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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The Derivational Complexity (full) 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), 187 ms]
(4) CpxRelTRS
(5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(6) CpxTRS
    (7) CpxTrsMatchBoundsProof [FINISHED, 129 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 (full) 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: FULL
----------------------------------------

(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 (full) 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: FULL
----------------------------------------

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

(4)
Obligation:
The Runtime Complexity (full) 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: FULL
----------------------------------------

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

(6)
Obligation:
The Runtime Complexity (full) 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: FULL
----------------------------------------

(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, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 134, 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]
{(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]), (54,112,[0_1|2]), (54,115,[0_1|2]), (54,120,[0_1|2]), (54,125,[2_1|2]), (54,130,[0_1|2]), (54,141,[0_1|2]), (54,145,[1_1|2]), (54,150,[0_1|2]), (54,155,[0_1|2]), (54,158,[0_1|2]), (54,162,[0_1|2]), (54,166,[0_1|2]), (54,170,[0_1|2]), (54,175,[0_1|2]), (54,180,[2_1|2]), (54,185,[0_1|2]), (54,190,[1_1|2]), (54,195,[0_1|2]), (54,200,[0_1|2]), (54,203,[0_1|2]), (54,206,[1_1|2]), (54,210,[0_1|2]), (54,213,[2_1|2]), (54,218,[5_1|2]), (54,222,[0_1|2]), (54,227,[0_1|2]), (54,232,[0_1|2]), (54,236,[0_1|2]), (54,240,[0_1|2]), (54,245,[0_1|2]), (54,250,[0_1|2]), (54,255,[0_1|2]), (54,260,[0_1|2]), (54,265,[5_1|2]), (54,268,[2_1|2]), (54,273,[2_1|2]), (54,278,[2_1|2]), (54,282,[1_1|2]), (54,285,[0_1|2]), (54,289,[1_1|2]), (54,293,[2_1|2]), (54,297,[0_1|2]), (54,301,[5_1|2]), (54,306,[1_1|2]), (54,311,[2_1|2]), (54,316,[0_1|2]), (54,319,[1_1|3]), (54,322,[0_1|3]), (54,326,[1_1|3]), (54,330,[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]), (106,112,[0_1|2]), (106,115,[0_1|2]), (106,120,[0_1|2]), (106,125,[2_1|2]), (106,130,[0_1|2]), (106,141,[0_1|2]), (106,145,[1_1|2]), (106,150,[0_1|2]), (106,155,[0_1|2]), (106,158,[0_1|2]), (106,162,[0_1|2]), (106,166,[0_1|2]), (106,170,[0_1|2]), (106,175,[0_1|2]), (106,180,[2_1|2]), (106,185,[0_1|2]), (106,190,[1_1|2]), (106,195,[0_1|2]), (106,200,[0_1|2]), (106,203,[0_1|2]), (106,206,[1_1|2]), (106,210,[0_1|2]), (106,213,[2_1|2]), (106,218,[5_1|2]), (106,222,[0_1|2]), (106,227,[0_1|2]), (106,232,[0_1|2]), (106,236,[0_1|2]), (106,240,[0_1|2]), (106,245,[0_1|2]), (106,250,[0_1|2]), (106,255,[0_1|2]), (106,260,[0_1|2]), (106,265,[5_1|2]), (106,268,[2_1|2]), (106,273,[2_1|2]), (106,278,[2_1|2]), (106,282,[1_1|2]), (106,285,[0_1|2]), (106,289,[1_1|2]), (106,293,[2_1|2]), (106,297,[0_1|2]), (106,301,[5_1|2]), (106,306,[1_1|2]), (106,311,[2_1|2]), (106,316,[0_1|2]), (106,319,[1_1|3]), (106,322,[0_1|3]), (106,326,[1_1|3]), (106,330,[5_1|3]), (107,108,[0_1|2]), (108,109,[2_1|2]), (109,106,[1_1|2]), (109,125,[1_1|2]), (109,180,[1_1|2]), (109,213,[1_1|2]), (109,268,[1_1|2]), (109,273,[1_1|2]), (109,278,[1_1|2]), (109,293,[1_1|2]), (109,311,[1_1|2]), (112,113,[2_1|2]), (113,114,[1_1|2]), (114,106,[3_1|2]), (114,125,[3_1|2]), (114,180,[3_1|2]), (114,213,[3_1|2]), (114,268,[3_1|2]), (114,273,[3_1|2]), (114,278,[3_1|2]), (114,293,[3_1|2]), (114,311,[3_1|2]), (115,116,[0_1|2]), (116,117,[2_1|2]), (117,118,[1_1|2]), (118,119,[4_1|2]), (119,106,[4_1|2]), (119,125,[4_1|2]), (119,180,[4_1|2]), (119,213,[4_1|2]), (119,268,[4_1|2]), (119,273,[4_1|2]), (119,278,[4_1|2]), (119,293,[4_1|2]), (119,311,[4_1|2]), (120,121,[1_1|2]), (121,122,[4_1|2]), (122,123,[3_1|2]), (123,124,[2_1|2]), (123,265,[5_1|2]), (123,268,[2_1|2]), (123,273,[2_1|2]), (123,278,[2_1|2]), (123,333,[5_1|3]), (123,343,[2_1|3]), (123,371,[5_1|4]), (124,106,[0_1|2]), (124,125,[0_1|2, 2_1|2]), (124,180,[0_1|2, 2_1|2]), (124,213,[0_1|2, 2_1|2]), (124,268,[0_1|2]), (124,273,[0_1|2]), (124,278,[0_1|2]), (124,293,[0_1|2]), (124,311,[0_1|2]), (124,107,[0_1|2]), (124,112,[0_1|2]), (124,115,[0_1|2]), (124,120,[0_1|2]), (124,130,[0_1|2]), (124,141,[0_1|2]), (124,145,[1_1|2]), (124,150,[0_1|2]), (124,155,[0_1|2]), (124,158,[0_1|2]), (124,162,[0_1|2]), (124,166,[0_1|2]), (124,170,[0_1|2]), (124,175,[0_1|2]), (124,185,[0_1|2]), (124,190,[1_1|2]), (124,195,[0_1|2]), (124,200,[0_1|2]), (124,203,[0_1|2]), (124,206,[1_1|2]), (124,210,[0_1|2]), (124,316,[0_1|2]), (124,218,[5_1|2]), (124,222,[0_1|2]), (124,227,[0_1|2]), (124,232,[0_1|2]), (124,236,[0_1|2]), (124,240,[0_1|2]), (124,245,[0_1|2]), (124,250,[0_1|2]), (124,255,[0_1|2]), (124,260,[0_1|2]), (124,336,[5_1|3]), (124,348,[0_1|3]), (124,352,[0_1|3]), (124,356,[1_1|3]), (124,319,[1_1|3]), (124,322,[0_1|3]), (124,326,[1_1|3]), (125,126,[3_1|2]), (126,127,[1_1|2]), (127,128,[0_1|2]), (128,129,[0_1|2]), (128,222,[0_1|2]), (128,227,[0_1|2]), (128,232,[0_1|2]), (128,236,[0_1|2]), (128,240,[0_1|2]), (128,245,[0_1|2]), (128,250,[0_1|2]), (128,255,[0_1|2]), (128,361,[0_1|3]), (128,366,[0_1|3]), (129,106,[5_1|2]), (129,125,[5_1|2]), (129,180,[5_1|2]), (129,213,[5_1|2]), (129,268,[5_1|2]), (129,273,[5_1|2]), (129,278,[5_1|2]), (129,293,[5_1|2]), (129,311,[5_1|2]), (130,131,[1_1|2]), (131,133,[3_1|2]), (133,134,[4_1|2]), (134,106,[0_1|2]), (134,145,[0_1|2, 1_1|2]), (134,190,[0_1|2, 1_1|2]), (134,206,[0_1|2, 1_1|2]), (134,282,[0_1|2]), (134,289,[0_1|2]), (134,306,[0_1|2]), (134,107,[0_1|2]), (134,112,[0_1|2]), (134,115,[0_1|2]), (134,120,[0_1|2]), (134,125,[2_1|2]), (134,130,[0_1|2]), (134,141,[0_1|2]), (134,150,[0_1|2]), (134,155,[0_1|2]), (134,158,[0_1|2]), (134,162,[0_1|2]), (134,166,[0_1|2]), (134,170,[0_1|2]), (134,175,[0_1|2]), (134,180,[2_1|2]), (134,185,[0_1|2]), (134,195,[0_1|2]), (134,200,[0_1|2]), (134,203,[0_1|2]), (134,210,[0_1|2]), (134,213,[2_1|2]), (134,316,[0_1|2]), (134,218,[5_1|2]), (134,222,[0_1|2]), (134,227,[0_1|2]), (134,232,[0_1|2]), (134,236,[0_1|2]), (134,240,[0_1|2]), (134,245,[0_1|2]), (134,250,[0_1|2]), (134,255,[0_1|2]), (134,260,[0_1|2]), (134,336,[5_1|3]), (134,319,[0_1|2, 1_1|3]), (134,326,[0_1|2, 1_1|3]), (134,322,[0_1|3]), (141,142,[1_1|2]), (142,143,[3_1|2]), (143,144,[4_1|2]), (144,106,[4_1|2]), (144,145,[4_1|2]), (144,190,[4_1|2]), (144,206,[4_1|2]), (144,282,[4_1|2]), (144,289,[4_1|2]), (144,306,[4_1|2]), (144,319,[4_1|2]), (144,326,[4_1|2]), (145,146,[3_1|2]), (146,147,[4_1|2]), (147,148,[4_1|2]), (148,149,[4_1|2]), (149,106,[0_1|2]), (149,145,[0_1|2, 1_1|2]), (149,190,[0_1|2, 1_1|2]), (149,206,[0_1|2, 1_1|2]), (149,282,[0_1|2]), (149,289,[0_1|2]), (149,306,[0_1|2]), (149,107,[0_1|2]), (149,112,[0_1|2]), (149,115,[0_1|2]), (149,120,[0_1|2]), (149,125,[2_1|2]), (149,130,[0_1|2]), (149,141,[0_1|2]), (149,150,[0_1|2]), (149,155,[0_1|2]), (149,158,[0_1|2]), (149,162,[0_1|2]), (149,166,[0_1|2]), (149,170,[0_1|2]), (149,175,[0_1|2]), (149,180,[2_1|2]), (149,185,[0_1|2]), (149,195,[0_1|2]), (149,200,[0_1|2]), (149,203,[0_1|2]), (149,210,[0_1|2]), (149,213,[2_1|2]), (149,316,[0_1|2]), (149,218,[5_1|2]), (149,222,[0_1|2]), (149,227,[0_1|2]), (149,232,[0_1|2]), (149,236,[0_1|2]), (149,240,[0_1|2]), (149,245,[0_1|2]), (149,250,[0_1|2]), (149,255,[0_1|2]), (149,260,[0_1|2]), (149,336,[5_1|3]), (149,319,[0_1|2, 1_1|3]), (149,326,[0_1|2, 1_1|3]), (149,322,[0_1|3]), (150,151,[1_1|2]), (151,152,[4_1|2]), (152,153,[1_1|2]), (153,154,[3_1|2]), (154,106,[4_1|2]), (154,145,[4_1|2]), (154,190,[4_1|2]), (154,206,[4_1|2]), (154,282,[4_1|2]), (154,289,[4_1|2]), (154,306,[4_1|2]), (154,319,[4_1|2]), (154,326,[4_1|2]), (155,156,[2_1|2]), (156,157,[3_1|2]), (157,106,[4_1|2]), (157,125,[4_1|2]), (157,180,[4_1|2]), (157,213,[4_1|2]), (157,268,[4_1|2]), (157,273,[4_1|2]), (157,278,[4_1|2]), (157,293,[4_1|2]), (157,311,[4_1|2]), (158,159,[0_1|2]), (159,160,[2_1|2]), (160,161,[4_1|2]), (161,106,[3_1|2]), (161,125,[3_1|2]), (161,180,[3_1|2]), (161,213,[3_1|2]), (161,268,[3_1|2]), (161,273,[3_1|2]), (161,278,[3_1|2]), (161,293,[3_1|2]), (161,311,[3_1|2]), (162,163,[2_1|2]), (163,164,[1_1|2]), (164,165,[4_1|2]), (165,106,[3_1|2]), (165,125,[3_1|2]), (165,180,[3_1|2]), (165,213,[3_1|2]), (165,268,[3_1|2]), (165,273,[3_1|2]), (165,278,[3_1|2]), (165,293,[3_1|2]), (165,311,[3_1|2]), (166,167,[2_1|2]), (167,168,[4_1|2]), (168,169,[3_1|2]), (169,106,[3_1|2]), (169,125,[3_1|2]), (169,180,[3_1|2]), (169,213,[3_1|2]), (169,268,[3_1|2]), (169,273,[3_1|2]), (169,278,[3_1|2]), (169,293,[3_1|2]), (169,311,[3_1|2]), (170,171,[2_1|2]), (171,172,[1_1|2]), (172,173,[3_1|2]), (173,174,[3_1|2]), (174,106,[4_1|2]), (174,125,[4_1|2]), (174,180,[4_1|2]), (174,213,[4_1|2]), (174,268,[4_1|2]), (174,273,[4_1|2]), (174,278,[4_1|2]), (174,293,[4_1|2]), (174,311,[4_1|2]), (175,176,[2_1|2]), (176,177,[3_1|2]), (177,178,[4_1|2]), (178,179,[5_1|2]), (179,106,[5_1|2]), (179,125,[5_1|2]), (179,180,[5_1|2]), (179,213,[5_1|2]), (179,268,[5_1|2]), (179,273,[5_1|2]), (179,278,[5_1|2]), (179,293,[5_1|2]), (179,311,[5_1|2]), (180,181,[4_1|2]), (181,182,[4_1|2]), (182,183,[3_1|2]), (183,184,[4_1|2]), (184,106,[0_1|2]), (184,125,[0_1|2, 2_1|2]), (184,180,[0_1|2, 2_1|2]), (184,213,[0_1|2, 2_1|2]), (184,268,[0_1|2]), (184,273,[0_1|2]), (184,278,[0_1|2]), (184,293,[0_1|2]), (184,311,[0_1|2]), (184,107,[0_1|2]), (184,112,[0_1|2]), (184,115,[0_1|2]), (184,120,[0_1|2]), (184,130,[0_1|2]), (184,141,[0_1|2]), (184,145,[1_1|2]), (184,150,[0_1|2]), (184,155,[0_1|2]), (184,158,[0_1|2]), (184,162,[0_1|2]), (184,166,[0_1|2]), (184,170,[0_1|2]), (184,175,[0_1|2]), (184,185,[0_1|2]), (184,190,[1_1|2]), (184,195,[0_1|2]), (184,200,[0_1|2]), (184,203,[0_1|2]), (184,206,[1_1|2]), (184,210,[0_1|2]), (184,316,[0_1|2]), (184,218,[5_1|2]), (184,222,[0_1|2]), (184,227,[0_1|2]), (184,232,[0_1|2]), (184,236,[0_1|2]), (184,240,[0_1|2]), (184,245,[0_1|2]), (184,250,[0_1|2]), (184,255,[0_1|2]), (184,260,[0_1|2]), (184,336,[5_1|3]), (184,348,[0_1|3]), (184,352,[0_1|3]), (184,356,[1_1|3]), (184,319,[1_1|3]), (184,322,[0_1|3]), (184,326,[1_1|3]), (185,186,[0_1|2]), (186,187,[3_1|2]), (187,188,[4_1|2]), (188,189,[2_1|2]), (189,106,[1_1|2]), (189,145,[1_1|2]), (189,190,[1_1|2]), (189,206,[1_1|2]), (189,282,[1_1|2]), (189,289,[1_1|2]), (189,306,[1_1|2]), (189,274,[1_1|2]), (189,319,[1_1|2]), (189,326,[1_1|2]), (190,191,[3_1|2]), (191,192,[4_1|2]), (192,193,[0_1|2]), (193,194,[2_1|2]), (193,306,[1_1|2]), (193,311,[2_1|2]), (194,106,[2_1|2]), (194,125,[2_1|2]), (194,180,[2_1|2]), (194,213,[2_1|2]), (194,268,[2_1|2]), (194,273,[2_1|2]), (194,278,[2_1|2]), (194,293,[2_1|2]), (194,311,[2_1|2]), (194,265,[5_1|2]), (194,282,[1_1|2]), (194,285,[0_1|2]), (194,289,[1_1|2]), (194,297,[0_1|2]), (194,301,[5_1|2]), (194,306,[1_1|2]), (194,340,[5_1|3]), (194,319,[1_1|3]), (194,322,[0_1|3]), (194,326,[1_1|3]), (195,196,[2_1|2]), (196,197,[5_1|2]), (197,198,[1_1|2]), (198,199,[3_1|2]), (199,106,[3_1|2]), (199,145,[3_1|2]), (199,190,[3_1|2]), (199,206,[3_1|2]), (199,282,[3_1|2]), (199,289,[3_1|2]), (199,306,[3_1|2]), (199,319,[3_1|2]), (199,326,[3_1|2]), (200,201,[1_1|2]), (201,202,[4_1|2]), (202,106,[4_1|2]), (202,145,[4_1|2]), (202,190,[4_1|2]), (202,206,[4_1|2]), (202,282,[4_1|2]), (202,289,[4_1|2]), (202,306,[4_1|2]), (202,319,[4_1|2]), (202,326,[4_1|2]), (203,204,[2_1|2]), (204,205,[1_1|2]), (205,106,[4_1|2]), (205,145,[4_1|2]), (205,190,[4_1|2]), (205,206,[4_1|2]), (205,282,[4_1|2]), (205,289,[4_1|2]), (205,306,[4_1|2]), (205,319,[4_1|2]), (205,326,[4_1|2]), (206,207,[4_1|2]), (207,208,[0_1|2]), (208,209,[2_1|2]), (208,293,[2_1|2]), (208,297,[0_1|2]), (208,301,[5_1|2]), (209,106,[5_1|2]), (209,125,[5_1|2]), (209,180,[5_1|2]), (209,213,[5_1|2]), (209,268,[5_1|2]), (209,273,[5_1|2]), (209,278,[5_1|2]), (209,293,[5_1|2]), (209,311,[5_1|2]), (210,211,[2_1|2]), (211,212,[4_1|2]), (212,106,[3_1|2]), (212,125,[3_1|2]), (212,180,[3_1|2]), (212,213,[3_1|2]), (212,268,[3_1|2]), (212,273,[3_1|2]), (212,278,[3_1|2]), (212,293,[3_1|2]), (212,311,[3_1|2]), (213,214,[3_1|2]), (214,215,[4_1|2]), (215,216,[4_1|2]), (216,217,[0_1|2]), (216,260,[0_1|2]), (217,106,[0_1|2]), (217,125,[0_1|2, 2_1|2]), (217,180,[0_1|2, 2_1|2]), (217,213,[0_1|2, 2_1|2]), (217,268,[0_1|2]), (217,273,[0_1|2]), (217,278,[0_1|2]), (217,293,[0_1|2]), (217,311,[0_1|2]), (217,107,[0_1|2]), (217,112,[0_1|2]), (217,115,[0_1|2]), (217,120,[0_1|2]), (217,130,[0_1|2]), (217,141,[0_1|2]), (217,145,[1_1|2]), (217,150,[0_1|2]), (217,155,[0_1|2]), (217,158,[0_1|2]), (217,162,[0_1|2]), (217,166,[0_1|2]), (217,170,[0_1|2]), (217,175,[0_1|2]), (217,185,[0_1|2]), (217,190,[1_1|2]), (217,195,[0_1|2]), (217,200,[0_1|2]), (217,203,[0_1|2]), (217,206,[1_1|2]), (217,210,[0_1|2]), (217,316,[0_1|2]), (217,218,[5_1|2]), (217,222,[0_1|2]), (217,227,[0_1|2]), (217,232,[0_1|2]), (217,236,[0_1|2]), (217,240,[0_1|2]), (217,245,[0_1|2]), (217,250,[0_1|2]), (217,255,[0_1|2]), (217,260,[0_1|2]), (217,336,[5_1|3]), (217,348,[0_1|3]), (217,352,[0_1|3]), (217,356,[1_1|3]), (217,319,[1_1|3]), (217,322,[0_1|3]), (217,326,[1_1|3]), (218,219,[0_1|2]), (219,220,[0_1|2]), (220,221,[2_1|2]), (221,106,[1_1|2]), (221,145,[1_1|2]), (221,190,[1_1|2]), (221,206,[1_1|2]), (221,282,[1_1|2]), (221,289,[1_1|2]), (221,306,[1_1|2]), (221,121,[1_1|2]), (221,131,[1_1|2]), (221,142,[1_1|2]), (221,151,[1_1|2]), (221,201,[1_1|2]), (221,223,[1_1|2]), (221,228,[1_1|2]), (221,241,[1_1|2]), (221,270,[1_1|2]), (221,280,[1_1|2]), (221,319,[1_1|2]), (221,326,[1_1|2]), (222,223,[1_1|2]), (223,224,[4_1|2]), (224,225,[3_1|2]), (225,226,[5_1|2]), (226,106,[4_1|2]), (226,145,[4_1|2]), (226,190,[4_1|2]), (226,206,[4_1|2]), (226,282,[4_1|2]), (226,289,[4_1|2]), (226,306,[4_1|2]), (226,319,[4_1|2]), (226,326,[4_1|2]), (227,228,[1_1|2]), (228,229,[5_1|2]), (229,230,[3_1|2]), (230,231,[4_1|2]), (231,106,[0_1|2]), (231,145,[0_1|2, 1_1|2]), (231,190,[0_1|2, 1_1|2]), (231,206,[0_1|2, 1_1|2]), (231,282,[0_1|2]), (231,289,[0_1|2]), (231,306,[0_1|2]), (231,107,[0_1|2]), (231,112,[0_1|2]), (231,115,[0_1|2]), (231,120,[0_1|2]), (231,125,[2_1|2]), (231,130,[0_1|2]), (231,141,[0_1|2]), (231,150,[0_1|2]), (231,155,[0_1|2]), (231,158,[0_1|2]), (231,162,[0_1|2]), (231,166,[0_1|2]), (231,170,[0_1|2]), (231,175,[0_1|2]), (231,180,[2_1|2]), (231,185,[0_1|2]), (231,195,[0_1|2]), (231,200,[0_1|2]), (231,203,[0_1|2]), (231,210,[0_1|2]), (231,213,[2_1|2]), (231,316,[0_1|2]), (231,218,[5_1|2]), (231,222,[0_1|2]), (231,227,[0_1|2]), (231,232,[0_1|2]), (231,236,[0_1|2]), (231,240,[0_1|2]), (231,245,[0_1|2]), (231,250,[0_1|2]), (231,255,[0_1|2]), (231,260,[0_1|2]), (231,336,[5_1|3]), (231,319,[0_1|2, 1_1|3]), (231,326,[0_1|2, 1_1|3]), (231,322,[0_1|3]), (232,233,[2_1|2]), (233,234,[4_1|2]), (234,235,[5_1|2]), (235,106,[3_1|2]), (235,125,[3_1|2]), (235,180,[3_1|2]), (235,213,[3_1|2]), (235,268,[3_1|2]), (235,273,[3_1|2]), (235,278,[3_1|2]), (235,293,[3_1|2]), (235,311,[3_1|2]), (236,237,[2_1|2]), (237,238,[5_1|2]), (238,239,[3_1|2]), (239,106,[3_1|2]), (239,125,[3_1|2]), (239,180,[3_1|2]), (239,213,[3_1|2]), (239,268,[3_1|2]), (239,273,[3_1|2]), (239,278,[3_1|2]), (239,293,[3_1|2]), (239,311,[3_1|2]), (240,241,[1_1|2]), (241,242,[3_1|2]), (242,243,[4_1|2]), (243,244,[2_1|2]), (243,293,[2_1|2]), (243,297,[0_1|2]), (243,301,[5_1|2]), (244,106,[5_1|2]), (244,145,[5_1|2]), (244,190,[5_1|2]), (244,206,[5_1|2]), (244,282,[5_1|2]), (244,289,[5_1|2]), (244,306,[5_1|2]), (244,274,[5_1|2]), (244,319,[5_1|2]), (244,326,[5_1|2]), (245,246,[2_1|2]), (246,247,[4_1|2]), (247,248,[1_1|2]), (248,249,[1_1|2]), (249,106,[5_1|2]), (249,125,[5_1|2]), (249,180,[5_1|2]), (249,213,[5_1|2]), (249,268,[5_1|2]), (249,273,[5_1|2]), (249,278,[5_1|2]), (249,293,[5_1|2]), (249,311,[5_1|2]), (250,251,[2_1|2]), (251,252,[5_1|2]), (252,253,[2_1|2]), (253,254,[1_1|2]), (254,106,[2_1|2]), (254,125,[2_1|2]), (254,180,[2_1|2]), (254,213,[2_1|2]), (254,268,[2_1|2]), (254,273,[2_1|2]), (254,278,[2_1|2]), (254,293,[2_1|2]), (254,311,[2_1|2]), (254,265,[5_1|2]), (254,282,[1_1|2]), (254,285,[0_1|2]), (254,289,[1_1|2]), (254,297,[0_1|2]), (254,301,[5_1|2]), (254,306,[1_1|2]), (254,340,[5_1|3]), (254,319,[1_1|3]), (254,322,[0_1|3]), (254,326,[1_1|3]), (255,256,[2_1|2]), (256,257,[5_1|2]), (257,258,[1_1|2]), (258,259,[3_1|2]), (259,106,[5_1|2]), (259,125,[5_1|2]), (259,180,[5_1|2]), (259,213,[5_1|2]), (259,268,[5_1|2]), (259,273,[5_1|2]), (259,278,[5_1|2]), (259,293,[5_1|2]), (259,311,[5_1|2]), (260,261,[0_1|2]), (261,262,[1_1|2]), (262,263,[3_1|2]), (263,264,[5_1|2]), (264,106,[2_1|2]), (264,145,[2_1|2]), (264,190,[2_1|2]), (264,206,[2_1|2]), (264,282,[2_1|2, 1_1|2]), (264,289,[2_1|2, 1_1|2]), (264,306,[2_1|2, 1_1|2]), (264,274,[2_1|2]), (264,265,[5_1|2]), (264,268,[2_1|2]), (264,273,[2_1|2]), (264,278,[2_1|2]), (264,285,[0_1|2]), (264,293,[2_1|2]), (264,297,[0_1|2]), (264,301,[5_1|2]), (264,311,[2_1|2]), (264,340,[5_1|3]), (264,319,[2_1|2]), (264,326,[2_1|2]), (265,266,[0_1|2]), (266,267,[2_1|2]), (267,106,[1_1|2]), (267,145,[1_1|2]), (267,190,[1_1|2]), (267,206,[1_1|2]), (267,282,[1_1|2]), (267,289,[1_1|2]), (267,306,[1_1|2]), (267,121,[1_1|2]), (267,131,[1_1|2]), (267,142,[1_1|2]), (267,151,[1_1|2]), (267,201,[1_1|2]), (267,223,[1_1|2]), (267,228,[1_1|2]), (267,241,[1_1|2]), (267,319,[1_1|2]), (267,326,[1_1|2]), (268,269,[0_1|2]), (269,270,[1_1|2]), (270,271,[3_1|2]), (271,272,[5_1|2]), (272,106,[2_1|2]), (272,145,[2_1|2]), (272,190,[2_1|2]), (272,206,[2_1|2]), (272,282,[2_1|2, 1_1|2]), (272,289,[2_1|2, 1_1|2]), (272,306,[2_1|2, 1_1|2]), (272,265,[5_1|2]), (272,268,[2_1|2]), (272,273,[2_1|2]), (272,278,[2_1|2]), (272,285,[0_1|2]), (272,293,[2_1|2]), (272,297,[0_1|2]), (272,301,[5_1|2]), (272,311,[2_1|2]), (272,340,[5_1|3]), (272,319,[2_1|2]), (272,326,[2_1|2]), (273,274,[1_1|2]), (274,275,[0_1|2]), (275,276,[1_1|2]), (276,277,[3_1|2]), (277,106,[4_1|2]), (277,145,[4_1|2]), (277,190,[4_1|2]), (277,206,[4_1|2]), (277,282,[4_1|2]), (277,289,[4_1|2]), (277,306,[4_1|2]), (277,319,[4_1|2]), (277,326,[4_1|2]), (278,279,[0_1|2]), (279,280,[1_1|2]), (280,281,[4_1|2]), (281,106,[5_1|2]), (281,145,[5_1|2]), (281,190,[5_1|2]), (281,206,[5_1|2]), (281,282,[5_1|2]), (281,289,[5_1|2]), (281,306,[5_1|2]), (281,319,[5_1|2]), (281,326,[5_1|2]), (282,283,[3_1|2]), (283,284,[5_1|2]), (284,106,[2_1|2]), (284,145,[2_1|2]), (284,190,[2_1|2]), (284,206,[2_1|2]), (284,282,[2_1|2, 1_1|2]), (284,289,[2_1|2, 1_1|2]), (284,306,[2_1|2, 1_1|2]), (284,265,[5_1|2]), (284,268,[2_1|2]), (284,273,[2_1|2]), (284,278,[2_1|2]), (284,285,[0_1|2]), (284,293,[2_1|2]), (284,297,[0_1|2]), (284,301,[5_1|2]), (284,311,[2_1|2]), (284,340,[5_1|3]), (284,319,[2_1|2]), (284,326,[2_1|2]), (285,286,[2_1|2]), (286,287,[1_1|2]), (287,288,[3_1|2]), (288,106,[5_1|2]), (288,145,[5_1|2]), (288,190,[5_1|2]), (288,206,[5_1|2]), (288,282,[5_1|2]), (288,289,[5_1|2]), (288,306,[5_1|2]), (288,319,[5_1|2]), (288,326,[5_1|2]), (289,290,[4_1|2]), (290,291,[3_1|2]), (291,292,[5_1|2]), (292,106,[2_1|2]), (292,145,[2_1|2]), (292,190,[2_1|2]), (292,206,[2_1|2]), (292,282,[2_1|2, 1_1|2]), (292,289,[2_1|2, 1_1|2]), (292,306,[2_1|2, 1_1|2]), (292,265,[5_1|2]), (292,268,[2_1|2]), (292,273,[2_1|2]), (292,278,[2_1|2]), (292,285,[0_1|2]), (292,293,[2_1|2]), (292,297,[0_1|2]), (292,301,[5_1|2]), (292,311,[2_1|2]), (292,340,[5_1|3]), (292,319,[2_1|2]), (292,326,[2_1|2]), (293,294,[5_1|2]), (294,295,[2_1|2]), (295,296,[3_1|2]), (296,106,[3_1|2]), (296,125,[3_1|2]), (296,180,[3_1|2]), (296,213,[3_1|2]), (296,268,[3_1|2]), (296,273,[3_1|2]), (296,278,[3_1|2]), (296,293,[3_1|2]), (296,311,[3_1|2]), (297,298,[2_1|2]), (298,299,[5_1|2]), (299,300,[2_1|2]), (300,106,[4_1|2]), (300,125,[4_1|2]), (300,180,[4_1|2]), (300,213,[4_1|2]), (300,268,[4_1|2]), (300,273,[4_1|2]), (300,278,[4_1|2]), (300,293,[4_1|2]), (300,311,[4_1|2]), (301,302,[5_1|2]), (302,303,[2_1|2]), (303,304,[1_1|2]), (304,305,[3_1|2]), (305,106,[4_1|2]), (305,145,[4_1|2]), (305,190,[4_1|2]), (305,206,[4_1|2]), (305,282,[4_1|2]), (305,289,[4_1|2]), (305,306,[4_1|2]), (305,319,[4_1|2]), (305,326,[4_1|2]), (306,307,[3_1|2]), (307,308,[0_1|2]), (308,309,[2_1|2]), (309,310,[5_1|2]), (310,106,[2_1|2]), (310,145,[2_1|2]), (310,190,[2_1|2]), (310,206,[2_1|2]), (310,282,[2_1|2, 1_1|2]), (310,289,[2_1|2, 1_1|2]), (310,306,[2_1|2, 1_1|2]), (310,265,[5_1|2]), (310,268,[2_1|2]), (310,273,[2_1|2]), (310,278,[2_1|2]), (310,285,[0_1|2]), (310,293,[2_1|2]), (310,297,[0_1|2]), (310,301,[5_1|2]), (310,311,[2_1|2]), (310,340,[5_1|3]), (310,319,[2_1|2]), (310,326,[2_1|2]), (311,312,[0_1|2]), (312,313,[2_1|2]), (313,314,[1_1|2]), (314,315,[5_1|2]), (315,106,[1_1|2]), (315,145,[1_1|2]), (315,190,[1_1|2]), (315,206,[1_1|2]), (315,282,[1_1|2]), (315,289,[1_1|2]), (315,306,[1_1|2]), (315,319,[1_1|2]), (315,326,[1_1|2]), (316,317,[2_1|2]), (317,318,[1_1|2]), (318,125,[4_1|2]), (318,180,[4_1|2]), (318,213,[4_1|2]), (318,268,[4_1|2]), (318,273,[4_1|2]), (318,278,[4_1|2]), (318,293,[4_1|2]), (318,311,[4_1|2]), (319,320,[3_1|3]), (320,321,[5_1|3]), (321,127,[2_1|3]), (322,323,[2_1|3]), (323,324,[1_1|3]), (324,325,[3_1|3]), (325,127,[5_1|3]), (326,327,[4_1|3]), (327,328,[3_1|3]), (328,329,[5_1|3]), (329,127,[2_1|3]), (330,331,[0_1|3]), (331,332,[2_1|3]), (332,270,[1_1|3]), (332,280,[1_1|3]), (333,334,[0_1|3]), (334,335,[2_1|3]), (335,145,[1_1|3]), (335,190,[1_1|3]), (335,206,[1_1|3]), (335,282,[1_1|3]), (335,289,[1_1|3]), (335,306,[1_1|3]), (335,319,[1_1|3]), (335,326,[1_1|3]), (335,274,[1_1|3]), (335,121,[1_1|3]), (335,131,[1_1|3]), (335,142,[1_1|3]), (335,151,[1_1|3]), (335,201,[1_1|3]), (335,223,[1_1|3]), (335,228,[1_1|3]), (335,241,[1_1|3]), (335,270,[1_1|3]), (335,280,[1_1|3]), (335,349,[1_1|3]), (335,353,[1_1|3]), (336,337,[0_1|3]), (337,338,[0_1|3]), (338,339,[2_1|3]), (339,270,[1_1|3]), (339,280,[1_1|3]), (340,341,[0_1|3]), (341,342,[2_1|3]), (342,121,[1_1|3]), (342,131,[1_1|3]), (342,142,[1_1|3]), (342,151,[1_1|3]), (342,201,[1_1|3]), (342,223,[1_1|3]), (342,228,[1_1|3]), (342,241,[1_1|3]), (342,270,[1_1|3]), (342,280,[1_1|3]), (342,276,[1_1|3]), (343,344,[0_1|3]), (344,345,[1_1|3]), (345,346,[3_1|3]), (346,347,[5_1|3]), (347,127,[2_1|3]), (348,349,[1_1|3]), (349,350,[3_1|3]), (350,351,[4_1|3]), (351,127,[0_1|3]), (352,353,[1_1|3]), (353,354,[3_1|3]), (354,355,[4_1|3]), (355,127,[4_1|3]), (356,357,[3_1|3]), (357,358,[4_1|3]), (358,359,[4_1|3]), (359,360,[4_1|3]), (360,127,[0_1|3]), (361,362,[1_1|3]), (362,363,[4_1|3]), (363,364,[3_1|3]), (364,365,[5_1|3]), (365,127,[4_1|3]), (366,367,[1_1|3]), (367,368,[5_1|3]), (368,369,[3_1|3]), (369,370,[4_1|3]), (370,127,[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 (full) 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: FULL
----------------------------------------

(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 (full) 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: FULL
----------------------------------------

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

(15)
BOUNDS(n^1, INF)

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

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

The Runtime Complexity (full) 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: FULL