/export/starexec/sandbox2/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 92 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 210 ms] (8) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(0(1(x1))) -> 0(1(2(0(3(x1))))) 0(0(1(x1))) -> 0(1(2(0(3(2(x1)))))) 0(0(1(x1))) -> 1(2(0(0(3(2(x1)))))) 0(1(0(x1))) -> 2(0(3(1(2(0(x1)))))) 0(4(1(x1))) -> 4(0(3(1(x1)))) 0(4(1(x1))) -> 2(4(0(3(2(1(x1)))))) 0(4(1(x1))) -> 2(4(0(5(3(1(x1)))))) 0(4(1(x1))) -> 4(2(1(2(0(3(x1)))))) 4(1(0(x1))) -> 1(2(0(4(x1)))) 0(0(1(1(x1)))) -> 1(2(0(0(3(1(x1)))))) 0(0(2(1(x1)))) -> 2(2(0(3(0(1(x1)))))) 0(0(4(1(x1)))) -> 1(4(0(3(0(3(x1)))))) 0(0(5(1(x1)))) -> 0(0(3(1(2(5(x1)))))) 0(1(1(0(x1)))) -> 1(2(0(0(1(2(x1)))))) 0(1(4(1(x1)))) -> 0(1(2(4(1(2(x1)))))) 0(1(5(0(x1)))) -> 1(2(5(0(0(3(x1)))))) 0(2(4(1(x1)))) -> 4(0(5(3(1(2(x1)))))) 0(4(1(0(x1)))) -> 0(4(0(1(2(x1))))) 0(4(2(1(x1)))) -> 4(0(3(2(2(1(x1)))))) 0(4(2(1(x1)))) -> 4(0(3(5(1(2(x1)))))) 0(4(4(1(x1)))) -> 2(4(0(3(4(1(x1)))))) 0(5(0(1(x1)))) -> 0(2(0(3(5(1(x1)))))) 0(5(0(1(x1)))) -> 5(2(0(3(0(1(x1)))))) 0(5(1(0(x1)))) -> 0(1(2(0(3(5(x1)))))) 0(5(1(0(x1)))) -> 2(0(1(3(5(0(x1)))))) 4(0(5(1(x1)))) -> 1(4(0(5(3(2(x1)))))) 4(1(0(0(x1)))) -> 0(4(1(2(0(x1))))) 4(1(0(1(x1)))) -> 1(1(2(0(4(x1))))) 4(1(5(0(x1)))) -> 1(2(0(5(4(x1))))) 4(1(5(0(x1)))) -> 1(4(0(3(5(x1))))) 4(3(1(0(x1)))) -> 1(4(2(0(3(x1))))) 4(3(1(0(x1)))) -> 2(0(2(1(3(4(x1)))))) 4(3(1(0(x1)))) -> 2(1(4(2(0(3(x1)))))) 4(3(1(0(x1)))) -> 2(2(4(0(1(3(x1)))))) 5(0(1(0(x1)))) -> 0(3(5(1(2(0(x1)))))) 5(0(1(0(x1)))) -> 1(5(2(0(3(0(x1)))))) 5(4(1(0(x1)))) -> 0(1(2(4(5(2(x1)))))) 0(0(5(5(1(x1))))) -> 1(0(0(3(5(5(x1)))))) 0(1(0(5(0(x1))))) -> 0(1(5(2(0(0(x1)))))) 0(2(5(0(1(x1))))) -> 2(0(3(5(0(1(x1)))))) 0(3(1(0(0(x1))))) -> 0(0(3(0(1(2(x1)))))) 0(4(1(4(1(x1))))) -> 4(4(0(1(2(1(x1)))))) 0(5(5(4(1(x1))))) -> 4(1(0(5(5(3(x1)))))) 4(1(5(0(0(x1))))) -> 1(2(0(4(5(0(x1)))))) 4(1(5(5(0(x1))))) -> 5(1(3(0(5(4(x1)))))) 4(3(1(0(1(x1))))) -> 1(1(2(3(0(4(x1)))))) 4(3(1(1(0(x1))))) -> 1(2(0(1(4(3(x1)))))) 4(3(1(5(0(x1))))) -> 5(1(0(3(2(4(x1)))))) 4(4(1(0(5(x1))))) -> 4(0(5(3(4(1(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(2(x_1)) -> 2(encArg(x_1)) encArg(3(x_1)) -> 3(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_4(x_1)) -> 4(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 (full) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(0(1(x1))) -> 0(1(2(0(3(x1))))) 0(0(1(x1))) -> 0(1(2(0(3(2(x1)))))) 0(0(1(x1))) -> 1(2(0(0(3(2(x1)))))) 0(1(0(x1))) -> 2(0(3(1(2(0(x1)))))) 0(4(1(x1))) -> 4(0(3(1(x1)))) 0(4(1(x1))) -> 2(4(0(3(2(1(x1)))))) 0(4(1(x1))) -> 2(4(0(5(3(1(x1)))))) 0(4(1(x1))) -> 4(2(1(2(0(3(x1)))))) 4(1(0(x1))) -> 1(2(0(4(x1)))) 0(0(1(1(x1)))) -> 1(2(0(0(3(1(x1)))))) 0(0(2(1(x1)))) -> 2(2(0(3(0(1(x1)))))) 0(0(4(1(x1)))) -> 1(4(0(3(0(3(x1)))))) 0(0(5(1(x1)))) -> 0(0(3(1(2(5(x1)))))) 0(1(1(0(x1)))) -> 1(2(0(0(1(2(x1)))))) 0(1(4(1(x1)))) -> 0(1(2(4(1(2(x1)))))) 0(1(5(0(x1)))) -> 1(2(5(0(0(3(x1)))))) 0(2(4(1(x1)))) -> 4(0(5(3(1(2(x1)))))) 0(4(1(0(x1)))) -> 0(4(0(1(2(x1))))) 0(4(2(1(x1)))) -> 4(0(3(2(2(1(x1)))))) 0(4(2(1(x1)))) -> 4(0(3(5(1(2(x1)))))) 0(4(4(1(x1)))) -> 2(4(0(3(4(1(x1)))))) 0(5(0(1(x1)))) -> 0(2(0(3(5(1(x1)))))) 0(5(0(1(x1)))) -> 5(2(0(3(0(1(x1)))))) 0(5(1(0(x1)))) -> 0(1(2(0(3(5(x1)))))) 0(5(1(0(x1)))) -> 2(0(1(3(5(0(x1)))))) 4(0(5(1(x1)))) -> 1(4(0(5(3(2(x1)))))) 4(1(0(0(x1)))) -> 0(4(1(2(0(x1))))) 4(1(0(1(x1)))) -> 1(1(2(0(4(x1))))) 4(1(5(0(x1)))) -> 1(2(0(5(4(x1))))) 4(1(5(0(x1)))) -> 1(4(0(3(5(x1))))) 4(3(1(0(x1)))) -> 1(4(2(0(3(x1))))) 4(3(1(0(x1)))) -> 2(0(2(1(3(4(x1)))))) 4(3(1(0(x1)))) -> 2(1(4(2(0(3(x1)))))) 4(3(1(0(x1)))) -> 2(2(4(0(1(3(x1)))))) 5(0(1(0(x1)))) -> 0(3(5(1(2(0(x1)))))) 5(0(1(0(x1)))) -> 1(5(2(0(3(0(x1)))))) 5(4(1(0(x1)))) -> 0(1(2(4(5(2(x1)))))) 0(0(5(5(1(x1))))) -> 1(0(0(3(5(5(x1)))))) 0(1(0(5(0(x1))))) -> 0(1(5(2(0(0(x1)))))) 0(2(5(0(1(x1))))) -> 2(0(3(5(0(1(x1)))))) 0(3(1(0(0(x1))))) -> 0(0(3(0(1(2(x1)))))) 0(4(1(4(1(x1))))) -> 4(4(0(1(2(1(x1)))))) 0(5(5(4(1(x1))))) -> 4(1(0(5(5(3(x1)))))) 4(1(5(0(0(x1))))) -> 1(2(0(4(5(0(x1)))))) 4(1(5(5(0(x1))))) -> 5(1(3(0(5(4(x1)))))) 4(3(1(0(1(x1))))) -> 1(1(2(3(0(4(x1)))))) 4(3(1(1(0(x1))))) -> 1(2(0(1(4(3(x1)))))) 4(3(1(5(0(x1))))) -> 5(1(0(3(2(4(x1)))))) 4(4(1(0(5(x1))))) -> 4(0(5(3(4(1(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(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_4(x_1)) -> 4(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: 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(1, n^1). The TRS R consists of the following rules: 0(0(1(x1))) -> 0(1(2(0(3(x1))))) 0(0(1(x1))) -> 0(1(2(0(3(2(x1)))))) 0(0(1(x1))) -> 1(2(0(0(3(2(x1)))))) 0(1(0(x1))) -> 2(0(3(1(2(0(x1)))))) 0(4(1(x1))) -> 4(0(3(1(x1)))) 0(4(1(x1))) -> 2(4(0(3(2(1(x1)))))) 0(4(1(x1))) -> 2(4(0(5(3(1(x1)))))) 0(4(1(x1))) -> 4(2(1(2(0(3(x1)))))) 4(1(0(x1))) -> 1(2(0(4(x1)))) 0(0(1(1(x1)))) -> 1(2(0(0(3(1(x1)))))) 0(0(2(1(x1)))) -> 2(2(0(3(0(1(x1)))))) 0(0(4(1(x1)))) -> 1(4(0(3(0(3(x1)))))) 0(0(5(1(x1)))) -> 0(0(3(1(2(5(x1)))))) 0(1(1(0(x1)))) -> 1(2(0(0(1(2(x1)))))) 0(1(4(1(x1)))) -> 0(1(2(4(1(2(x1)))))) 0(1(5(0(x1)))) -> 1(2(5(0(0(3(x1)))))) 0(2(4(1(x1)))) -> 4(0(5(3(1(2(x1)))))) 0(4(1(0(x1)))) -> 0(4(0(1(2(x1))))) 0(4(2(1(x1)))) -> 4(0(3(2(2(1(x1)))))) 0(4(2(1(x1)))) -> 4(0(3(5(1(2(x1)))))) 0(4(4(1(x1)))) -> 2(4(0(3(4(1(x1)))))) 0(5(0(1(x1)))) -> 0(2(0(3(5(1(x1)))))) 0(5(0(1(x1)))) -> 5(2(0(3(0(1(x1)))))) 0(5(1(0(x1)))) -> 0(1(2(0(3(5(x1)))))) 0(5(1(0(x1)))) -> 2(0(1(3(5(0(x1)))))) 4(0(5(1(x1)))) -> 1(4(0(5(3(2(x1)))))) 4(1(0(0(x1)))) -> 0(4(1(2(0(x1))))) 4(1(0(1(x1)))) -> 1(1(2(0(4(x1))))) 4(1(5(0(x1)))) -> 1(2(0(5(4(x1))))) 4(1(5(0(x1)))) -> 1(4(0(3(5(x1))))) 4(3(1(0(x1)))) -> 1(4(2(0(3(x1))))) 4(3(1(0(x1)))) -> 2(0(2(1(3(4(x1)))))) 4(3(1(0(x1)))) -> 2(1(4(2(0(3(x1)))))) 4(3(1(0(x1)))) -> 2(2(4(0(1(3(x1)))))) 5(0(1(0(x1)))) -> 0(3(5(1(2(0(x1)))))) 5(0(1(0(x1)))) -> 1(5(2(0(3(0(x1)))))) 5(4(1(0(x1)))) -> 0(1(2(4(5(2(x1)))))) 0(0(5(5(1(x1))))) -> 1(0(0(3(5(5(x1)))))) 0(1(0(5(0(x1))))) -> 0(1(5(2(0(0(x1)))))) 0(2(5(0(1(x1))))) -> 2(0(3(5(0(1(x1)))))) 0(3(1(0(0(x1))))) -> 0(0(3(0(1(2(x1)))))) 0(4(1(4(1(x1))))) -> 4(4(0(1(2(1(x1)))))) 0(5(5(4(1(x1))))) -> 4(1(0(5(5(3(x1)))))) 4(1(5(0(0(x1))))) -> 1(2(0(4(5(0(x1)))))) 4(1(5(5(0(x1))))) -> 5(1(3(0(5(4(x1)))))) 4(3(1(0(1(x1))))) -> 1(1(2(3(0(4(x1)))))) 4(3(1(1(0(x1))))) -> 1(2(0(1(4(3(x1)))))) 4(3(1(5(0(x1))))) -> 5(1(0(3(2(4(x1)))))) 4(4(1(0(5(x1))))) -> 4(0(5(3(4(1(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(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_4(x_1)) -> 4(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: 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(0(1(x1))) -> 0(1(2(0(3(x1))))) 0(0(1(x1))) -> 0(1(2(0(3(2(x1)))))) 0(0(1(x1))) -> 1(2(0(0(3(2(x1)))))) 0(1(0(x1))) -> 2(0(3(1(2(0(x1)))))) 0(4(1(x1))) -> 4(0(3(1(x1)))) 0(4(1(x1))) -> 2(4(0(3(2(1(x1)))))) 0(4(1(x1))) -> 2(4(0(5(3(1(x1)))))) 0(4(1(x1))) -> 4(2(1(2(0(3(x1)))))) 4(1(0(x1))) -> 1(2(0(4(x1)))) 0(0(1(1(x1)))) -> 1(2(0(0(3(1(x1)))))) 0(0(2(1(x1)))) -> 2(2(0(3(0(1(x1)))))) 0(0(4(1(x1)))) -> 1(4(0(3(0(3(x1)))))) 0(0(5(1(x1)))) -> 0(0(3(1(2(5(x1)))))) 0(1(1(0(x1)))) -> 1(2(0(0(1(2(x1)))))) 0(1(4(1(x1)))) -> 0(1(2(4(1(2(x1)))))) 0(1(5(0(x1)))) -> 1(2(5(0(0(3(x1)))))) 0(2(4(1(x1)))) -> 4(0(5(3(1(2(x1)))))) 0(4(1(0(x1)))) -> 0(4(0(1(2(x1))))) 0(4(2(1(x1)))) -> 4(0(3(2(2(1(x1)))))) 0(4(2(1(x1)))) -> 4(0(3(5(1(2(x1)))))) 0(4(4(1(x1)))) -> 2(4(0(3(4(1(x1)))))) 0(5(0(1(x1)))) -> 0(2(0(3(5(1(x1)))))) 0(5(0(1(x1)))) -> 5(2(0(3(0(1(x1)))))) 0(5(1(0(x1)))) -> 0(1(2(0(3(5(x1)))))) 0(5(1(0(x1)))) -> 2(0(1(3(5(0(x1)))))) 4(0(5(1(x1)))) -> 1(4(0(5(3(2(x1)))))) 4(1(0(0(x1)))) -> 0(4(1(2(0(x1))))) 4(1(0(1(x1)))) -> 1(1(2(0(4(x1))))) 4(1(5(0(x1)))) -> 1(2(0(5(4(x1))))) 4(1(5(0(x1)))) -> 1(4(0(3(5(x1))))) 4(3(1(0(x1)))) -> 1(4(2(0(3(x1))))) 4(3(1(0(x1)))) -> 2(0(2(1(3(4(x1)))))) 4(3(1(0(x1)))) -> 2(1(4(2(0(3(x1)))))) 4(3(1(0(x1)))) -> 2(2(4(0(1(3(x1)))))) 5(0(1(0(x1)))) -> 0(3(5(1(2(0(x1)))))) 5(0(1(0(x1)))) -> 1(5(2(0(3(0(x1)))))) 5(4(1(0(x1)))) -> 0(1(2(4(5(2(x1)))))) 0(0(5(5(1(x1))))) -> 1(0(0(3(5(5(x1)))))) 0(1(0(5(0(x1))))) -> 0(1(5(2(0(0(x1)))))) 0(2(5(0(1(x1))))) -> 2(0(3(5(0(1(x1)))))) 0(3(1(0(0(x1))))) -> 0(0(3(0(1(2(x1)))))) 0(4(1(4(1(x1))))) -> 4(4(0(1(2(1(x1)))))) 0(5(5(4(1(x1))))) -> 4(1(0(5(5(3(x1)))))) 4(1(5(0(0(x1))))) -> 1(2(0(4(5(0(x1)))))) 4(1(5(5(0(x1))))) -> 5(1(3(0(5(4(x1)))))) 4(3(1(0(1(x1))))) -> 1(1(2(3(0(4(x1)))))) 4(3(1(1(0(x1))))) -> 1(2(0(1(4(3(x1)))))) 4(3(1(5(0(x1))))) -> 5(1(0(3(2(4(x1)))))) 4(4(1(0(5(x1))))) -> 4(0(5(3(4(1(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(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_4(x_1)) -> 4(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: 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. 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(317,318,[0_1|3]), (318,319,[3_1|3]), (319,320,[0_1|3]), (320,321,[1_1|3]), (321,98,[2_1|3]), (322,323,[0_1|3]), (323,324,[3_1|3]), (324,325,[0_1|3]), (325,326,[1_1|3]), (326,92,[2_1|3]), (326,204,[2_1|3]), (326,98,[2_1|3]), (327,328,[0_1|3]), (328,329,[3_1|3]), (329,330,[1_1|3]), (330,331,[2_1|3]), (331,62,[0_1|3]), (331,66,[0_1|3]), (331,91,[0_1|3]), (331,106,[0_1|3]), (331,116,[0_1|3]), (331,144,[0_1|3]), (331,178,[0_1|3]), (331,188,[0_1|3]), (331,203,[0_1|3]), (331,211,[0_1|3]), (331,281,[0_1|3]), (331,291,[0_1|3]), (331,97,[0_1|3]), (331,299,[4_1|3]), (331,302,[2_1|3]), (331,307,[2_1|3]), (331,312,[4_1|3]), (332,333,[2_1|3]), (333,334,[0_1|3]), (333,601,[0_1|4]), (333,605,[0_1|4]), (333,610,[1_1|4]), (334,335,[0_1|3]), (335,336,[1_1|3]), (336,97,[2_1|3]), (337,338,[1_1|3]), (338,339,[2_1|3]), (339,340,[4_1|3]), (340,341,[1_1|3]), (341,199,[2_1|3]), (342,343,[1_1|3]), (343,344,[2_1|3]), (344,345,[4_1|3]), (345,346,[5_1|3]), (346,200,[2_1|3]), (347,348,[1_1|3]), (348,349,[2_1|3]), (349,350,[0_1|3]), (350,63,[3_1|3]), (350,67,[3_1|3]), (350,107,[3_1|3]), (350,117,[3_1|3]), (350,189,[3_1|3]), (350,292,[3_1|3]), (350,542,[3_1|3]), (351,352,[1_1|3]), (352,353,[2_1|3]), (353,354,[0_1|3]), (354,355,[3_1|3]), (355,63,[2_1|3]), (355,67,[2_1|3]), (355,107,[2_1|3]), (355,117,[2_1|3]), (355,189,[2_1|3]), (355,292,[2_1|3]), (355,542,[2_1|3]), (356,357,[2_1|3]), (357,358,[0_1|3]), (358,359,[0_1|3]), (359,360,[3_1|3]), (360,63,[2_1|3]), (360,67,[2_1|3]), (360,107,[2_1|3]), (360,117,[2_1|3]), (360,189,[2_1|3]), (360,292,[2_1|3]), (360,542,[2_1|3]), (361,362,[0_1|3]), (362,363,[3_1|3]), (363,364,[1_1|3]), (364,365,[2_1|3]), (365,97,[0_1|3]), (366,367,[0_1|3]), (367,368,[3_1|3]), (368,369,[2_1|3]), (369,370,[2_1|3]), (370,141,[1_1|3]), (370,314,[1_1|3]), (370,391,[1_1|3]), (371,372,[0_1|3]), (372,373,[3_1|3]), (373,374,[5_1|3]), (374,375,[1_1|3]), (375,141,[2_1|3]), (375,314,[2_1|3]), (375,391,[2_1|3]), (376,377,[0_1|3]), (377,378,[3_1|3]), (378,199,[1_1|3]), (378,213,[1_1|3]), (379,380,[4_1|3]), (380,381,[0_1|3]), (381,382,[3_1|3]), (382,383,[2_1|3]), (383,199,[1_1|3]), (383,213,[1_1|3]), (384,385,[4_1|3]), (385,386,[0_1|3]), (386,387,[5_1|3]), (387,388,[3_1|3]), (388,199,[1_1|3]), (388,213,[1_1|3]), (389,390,[2_1|3]), (390,391,[1_1|3]), (391,392,[2_1|3]), (392,393,[0_1|3]), (393,199,[3_1|3]), (393,213,[3_1|3]), (394,395,[4_1|3]), (395,396,[0_1|3]), (396,397,[1_1|3]), (397,200,[2_1|3]), (398,399,[4_1|3]), (399,400,[0_1|3]), (400,401,[3_1|3]), (401,402,[0_1|3]), (402,213,[3_1|3]), (402,534,[3_1|3]), (403,404,[1_1|3]), (404,405,[2_1|3]), (405,406,[0_1|3]), (406,407,[3_1|3]), (407,273,[5_1|3]), (408,409,[0_1|3]), (409,410,[1_1|3]), (410,411,[3_1|3]), (411,412,[5_1|3]), (412,273,[0_1|3]), (413,414,[1_1|3]), (414,415,[2_1|3]), (415,416,[0_1|3]), (416,71,[3_1|3]), (416,76,[3_1|3]), (416,86,[3_1|3]), (416,96,[3_1|3]), (416,111,[3_1|3]), (416,121,[3_1|3]), (416,208,[3_1|3]), (416,215,[3_1|3]), (416,219,[3_1|3]), (416,223,[3_1|3]), (416,227,[3_1|3]), (416,237,[3_1|3]), (416,242,[3_1|3]), (416,261,[3_1|3]), (416,266,[3_1|3]), (416,286,[3_1|3]), (416,296,[3_1|3]), (416,63,[3_1|3]), (416,67,[3_1|3]), (416,107,[3_1|3]), (416,117,[3_1|3]), (416,189,[3_1|3]), (416,292,[3_1|3]), (416,348,[3_1|3]), (416,352,[3_1|3]), (416,404,[3_1|3]), (417,418,[1_1|3]), (418,419,[2_1|3]), (419,420,[0_1|3]), (420,421,[3_1|3]), (421,71,[2_1|3]), (421,76,[2_1|3]), (421,86,[2_1|3]), (421,96,[2_1|3]), (421,111,[2_1|3]), (421,121,[2_1|3]), (421,208,[2_1|3]), (421,215,[2_1|3]), (421,219,[2_1|3]), (421,223,[2_1|3]), (421,227,[2_1|3]), (421,237,[2_1|3]), (421,242,[2_1|3]), (421,261,[2_1|3]), (421,266,[2_1|3]), (421,286,[2_1|3]), (421,296,[2_1|3]), (421,63,[2_1|3]), (421,67,[2_1|3]), (421,107,[2_1|3]), (421,117,[2_1|3]), (421,189,[2_1|3]), (421,292,[2_1|3]), (421,348,[2_1|3]), (421,352,[2_1|3]), (421,404,[2_1|3]), (422,423,[2_1|3]), (423,424,[0_1|3]), (424,425,[0_1|3]), (425,426,[3_1|3]), (426,71,[2_1|3]), (426,76,[2_1|3]), (426,86,[2_1|3]), (426,96,[2_1|3]), (426,111,[2_1|3]), (426,121,[2_1|3]), (426,208,[2_1|3]), (426,215,[2_1|3]), (426,219,[2_1|3]), (426,223,[2_1|3]), (426,227,[2_1|3]), (426,237,[2_1|3]), (426,242,[2_1|3]), (426,261,[2_1|3]), (426,266,[2_1|3]), (426,286,[2_1|3]), (426,296,[2_1|3]), (426,63,[2_1|3]), (426,67,[2_1|3]), (426,107,[2_1|3]), (426,117,[2_1|3]), (426,189,[2_1|3]), (426,292,[2_1|3]), (426,348,[2_1|3]), (426,352,[2_1|3]), (426,404,[2_1|3]), (427,428,[4_1|3]), (428,429,[0_1|3]), (429,430,[3_1|3]), (430,431,[0_1|3]), (431,199,[3_1|3]), (431,213,[3_1|3]), (432,433,[2_1|3]), (433,434,[0_1|3]), (434,435,[0_1|3]), (435,436,[3_1|3]), (436,216,[1_1|3]), (436,262,[1_1|3]), (437,438,[0_1|3]), (438,439,[3_1|3]), (439,440,[1_1|3]), (440,441,[2_1|3]), (441,233,[5_1|3]), (441,272,[5_1|3]), (442,443,[2_1|3]), (443,444,[0_1|3]), (444,445,[3_1|3]), (445,446,[0_1|3]), (446,252,[1_1|3]), (447,448,[1_1|3]), (448,449,[2_1|3]), (449,450,[0_1|3]), (450,115,[3_1|3]), (451,452,[1_1|3]), (452,453,[2_1|3]), (453,454,[0_1|3]), (454,455,[3_1|3]), (455,115,[2_1|3]), (456,457,[2_1|3]), (457,458,[0_1|3]), (458,459,[0_1|3]), (459,460,[3_1|3]), (460,115,[2_1|3]), (461,462,[2_1|3]), (462,463,[0_1|3]), (462,492,[4_1|3]), (462,495,[2_1|3]), (462,500,[2_1|3]), (462,505,[4_1|3]), (462,514,[2_1|3]), (463,62,[4_1|3]), (463,66,[4_1|3]), (463,91,[4_1|3]), (463,106,[4_1|3]), (463,116,[4_1|3]), (463,144,[4_1|3]), (463,178,[4_1|3]), (463,188,[4_1|3]), (463,203,[4_1|3]), (463,211,[4_1|3]), (463,281,[4_1|3]), (463,291,[4_1|3]), (463,97,[4_1|3]), (463,200,[4_1|3]), (464,465,[1_1|3]), (465,466,[2_1|3]), (466,467,[0_1|3]), (467,63,[4_1|3]), (467,67,[4_1|3]), (467,107,[4_1|3]), (467,117,[4_1|3]), (467,189,[4_1|3]), (467,292,[4_1|3]), (468,469,[4_1|3]), (469,470,[1_1|3]), (470,471,[2_1|3]), (471,92,[0_1|3]), (471,204,[0_1|3]), (471,98,[0_1|3]), (472,473,[3_1|3]), (473,474,[5_1|3]), (474,475,[1_1|3]), (475,476,[2_1|3]), (476,62,[0_1|3]), (476,66,[0_1|3]), (476,91,[0_1|3]), (476,106,[0_1|3]), (476,116,[0_1|3]), (476,144,[0_1|3]), (476,178,[0_1|3]), (476,188,[0_1|3]), (476,203,[0_1|3]), (476,211,[0_1|3]), (476,281,[0_1|3]), (476,291,[0_1|3]), (476,97,[0_1|3]), (476,299,[4_1|3]), (476,302,[2_1|3]), (476,307,[2_1|3]), (476,312,[4_1|3]), (477,478,[5_1|3]), (478,479,[2_1|3]), (479,480,[0_1|3]), (480,481,[3_1|3]), (481,62,[0_1|3]), (481,66,[0_1|3]), (481,91,[0_1|3]), (481,106,[0_1|3]), (481,116,[0_1|3]), (481,144,[0_1|3]), (481,178,[0_1|3]), (481,188,[0_1|3]), (481,203,[0_1|3]), (481,211,[0_1|3]), (481,281,[0_1|3]), (481,291,[0_1|3]), (481,97,[0_1|3]), (481,299,[4_1|3]), (481,302,[2_1|3]), (481,307,[2_1|3]), (481,312,[4_1|3]), (482,483,[3_1|3]), (483,484,[5_1|3]), (484,485,[1_1|3]), (485,486,[2_1|3]), (486,97,[0_1|3]), (487,488,[5_1|3]), (488,489,[2_1|3]), (489,490,[0_1|3]), (490,491,[3_1|3]), (491,97,[0_1|3]), (492,493,[0_1|3]), (492,317,[0_1|3]), (493,494,[3_1|3]), (494,71,[1_1|3]), (494,76,[1_1|3]), (494,86,[1_1|3]), (494,96,[1_1|3]), (494,111,[1_1|3]), (494,121,[1_1|3]), (494,208,[1_1|3]), (494,215,[1_1|3]), (494,219,[1_1|3]), (494,223,[1_1|3]), (494,227,[1_1|3]), (494,237,[1_1|3]), (494,242,[1_1|3]), (494,261,[1_1|3]), (494,266,[1_1|3]), (494,286,[1_1|3]), (494,296,[1_1|3]), (494,63,[1_1|3]), (494,67,[1_1|3]), (494,107,[1_1|3]), (494,117,[1_1|3]), (494,189,[1_1|3]), (494,292,[1_1|3]), (494,216,[1_1|3]), (494,262,[1_1|3]), (494,487,[1_1|3]), (495,496,[4_1|3]), (496,497,[0_1|3]), (497,498,[3_1|3]), (498,499,[2_1|3]), (499,71,[1_1|3]), (499,76,[1_1|3]), (499,86,[1_1|3]), (499,96,[1_1|3]), (499,111,[1_1|3]), (499,121,[1_1|3]), (499,208,[1_1|3]), (499,215,[1_1|3]), (499,219,[1_1|3]), (499,223,[1_1|3]), (499,227,[1_1|3]), (499,237,[1_1|3]), (499,242,[1_1|3]), (499,261,[1_1|3]), (499,266,[1_1|3]), (499,286,[1_1|3]), (499,296,[1_1|3]), (499,63,[1_1|3]), (499,67,[1_1|3]), (499,107,[1_1|3]), (499,117,[1_1|3]), (499,189,[1_1|3]), (499,292,[1_1|3]), (499,216,[1_1|3]), (499,262,[1_1|3]), (499,487,[1_1|3]), (500,501,[4_1|3]), (501,502,[0_1|3]), (502,503,[5_1|3]), (503,504,[3_1|3]), (504,71,[1_1|3]), (504,76,[1_1|3]), (504,86,[1_1|3]), (504,96,[1_1|3]), (504,111,[1_1|3]), (504,121,[1_1|3]), (504,208,[1_1|3]), (504,215,[1_1|3]), (504,219,[1_1|3]), (504,223,[1_1|3]), (504,227,[1_1|3]), (504,237,[1_1|3]), (504,242,[1_1|3]), (504,261,[1_1|3]), (504,266,[1_1|3]), (504,286,[1_1|3]), (504,296,[1_1|3]), (504,63,[1_1|3]), (504,67,[1_1|3]), (504,107,[1_1|3]), (504,117,[1_1|3]), (504,189,[1_1|3]), (504,292,[1_1|3]), (504,216,[1_1|3]), (504,262,[1_1|3]), (504,487,[1_1|3]), (505,506,[2_1|3]), (506,507,[1_1|3]), (507,508,[2_1|3]), (508,509,[0_1|3]), (509,71,[3_1|3]), (509,76,[3_1|3]), (509,86,[3_1|3]), (509,96,[3_1|3]), (509,111,[3_1|3]), (509,121,[3_1|3]), (509,208,[3_1|3]), (509,215,[3_1|3]), (509,219,[3_1|3]), (509,223,[3_1|3]), (509,227,[3_1|3]), (509,237,[3_1|3]), (509,242,[3_1|3]), (509,261,[3_1|3]), (509,266,[3_1|3]), (509,286,[3_1|3]), (509,296,[3_1|3]), (509,63,[3_1|3]), (509,67,[3_1|3]), (509,107,[3_1|3]), (509,117,[3_1|3]), (509,189,[3_1|3]), (509,292,[3_1|3]), (509,216,[3_1|3]), (509,262,[3_1|3]), (509,487,[3_1|3]), (510,511,[4_1|3]), (511,512,[0_1|3]), (512,513,[1_1|3]), (513,97,[2_1|3]), (514,515,[4_1|3]), (515,516,[0_1|3]), (516,517,[3_1|3]), (517,518,[4_1|3]), (517,296,[1_1|3]), (518,199,[1_1|3]), (518,213,[1_1|3]), (519,520,[0_1|3]), (520,521,[3_1|3]), (521,522,[2_1|3]), (522,523,[2_1|3]), (523,252,[1_1|3]), (523,456,[1_1|3]), (523,314,[1_1|3]), (523,598,[1_1|3]), (523,398,[1_1|3]), (523,356,[1_1|3]), (524,525,[0_1|3]), (525,526,[3_1|3]), (526,527,[5_1|3]), (527,528,[1_1|3]), (528,252,[2_1|3]), (528,456,[2_1|3]), (528,314,[2_1|3]), (528,598,[2_1|3]), (528,398,[2_1|3]), (528,356,[2_1|3]), (529,530,[2_1|3]), (530,531,[0_1|3]), (531,97,[4_1|3]), (532,533,[4_1|3]), (533,534,[1_1|3]), (534,535,[2_1|3]), (535,98,[0_1|3]), (536,537,[0_1|3]), (537,538,[5_1|3]), (538,539,[3_1|3]), (539,540,[4_1|3]), (540,201,[1_1|3]), (541,542,[1_1|3]), (542,543,[2_1|3]), (543,544,[4_1|3]), (544,545,[5_1|3]), (545,97,[2_1|3]), (546,547,[4_1|3]), (547,548,[2_1|3]), (548,549,[0_1|3]), (549,97,[3_1|3]), (550,551,[0_1|3]), (551,552,[2_1|3]), (552,553,[1_1|3]), (553,554,[3_1|3]), (554,97,[4_1|3]), (555,556,[1_1|3]), (556,557,[4_1|3]), (557,558,[2_1|3]), (558,559,[0_1|3]), (559,97,[3_1|3]), (560,561,[2_1|3]), (561,562,[4_1|3]), (562,563,[0_1|3]), (563,564,[1_1|3]), (564,97,[3_1|3]), (565,566,[0_1|4]), (566,567,[3_1|4]), (567,470,[1_1|4]), (568,569,[4_1|4]), (569,570,[0_1|4]), (570,571,[3_1|4]), (571,572,[2_1|4]), (572,470,[1_1|4]), (573,574,[4_1|4]), (574,575,[0_1|4]), (575,576,[5_1|4]), (576,577,[3_1|4]), (577,470,[1_1|4]), (578,579,[2_1|4]), (579,580,[1_1|4]), (580,581,[2_1|4]), (581,582,[0_1|4]), (582,470,[3_1|4]), (583,584,[0_1|4]), (584,585,[3_1|4]), (585,534,[1_1|4]), (586,587,[4_1|4]), (587,588,[0_1|4]), (588,589,[3_1|4]), (589,590,[2_1|4]), (590,534,[1_1|4]), (591,592,[4_1|4]), (592,593,[0_1|4]), (593,594,[5_1|4]), (594,595,[3_1|4]), (595,534,[1_1|4]), (596,597,[2_1|4]), (597,598,[1_1|4]), (598,599,[2_1|4]), (599,600,[0_1|4]), (600,534,[3_1|4]), (601,602,[1_1|4]), (602,603,[2_1|4]), (603,604,[0_1|4]), (604,336,[3_1|4]), (605,606,[1_1|4]), (606,607,[2_1|4]), (607,608,[0_1|4]), (608,609,[3_1|4]), (609,336,[2_1|4]), (610,611,[2_1|4]), (611,612,[0_1|4]), (612,613,[0_1|4]), (613,614,[3_1|4]), (614,336,[2_1|4])}" ---------------------------------------- (8) BOUNDS(1, n^1)