/export/starexec/sandbox/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^1).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), 83 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 91 ms] (8) BOUNDS(1, n^1) (9) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 4 ms] (10) TRS for Loop Detection (11) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (12) BEST (13) proven lower bound (14) LowerBoundPropagationProof [FINISHED, 0 ms] (15) BOUNDS(n^1, INF) (16) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: 0(1(1(2(x1)))) -> 1(3(0(1(2(x1))))) 0(1(1(2(x1)))) -> 1(3(1(0(2(x1))))) 0(1(1(2(x1)))) -> 2(3(1(3(0(1(x1)))))) 0(1(2(0(x1)))) -> 1(0(0(2(2(x1))))) 0(1(2(4(x1)))) -> 0(2(3(4(1(x1))))) 0(1(2(4(x1)))) -> 1(0(4(2(3(x1))))) 0(1(2(4(x1)))) -> 1(2(3(0(4(x1))))) 0(1(2(4(x1)))) -> 2(1(4(0(3(x1))))) 0(1(2(4(x1)))) -> 1(2(3(4(0(5(x1)))))) 0(1(2(4(x1)))) -> 2(1(1(0(3(4(x1)))))) 0(1(2(4(x1)))) -> 4(1(2(2(3(0(x1)))))) 0(1(2(4(x1)))) -> 4(5(0(2(3(1(x1)))))) 0(4(2(0(x1)))) -> 0(4(2(3(0(x1))))) 0(4(2(0(x1)))) -> 2(3(0(4(0(0(x1)))))) 0(4(2(0(x1)))) -> 3(4(0(2(3(0(x1)))))) 0(4(2(0(x1)))) -> 4(2(3(0(4(0(x1)))))) 0(4(2(0(x1)))) -> 4(3(0(0(5(2(x1)))))) 0(4(2(4(x1)))) -> 4(0(2(3(1(4(x1)))))) 0(4(2(4(x1)))) -> 4(0(4(2(0(3(x1)))))) 5(1(2(0(x1)))) -> 2(1(3(5(0(x1))))) 5(1(2(0(x1)))) -> 3(1(0(2(5(x1))))) 5(1(2(0(x1)))) -> 2(3(0(0(1(5(x1)))))) 5(1(2(4(x1)))) -> 3(2(5(1(4(x1))))) 5(1(2(4(x1)))) -> 5(2(1(3(4(x1))))) 5(1(2(4(x1)))) -> 5(5(2(1(4(x1))))) 5(1(2(4(x1)))) -> 0(3(4(5(2(1(x1)))))) 5(1(4(2(x1)))) -> 3(4(5(2(1(x1))))) 5(1(4(2(x1)))) -> 2(1(3(4(5(4(x1)))))) 5(1(4(2(x1)))) -> 3(3(4(2(1(5(x1)))))) 5(4(1(4(x1)))) -> 3(4(4(1(5(4(x1)))))) 5(4(1(4(x1)))) -> 4(1(3(5(0(4(x1)))))) 5(4(1(4(x1)))) -> 5(1(3(4(5(4(x1)))))) 5(4(1(4(x1)))) -> 5(1(5(3(4(4(x1)))))) 5(4(2(0(x1)))) -> 5(4(2(3(0(x1))))) 5(4(2(0(x1)))) -> 0(1(2(3(4(5(x1)))))) 5(4(2(0(x1)))) -> 4(5(3(3(0(2(x1)))))) 0(1(2(0(4(x1))))) -> 0(2(4(1(3(0(x1)))))) 0(1(2(0(4(x1))))) -> 2(0(3(4(0(1(x1)))))) 0(1(2(0(4(x1))))) -> 4(0(2(3(1(0(x1)))))) 0(1(4(2(2(x1))))) -> 1(2(3(4(0(2(x1)))))) 5(0(1(2(4(x1))))) -> 3(0(2(1(4(5(x1)))))) 5(1(2(2(4(x1))))) -> 5(2(2(1(4(5(x1)))))) 5(1(2(4(0(x1))))) -> 5(0(2(1(3(4(x1)))))) 5(1(2(4(0(x1))))) -> 5(0(3(2(1(4(x1)))))) 5(1(3(1(4(x1))))) -> 1(5(1(3(4(0(x1)))))) 5(1(4(1(2(x1))))) -> 2(1(5(3(4(1(x1)))))) 5(4(1(1(4(x1))))) -> 1(1(3(4(5(4(x1)))))) 5(4(1(4(0(x1))))) -> 3(4(0(4(5(1(x1)))))) 5(4(3(2(0(x1))))) -> 5(4(0(3(2(3(x1)))))) 5(4(5(2(0(x1))))) -> 5(0(5(4(4(2(x1)))))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(1(x_1)) -> 1(encArg(x_1)) encArg(2(x_1)) -> 2(encArg(x_1)) encArg(3(x_1)) -> 3(encArg(x_1)) encArg(4(x_1)) -> 4(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: 0(1(1(2(x1)))) -> 1(3(0(1(2(x1))))) 0(1(1(2(x1)))) -> 1(3(1(0(2(x1))))) 0(1(1(2(x1)))) -> 2(3(1(3(0(1(x1)))))) 0(1(2(0(x1)))) -> 1(0(0(2(2(x1))))) 0(1(2(4(x1)))) -> 0(2(3(4(1(x1))))) 0(1(2(4(x1)))) -> 1(0(4(2(3(x1))))) 0(1(2(4(x1)))) -> 1(2(3(0(4(x1))))) 0(1(2(4(x1)))) -> 2(1(4(0(3(x1))))) 0(1(2(4(x1)))) -> 1(2(3(4(0(5(x1)))))) 0(1(2(4(x1)))) -> 2(1(1(0(3(4(x1)))))) 0(1(2(4(x1)))) -> 4(1(2(2(3(0(x1)))))) 0(1(2(4(x1)))) -> 4(5(0(2(3(1(x1)))))) 0(4(2(0(x1)))) -> 0(4(2(3(0(x1))))) 0(4(2(0(x1)))) -> 2(3(0(4(0(0(x1)))))) 0(4(2(0(x1)))) -> 3(4(0(2(3(0(x1)))))) 0(4(2(0(x1)))) -> 4(2(3(0(4(0(x1)))))) 0(4(2(0(x1)))) -> 4(3(0(0(5(2(x1)))))) 0(4(2(4(x1)))) -> 4(0(2(3(1(4(x1)))))) 0(4(2(4(x1)))) -> 4(0(4(2(0(3(x1)))))) 5(1(2(0(x1)))) -> 2(1(3(5(0(x1))))) 5(1(2(0(x1)))) -> 3(1(0(2(5(x1))))) 5(1(2(0(x1)))) -> 2(3(0(0(1(5(x1)))))) 5(1(2(4(x1)))) -> 3(2(5(1(4(x1))))) 5(1(2(4(x1)))) -> 5(2(1(3(4(x1))))) 5(1(2(4(x1)))) -> 5(5(2(1(4(x1))))) 5(1(2(4(x1)))) -> 0(3(4(5(2(1(x1)))))) 5(1(4(2(x1)))) -> 3(4(5(2(1(x1))))) 5(1(4(2(x1)))) -> 2(1(3(4(5(4(x1)))))) 5(1(4(2(x1)))) -> 3(3(4(2(1(5(x1)))))) 5(4(1(4(x1)))) -> 3(4(4(1(5(4(x1)))))) 5(4(1(4(x1)))) -> 4(1(3(5(0(4(x1)))))) 5(4(1(4(x1)))) -> 5(1(3(4(5(4(x1)))))) 5(4(1(4(x1)))) -> 5(1(5(3(4(4(x1)))))) 5(4(2(0(x1)))) -> 5(4(2(3(0(x1))))) 5(4(2(0(x1)))) -> 0(1(2(3(4(5(x1)))))) 5(4(2(0(x1)))) -> 4(5(3(3(0(2(x1)))))) 0(1(2(0(4(x1))))) -> 0(2(4(1(3(0(x1)))))) 0(1(2(0(4(x1))))) -> 2(0(3(4(0(1(x1)))))) 0(1(2(0(4(x1))))) -> 4(0(2(3(1(0(x1)))))) 0(1(4(2(2(x1))))) -> 1(2(3(4(0(2(x1)))))) 5(0(1(2(4(x1))))) -> 3(0(2(1(4(5(x1)))))) 5(1(2(2(4(x1))))) -> 5(2(2(1(4(5(x1)))))) 5(1(2(4(0(x1))))) -> 5(0(2(1(3(4(x1)))))) 5(1(2(4(0(x1))))) -> 5(0(3(2(1(4(x1)))))) 5(1(3(1(4(x1))))) -> 1(5(1(3(4(0(x1)))))) 5(1(4(1(2(x1))))) -> 2(1(5(3(4(1(x1)))))) 5(4(1(1(4(x1))))) -> 1(1(3(4(5(4(x1)))))) 5(4(1(4(0(x1))))) -> 3(4(0(4(5(1(x1)))))) 5(4(3(2(0(x1))))) -> 5(4(0(3(2(3(x1)))))) 5(4(5(2(0(x1))))) -> 5(0(5(4(4(2(x1)))))) The (relative) TRS S consists of the following rules: encArg(1(x_1)) -> 1(encArg(x_1)) encArg(2(x_1)) -> 2(encArg(x_1)) encArg(3(x_1)) -> 3(encArg(x_1)) encArg(4(x_1)) -> 4(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: 0(1(1(2(x1)))) -> 1(3(0(1(2(x1))))) 0(1(1(2(x1)))) -> 1(3(1(0(2(x1))))) 0(1(1(2(x1)))) -> 2(3(1(3(0(1(x1)))))) 0(1(2(0(x1)))) -> 1(0(0(2(2(x1))))) 0(1(2(4(x1)))) -> 0(2(3(4(1(x1))))) 0(1(2(4(x1)))) -> 1(0(4(2(3(x1))))) 0(1(2(4(x1)))) -> 1(2(3(0(4(x1))))) 0(1(2(4(x1)))) -> 2(1(4(0(3(x1))))) 0(1(2(4(x1)))) -> 1(2(3(4(0(5(x1)))))) 0(1(2(4(x1)))) -> 2(1(1(0(3(4(x1)))))) 0(1(2(4(x1)))) -> 4(1(2(2(3(0(x1)))))) 0(1(2(4(x1)))) -> 4(5(0(2(3(1(x1)))))) 0(4(2(0(x1)))) -> 0(4(2(3(0(x1))))) 0(4(2(0(x1)))) -> 2(3(0(4(0(0(x1)))))) 0(4(2(0(x1)))) -> 3(4(0(2(3(0(x1)))))) 0(4(2(0(x1)))) -> 4(2(3(0(4(0(x1)))))) 0(4(2(0(x1)))) -> 4(3(0(0(5(2(x1)))))) 0(4(2(4(x1)))) -> 4(0(2(3(1(4(x1)))))) 0(4(2(4(x1)))) -> 4(0(4(2(0(3(x1)))))) 5(1(2(0(x1)))) -> 2(1(3(5(0(x1))))) 5(1(2(0(x1)))) -> 3(1(0(2(5(x1))))) 5(1(2(0(x1)))) -> 2(3(0(0(1(5(x1)))))) 5(1(2(4(x1)))) -> 3(2(5(1(4(x1))))) 5(1(2(4(x1)))) -> 5(2(1(3(4(x1))))) 5(1(2(4(x1)))) -> 5(5(2(1(4(x1))))) 5(1(2(4(x1)))) -> 0(3(4(5(2(1(x1)))))) 5(1(4(2(x1)))) -> 3(4(5(2(1(x1))))) 5(1(4(2(x1)))) -> 2(1(3(4(5(4(x1)))))) 5(1(4(2(x1)))) -> 3(3(4(2(1(5(x1)))))) 5(4(1(4(x1)))) -> 3(4(4(1(5(4(x1)))))) 5(4(1(4(x1)))) -> 4(1(3(5(0(4(x1)))))) 5(4(1(4(x1)))) -> 5(1(3(4(5(4(x1)))))) 5(4(1(4(x1)))) -> 5(1(5(3(4(4(x1)))))) 5(4(2(0(x1)))) -> 5(4(2(3(0(x1))))) 5(4(2(0(x1)))) -> 0(1(2(3(4(5(x1)))))) 5(4(2(0(x1)))) -> 4(5(3(3(0(2(x1)))))) 0(1(2(0(4(x1))))) -> 0(2(4(1(3(0(x1)))))) 0(1(2(0(4(x1))))) -> 2(0(3(4(0(1(x1)))))) 0(1(2(0(4(x1))))) -> 4(0(2(3(1(0(x1)))))) 0(1(4(2(2(x1))))) -> 1(2(3(4(0(2(x1)))))) 5(0(1(2(4(x1))))) -> 3(0(2(1(4(5(x1)))))) 5(1(2(2(4(x1))))) -> 5(2(2(1(4(5(x1)))))) 5(1(2(4(0(x1))))) -> 5(0(2(1(3(4(x1)))))) 5(1(2(4(0(x1))))) -> 5(0(3(2(1(4(x1)))))) 5(1(3(1(4(x1))))) -> 1(5(1(3(4(0(x1)))))) 5(1(4(1(2(x1))))) -> 2(1(5(3(4(1(x1)))))) 5(4(1(1(4(x1))))) -> 1(1(3(4(5(4(x1)))))) 5(4(1(4(0(x1))))) -> 3(4(0(4(5(1(x1)))))) 5(4(3(2(0(x1))))) -> 5(4(0(3(2(3(x1)))))) 5(4(5(2(0(x1))))) -> 5(0(5(4(4(2(x1)))))) The (relative) TRS S consists of the following rules: encArg(1(x_1)) -> 1(encArg(x_1)) encArg(2(x_1)) -> 2(encArg(x_1)) encArg(3(x_1)) -> 3(encArg(x_1)) encArg(4(x_1)) -> 4(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (5) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(1(2(x1)))) -> 1(3(0(1(2(x1))))) 0(1(1(2(x1)))) -> 1(3(1(0(2(x1))))) 0(1(1(2(x1)))) -> 2(3(1(3(0(1(x1)))))) 0(1(2(0(x1)))) -> 1(0(0(2(2(x1))))) 0(1(2(4(x1)))) -> 0(2(3(4(1(x1))))) 0(1(2(4(x1)))) -> 1(0(4(2(3(x1))))) 0(1(2(4(x1)))) -> 1(2(3(0(4(x1))))) 0(1(2(4(x1)))) -> 2(1(4(0(3(x1))))) 0(1(2(4(x1)))) -> 1(2(3(4(0(5(x1)))))) 0(1(2(4(x1)))) -> 2(1(1(0(3(4(x1)))))) 0(1(2(4(x1)))) -> 4(1(2(2(3(0(x1)))))) 0(1(2(4(x1)))) -> 4(5(0(2(3(1(x1)))))) 0(4(2(0(x1)))) -> 0(4(2(3(0(x1))))) 0(4(2(0(x1)))) -> 2(3(0(4(0(0(x1)))))) 0(4(2(0(x1)))) -> 3(4(0(2(3(0(x1)))))) 0(4(2(0(x1)))) -> 4(2(3(0(4(0(x1)))))) 0(4(2(0(x1)))) -> 4(3(0(0(5(2(x1)))))) 0(4(2(4(x1)))) -> 4(0(2(3(1(4(x1)))))) 0(4(2(4(x1)))) -> 4(0(4(2(0(3(x1)))))) 5(1(2(0(x1)))) -> 2(1(3(5(0(x1))))) 5(1(2(0(x1)))) -> 3(1(0(2(5(x1))))) 5(1(2(0(x1)))) -> 2(3(0(0(1(5(x1)))))) 5(1(2(4(x1)))) -> 3(2(5(1(4(x1))))) 5(1(2(4(x1)))) -> 5(2(1(3(4(x1))))) 5(1(2(4(x1)))) -> 5(5(2(1(4(x1))))) 5(1(2(4(x1)))) -> 0(3(4(5(2(1(x1)))))) 5(1(4(2(x1)))) -> 3(4(5(2(1(x1))))) 5(1(4(2(x1)))) -> 2(1(3(4(5(4(x1)))))) 5(1(4(2(x1)))) -> 3(3(4(2(1(5(x1)))))) 5(4(1(4(x1)))) -> 3(4(4(1(5(4(x1)))))) 5(4(1(4(x1)))) -> 4(1(3(5(0(4(x1)))))) 5(4(1(4(x1)))) -> 5(1(3(4(5(4(x1)))))) 5(4(1(4(x1)))) -> 5(1(5(3(4(4(x1)))))) 5(4(2(0(x1)))) -> 5(4(2(3(0(x1))))) 5(4(2(0(x1)))) -> 0(1(2(3(4(5(x1)))))) 5(4(2(0(x1)))) -> 4(5(3(3(0(2(x1)))))) 0(1(2(0(4(x1))))) -> 0(2(4(1(3(0(x1)))))) 0(1(2(0(4(x1))))) -> 2(0(3(4(0(1(x1)))))) 0(1(2(0(4(x1))))) -> 4(0(2(3(1(0(x1)))))) 0(1(4(2(2(x1))))) -> 1(2(3(4(0(2(x1)))))) 5(0(1(2(4(x1))))) -> 3(0(2(1(4(5(x1)))))) 5(1(2(2(4(x1))))) -> 5(2(2(1(4(5(x1)))))) 5(1(2(4(0(x1))))) -> 5(0(2(1(3(4(x1)))))) 5(1(2(4(0(x1))))) -> 5(0(3(2(1(4(x1)))))) 5(1(3(1(4(x1))))) -> 1(5(1(3(4(0(x1)))))) 5(1(4(1(2(x1))))) -> 2(1(5(3(4(1(x1)))))) 5(4(1(1(4(x1))))) -> 1(1(3(4(5(4(x1)))))) 5(4(1(4(0(x1))))) -> 3(4(0(4(5(1(x1)))))) 5(4(3(2(0(x1))))) -> 5(4(0(3(2(3(x1)))))) 5(4(5(2(0(x1))))) -> 5(0(5(4(4(2(x1)))))) encArg(1(x_1)) -> 1(encArg(x_1)) encArg(2(x_1)) -> 2(encArg(x_1)) encArg(3(x_1)) -> 3(encArg(x_1)) encArg(4(x_1)) -> 4(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (7) CpxTrsMatchBoundsProof (FINISHED) A linear upper bound on the runtime complexity of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. The certificate found is represented by the following graph. "[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, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 680] {(52,53,[0_1|0, 5_1|0, encArg_1|0, encode_0_1|0, encode_1_1|0, encode_2_1|0, encode_3_1|0, encode_4_1|0, encode_5_1|0]), (52,54,[1_1|1]), (52,58,[1_1|1]), (52,62,[2_1|1]), (52,67,[0_1|1]), (52,71,[1_1|1]), (52,75,[1_1|1]), (52,79,[2_1|1]), (52,83,[1_1|1]), (52,88,[2_1|1]), (52,93,[4_1|1]), (52,98,[4_1|1]), (52,103,[1_1|1]), (52,108,[4_1|1]), (52,113,[4_1|1]), (52,118,[3_1|1]), (52,122,[5_1|1]), (52,126,[5_1|1]), (52,130,[0_1|1]), (52,135,[5_1|1]), (52,140,[3_1|1]), (52,144,[2_1|1]), (52,149,[3_1|1]), (52,154,[2_1|1]), (52,159,[1_1|1]), (52,164,[3_1|1]), (52,169,[4_1|1]), (52,174,[5_1|1]), (52,179,[5_1|1]), (52,184,[1_1|1]), (52,189,[1_1|1, 2_1|1, 3_1|1, 4_1|1, 0_1|1, 5_1|1]), (52,214,[1_1|2]), (52,218,[1_1|2]), (52,222,[2_1|2]), (52,227,[1_1|2]), (52,231,[0_1|2]), (52,236,[2_1|2]), (52,241,[4_1|2]), (52,246,[0_1|2]), (52,250,[1_1|2]), (52,254,[1_1|2]), (52,258,[2_1|2]), (52,262,[1_1|2]), (52,267,[2_1|2]), (52,272,[4_1|2]), (52,277,[4_1|2]), (52,282,[1_1|2]), (52,287,[0_1|2]), (52,291,[2_1|2]), (52,296,[3_1|2]), (52,301,[4_1|2]), (52,306,[4_1|2]), (52,311,[4_1|2]), (52,316,[4_1|2]), (52,321,[2_1|2]), (52,325,[3_1|2]), (52,329,[2_1|2]), (52,334,[3_1|2]), (52,338,[5_1|2]), (52,342,[5_1|2]), (52,346,[0_1|2]), (52,351,[5_1|2]), (52,356,[5_1|2]), (52,361,[5_1|2]), (52,366,[3_1|2]), (52,370,[2_1|2]), (52,375,[3_1|2]), (52,380,[2_1|2]), (52,385,[1_1|2]), (52,390,[3_1|2]), (52,395,[4_1|2]), (52,400,[5_1|2]), (52,405,[5_1|2]), (52,410,[3_1|2]), (52,415,[1_1|2]), (52,420,[5_1|2]), (52,424,[0_1|2]), (52,429,[4_1|2]), (52,434,[5_1|2]), (52,439,[5_1|2]), (52,444,[3_1|2]), (53,53,[1_1|0, 2_1|0, 3_1|0, 4_1|0, cons_0_1|0, cons_5_1|0]), (54,55,[3_1|1]), (55,56,[0_1|1]), (55,67,[0_1|1]), (55,71,[1_1|1]), (55,75,[1_1|1]), (55,79,[2_1|1]), (55,83,[1_1|1]), (55,88,[2_1|1]), (55,93,[4_1|1]), (55,98,[4_1|1]), (56,57,[1_1|1]), (57,53,[2_1|1]), (58,59,[3_1|1]), (59,60,[1_1|1]), (60,61,[0_1|1]), (61,53,[2_1|1]), (62,63,[3_1|1]), (63,64,[1_1|1]), (64,65,[3_1|1]), (65,66,[0_1|1]), (65,54,[1_1|1]), (65,58,[1_1|1]), (65,62,[2_1|1]), (65,67,[0_1|1]), (65,71,[1_1|1]), (65,75,[1_1|1]), (65,79,[2_1|1]), (65,83,[1_1|1]), (65,88,[2_1|1]), (65,93,[4_1|1]), (65,98,[4_1|1]), (65,103,[1_1|1]), (66,53,[1_1|1]), (67,68,[2_1|1]), (68,69,[3_1|1]), (69,70,[4_1|1]), (70,53,[1_1|1]), (71,72,[0_1|1]), (72,73,[4_1|1]), (73,74,[2_1|1]), (74,53,[3_1|1]), (75,76,[2_1|1]), (76,77,[3_1|1]), (77,78,[0_1|1]), (77,108,[4_1|1]), (77,113,[4_1|1]), (78,53,[4_1|1]), (79,80,[1_1|1]), (80,81,[4_1|1]), (81,82,[0_1|1]), (82,53,[3_1|1]), (83,84,[2_1|1]), (84,85,[3_1|1]), (85,86,[4_1|1]), (86,87,[0_1|1]), (87,53,[5_1|1]), (87,118,[3_1|1]), (87,122,[5_1|1]), (87,126,[5_1|1]), (87,130,[0_1|1]), (87,135,[5_1|1]), (87,140,[3_1|1]), (87,144,[2_1|1]), (87,149,[3_1|1]), (87,154,[2_1|1]), (87,159,[1_1|1]), (87,164,[3_1|1]), (87,169,[4_1|1]), (87,174,[5_1|1]), (87,179,[5_1|1]), (87,184,[1_1|1]), (88,89,[1_1|1]), (89,90,[1_1|1]), (90,91,[0_1|1]), (91,92,[3_1|1]), (92,53,[4_1|1]), (93,94,[1_1|1]), (94,95,[2_1|1]), (95,96,[2_1|1]), (96,97,[3_1|1]), (97,53,[0_1|1]), (97,54,[1_1|1]), (97,58,[1_1|1]), (97,62,[2_1|1]), (97,67,[0_1|1]), (97,71,[1_1|1]), (97,75,[1_1|1]), (97,79,[2_1|1]), (97,83,[1_1|1]), (97,88,[2_1|1]), (97,93,[4_1|1]), (97,98,[4_1|1]), (97,103,[1_1|1]), (97,108,[4_1|1]), (97,113,[4_1|1]), (98,99,[5_1|1]), (99,100,[0_1|1]), (100,101,[2_1|1]), (101,102,[3_1|1]), (102,53,[1_1|1]), (103,104,[2_1|1]), (104,105,[3_1|1]), (105,106,[4_1|1]), (106,107,[0_1|1]), (107,53,[2_1|1]), (108,109,[0_1|1]), (109,110,[2_1|1]), (110,111,[3_1|1]), (111,112,[1_1|1]), (112,53,[4_1|1]), (113,114,[0_1|1]), (113,190,[0_1|2]), (113,194,[2_1|2]), (113,199,[3_1|2]), (113,204,[4_1|2]), (113,209,[4_1|2]), (114,115,[4_1|1]), (115,116,[2_1|1]), (116,117,[0_1|1]), (117,53,[3_1|1]), (118,119,[2_1|1]), (119,120,[5_1|1]), (119,140,[3_1|1]), (119,144,[2_1|1]), (119,149,[3_1|1]), (119,154,[2_1|1]), (120,121,[1_1|1]), (121,53,[4_1|1]), (122,123,[2_1|1]), (123,124,[1_1|1]), (124,125,[3_1|1]), (125,53,[4_1|1]), (126,127,[5_1|1]), (127,128,[2_1|1]), (128,129,[1_1|1]), (129,53,[4_1|1]), (130,131,[3_1|1]), (131,132,[4_1|1]), (132,133,[5_1|1]), (133,134,[2_1|1]), (134,53,[1_1|1]), (135,136,[2_1|1]), (136,137,[2_1|1]), (137,138,[1_1|1]), (138,139,[4_1|1]), (139,53,[5_1|1]), (139,118,[3_1|1]), (139,122,[5_1|1]), (139,126,[5_1|1]), (139,130,[0_1|1]), (139,135,[5_1|1]), (139,140,[3_1|1]), (139,144,[2_1|1]), (139,149,[3_1|1]), (139,154,[2_1|1]), (139,159,[1_1|1]), (139,164,[3_1|1]), (139,169,[4_1|1]), (139,174,[5_1|1]), (139,179,[5_1|1]), (139,184,[1_1|1]), (140,141,[4_1|1]), (141,142,[5_1|1]), (142,143,[2_1|1]), (143,53,[1_1|1]), (144,145,[1_1|1]), (145,146,[3_1|1]), (146,147,[4_1|1]), (147,148,[5_1|1]), (147,164,[3_1|1]), (147,169,[4_1|1]), (147,174,[5_1|1]), (147,179,[5_1|1]), (147,184,[1_1|1]), (148,53,[4_1|1]), (149,150,[3_1|1]), (150,151,[4_1|1]), (151,152,[2_1|1]), (152,153,[1_1|1]), (153,53,[5_1|1]), (153,118,[3_1|1]), (153,122,[5_1|1]), (153,126,[5_1|1]), (153,130,[0_1|1]), (153,135,[5_1|1]), (153,140,[3_1|1]), (153,144,[2_1|1]), (153,149,[3_1|1]), (153,154,[2_1|1]), (153,159,[1_1|1]), (153,164,[3_1|1]), (153,169,[4_1|1]), (153,174,[5_1|1]), (153,179,[5_1|1]), (153,184,[1_1|1]), (154,155,[1_1|1]), (155,156,[5_1|1]), (156,157,[3_1|1]), (157,158,[4_1|1]), (158,53,[1_1|1]), (159,160,[5_1|1]), (160,161,[1_1|1]), (161,162,[3_1|1]), (162,163,[4_1|1]), (163,53,[0_1|1]), (163,54,[1_1|1]), (163,58,[1_1|1]), (163,62,[2_1|1]), (163,67,[0_1|1]), (163,71,[1_1|1]), (163,75,[1_1|1]), (163,79,[2_1|1]), (163,83,[1_1|1]), (163,88,[2_1|1]), (163,93,[4_1|1]), (163,98,[4_1|1]), (163,103,[1_1|1]), (163,108,[4_1|1]), (163,113,[4_1|1]), (164,165,[4_1|1]), (165,166,[4_1|1]), (166,167,[1_1|1]), (167,168,[5_1|1]), (167,164,[3_1|1]), (167,169,[4_1|1]), (167,174,[5_1|1]), (167,179,[5_1|1]), (167,184,[1_1|1]), (168,53,[4_1|1]), (169,170,[1_1|1]), (170,171,[3_1|1]), (171,172,[5_1|1]), (172,173,[0_1|1]), (172,108,[4_1|1]), (172,113,[4_1|1]), (173,53,[4_1|1]), (174,175,[1_1|1]), (175,176,[3_1|1]), (176,177,[4_1|1]), (177,178,[5_1|1]), (177,164,[3_1|1]), (177,169,[4_1|1]), (177,174,[5_1|1]), (177,179,[5_1|1]), (177,184,[1_1|1]), (178,53,[4_1|1]), (179,180,[1_1|1]), (180,181,[5_1|1]), (181,182,[3_1|1]), (182,183,[4_1|1]), (183,53,[4_1|1]), (184,185,[1_1|1]), (185,186,[3_1|1]), (186,187,[4_1|1]), (187,188,[5_1|1]), (187,164,[3_1|1]), (187,169,[4_1|1]), (187,174,[5_1|1]), (187,179,[5_1|1]), (187,184,[1_1|1]), (188,53,[4_1|1]), (189,53,[encArg_1|1]), (189,189,[1_1|1, 2_1|1, 3_1|1, 4_1|1, 0_1|1, 5_1|1]), (189,214,[1_1|2]), (189,218,[1_1|2]), (189,222,[2_1|2]), (189,227,[1_1|2]), (189,231,[0_1|2]), (189,236,[2_1|2]), (189,241,[4_1|2]), (189,246,[0_1|2]), (189,250,[1_1|2]), (189,254,[1_1|2]), (189,258,[2_1|2]), (189,262,[1_1|2]), (189,267,[2_1|2]), (189,272,[4_1|2]), (189,277,[4_1|2]), (189,282,[1_1|2]), (189,287,[0_1|2]), (189,291,[2_1|2]), (189,296,[3_1|2]), (189,301,[4_1|2]), (189,306,[4_1|2]), (189,311,[4_1|2]), (189,316,[4_1|2]), (189,321,[2_1|2]), (189,325,[3_1|2]), (189,329,[2_1|2]), (189,334,[3_1|2]), (189,338,[5_1|2]), (189,342,[5_1|2]), (189,346,[0_1|2]), (189,351,[5_1|2]), (189,356,[5_1|2]), (189,361,[5_1|2]), (189,366,[3_1|2]), (189,370,[2_1|2]), (189,375,[3_1|2]), (189,380,[2_1|2]), (189,385,[1_1|2]), (189,390,[3_1|2]), (189,395,[4_1|2]), (189,400,[5_1|2]), (189,405,[5_1|2]), (189,410,[3_1|2]), (189,415,[1_1|2]), (189,420,[5_1|2]), (189,424,[0_1|2]), (189,429,[4_1|2]), (189,434,[5_1|2]), (189,439,[5_1|2]), (189,444,[3_1|2]), (190,191,[4_1|2]), (191,192,[2_1|2]), (192,193,[3_1|2]), (193,117,[0_1|2]), (194,195,[3_1|2]), (195,196,[0_1|2]), (196,197,[4_1|2]), (197,198,[0_1|2]), (198,117,[0_1|2]), (199,200,[4_1|2]), (200,201,[0_1|2]), (201,202,[2_1|2]), (202,203,[3_1|2]), (203,117,[0_1|2]), (204,205,[2_1|2]), (205,206,[3_1|2]), (206,207,[0_1|2]), (207,208,[4_1|2]), (208,117,[0_1|2]), (209,210,[3_1|2]), (210,211,[0_1|2]), (211,212,[0_1|2]), (212,213,[5_1|2]), (213,117,[2_1|2]), (214,215,[3_1|2]), (215,216,[0_1|2]), (215,227,[1_1|2]), (215,231,[0_1|2]), (215,236,[2_1|2]), (215,241,[4_1|2]), (215,246,[0_1|2]), (215,250,[1_1|2]), (215,254,[1_1|2]), (215,258,[2_1|2]), (215,262,[1_1|2]), (215,267,[2_1|2]), (215,272,[4_1|2]), (215,277,[4_1|2]), (215,449,[1_1|3]), (215,453,[0_1|3]), (215,457,[1_1|3]), (215,461,[1_1|3]), (215,465,[2_1|3]), (215,469,[1_1|3]), (215,474,[2_1|3]), (215,479,[4_1|3]), (215,484,[4_1|3]), (215,489,[0_1|3]), (215,494,[2_1|3]), (215,499,[4_1|3]), (216,217,[1_1|2]), (217,189,[2_1|2]), (217,222,[2_1|2]), (217,236,[2_1|2]), (217,258,[2_1|2]), (217,267,[2_1|2]), (217,291,[2_1|2]), (217,321,[2_1|2]), (217,329,[2_1|2]), (217,370,[2_1|2]), (217,380,[2_1|2]), (217,255,[2_1|2]), (217,263,[2_1|2]), (217,283,[2_1|2]), (218,219,[3_1|2]), (219,220,[1_1|2]), (220,221,[0_1|2]), (221,189,[2_1|2]), (221,222,[2_1|2]), (221,236,[2_1|2]), (221,258,[2_1|2]), (221,267,[2_1|2]), (221,291,[2_1|2]), (221,321,[2_1|2]), (221,329,[2_1|2]), (221,370,[2_1|2]), (221,380,[2_1|2]), (221,255,[2_1|2]), (221,263,[2_1|2]), (221,283,[2_1|2]), (222,223,[3_1|2]), (223,224,[1_1|2]), (224,225,[3_1|2]), (225,226,[0_1|2]), (225,214,[1_1|2]), (225,218,[1_1|2]), (225,222,[2_1|2]), (225,227,[1_1|2]), (225,231,[0_1|2]), (225,236,[2_1|2]), (225,241,[4_1|2]), (225,246,[0_1|2]), (225,250,[1_1|2]), (225,254,[1_1|2]), (225,258,[2_1|2]), (225,262,[1_1|2]), (225,267,[2_1|2]), (225,272,[4_1|2]), (225,277,[4_1|2]), (225,282,[1_1|2]), (225,504,[1_1|3]), (225,508,[1_1|3]), (225,512,[1_1|3]), (225,516,[2_1|3]), (226,189,[1_1|2]), (226,222,[1_1|2]), (226,236,[1_1|2]), (226,258,[1_1|2]), (226,267,[1_1|2]), (226,291,[1_1|2]), (226,321,[1_1|2]), (226,329,[1_1|2]), (226,370,[1_1|2]), (226,380,[1_1|2]), (226,255,[1_1|2]), (226,263,[1_1|2]), (226,283,[1_1|2]), (227,228,[0_1|2]), (228,229,[0_1|2]), (229,230,[2_1|2]), (230,189,[2_1|2]), (230,231,[2_1|2]), (230,246,[2_1|2]), (230,287,[2_1|2]), (230,346,[2_1|2]), (230,424,[2_1|2]), (230,237,[2_1|2]), (231,232,[2_1|2]), (232,233,[4_1|2]), (233,234,[1_1|2]), (234,235,[3_1|2]), (235,189,[0_1|2]), (235,241,[0_1|2, 4_1|2]), (235,272,[0_1|2, 4_1|2]), (235,277,[0_1|2, 4_1|2]), (235,301,[0_1|2, 4_1|2]), (235,306,[0_1|2, 4_1|2]), (235,311,[0_1|2, 4_1|2]), (235,316,[0_1|2, 4_1|2]), (235,395,[0_1|2]), (235,429,[0_1|2]), (235,288,[0_1|2]), (235,214,[1_1|2]), (235,218,[1_1|2]), (235,222,[2_1|2]), (235,227,[1_1|2]), (235,231,[0_1|2]), (235,236,[2_1|2]), (235,246,[0_1|2]), (235,250,[1_1|2]), (235,254,[1_1|2]), (235,258,[2_1|2]), (235,262,[1_1|2]), (235,267,[2_1|2]), (235,282,[1_1|2]), (235,287,[0_1|2]), (235,291,[2_1|2]), (235,296,[3_1|2]), (236,237,[0_1|2]), (237,238,[3_1|2]), (238,239,[4_1|2]), (239,240,[0_1|2]), (239,214,[1_1|2]), (239,218,[1_1|2]), (239,222,[2_1|2]), (239,227,[1_1|2]), (239,231,[0_1|2]), (239,236,[2_1|2]), (239,241,[4_1|2]), (239,246,[0_1|2]), (239,250,[1_1|2]), (239,254,[1_1|2]), (239,258,[2_1|2]), (239,262,[1_1|2]), (239,267,[2_1|2]), (239,272,[4_1|2]), (239,277,[4_1|2]), (239,282,[1_1|2]), (239,504,[1_1|3]), (239,508,[1_1|3]), (239,512,[1_1|3]), (239,516,[2_1|3]), (240,189,[1_1|2]), (240,241,[1_1|2]), (240,272,[1_1|2]), (240,277,[1_1|2]), (240,301,[1_1|2]), (240,306,[1_1|2]), (240,311,[1_1|2]), (240,316,[1_1|2]), (240,395,[1_1|2]), (240,429,[1_1|2]), (240,288,[1_1|2]), (241,242,[0_1|2]), (242,243,[2_1|2]), (243,244,[3_1|2]), (244,245,[1_1|2]), (245,189,[0_1|2]), (245,241,[0_1|2, 4_1|2]), (245,272,[0_1|2, 4_1|2]), (245,277,[0_1|2, 4_1|2]), (245,301,[0_1|2, 4_1|2]), (245,306,[0_1|2, 4_1|2]), (245,311,[0_1|2, 4_1|2]), (245,316,[0_1|2, 4_1|2]), (245,395,[0_1|2]), (245,429,[0_1|2]), (245,288,[0_1|2]), (245,214,[1_1|2]), (245,218,[1_1|2]), (245,222,[2_1|2]), (245,227,[1_1|2]), (245,231,[0_1|2]), (245,236,[2_1|2]), (245,246,[0_1|2]), (245,250,[1_1|2]), (245,254,[1_1|2]), (245,258,[2_1|2]), (245,262,[1_1|2]), (245,267,[2_1|2]), (245,282,[1_1|2]), (245,287,[0_1|2]), (245,291,[2_1|2]), (245,296,[3_1|2]), (246,247,[2_1|2]), (247,248,[3_1|2]), (248,249,[4_1|2]), (249,189,[1_1|2]), (249,241,[1_1|2]), (249,272,[1_1|2]), (249,277,[1_1|2]), (249,301,[1_1|2]), (249,306,[1_1|2]), (249,311,[1_1|2]), (249,316,[1_1|2]), (249,395,[1_1|2]), (249,429,[1_1|2]), (250,251,[0_1|2]), (251,252,[4_1|2]), (252,253,[2_1|2]), (253,189,[3_1|2]), (253,241,[3_1|2]), (253,272,[3_1|2]), (253,277,[3_1|2]), (253,301,[3_1|2]), (253,306,[3_1|2]), (253,311,[3_1|2]), (253,316,[3_1|2]), (253,395,[3_1|2]), (253,429,[3_1|2]), (254,255,[2_1|2]), (255,256,[3_1|2]), (256,257,[0_1|2]), (256,287,[0_1|2]), (256,291,[2_1|2]), (256,296,[3_1|2]), (256,301,[4_1|2]), (256,306,[4_1|2]), (256,311,[4_1|2]), (256,316,[4_1|2]), (256,521,[0_1|3]), (256,525,[2_1|3]), (256,530,[3_1|3]), (256,535,[4_1|3]), (256,540,[4_1|3]), (257,189,[4_1|2]), (257,241,[4_1|2]), (257,272,[4_1|2]), (257,277,[4_1|2]), (257,301,[4_1|2]), (257,306,[4_1|2]), (257,311,[4_1|2]), (257,316,[4_1|2]), (257,395,[4_1|2]), (257,429,[4_1|2]), (258,259,[1_1|2]), (259,260,[4_1|2]), (260,261,[0_1|2]), (261,189,[3_1|2]), (261,241,[3_1|2]), (261,272,[3_1|2]), (261,277,[3_1|2]), (261,301,[3_1|2]), (261,306,[3_1|2]), (261,311,[3_1|2]), (261,316,[3_1|2]), (261,395,[3_1|2]), (261,429,[3_1|2]), (262,263,[2_1|2]), (263,264,[3_1|2]), (264,265,[4_1|2]), (265,266,[0_1|2]), (266,189,[5_1|2]), (266,241,[5_1|2]), (266,272,[5_1|2]), (266,277,[5_1|2]), (266,301,[5_1|2]), (266,306,[5_1|2]), (266,311,[5_1|2]), (266,316,[5_1|2]), (266,395,[5_1|2, 4_1|2]), (266,429,[5_1|2, 4_1|2]), (266,321,[2_1|2]), (266,325,[3_1|2]), (266,329,[2_1|2]), (266,334,[3_1|2]), (266,338,[5_1|2]), (266,342,[5_1|2]), (266,346,[0_1|2]), (266,351,[5_1|2]), (266,356,[5_1|2]), (266,361,[5_1|2]), (266,366,[3_1|2]), (266,370,[2_1|2]), (266,375,[3_1|2]), (266,380,[2_1|2]), (266,385,[1_1|2]), (266,390,[3_1|2]), (266,400,[5_1|2]), (266,405,[5_1|2]), (266,410,[3_1|2]), (266,415,[1_1|2]), (266,420,[5_1|2]), (266,424,[0_1|2]), (266,434,[5_1|2]), (266,439,[5_1|2]), (266,444,[3_1|2]), (267,268,[1_1|2]), (268,269,[1_1|2]), (269,270,[0_1|2]), (270,271,[3_1|2]), (271,189,[4_1|2]), (271,241,[4_1|2]), (271,272,[4_1|2]), (271,277,[4_1|2]), (271,301,[4_1|2]), (271,306,[4_1|2]), (271,311,[4_1|2]), (271,316,[4_1|2]), (271,395,[4_1|2]), (271,429,[4_1|2]), (272,273,[1_1|2]), (273,274,[2_1|2]), (274,275,[2_1|2]), (275,276,[3_1|2]), (276,189,[0_1|2]), (276,241,[0_1|2, 4_1|2]), (276,272,[0_1|2, 4_1|2]), (276,277,[0_1|2, 4_1|2]), (276,301,[0_1|2, 4_1|2]), (276,306,[0_1|2, 4_1|2]), (276,311,[0_1|2, 4_1|2]), (276,316,[0_1|2, 4_1|2]), (276,395,[0_1|2]), (276,429,[0_1|2]), (276,214,[1_1|2]), (276,218,[1_1|2]), (276,222,[2_1|2]), (276,227,[1_1|2]), (276,231,[0_1|2]), (276,236,[2_1|2]), (276,246,[0_1|2]), (276,250,[1_1|2]), (276,254,[1_1|2]), (276,258,[2_1|2]), (276,262,[1_1|2]), (276,267,[2_1|2]), (276,282,[1_1|2]), (276,287,[0_1|2]), (276,291,[2_1|2]), (276,296,[3_1|2]), (277,278,[5_1|2]), (278,279,[0_1|2]), (279,280,[2_1|2]), (280,281,[3_1|2]), (281,189,[1_1|2]), (281,241,[1_1|2]), (281,272,[1_1|2]), (281,277,[1_1|2]), (281,301,[1_1|2]), (281,306,[1_1|2]), (281,311,[1_1|2]), (281,316,[1_1|2]), (281,395,[1_1|2]), (281,429,[1_1|2]), (282,283,[2_1|2]), (283,284,[3_1|2]), (284,285,[4_1|2]), (285,286,[0_1|2]), (286,189,[2_1|2]), (286,222,[2_1|2]), (286,236,[2_1|2]), (286,258,[2_1|2]), (286,267,[2_1|2]), (286,291,[2_1|2]), (286,321,[2_1|2]), (286,329,[2_1|2]), (286,370,[2_1|2]), (286,380,[2_1|2]), (287,288,[4_1|2]), (288,289,[2_1|2]), (289,290,[3_1|2]), (290,189,[0_1|2]), (290,231,[0_1|2]), (290,246,[0_1|2]), (290,287,[0_1|2]), (290,346,[0_1|2]), (290,424,[0_1|2]), (290,237,[0_1|2]), (290,214,[1_1|2]), (290,218,[1_1|2]), (290,222,[2_1|2]), (290,227,[1_1|2]), (290,236,[2_1|2]), (290,241,[4_1|2]), (290,250,[1_1|2]), (290,254,[1_1|2]), (290,258,[2_1|2]), (290,262,[1_1|2]), (290,267,[2_1|2]), (290,272,[4_1|2]), (290,277,[4_1|2]), (290,282,[1_1|2]), (290,291,[2_1|2]), (290,296,[3_1|2]), (290,301,[4_1|2]), (290,306,[4_1|2]), (290,311,[4_1|2]), (290,316,[4_1|2]), (291,292,[3_1|2]), (292,293,[0_1|2]), (293,294,[4_1|2]), (294,295,[0_1|2]), (295,189,[0_1|2]), (295,231,[0_1|2]), (295,246,[0_1|2]), (295,287,[0_1|2]), (295,346,[0_1|2]), (295,424,[0_1|2]), (295,237,[0_1|2]), (295,214,[1_1|2]), (295,218,[1_1|2]), (295,222,[2_1|2]), (295,227,[1_1|2]), (295,236,[2_1|2]), (295,241,[4_1|2]), (295,250,[1_1|2]), (295,254,[1_1|2]), (295,258,[2_1|2]), (295,262,[1_1|2]), (295,267,[2_1|2]), (295,272,[4_1|2]), (295,277,[4_1|2]), (295,282,[1_1|2]), (295,291,[2_1|2]), (295,296,[3_1|2]), (295,301,[4_1|2]), (295,306,[4_1|2]), (295,311,[4_1|2]), (295,316,[4_1|2]), (296,297,[4_1|2]), (297,298,[0_1|2]), (298,299,[2_1|2]), (299,300,[3_1|2]), (300,189,[0_1|2]), (300,231,[0_1|2]), (300,246,[0_1|2]), (300,287,[0_1|2]), (300,346,[0_1|2]), (300,424,[0_1|2]), (300,237,[0_1|2]), (300,214,[1_1|2]), (300,218,[1_1|2]), (300,222,[2_1|2]), (300,227,[1_1|2]), (300,236,[2_1|2]), (300,241,[4_1|2]), (300,250,[1_1|2]), (300,254,[1_1|2]), (300,258,[2_1|2]), (300,262,[1_1|2]), (300,267,[2_1|2]), (300,272,[4_1|2]), (300,277,[4_1|2]), (300,282,[1_1|2]), (300,291,[2_1|2]), (300,296,[3_1|2]), (300,301,[4_1|2]), (300,306,[4_1|2]), (300,311,[4_1|2]), (300,316,[4_1|2]), (301,302,[2_1|2]), (302,303,[3_1|2]), (303,304,[0_1|2]), (303,521,[0_1|3]), (303,525,[2_1|3]), (303,530,[3_1|3]), (303,535,[4_1|3]), (303,540,[4_1|3]), (304,305,[4_1|2]), (305,189,[0_1|2]), (305,231,[0_1|2]), (305,246,[0_1|2]), (305,287,[0_1|2]), (305,346,[0_1|2]), (305,424,[0_1|2]), (305,237,[0_1|2]), (305,214,[1_1|2]), (305,218,[1_1|2]), (305,222,[2_1|2]), (305,227,[1_1|2]), (305,236,[2_1|2]), (305,241,[4_1|2]), (305,250,[1_1|2]), (305,254,[1_1|2]), (305,258,[2_1|2]), (305,262,[1_1|2]), (305,267,[2_1|2]), (305,272,[4_1|2]), (305,277,[4_1|2]), (305,282,[1_1|2]), (305,291,[2_1|2]), (305,296,[3_1|2]), (305,301,[4_1|2]), (305,306,[4_1|2]), (305,311,[4_1|2]), (305,316,[4_1|2]), (306,307,[3_1|2]), (307,308,[0_1|2]), (308,309,[0_1|2]), (309,310,[5_1|2]), (310,189,[2_1|2]), (310,231,[2_1|2]), (310,246,[2_1|2]), (310,287,[2_1|2]), (310,346,[2_1|2]), (310,424,[2_1|2]), (310,237,[2_1|2]), (311,312,[0_1|2]), (312,313,[2_1|2]), (313,314,[3_1|2]), (314,315,[1_1|2]), (315,189,[4_1|2]), (315,241,[4_1|2]), (315,272,[4_1|2]), (315,277,[4_1|2]), (315,301,[4_1|2]), (315,306,[4_1|2]), (315,311,[4_1|2]), (315,316,[4_1|2]), (315,395,[4_1|2]), (315,429,[4_1|2]), (316,317,[0_1|2]), (316,545,[0_1|3]), (316,549,[2_1|3]), (316,554,[3_1|3]), (316,559,[4_1|3]), (316,564,[4_1|3]), (317,318,[4_1|2]), (318,319,[2_1|2]), (319,320,[0_1|2]), (320,189,[3_1|2]), (320,241,[3_1|2]), (320,272,[3_1|2]), (320,277,[3_1|2]), (320,301,[3_1|2]), (320,306,[3_1|2]), (320,311,[3_1|2]), (320,316,[3_1|2]), (320,395,[3_1|2]), (320,429,[3_1|2]), (321,322,[1_1|2]), (322,323,[3_1|2]), (323,324,[5_1|2]), (323,444,[3_1|2]), (324,189,[0_1|2]), (324,231,[0_1|2]), (324,246,[0_1|2]), (324,287,[0_1|2]), (324,346,[0_1|2]), (324,424,[0_1|2]), (324,237,[0_1|2]), (324,214,[1_1|2]), (324,218,[1_1|2]), (324,222,[2_1|2]), (324,227,[1_1|2]), (324,236,[2_1|2]), (324,241,[4_1|2]), (324,250,[1_1|2]), (324,254,[1_1|2]), (324,258,[2_1|2]), (324,262,[1_1|2]), (324,267,[2_1|2]), (324,272,[4_1|2]), (324,277,[4_1|2]), (324,282,[1_1|2]), (324,291,[2_1|2]), (324,296,[3_1|2]), (324,301,[4_1|2]), (324,306,[4_1|2]), (324,311,[4_1|2]), (324,316,[4_1|2]), (325,326,[1_1|2]), (326,327,[0_1|2]), (327,328,[2_1|2]), (328,189,[5_1|2]), (328,231,[5_1|2]), (328,246,[5_1|2]), (328,287,[5_1|2]), (328,346,[5_1|2, 0_1|2]), (328,424,[5_1|2, 0_1|2]), (328,237,[5_1|2]), (328,321,[2_1|2]), (328,325,[3_1|2]), (328,329,[2_1|2]), (328,334,[3_1|2]), (328,338,[5_1|2]), (328,342,[5_1|2]), (328,351,[5_1|2]), (328,356,[5_1|2]), (328,361,[5_1|2]), (328,366,[3_1|2]), (328,370,[2_1|2]), (328,375,[3_1|2]), (328,380,[2_1|2]), (328,385,[1_1|2]), (328,390,[3_1|2]), (328,395,[4_1|2]), (328,400,[5_1|2]), (328,405,[5_1|2]), (328,410,[3_1|2]), (328,415,[1_1|2]), (328,420,[5_1|2]), (328,429,[4_1|2]), (328,434,[5_1|2]), (328,439,[5_1|2]), (328,444,[3_1|2]), (329,330,[3_1|2]), (330,331,[0_1|2]), (331,332,[0_1|2]), (332,333,[1_1|2]), (333,189,[5_1|2]), (333,231,[5_1|2]), (333,246,[5_1|2]), (333,287,[5_1|2]), (333,346,[5_1|2, 0_1|2]), (333,424,[5_1|2, 0_1|2]), (333,237,[5_1|2]), (333,321,[2_1|2]), (333,325,[3_1|2]), (333,329,[2_1|2]), (333,334,[3_1|2]), (333,338,[5_1|2]), (333,342,[5_1|2]), (333,351,[5_1|2]), (333,356,[5_1|2]), (333,361,[5_1|2]), (333,366,[3_1|2]), (333,370,[2_1|2]), (333,375,[3_1|2]), (333,380,[2_1|2]), (333,385,[1_1|2]), (333,390,[3_1|2]), (333,395,[4_1|2]), (333,400,[5_1|2]), (333,405,[5_1|2]), (333,410,[3_1|2]), (333,415,[1_1|2]), (333,420,[5_1|2]), (333,429,[4_1|2]), (333,434,[5_1|2]), (333,439,[5_1|2]), (333,444,[3_1|2]), (334,335,[2_1|2]), (335,336,[5_1|2]), (335,366,[3_1|2]), (335,370,[2_1|2]), (335,375,[3_1|2]), (335,380,[2_1|2]), (335,569,[3_1|3]), (335,573,[2_1|3]), (335,578,[3_1|3]), (335,583,[2_1|3]), (336,337,[1_1|2]), (337,189,[4_1|2]), (337,241,[4_1|2]), (337,272,[4_1|2]), (337,277,[4_1|2]), (337,301,[4_1|2]), (337,306,[4_1|2]), (337,311,[4_1|2]), (337,316,[4_1|2]), (337,395,[4_1|2]), (337,429,[4_1|2]), (338,339,[2_1|2]), (339,340,[1_1|2]), (340,341,[3_1|2]), (341,189,[4_1|2]), (341,241,[4_1|2]), (341,272,[4_1|2]), (341,277,[4_1|2]), (341,301,[4_1|2]), (341,306,[4_1|2]), (341,311,[4_1|2]), (341,316,[4_1|2]), (341,395,[4_1|2]), (341,429,[4_1|2]), (342,343,[5_1|2]), (343,344,[2_1|2]), (344,345,[1_1|2]), (345,189,[4_1|2]), (345,241,[4_1|2]), (345,272,[4_1|2]), (345,277,[4_1|2]), (345,301,[4_1|2]), (345,306,[4_1|2]), (345,311,[4_1|2]), (345,316,[4_1|2]), (345,395,[4_1|2]), (345,429,[4_1|2]), (346,347,[3_1|2]), (347,348,[4_1|2]), (348,349,[5_1|2]), (349,350,[2_1|2]), (350,189,[1_1|2]), (350,241,[1_1|2]), (350,272,[1_1|2]), (350,277,[1_1|2]), (350,301,[1_1|2]), (350,306,[1_1|2]), (350,311,[1_1|2]), (350,316,[1_1|2]), (350,395,[1_1|2]), (350,429,[1_1|2]), (351,352,[0_1|2]), (352,353,[2_1|2]), (353,354,[1_1|2]), (354,355,[3_1|2]), (355,189,[4_1|2]), (355,231,[4_1|2]), (355,246,[4_1|2]), (355,287,[4_1|2]), (355,346,[4_1|2]), (355,424,[4_1|2]), (355,242,[4_1|2]), (355,312,[4_1|2]), (355,317,[4_1|2]), (355,545,[4_1|2]), (356,357,[0_1|2]), (357,358,[3_1|2]), (358,359,[2_1|2]), (359,360,[1_1|2]), (360,189,[4_1|2]), (360,231,[4_1|2]), (360,246,[4_1|2]), (360,287,[4_1|2]), (360,346,[4_1|2]), (360,424,[4_1|2]), (360,242,[4_1|2]), (360,312,[4_1|2]), (360,317,[4_1|2]), (360,545,[4_1|2]), (361,362,[2_1|2]), (362,363,[2_1|2]), (363,364,[1_1|2]), (364,365,[4_1|2]), (365,189,[5_1|2]), (365,241,[5_1|2]), (365,272,[5_1|2]), (365,277,[5_1|2]), (365,301,[5_1|2]), (365,306,[5_1|2]), (365,311,[5_1|2]), (365,316,[5_1|2]), (365,395,[5_1|2, 4_1|2]), (365,429,[5_1|2, 4_1|2]), (365,321,[2_1|2]), (365,325,[3_1|2]), (365,329,[2_1|2]), (365,334,[3_1|2]), (365,338,[5_1|2]), (365,342,[5_1|2]), (365,346,[0_1|2]), (365,351,[5_1|2]), (365,356,[5_1|2]), (365,361,[5_1|2]), (365,366,[3_1|2]), (365,370,[2_1|2]), (365,375,[3_1|2]), (365,380,[2_1|2]), (365,385,[1_1|2]), (365,390,[3_1|2]), (365,400,[5_1|2]), (365,405,[5_1|2]), (365,410,[3_1|2]), (365,415,[1_1|2]), (365,420,[5_1|2]), (365,424,[0_1|2]), (365,434,[5_1|2]), (365,439,[5_1|2]), (365,444,[3_1|2]), (366,367,[4_1|2]), (367,368,[5_1|2]), (368,369,[2_1|2]), (369,189,[1_1|2]), (369,222,[1_1|2]), (369,236,[1_1|2]), (369,258,[1_1|2]), (369,267,[1_1|2]), (369,291,[1_1|2]), (369,321,[1_1|2]), (369,329,[1_1|2]), (369,370,[1_1|2]), (369,380,[1_1|2]), (369,302,[1_1|2]), (369,549,[1_1|2]), (370,371,[1_1|2]), (371,372,[3_1|2]), (372,373,[4_1|2]), (373,374,[5_1|2]), (373,390,[3_1|2]), (373,395,[4_1|2]), (373,400,[5_1|2]), (373,405,[5_1|2]), (373,410,[3_1|2]), (373,415,[1_1|2]), (373,420,[5_1|2]), (373,424,[0_1|2]), (373,429,[4_1|2]), (373,434,[5_1|2]), (373,439,[5_1|2]), (373,588,[5_1|3]), (373,592,[0_1|3]), (373,597,[4_1|3]), (373,634,[3_1|3]), (373,639,[4_1|3]), (373,644,[5_1|3]), (373,649,[5_1|3]), (373,654,[3_1|3]), (374,189,[4_1|2]), (374,222,[4_1|2]), (374,236,[4_1|2]), (374,258,[4_1|2]), (374,267,[4_1|2]), (374,291,[4_1|2]), (374,321,[4_1|2]), (374,329,[4_1|2]), (374,370,[4_1|2]), (374,380,[4_1|2]), (374,302,[4_1|2]), (374,549,[4_1|2]), (375,376,[3_1|2]), (376,377,[4_1|2]), (377,378,[2_1|2]), (378,379,[1_1|2]), (379,189,[5_1|2]), (379,222,[5_1|2]), (379,236,[5_1|2]), (379,258,[5_1|2]), (379,267,[5_1|2]), (379,291,[5_1|2]), (379,321,[5_1|2, 2_1|2]), (379,329,[5_1|2, 2_1|2]), (379,370,[5_1|2, 2_1|2]), (379,380,[5_1|2, 2_1|2]), (379,302,[5_1|2]), (379,325,[3_1|2]), (379,334,[3_1|2]), (379,338,[5_1|2]), (379,342,[5_1|2]), (379,346,[0_1|2]), (379,351,[5_1|2]), (379,356,[5_1|2]), (379,361,[5_1|2]), (379,366,[3_1|2]), (379,375,[3_1|2]), (379,385,[1_1|2]), (379,390,[3_1|2]), (379,395,[4_1|2]), (379,400,[5_1|2]), (379,405,[5_1|2]), (379,410,[3_1|2]), (379,415,[1_1|2]), (379,420,[5_1|2]), (379,424,[0_1|2]), (379,429,[4_1|2]), (379,434,[5_1|2]), (379,439,[5_1|2]), (379,444,[3_1|2]), (379,549,[5_1|2]), (380,381,[1_1|2]), (381,382,[5_1|2]), (382,383,[3_1|2]), (383,384,[4_1|2]), (384,189,[1_1|2]), (384,222,[1_1|2]), (384,236,[1_1|2]), (384,258,[1_1|2]), (384,267,[1_1|2]), (384,291,[1_1|2]), (384,321,[1_1|2]), (384,329,[1_1|2]), (384,370,[1_1|2]), (384,380,[1_1|2]), (384,255,[1_1|2]), (384,263,[1_1|2]), (384,283,[1_1|2]), (384,274,[1_1|2]), (385,386,[5_1|2]), (386,387,[1_1|2]), (387,388,[3_1|2]), (388,389,[4_1|2]), (389,189,[0_1|2]), (389,241,[0_1|2, 4_1|2]), (389,272,[0_1|2, 4_1|2]), (389,277,[0_1|2, 4_1|2]), (389,301,[0_1|2, 4_1|2]), (389,306,[0_1|2, 4_1|2]), (389,311,[0_1|2, 4_1|2]), (389,316,[0_1|2, 4_1|2]), (389,395,[0_1|2]), (389,429,[0_1|2]), (389,214,[1_1|2]), (389,218,[1_1|2]), (389,222,[2_1|2]), (389,227,[1_1|2]), (389,231,[0_1|2]), (389,236,[2_1|2]), (389,246,[0_1|2]), (389,250,[1_1|2]), (389,254,[1_1|2]), (389,258,[2_1|2]), (389,262,[1_1|2]), (389,267,[2_1|2]), (389,282,[1_1|2]), (389,287,[0_1|2]), (389,291,[2_1|2]), (389,296,[3_1|2]), (390,391,[4_1|2]), (391,392,[4_1|2]), (392,393,[1_1|2]), (393,394,[5_1|2]), (393,390,[3_1|2]), (393,395,[4_1|2]), (393,400,[5_1|2]), (393,405,[5_1|2]), (393,410,[3_1|2]), (393,415,[1_1|2]), (393,420,[5_1|2]), (393,424,[0_1|2]), (393,429,[4_1|2]), (393,434,[5_1|2]), (393,439,[5_1|2]), (393,588,[5_1|3]), (393,592,[0_1|3]), (393,597,[4_1|3]), (394,189,[4_1|2]), (394,241,[4_1|2]), (394,272,[4_1|2]), (394,277,[4_1|2]), (394,301,[4_1|2]), (394,306,[4_1|2]), (394,311,[4_1|2]), (394,316,[4_1|2]), (394,395,[4_1|2]), (394,429,[4_1|2]), (395,396,[1_1|2]), (396,397,[3_1|2]), (397,398,[5_1|2]), (398,399,[0_1|2]), (398,287,[0_1|2]), (398,291,[2_1|2]), (398,296,[3_1|2]), (398,301,[4_1|2]), (398,306,[4_1|2]), (398,311,[4_1|2]), (398,316,[4_1|2]), (398,521,[0_1|3]), (398,525,[2_1|3]), (398,530,[3_1|3]), (398,535,[4_1|3]), (398,540,[4_1|3]), (399,189,[4_1|2]), (399,241,[4_1|2]), (399,272,[4_1|2]), (399,277,[4_1|2]), (399,301,[4_1|2]), (399,306,[4_1|2]), (399,311,[4_1|2]), (399,316,[4_1|2]), (399,395,[4_1|2]), (399,429,[4_1|2]), (400,401,[1_1|2]), (401,402,[3_1|2]), (402,403,[4_1|2]), (403,404,[5_1|2]), (403,390,[3_1|2]), (403,395,[4_1|2]), (403,400,[5_1|2]), (403,405,[5_1|2]), (403,410,[3_1|2]), (403,415,[1_1|2]), (403,420,[5_1|2]), (403,424,[0_1|2]), (403,429,[4_1|2]), (403,434,[5_1|2]), (403,439,[5_1|2]), (403,588,[5_1|3]), (403,592,[0_1|3]), (403,597,[4_1|3]), (404,189,[4_1|2]), (404,241,[4_1|2]), (404,272,[4_1|2]), (404,277,[4_1|2]), (404,301,[4_1|2]), (404,306,[4_1|2]), (404,311,[4_1|2]), (404,316,[4_1|2]), (404,395,[4_1|2]), (404,429,[4_1|2]), (405,406,[1_1|2]), (406,407,[5_1|2]), (407,408,[3_1|2]), (408,409,[4_1|2]), (409,189,[4_1|2]), (409,241,[4_1|2]), (409,272,[4_1|2]), (409,277,[4_1|2]), (409,301,[4_1|2]), (409,306,[4_1|2]), (409,311,[4_1|2]), (409,316,[4_1|2]), (409,395,[4_1|2]), (409,429,[4_1|2]), (410,411,[4_1|2]), (411,412,[0_1|2]), (412,413,[4_1|2]), (413,414,[5_1|2]), (413,321,[2_1|2]), (413,325,[3_1|2]), (413,329,[2_1|2]), (413,334,[3_1|2]), (413,338,[5_1|2]), (413,342,[5_1|2]), (413,346,[0_1|2]), (413,351,[5_1|2]), (413,356,[5_1|2]), (413,361,[5_1|2]), (413,366,[3_1|2]), (413,370,[2_1|2]), (413,375,[3_1|2]), (413,380,[2_1|2]), (413,385,[1_1|2]), (413,602,[2_1|3]), (413,606,[3_1|3]), (413,610,[2_1|3]), (413,615,[2_1|3]), (413,620,[3_1|3]), (413,624,[2_1|3]), (413,629,[3_1|3]), (413,659,[3_1|3]), (413,663,[5_1|3]), (413,667,[5_1|3]), (413,671,[0_1|3]), (414,189,[1_1|2]), (414,231,[1_1|2]), (414,246,[1_1|2]), (414,287,[1_1|2]), (414,346,[1_1|2]), (414,424,[1_1|2]), (414,242,[1_1|2]), (414,312,[1_1|2]), (414,317,[1_1|2]), (414,545,[1_1|2]), (415,416,[1_1|2]), (416,417,[3_1|2]), (417,418,[4_1|2]), (418,419,[5_1|2]), (418,390,[3_1|2]), (418,395,[4_1|2]), (418,400,[5_1|2]), (418,405,[5_1|2]), (418,410,[3_1|2]), (418,415,[1_1|2]), (418,420,[5_1|2]), (418,424,[0_1|2]), (418,429,[4_1|2]), (418,434,[5_1|2]), (418,439,[5_1|2]), (418,588,[5_1|3]), (418,592,[0_1|3]), (418,597,[4_1|3]), (419,189,[4_1|2]), (419,241,[4_1|2]), (419,272,[4_1|2]), (419,277,[4_1|2]), (419,301,[4_1|2]), (419,306,[4_1|2]), (419,311,[4_1|2]), (419,316,[4_1|2]), (419,395,[4_1|2]), (419,429,[4_1|2]), (420,421,[4_1|2]), (421,422,[2_1|2]), (422,423,[3_1|2]), (423,189,[0_1|2]), (423,231,[0_1|2]), (423,246,[0_1|2]), (423,287,[0_1|2]), (423,346,[0_1|2]), (423,424,[0_1|2]), (423,237,[0_1|2]), (423,214,[1_1|2]), (423,218,[1_1|2]), (423,222,[2_1|2]), (423,227,[1_1|2]), (423,236,[2_1|2]), (423,241,[4_1|2]), (423,250,[1_1|2]), (423,254,[1_1|2]), (423,258,[2_1|2]), (423,262,[1_1|2]), (423,267,[2_1|2]), (423,272,[4_1|2]), (423,277,[4_1|2]), (423,282,[1_1|2]), (423,291,[2_1|2]), (423,296,[3_1|2]), (423,301,[4_1|2]), (423,306,[4_1|2]), (423,311,[4_1|2]), (423,316,[4_1|2]), (424,425,[1_1|2]), (425,426,[2_1|2]), (426,427,[3_1|2]), (427,428,[4_1|2]), (428,189,[5_1|2]), (428,231,[5_1|2]), (428,246,[5_1|2]), (428,287,[5_1|2]), (428,346,[5_1|2, 0_1|2]), (428,424,[5_1|2, 0_1|2]), (428,237,[5_1|2]), (428,321,[2_1|2]), (428,325,[3_1|2]), (428,329,[2_1|2]), (428,334,[3_1|2]), (428,338,[5_1|2]), (428,342,[5_1|2]), (428,351,[5_1|2]), (428,356,[5_1|2]), (428,361,[5_1|2]), (428,366,[3_1|2]), (428,370,[2_1|2]), (428,375,[3_1|2]), (428,380,[2_1|2]), (428,385,[1_1|2]), (428,390,[3_1|2]), (428,395,[4_1|2]), (428,400,[5_1|2]), (428,405,[5_1|2]), (428,410,[3_1|2]), (428,415,[1_1|2]), (428,420,[5_1|2]), (428,429,[4_1|2]), (428,434,[5_1|2]), (428,439,[5_1|2]), (428,444,[3_1|2]), (429,430,[5_1|2]), (430,431,[3_1|2]), (431,432,[3_1|2]), (432,433,[0_1|2]), (433,189,[2_1|2]), (433,231,[2_1|2]), (433,246,[2_1|2]), (433,287,[2_1|2]), (433,346,[2_1|2]), (433,424,[2_1|2]), (433,237,[2_1|2]), (434,435,[4_1|2]), (435,436,[0_1|2]), (436,437,[3_1|2]), (437,438,[2_1|2]), (438,189,[3_1|2]), (438,231,[3_1|2]), (438,246,[3_1|2]), (438,287,[3_1|2]), (438,346,[3_1|2]), (438,424,[3_1|2]), (438,237,[3_1|2]), (439,440,[0_1|2]), (440,441,[5_1|2]), (441,442,[4_1|2]), (442,443,[4_1|2]), (443,189,[2_1|2]), (443,231,[2_1|2]), (443,246,[2_1|2]), (443,287,[2_1|2]), (443,346,[2_1|2]), (443,424,[2_1|2]), (443,237,[2_1|2]), (444,445,[0_1|2]), (445,446,[2_1|2]), (446,447,[1_1|2]), (447,448,[4_1|2]), (448,189,[5_1|2]), (448,241,[5_1|2]), (448,272,[5_1|2]), (448,277,[5_1|2]), (448,301,[5_1|2]), (448,306,[5_1|2]), (448,311,[5_1|2]), (448,316,[5_1|2]), (448,395,[5_1|2, 4_1|2]), (448,429,[5_1|2, 4_1|2]), (448,321,[2_1|2]), (448,325,[3_1|2]), (448,329,[2_1|2]), (448,334,[3_1|2]), (448,338,[5_1|2]), (448,342,[5_1|2]), (448,346,[0_1|2]), (448,351,[5_1|2]), (448,356,[5_1|2]), (448,361,[5_1|2]), (448,366,[3_1|2]), (448,370,[2_1|2]), (448,375,[3_1|2]), (448,380,[2_1|2]), (448,385,[1_1|2]), (448,390,[3_1|2]), (448,400,[5_1|2]), (448,405,[5_1|2]), (448,410,[3_1|2]), (448,415,[1_1|2]), (448,420,[5_1|2]), (448,424,[0_1|2]), (448,434,[5_1|2]), (448,439,[5_1|2]), (448,444,[3_1|2]), (449,450,[0_1|3]), (450,451,[0_1|3]), (451,452,[2_1|3]), (452,231,[2_1|3]), (452,246,[2_1|3]), (452,287,[2_1|3]), (452,346,[2_1|3]), (452,424,[2_1|3]), (452,237,[2_1|3]), (453,454,[2_1|3]), (454,455,[3_1|3]), (455,456,[4_1|3]), (456,241,[1_1|3]), (456,272,[1_1|3]), (456,277,[1_1|3]), (456,301,[1_1|3]), (456,306,[1_1|3]), (456,311,[1_1|3]), (456,316,[1_1|3]), (456,395,[1_1|3]), (456,429,[1_1|3]), (457,458,[0_1|3]), (458,459,[4_1|3]), (459,460,[2_1|3]), (460,241,[3_1|3]), (460,272,[3_1|3]), (460,277,[3_1|3]), (460,301,[3_1|3]), (460,306,[3_1|3]), (460,311,[3_1|3]), (460,316,[3_1|3]), (460,395,[3_1|3]), (460,429,[3_1|3]), (461,462,[2_1|3]), (462,463,[3_1|3]), (463,464,[0_1|3]), (464,241,[4_1|3]), (464,272,[4_1|3]), (464,277,[4_1|3]), (464,301,[4_1|3]), (464,306,[4_1|3]), (464,311,[4_1|3]), (464,316,[4_1|3]), (464,395,[4_1|3]), (464,429,[4_1|3]), (465,466,[1_1|3]), (466,467,[4_1|3]), (467,468,[0_1|3]), (468,241,[3_1|3]), (468,272,[3_1|3]), (468,277,[3_1|3]), (468,301,[3_1|3]), (468,306,[3_1|3]), (468,311,[3_1|3]), (468,316,[3_1|3]), (468,395,[3_1|3]), (468,429,[3_1|3]), (469,470,[2_1|3]), (470,471,[3_1|3]), (471,472,[4_1|3]), (472,473,[0_1|3]), (473,241,[5_1|3]), (473,272,[5_1|3]), (473,277,[5_1|3]), (473,301,[5_1|3]), (473,306,[5_1|3]), (473,311,[5_1|3]), (473,316,[5_1|3]), (473,395,[5_1|3]), (473,429,[5_1|3]), (474,475,[1_1|3]), (475,476,[1_1|3]), (476,477,[0_1|3]), (477,478,[3_1|3]), (478,241,[4_1|3]), (478,272,[4_1|3]), (478,277,[4_1|3]), (478,301,[4_1|3]), (478,306,[4_1|3]), (478,311,[4_1|3]), (478,316,[4_1|3]), (478,395,[4_1|3]), (478,429,[4_1|3]), (479,480,[1_1|3]), (480,481,[2_1|3]), (481,482,[2_1|3]), (482,483,[3_1|3]), (483,241,[0_1|3]), (483,272,[0_1|3]), (483,277,[0_1|3]), (483,301,[0_1|3]), (483,306,[0_1|3]), (483,311,[0_1|3]), (483,316,[0_1|3]), (483,395,[0_1|3]), (483,429,[0_1|3]), (484,485,[5_1|3]), (485,486,[0_1|3]), (486,487,[2_1|3]), (487,488,[3_1|3]), (488,241,[1_1|3]), (488,272,[1_1|3]), (488,277,[1_1|3]), (488,301,[1_1|3]), (488,306,[1_1|3]), (488,311,[1_1|3]), (488,316,[1_1|3]), (488,395,[1_1|3]), (488,429,[1_1|3]), (489,490,[2_1|3]), (490,491,[4_1|3]), (491,492,[1_1|3]), (492,493,[3_1|3]), (493,288,[0_1|3]), (494,495,[0_1|3]), (495,496,[3_1|3]), (496,497,[4_1|3]), (497,498,[0_1|3]), (498,288,[1_1|3]), (499,500,[0_1|3]), (500,501,[2_1|3]), (501,502,[3_1|3]), (502,503,[1_1|3]), (503,288,[0_1|3]), (504,505,[0_1|3]), (505,506,[0_1|3]), (506,507,[2_1|3]), (507,237,[2_1|3]), (508,509,[3_1|3]), (509,510,[0_1|3]), (510,511,[1_1|3]), (511,255,[2_1|3]), (511,263,[2_1|3]), (511,283,[2_1|3]), (511,274,[2_1|3]), (512,513,[3_1|3]), (513,514,[1_1|3]), (514,515,[0_1|3]), (515,255,[2_1|3]), (515,263,[2_1|3]), (515,283,[2_1|3]), (515,274,[2_1|3]), (516,517,[3_1|3]), (517,518,[1_1|3]), (518,519,[3_1|3]), (519,520,[0_1|3]), (520,255,[1_1|3]), (520,263,[1_1|3]), (520,283,[1_1|3]), (520,274,[1_1|3]), (521,522,[4_1|3]), (522,523,[2_1|3]), (523,524,[3_1|3]), (524,237,[0_1|3]), (525,526,[3_1|3]), (526,527,[0_1|3]), (527,528,[4_1|3]), (528,529,[0_1|3]), (529,237,[0_1|3]), (530,531,[4_1|3]), (531,532,[0_1|3]), (532,533,[2_1|3]), (533,534,[3_1|3]), (534,237,[0_1|3]), (535,536,[2_1|3]), (536,537,[3_1|3]), (537,538,[0_1|3]), (538,539,[4_1|3]), (539,237,[0_1|3]), (540,541,[3_1|3]), (541,542,[0_1|3]), (542,543,[0_1|3]), (543,544,[5_1|3]), (544,237,[2_1|3]), (545,546,[4_1|3]), (546,547,[2_1|3]), (547,548,[3_1|3]), (548,320,[0_1|3]), (549,550,[3_1|3]), (550,551,[0_1|3]), (551,552,[4_1|3]), (552,553,[0_1|3]), (553,320,[0_1|3]), (554,555,[4_1|3]), (555,556,[0_1|3]), (556,557,[2_1|3]), (557,558,[3_1|3]), (558,320,[0_1|3]), (559,560,[2_1|3]), (560,561,[3_1|3]), (561,562,[0_1|3]), (562,563,[4_1|3]), (563,320,[0_1|3]), (564,565,[3_1|3]), (565,566,[0_1|3]), (566,567,[0_1|3]), (567,568,[5_1|3]), (568,320,[2_1|3]), (569,570,[4_1|3]), (570,571,[5_1|3]), (571,572,[2_1|3]), (572,222,[1_1|3]), (572,236,[1_1|3]), (572,258,[1_1|3]), (572,267,[1_1|3]), (572,291,[1_1|3]), (572,321,[1_1|3]), (572,329,[1_1|3]), (572,370,[1_1|3]), (572,380,[1_1|3]), (572,302,[1_1|3]), (572,549,[1_1|3]), (573,574,[1_1|3]), (574,575,[3_1|3]), (575,576,[4_1|3]), (576,577,[5_1|3]), (576,634,[3_1|3]), (576,639,[4_1|3]), (576,644,[5_1|3]), (576,649,[5_1|3]), (576,654,[3_1|3]), (577,222,[4_1|3]), (577,236,[4_1|3]), (577,258,[4_1|3]), (577,267,[4_1|3]), (577,291,[4_1|3]), (577,321,[4_1|3]), (577,329,[4_1|3]), (577,370,[4_1|3]), (577,380,[4_1|3]), (577,302,[4_1|3]), (577,549,[4_1|3]), (578,579,[3_1|3]), (579,580,[4_1|3]), (580,581,[2_1|3]), (581,582,[1_1|3]), (582,222,[5_1|3]), (582,236,[5_1|3]), (582,258,[5_1|3]), (582,267,[5_1|3]), (582,291,[5_1|3]), (582,321,[5_1|3]), (582,329,[5_1|3]), (582,370,[5_1|3]), (582,380,[5_1|3]), (582,302,[5_1|3]), (582,549,[5_1|3]), (583,584,[1_1|3]), (584,585,[5_1|3]), (585,586,[3_1|3]), (586,587,[4_1|3]), (587,255,[1_1|3]), (587,263,[1_1|3]), (587,283,[1_1|3]), (587,274,[1_1|3]), (588,589,[4_1|3]), (589,590,[2_1|3]), (590,591,[3_1|3]), (591,237,[0_1|3]), (592,593,[1_1|3]), (593,594,[2_1|3]), (594,595,[3_1|3]), (595,596,[4_1|3]), (596,237,[5_1|3]), (597,598,[5_1|3]), (598,599,[3_1|3]), (599,600,[3_1|3]), (600,601,[0_1|3]), (601,237,[2_1|3]), (602,603,[1_1|3]), (603,604,[3_1|3]), (604,605,[5_1|3]), (605,237,[0_1|3]), (606,607,[1_1|3]), (607,608,[0_1|3]), (608,609,[2_1|3]), (609,237,[5_1|3]), (610,611,[3_1|3]), (611,612,[0_1|3]), (612,613,[0_1|3]), (613,614,[1_1|3]), (614,237,[5_1|3]), (615,616,[1_1|3]), (616,617,[5_1|3]), (617,618,[3_1|3]), (618,619,[4_1|3]), (619,274,[1_1|3]), (620,621,[4_1|3]), (621,622,[5_1|3]), (622,623,[2_1|3]), (623,302,[1_1|3]), (623,549,[1_1|3]), (623,289,[1_1|3]), (623,319,[1_1|3]), (623,547,[1_1|3]), (624,625,[1_1|3]), (625,626,[3_1|3]), (626,627,[4_1|3]), (627,628,[5_1|3]), (627,676,[5_1|3]), (628,302,[4_1|3]), (628,549,[4_1|3]), (628,289,[4_1|3]), (628,319,[4_1|3]), (628,547,[4_1|3]), (629,630,[3_1|3]), (630,631,[4_1|3]), (631,632,[2_1|3]), (632,633,[1_1|3]), (633,302,[5_1|3]), (633,549,[5_1|3]), (633,289,[5_1|3]), (633,319,[5_1|3]), (633,547,[5_1|3]), (634,635,[4_1|3]), (635,636,[4_1|3]), (636,637,[1_1|3]), (637,638,[5_1|3]), (638,260,[4_1|3]), (639,640,[1_1|3]), (640,641,[3_1|3]), (641,642,[5_1|3]), (642,643,[0_1|3]), (643,260,[4_1|3]), (644,645,[1_1|3]), (645,646,[3_1|3]), (646,647,[4_1|3]), (647,648,[5_1|3]), (648,260,[4_1|3]), (649,650,[1_1|3]), (650,651,[5_1|3]), (651,652,[3_1|3]), (652,653,[4_1|3]), (653,260,[4_1|3]), (654,655,[4_1|3]), (655,656,[0_1|3]), (656,657,[4_1|3]), (657,658,[5_1|3]), (657,385,[1_1|2]), (658,261,[1_1|3]), (659,660,[2_1|3]), (660,661,[5_1|3]), (661,662,[1_1|3]), (662,233,[4_1|3]), (663,664,[2_1|3]), (664,665,[1_1|3]), (665,666,[3_1|3]), (666,233,[4_1|3]), (667,668,[5_1|3]), (668,669,[2_1|3]), (669,670,[1_1|3]), (670,233,[4_1|3]), (671,672,[3_1|3]), (672,673,[4_1|3]), (673,674,[5_1|3]), (674,675,[2_1|3]), (675,233,[1_1|3]), (676,677,[4_1|3]), (677,678,[0_1|3]), (678,679,[3_1|3]), (679,680,[2_1|3]), (680,237,[3_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1) ---------------------------------------- (9) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (10) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: 0(1(1(2(x1)))) -> 1(3(0(1(2(x1))))) 0(1(1(2(x1)))) -> 1(3(1(0(2(x1))))) 0(1(1(2(x1)))) -> 2(3(1(3(0(1(x1)))))) 0(1(2(0(x1)))) -> 1(0(0(2(2(x1))))) 0(1(2(4(x1)))) -> 0(2(3(4(1(x1))))) 0(1(2(4(x1)))) -> 1(0(4(2(3(x1))))) 0(1(2(4(x1)))) -> 1(2(3(0(4(x1))))) 0(1(2(4(x1)))) -> 2(1(4(0(3(x1))))) 0(1(2(4(x1)))) -> 1(2(3(4(0(5(x1)))))) 0(1(2(4(x1)))) -> 2(1(1(0(3(4(x1)))))) 0(1(2(4(x1)))) -> 4(1(2(2(3(0(x1)))))) 0(1(2(4(x1)))) -> 4(5(0(2(3(1(x1)))))) 0(4(2(0(x1)))) -> 0(4(2(3(0(x1))))) 0(4(2(0(x1)))) -> 2(3(0(4(0(0(x1)))))) 0(4(2(0(x1)))) -> 3(4(0(2(3(0(x1)))))) 0(4(2(0(x1)))) -> 4(2(3(0(4(0(x1)))))) 0(4(2(0(x1)))) -> 4(3(0(0(5(2(x1)))))) 0(4(2(4(x1)))) -> 4(0(2(3(1(4(x1)))))) 0(4(2(4(x1)))) -> 4(0(4(2(0(3(x1)))))) 5(1(2(0(x1)))) -> 2(1(3(5(0(x1))))) 5(1(2(0(x1)))) -> 3(1(0(2(5(x1))))) 5(1(2(0(x1)))) -> 2(3(0(0(1(5(x1)))))) 5(1(2(4(x1)))) -> 3(2(5(1(4(x1))))) 5(1(2(4(x1)))) -> 5(2(1(3(4(x1))))) 5(1(2(4(x1)))) -> 5(5(2(1(4(x1))))) 5(1(2(4(x1)))) -> 0(3(4(5(2(1(x1)))))) 5(1(4(2(x1)))) -> 3(4(5(2(1(x1))))) 5(1(4(2(x1)))) -> 2(1(3(4(5(4(x1)))))) 5(1(4(2(x1)))) -> 3(3(4(2(1(5(x1)))))) 5(4(1(4(x1)))) -> 3(4(4(1(5(4(x1)))))) 5(4(1(4(x1)))) -> 4(1(3(5(0(4(x1)))))) 5(4(1(4(x1)))) -> 5(1(3(4(5(4(x1)))))) 5(4(1(4(x1)))) -> 5(1(5(3(4(4(x1)))))) 5(4(2(0(x1)))) -> 5(4(2(3(0(x1))))) 5(4(2(0(x1)))) -> 0(1(2(3(4(5(x1)))))) 5(4(2(0(x1)))) -> 4(5(3(3(0(2(x1)))))) 0(1(2(0(4(x1))))) -> 0(2(4(1(3(0(x1)))))) 0(1(2(0(4(x1))))) -> 2(0(3(4(0(1(x1)))))) 0(1(2(0(4(x1))))) -> 4(0(2(3(1(0(x1)))))) 0(1(4(2(2(x1))))) -> 1(2(3(4(0(2(x1)))))) 5(0(1(2(4(x1))))) -> 3(0(2(1(4(5(x1)))))) 5(1(2(2(4(x1))))) -> 5(2(2(1(4(5(x1)))))) 5(1(2(4(0(x1))))) -> 5(0(2(1(3(4(x1)))))) 5(1(2(4(0(x1))))) -> 5(0(3(2(1(4(x1)))))) 5(1(3(1(4(x1))))) -> 1(5(1(3(4(0(x1)))))) 5(1(4(1(2(x1))))) -> 2(1(5(3(4(1(x1)))))) 5(4(1(1(4(x1))))) -> 1(1(3(4(5(4(x1)))))) 5(4(1(4(0(x1))))) -> 3(4(0(4(5(1(x1)))))) 5(4(3(2(0(x1))))) -> 5(4(0(3(2(3(x1)))))) 5(4(5(2(0(x1))))) -> 5(0(5(4(4(2(x1)))))) The (relative) TRS S consists of the following rules: encArg(1(x_1)) -> 1(encArg(x_1)) encArg(2(x_1)) -> 2(encArg(x_1)) encArg(3(x_1)) -> 3(encArg(x_1)) encArg(4(x_1)) -> 4(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (11) DecreasingLoopProof (LOWER BOUND(ID)) The following loop(s) give(s) rise to the lower bound Omega(n^1): The rewrite sequence 5(1(4(2(x1)))) ->^+ 3(3(4(2(1(5(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 / 1(4(2(x1)))]. The result substitution is [ ]. ---------------------------------------- (12) Complex Obligation (BEST) ---------------------------------------- (13) Obligation: Proved the lower bound n^1 for the following obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: 0(1(1(2(x1)))) -> 1(3(0(1(2(x1))))) 0(1(1(2(x1)))) -> 1(3(1(0(2(x1))))) 0(1(1(2(x1)))) -> 2(3(1(3(0(1(x1)))))) 0(1(2(0(x1)))) -> 1(0(0(2(2(x1))))) 0(1(2(4(x1)))) -> 0(2(3(4(1(x1))))) 0(1(2(4(x1)))) -> 1(0(4(2(3(x1))))) 0(1(2(4(x1)))) -> 1(2(3(0(4(x1))))) 0(1(2(4(x1)))) -> 2(1(4(0(3(x1))))) 0(1(2(4(x1)))) -> 1(2(3(4(0(5(x1)))))) 0(1(2(4(x1)))) -> 2(1(1(0(3(4(x1)))))) 0(1(2(4(x1)))) -> 4(1(2(2(3(0(x1)))))) 0(1(2(4(x1)))) -> 4(5(0(2(3(1(x1)))))) 0(4(2(0(x1)))) -> 0(4(2(3(0(x1))))) 0(4(2(0(x1)))) -> 2(3(0(4(0(0(x1)))))) 0(4(2(0(x1)))) -> 3(4(0(2(3(0(x1)))))) 0(4(2(0(x1)))) -> 4(2(3(0(4(0(x1)))))) 0(4(2(0(x1)))) -> 4(3(0(0(5(2(x1)))))) 0(4(2(4(x1)))) -> 4(0(2(3(1(4(x1)))))) 0(4(2(4(x1)))) -> 4(0(4(2(0(3(x1)))))) 5(1(2(0(x1)))) -> 2(1(3(5(0(x1))))) 5(1(2(0(x1)))) -> 3(1(0(2(5(x1))))) 5(1(2(0(x1)))) -> 2(3(0(0(1(5(x1)))))) 5(1(2(4(x1)))) -> 3(2(5(1(4(x1))))) 5(1(2(4(x1)))) -> 5(2(1(3(4(x1))))) 5(1(2(4(x1)))) -> 5(5(2(1(4(x1))))) 5(1(2(4(x1)))) -> 0(3(4(5(2(1(x1)))))) 5(1(4(2(x1)))) -> 3(4(5(2(1(x1))))) 5(1(4(2(x1)))) -> 2(1(3(4(5(4(x1)))))) 5(1(4(2(x1)))) -> 3(3(4(2(1(5(x1)))))) 5(4(1(4(x1)))) -> 3(4(4(1(5(4(x1)))))) 5(4(1(4(x1)))) -> 4(1(3(5(0(4(x1)))))) 5(4(1(4(x1)))) -> 5(1(3(4(5(4(x1)))))) 5(4(1(4(x1)))) -> 5(1(5(3(4(4(x1)))))) 5(4(2(0(x1)))) -> 5(4(2(3(0(x1))))) 5(4(2(0(x1)))) -> 0(1(2(3(4(5(x1)))))) 5(4(2(0(x1)))) -> 4(5(3(3(0(2(x1)))))) 0(1(2(0(4(x1))))) -> 0(2(4(1(3(0(x1)))))) 0(1(2(0(4(x1))))) -> 2(0(3(4(0(1(x1)))))) 0(1(2(0(4(x1))))) -> 4(0(2(3(1(0(x1)))))) 0(1(4(2(2(x1))))) -> 1(2(3(4(0(2(x1)))))) 5(0(1(2(4(x1))))) -> 3(0(2(1(4(5(x1)))))) 5(1(2(2(4(x1))))) -> 5(2(2(1(4(5(x1)))))) 5(1(2(4(0(x1))))) -> 5(0(2(1(3(4(x1)))))) 5(1(2(4(0(x1))))) -> 5(0(3(2(1(4(x1)))))) 5(1(3(1(4(x1))))) -> 1(5(1(3(4(0(x1)))))) 5(1(4(1(2(x1))))) -> 2(1(5(3(4(1(x1)))))) 5(4(1(1(4(x1))))) -> 1(1(3(4(5(4(x1)))))) 5(4(1(4(0(x1))))) -> 3(4(0(4(5(1(x1)))))) 5(4(3(2(0(x1))))) -> 5(4(0(3(2(3(x1)))))) 5(4(5(2(0(x1))))) -> 5(0(5(4(4(2(x1)))))) The (relative) TRS S consists of the following rules: encArg(1(x_1)) -> 1(encArg(x_1)) encArg(2(x_1)) -> 2(encArg(x_1)) encArg(3(x_1)) -> 3(encArg(x_1)) encArg(4(x_1)) -> 4(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (14) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (15) BOUNDS(n^1, INF) ---------------------------------------- (16) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: 0(1(1(2(x1)))) -> 1(3(0(1(2(x1))))) 0(1(1(2(x1)))) -> 1(3(1(0(2(x1))))) 0(1(1(2(x1)))) -> 2(3(1(3(0(1(x1)))))) 0(1(2(0(x1)))) -> 1(0(0(2(2(x1))))) 0(1(2(4(x1)))) -> 0(2(3(4(1(x1))))) 0(1(2(4(x1)))) -> 1(0(4(2(3(x1))))) 0(1(2(4(x1)))) -> 1(2(3(0(4(x1))))) 0(1(2(4(x1)))) -> 2(1(4(0(3(x1))))) 0(1(2(4(x1)))) -> 1(2(3(4(0(5(x1)))))) 0(1(2(4(x1)))) -> 2(1(1(0(3(4(x1)))))) 0(1(2(4(x1)))) -> 4(1(2(2(3(0(x1)))))) 0(1(2(4(x1)))) -> 4(5(0(2(3(1(x1)))))) 0(4(2(0(x1)))) -> 0(4(2(3(0(x1))))) 0(4(2(0(x1)))) -> 2(3(0(4(0(0(x1)))))) 0(4(2(0(x1)))) -> 3(4(0(2(3(0(x1)))))) 0(4(2(0(x1)))) -> 4(2(3(0(4(0(x1)))))) 0(4(2(0(x1)))) -> 4(3(0(0(5(2(x1)))))) 0(4(2(4(x1)))) -> 4(0(2(3(1(4(x1)))))) 0(4(2(4(x1)))) -> 4(0(4(2(0(3(x1)))))) 5(1(2(0(x1)))) -> 2(1(3(5(0(x1))))) 5(1(2(0(x1)))) -> 3(1(0(2(5(x1))))) 5(1(2(0(x1)))) -> 2(3(0(0(1(5(x1)))))) 5(1(2(4(x1)))) -> 3(2(5(1(4(x1))))) 5(1(2(4(x1)))) -> 5(2(1(3(4(x1))))) 5(1(2(4(x1)))) -> 5(5(2(1(4(x1))))) 5(1(2(4(x1)))) -> 0(3(4(5(2(1(x1)))))) 5(1(4(2(x1)))) -> 3(4(5(2(1(x1))))) 5(1(4(2(x1)))) -> 2(1(3(4(5(4(x1)))))) 5(1(4(2(x1)))) -> 3(3(4(2(1(5(x1)))))) 5(4(1(4(x1)))) -> 3(4(4(1(5(4(x1)))))) 5(4(1(4(x1)))) -> 4(1(3(5(0(4(x1)))))) 5(4(1(4(x1)))) -> 5(1(3(4(5(4(x1)))))) 5(4(1(4(x1)))) -> 5(1(5(3(4(4(x1)))))) 5(4(2(0(x1)))) -> 5(4(2(3(0(x1))))) 5(4(2(0(x1)))) -> 0(1(2(3(4(5(x1)))))) 5(4(2(0(x1)))) -> 4(5(3(3(0(2(x1)))))) 0(1(2(0(4(x1))))) -> 0(2(4(1(3(0(x1)))))) 0(1(2(0(4(x1))))) -> 2(0(3(4(0(1(x1)))))) 0(1(2(0(4(x1))))) -> 4(0(2(3(1(0(x1)))))) 0(1(4(2(2(x1))))) -> 1(2(3(4(0(2(x1)))))) 5(0(1(2(4(x1))))) -> 3(0(2(1(4(5(x1)))))) 5(1(2(2(4(x1))))) -> 5(2(2(1(4(5(x1)))))) 5(1(2(4(0(x1))))) -> 5(0(2(1(3(4(x1)))))) 5(1(2(4(0(x1))))) -> 5(0(3(2(1(4(x1)))))) 5(1(3(1(4(x1))))) -> 1(5(1(3(4(0(x1)))))) 5(1(4(1(2(x1))))) -> 2(1(5(3(4(1(x1)))))) 5(4(1(1(4(x1))))) -> 1(1(3(4(5(4(x1)))))) 5(4(1(4(0(x1))))) -> 3(4(0(4(5(1(x1)))))) 5(4(3(2(0(x1))))) -> 5(4(0(3(2(3(x1)))))) 5(4(5(2(0(x1))))) -> 5(0(5(4(4(2(x1)))))) The (relative) TRS S consists of the following rules: encArg(1(x_1)) -> 1(encArg(x_1)) encArg(2(x_1)) -> 2(encArg(x_1)) encArg(3(x_1)) -> 3(encArg(x_1)) encArg(4(x_1)) -> 4(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) Rewrite Strategy: INNERMOST