(3(4(4(x1)))))
   0(3(1(x1))) -> 1(3(4(4(4(0(x1))))))
   0(3(2(x1))) -> 0(2(1(3(x1))))
   0(3(2(x1))) -> 0(2(3(4(x1))))
   0(3(2(x1))) -> 0(0(2(4(3(x1)))))
   0(3(2(x1))) -> 0(2(1(4(3(x1)))))
   0(3(2(x1))) -> 0(2(4(3(3(x1)))))
   0(3(2(x1))) -> 0(2(1(3(3(4(x1))))))
   0(3(2(x1))) -> 0(2(3(4(5(5(x1))))))
   0(3(2(x1))) -> 2(4(4(3(4(0(x1))))))
   0(4(1(x1))) -> 0(1(4(4(x1))))
   0(4(1(x1))) -> 0(2(1(4(x1))))
   0(4(2(x1))) -> 0(2(1(4(x1))))
   0(4(2(x1))) -> 0(2(3(4(x1))))
   0(4(2(x1))) -> 0(2(4(3(x1))))
   2(0(1(x1))) -> 5(0(2(1(x1))))
   2(3(1(x1))) -> 1(3(5(2(x1))))
   2(3(1(x1))) -> 0(2(1(3(5(x1)))))
   2(3(1(x1))) -> 1(4(3(5(2(x1)))))
   0(2(0(1(x1)))) -> 5(0(0(2(1(x1)))))
   0(3(1(1(x1)))) -> 0(1(4(1(3(4(x1))))))
   0(3(2(1(x1)))) -> 0(0(3(4(2(1(x1))))))
   0(3(2(2(x1)))) -> 1(3(4(0(2(2(x1))))))
   0(4(1(2(x1)))) -> 1(4(0(2(5(x1)))))
   0(4(3(2(x1)))) -> 2(3(4(4(0(0(x1))))))
   0(5(3(1(x1)))) -> 0(1(4(3(5(4(x1))))))
   0(5(3(1(x1)))) -> 0(1(5(3(4(0(x1))))))
   0(5(3(2(x1)))) -> 0(2(4(5(3(x1)))))
   0(5(3(2(x1)))) -> 0(2(5(3(3(x1)))))
   2(0(3(1(x1)))) -> 2(0(1(3(5(2(x1))))))
   2(0(4(1(x1)))) -> 2(0(1(4(5(x1)))))
   2(5(3(2(x1)))) -> 2(5(2(3(3(x1)))))
   2(5(4(2(x1)))) -> 0(2(5(2(4(x1)))))
   0(0(3(2(1(x1))))) -> 0(0(1(3(5(2(x1))))))
   0(1(0(3(2(x1))))) -> 0(1(4(3(2(0(x1))))))
   0(1(0(3(2(x1))))) -> 2(3(1(0(0(5(x1))))))
   0(3(2(5(1(x1))))) -> 0(2(5(1(3(3(x1))))))
   0(5(1(1(2(x1))))) -> 0(2(4(1(1(5(x1))))))
   0(5(1(2(2(x1))))) -> 0(2(5(2(1(2(x1))))))
   0(5(3(2(1(x1))))) -> 0(1(3(4(2(5(x1))))))
   0(5(5(3(2(x1))))) -> 0(2(5(1(3(5(x1))))))
   2(0(3(1(1(x1))))) -> 2(1(0(1(3(4(x1))))))
   2(2(0(3(1(x1))))) -> 1(3(0(2(5(2(x1))))))
   2(2(0(5(1(x1))))) -> 2(0(2(1(5(1(x1))))))
   2(5(5(4(1(x1))))) -> 5(5(2(1(3(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(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(0(2(1(x1))))
   0(1(2(x1))) -> 0(2(1(3(x1))))
   0(1(2(x1))) -> 0(0(2(1(4(4(x1))))))
   0(3(1(x1))) -> 0(1(3(4(0(x1)))))
   0(3(1(x1))) -> 0(1(3(4(4(x1)))))
   0(3(1(x1))) -> 1(3(4(4(4(0(x1))))))
   0(3(2(x1))) -> 0(2(1(3(x1))))
   0(3(2(x1))) -> 0(2(3(4(x1))))
   0(3(2(x1))) -> 0(0(2(4(3(x1)))))
   0(3(2(x1))) -> 0(2(1(4(3(x1)))))
   0(3(2(x1))) -> 0(2(4(3(3(x1)))))
   0(3(2(x1))) -> 0(2(1(3(3(4(x1))))))
   0(3(2(x1))) -> 0(2(3(4(5(5(x1))))))
   0(3(2(x1))) -> 2(4(4(3(4(0(x1))))))
   0(4(1(x1))) -> 0(1(4(4(x1))))
   0(4(1(x1))) -> 0(2(1(4(x1))))
   0(4(2(x1))) -> 0(2(1(4(x1))))
   0(4(2(x1))) -> 0(2(3(4(x1))))
   0(4(2(x1))) -> 0(2(4(3(x1))))
   2(0(1(x1))) -> 5(0(2(1(x1))))
   2(3(1(x1))) -> 1(3(5(2(x1))))
   2(3(1(x1))) -> 0(2(1(3(5(x1)))))
   2(3(1(x1))) -> 1(4(3(5(2(x1)))))
   0(2(0(1(x1)))) -> 5(0(0(2(1(x1)))))
   0(3(1(1(x1)))) -> 0(1(4(1(3(4(x1))))))
   0(3(2(1(x1)))) -> 0(0(3(4(2(1(x1))))))
   0(3(2(2(x1)))) -> 1(3(4(0(2(2(x1))))))
   0(4(1(2(x1)))) -> 1(4(0(2(5(x1)))))
   0(4(3(2(x1)))) -> 2(3(4(4(0(0(x1))))))
   0(5(3(1(x1)))) -> 0(1(4(3(5(4(x1))))))
   0(5(3(1(x1)))) -> 0(1(5(3(4(0(x1))))))
   0(5(3(2(x1)))) -> 0(2(4(5(3(x1)))))
   0(5(3(2(x1)))) -> 0(2(5(3(3(x1)))))
   2(0(3(1(x1)))) -> 2(0(1(3(5(2(x1))))))
   2(0(4(1(x1)))) -> 2(0(1(4(5(x1)))))
   2(5(3(2(x1)))) -> 2(5(2(3(3(x1)))))
   2(5(4(2(x1)))) -> 0(2(5(2(4(x1)))))
   0(0(3(2(1(x1))))) -> 0(0(1(3(5(2(x1))))))
   0(1(0(3(2(x1))))) -> 0(1(4(3(2(0(x1))))))
   0(1(0(3(2(x1))))) -> 2(3(1(0(0(5(x1))))))
   0(3(2(5(1(x1))))) -> 0(2(5(1(3(3(x1))))))
   0(5(1(1(2(x1))))) -> 0(2(4(1(1(5(x1))))))
   0(5(1(2(2(x1))))) -> 0(2(5(2(1(2(x1))))))
   0(5(3(2(1(x1))))) -> 0(1(3(4(2(5(x1))))))
   0(5(5(3(2(x1))))) -> 0(2(5(1(3(5(x1))))))
   2(0(3(1(1(x1))))) -> 2(1(0(1(3(4(x1))))))
   2(2(0(3(1(x1))))) -> 1(3(0(2(5(2(x1))))))
   2(2(0(5(1(x1))))) -> 2(0(2(1(5(1(x1))))))
   2(5(5(4(1(x1))))) -> 5(5(2(1(3(4(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(0(2(1(x1))))
   0(1(2(x1))) -> 0(2(1(3(x1))))
   0(1(2(x1))) -> 0(0(2(1(4(4(x1))))))
   0(3(1(x1))) -> 0(1(3(4(0(x1)))))
   0(3(1(x1))) -> 0(1(3(4(4(x1)))))
   0(3(1(x1))) -> 1(3(4(4(4(0(x1))))))
   0(3(2(x1))) -> 0(2(1(3(x1))))
   0(3(2(x1))) -> 0(2(3(4(x1))))
   0(3(2(x1))) -> 0(0(2(4(3(x1)))))
   0(3(2(x1))) -> 0(2(1(4(3(x1)))))
   0(3(2(x1))) -> 0(2(4(3(3(x1)))))
   0(3(2(x1))) -> 0(2(1(3(3(4(x1))))))
   0(3(2(x1))) -> 0(2(3(4(5(5(x1))))))
   0(3(2(x1))) -> 2(4(4(3(4(0(x1))))))
   0(4(1(x1))) -> 0(1(4(4(x1))))
   0(4(1(x1))) -> 0(2(1(4(x1))))
   0(4(2(x1))) -> 0(2(1(4(x1))))
   0(4(2(x1))) -> 0(2(3(4(x1))))
   0(4(2(x1))) -> 0(2(4(3(x1))))
   2(0(1(x1))) -> 5(0(2(1(x1))))
   2(3(1(x1))) -> 1(3(5(2(x1))))
   2(3(1(x1))) -> 0(2(1(3(5(x1)))))
   2(3(1(x1))) -> 1(4(3(5(2(x1)))))
   0(2(0(1(x1)))) -> 5(0(0(2(1(x1)))))
   0(3(1(1(x1)))) -> 0(1(4(1(3(4(x1))))))
   0(3(2(1(x1)))) -> 0(0(3(4(2(1(x1))))))
   0(3(2(2(x1)))) -> 1(3(4(0(2(2(x1))))))
   0(4(1(2(x1)))) -> 1(4(0(2(5(x1)))))
   0(4(3(2(x1)))) -> 2(3(4(4(0(0(x1))))))
   0(5(3(1(x1)))) -> 0(1(4(3(5(4(x1))))))
   0(5(3(1(x1)))) -> 0(1(5(3(4(0(x1))))))
   0(5(3(2(x1)))) -> 0(2(4(5(3(x1)))))
   0(5(3(2(x1)))) -> 0(2(5(3(3(x1)))))
   2(0(3(1(x1)))) -> 2(0(1(3(5(2(x1))))))
   2(0(4(1(x1)))) -> 2(0(1(4(5(x1)))))
   2(5(3(2(x1)))) -> 2(5(2(3(3(x1)))))
   2(5(4(2(x1)))) -> 0(2(5(2(4(x1)))))
   0(0(3(2(1(x1))))) -> 0(0(1(3(5(2(x1))))))
   0(1(0(3(2(x1))))) -> 0(1(4(3(2(0(x1))))))
   0(1(0(3(2(x1))))) -> 2(3(1(0(0(5(x1))))))
   0(3(2(5(1(x1))))) -> 0(2(5(1(3(3(x1))))))
   0(5(1(1(2(x1))))) -> 0(2(4(1(1(5(x1))))))
   0(5(1(2(2(x1))))) -> 0(2(5(2(1(2(x1))))))
   0(5(3(2(1(x1))))) -> 0(1(3(4(2(5(x1))))))
   0(5(5(3(2(x1))))) -> 0(2(5(1(3(5(x1))))))
   2(0(3(1(1(x1))))) -> 2(1(0(1(3(4(x1))))))
   2(2(0(3(1(x1))))) -> 1(3(0(2(5(2(x1))))))
   2(2(0(5(1(x1))))) -> 2(0(2(1(5(1(x1))))))
   2(5(5(4(1(x1))))) -> 5(5(2(1(3(4(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(0(2(1(x1))))
   0(1(2(x1))) -> 0(2(1(3(x1))))
   0(1(2(x1))) -> 0(0(2(1(4(4(x1))))))
   0(3(1(x1))) -> 0(1(3(4(0(x1)))))
   0(3(1(x1))) -> 0(1(3(4(4(x1)))))
   0(3(1(x1))) -> 1(3(4(4(4(0(x1))))))
   0(3(2(x1))) -> 0(2(1(3(x1))))
   0(3(2(x1))) -> 0(2(3(4(x1))))
   0(3(2(x1))) -> 0(0(2(4(3(x1)))))
   0(3(2(x1))) -> 0(2(1(4(3(x1)))))
   0(3(2(x1))) -> 0(2(4(3(3(x1)))))
   0(3(2(x1))) -> 0(2(1(3(3(4(x1))))))
   0(3(2(x1))) -> 0(2(3(4(5(5(x1))))))
   0(3(2(x1))) -> 2(4(4(3(4(0(x1))))))
   0(4(1(x1))) -> 0(1(4(4(x1))))
   0(4(1(x1))) -> 0(2(1(4(x1))))
   0(4(2(x1))) -> 0(2(1(4(x1))))
   0(4(2(x1))) -> 0(2(3(4(x1))))
   0(4(2(x1))) -> 0(2(4(3(x1))))
   2(0(1(x1))) -> 5(0(2(1(x1))))
   2(3(1(x1))) -> 1(3(5(2(x1))))
   2(3(1(x1))) -> 0(2(1(3(5(x1)))))
   2(3(1(x1))) -> 1(4(3(5(2(x1)))))
   0(2(0(1(x1)))) -> 5(0(0(2(1(x1)))))
   0(3(1(1(x1)))) -> 0(1(4(1(3(4(x1))))))
   0(3(2(1(x1)))) -> 0(0(3(4(2(1(x1))))))
   0(3(2(2(x1)))) -> 1(3(4(0(2(2(x1))))))
   0(4(1(2(x1)))) -> 1(4(0(2(5(x1)))))
   0(4(3(2(x1)))) -> 2(3(4(4(0(0(x1))))))
   0(5(3(1(x1)))) -> 0(1(4(3(5(4(x1))))))
   0(5(3(1(x1)))) -> 0(1(5(3(4(0(x1))))))
   0(5(3(2(x1)))) -> 0(2(4(5(3(x1)))))
   0(5(3(2(x1)))) -> 0(2(5(3(3(x1)))))
   2(0(3(1(x1)))) -> 2(0(1(3(5(2(x1))))))
   2(0(4(1(x1)))) -> 2(0(1(4(5(x1)))))
   2(5(3(2(x1)))) -> 2(5(2(3(3(x1)))))
   2(5(4(2(x1)))) -> 0(2(5(2(4(x1)))))
   0(0(3(2(1(x1))))) -> 0(0(1(3(5(2(x1))))))
   0(1(0(3(2(x1))))) -> 0(1(4(3(2(0(x1))))))
   0(1(0(3(2(x1))))) -> 2(3(1(0(0(5(x1))))))
   0(3(2(5(1(x1))))) -> 0(2(5(1(3(3(x1))))))
   0(5(1(1(2(x1))))) -> 0(2(4(1(1(5(x1))))))
   0(5(1(2(2(x1))))) -> 0(2(5(2(1(2(x1))))))
   0(5(3(2(1(x1))))) -> 0(1(3(4(2(5(x1))))))
   0(5(5(3(2(x1))))) -> 0(2(5(1(3(5(x1))))))
   2(0(3(1(1(x1))))) -> 2(1(0(1(3(4(x1))))))
   2(2(0(3(1(x1))))) -> 1(3(0(2(5(2(x1))))))
   2(2(0(5(1(x1))))) -> 2(0(2(1(5(1(x1))))))
   2(5(5(4(1(x1))))) -> 5(5(2(1(3(4(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 4. 
The certificate found is represented by the following graph.

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

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

0(3(1(x1))) ->^+ 1(3(4(4(4(0(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 / 3(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(0(2(1(x1))))
   0(1(2(x1))) -> 0(2(1(3(x1))))
   0(1(2(x1))) -> 0(0(2(1(4(4(x1))))))
   0(3(1(x1))) -> 0(1(3(4(0(x1)))))
   0(3(1(x1))) -> 0(1(3(4(4(x1)))))
   0(3(1(x1))) -> 1(3(4(4(4(0(x1))))))
   0(3(2(x1))) -> 0(2(1(3(x1))))
   0(3(2(x1))) -> 0(2(3(4(x1))))
   0(3(2(x1))) -> 0(0(2(4(3(x1)))))
   0(3(2(x1))) -> 0(2(1(4(3(x1)))))
   0(3(2(x1))) -> 0(2(4(3(3(x1)))))
   0(3(2(x1))) -> 0(2(1(3(3(4(x1))))))
   0(3(2(x1))) -> 0(2(3(4(5(5(x1))))))
   0(3(2(x1))) -> 2(4(4(3(4(0(x1))))))
   0(4(1(x1))) -> 0(1(4(4(x1))))
   0(4(1(x1))) -> 0(2(1(4(x1))))
   0(4(2(x1))) -> 0(2(1(4(x1))))
   0(4(2(x1))) -> 0(2(3(4(x1))))
   0(4(2(x1))) -> 0(2(4(3(x1))))
   2(0(1(x1))) -> 5(0(2(1(x1))))
   2(3(1(x1))) -> 1(3(5(2(x1))))
   2(3(1(x1))) -> 0(2(1(3(5(x1)))))
   2(3(1(x1))) -> 1(4(3(5(2(x1)))))
   0(2(0(1(x1)))) -> 5(0(0(2(1(x1)))))
   0(3(1(1(x1)))) -> 0(1(4(1(3(4(x1))))))
   0(3(2(1(x1)))) -> 0(0(3(4(2(1(x1))))))
   0(3(2(2(x1)))) -> 1(3(4(0(2(2(x1))))))
   0(4(1(2(x1)))) -> 1(4(0(2(5(x1)))))
   0(4(3(2(x1)))) -> 2(3(4(4(0(0(x1))))))
   0(5(3(1(x1)))) -> 0(1(4(3(5(4(x1))))))
   0(5(3(1(x1)))) -> 0(1(5(3(4(0(x1))))))
   0(5(3(2(x1)))) -> 0(2(4(5(3(x1)))))
   0(5(3(2(x1)))) -> 0(2(5(3(3(x1)))))
   2(0(3(1(x1)))) -> 2(0(1(3(5(2(x1))))))
   2(0(4(1(x1)))) -> 2(0(1(4(5(x1)))))
   2(5(3(2(x1)))) -> 2(5(2(3(3(x1)))))
   2(5(4(2(x1)))) -> 0(2(5(2(4(x1)))))
   0(0(3(2(1(x1))))) -> 0(0(1(3(5(2(x1))))))
   0(1(0(3(2(x1))))) -> 0(1(4(3(2(0(x1))))))
   0(1(0(3(2(x1))))) -> 2(3(1(0(0(5(x1))))))
   0(3(2(5(1(x1))))) -> 0(2(5(1(3(3(x1))))))
   0(5(1(1(2(x1))))) -> 0(2(4(1(1(5(x1))))))
   0(5(1(2(2(x1))))) -> 0(2(5(2(1(2(x1))))))
   0(5(3(2(1(x1))))) -> 0(1(3(4(2(5(x1))))))
   0(5(5(3(2(x1))))) -> 0(2(5(1(3(5(x1))))))
   2(0(3(1(1(x1))))) -> 2(1(0(1(3(4(x1))))))
   2(2(0(3(1(x1))))) -> 1(3(0(2(5(2(x1))))))
   2(2(0(5(1(x1))))) -> 2(0(2(1(5(1(x1))))))
   2(5(5(4(1(x1))))) -> 5(5(2(1(3(4(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(0(2(1(x1))))
   0(1(2(x1))) -> 0(2(1(3(x1))))
   0(1(2(x1))) -> 0(0(2(1(4(4(x1))))))
   0(3(1(x1))) -> 0(1(3(4(0(x1)))))
   0(3(1(x1))) -> 0(1(3(4(4(x1)))))
   0(3(1(x1))) -> 1(3(4(4(4(0(x1))))))
   0(3(2(x1))) -> 0(2(1(3(x1))))
   0(3(2(x1))) -> 0(2(3(4(x1))))
   0(3(2(x1))) -> 0(0(2(4(3(x1)))))
   0(3(2(x1))) -> 0(2(1(4(3(x1)))))
   0(3(2(x1))) -> 0(2(4(3(3(x1)))))
   0(3(2(x1))) -> 0(2(1(3(3(4(x1))))))
   0(3(2(x1))) -> 0(2(3(4(5(5(x1))))))
   0(3(2(x1))) -> 2(4(4(3(4(0(x1))))))
   0(4(1(x1))) -> 0(1(4(4(x1))))
   0(4(1(x1))) -> 0(2(1(4(x1))))
   0(4(2(x1))) -> 0(2(1(4(x1))))
   0(4(2(x1))) -> 0(2(3(4(x1))))
   0(4(2(x1))) -> 0(2(4(3(x1))))
   2(0(1(x1))) -> 5(0(2(1(x1))))
   2(3(1(x1))) -> 1(3(5(2(x1))))
   2(3(1(x1))) -> 0(2(1(3(5(x1)))))
   2(3(1(x1))) -> 1(4(3(5(2(x1)))))
   0(2(0(1(x1)))) -> 5(0(0(2(1(x1)))))
   0(3(1(1(x1)))) -> 0(1(4(1(3(4(x1))))))
   0(3(2(1(x1)))) -> 0(0(3(4(2(1(x1))))))
   0(3(2(2(x1)))) -> 1(3(4(0(2(2(x1))))))
   0(4(1(2(x1)))) -> 1(4(0(2(5(x1)))))
   0(4(3(2(x1)))) -> 2(3(4(4(0(0(x1))))))
   0(5(3(1(x1)))) -> 0(1(4(3(5(4(x1))))))
   0(5(3(1(x1)))) -> 0(1(5(3(4(0(x1))))))
   0(5(3(2(x1)))) -> 0(2(4(5(3(x1)))))
   0(5(3(2(x1)))) -> 0(2(5(3(3(x1)))))
   2(0(3(1(x1)))) -> 2(0(1(3(5(2(x1))))))
   2(0(4(1(x1)))) -> 2(0(1(4(5(x1)))))
   2(5(3(2(x1)))) -> 2(5(2(3(3(x1)))))
   2(5(4(2(x1)))) -> 0(2(5(2(4(x1)))))
   0(0(3(2(1(x1))))) -> 0(0(1(3(5(2(x1))))))
   0(1(0(3(2(x1))))) -> 0(1(4(3(2(0(x1))))))
   0(1(0(3(2(x1))))) -> 2(3(1(0(0(5(x1))))))
   0(3(2(5(1(x1))))) -> 0(2(5(1(3(3(x1))))))
   0(5(1(1(2(x1))))) -> 0(2(4(1(1(5(x1))))))
   0(5(1(2(2(x1))))) -> 0(2(5(2(1(2(x1))))))
   0(5(3(2(1(x1))))) -> 0(1(3(4(2(5(x1))))))
   0(5(5(3(2(x1))))) -> 0(2(5(1(3(5(x1))))))
   2(0(3(1(1(x1))))) -> 2(1(0(1(3(4(x1))))))
   2(2(0(3(1(x1))))) -> 1(3(0(2(5(2(x1))))))
   2(2(0(5(1(x1))))) -> 2(0(2(1(5(1(x1))))))
   2(5(5(4(1(x1))))) -> 5(5(2(1(3(4(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