MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof [EQUIVALENT, 450 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 51 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 84 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (12) IRSwT ---------------------------------------- (0) Obligation: Rules: l0(iHAT0, jHAT0, xHAT0, yHAT0) -> l1(iHATpost, jHATpost, xHATpost, yHATpost) :|: jHAT0 = jHATpost && iHAT0 = iHATpost && yHATpost = -1 + yHAT0 && xHATpost = -1 + xHAT0 l2(x, x1, x2, x3) -> l3(x4, x5, x6, x7) :|: x3 = x7 && x2 = x6 && x1 = x5 && x = x4 && 0 <= x2 && x2 <= 0 l2(x8, x9, x10, x11) -> l0(x12, x13, x14, x15) :|: x11 = x15 && x10 = x14 && x9 = x13 && x8 = x12 && 1 <= x10 l2(x16, x17, x18, x19) -> l0(x20, x21, x22, x23) :|: x19 = x23 && x18 = x22 && x17 = x21 && x16 = x20 && 1 + x18 <= 0 l1(x24, x25, x26, x27) -> l2(x28, x29, x30, x31) :|: x27 = x31 && x26 = x30 && x25 = x29 && x24 = x28 l4(x32, x33, x34, x35) -> l5(x36, x37, x38, x39) :|: x35 = x39 && x34 = x38 && x33 = x37 && x32 = x36 l3(x40, x41, x42, x43) -> l4(x44, x45, x46, x47) :|: x43 = x47 && x42 = x46 && x41 = x45 && x40 = x44 && 1 + x41 <= x40 l3(x48, x49, x50, x51) -> l4(x52, x53, x54, x55) :|: x51 = x55 && x50 = x54 && x49 = x53 && x48 = x52 && 1 + x48 <= x49 l3(x56, x57, x58, x59) -> l4(x60, x61, x62, x63) :|: x59 = x63 && x58 = x62 && x57 = x61 && x56 = x60 && x57 <= x56 && x56 <= x57 l6(x64, x65, x66, x67) -> l1(x68, x69, x70, x71) :|: x65 = x69 && x64 = x68 && x71 = x65 && x70 = x64 l7(x72, x73, x74, x75) -> l6(x76, x77, x78, x79) :|: x75 = x79 && x74 = x78 && x73 = x77 && x72 = x76 Start term: l7(iHAT0, jHAT0, xHAT0, yHAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(iHAT0, jHAT0, xHAT0, yHAT0) -> l1(iHATpost, jHATpost, xHATpost, yHATpost) :|: jHAT0 = jHATpost && iHAT0 = iHATpost && yHATpost = -1 + yHAT0 && xHATpost = -1 + xHAT0 l2(x, x1, x2, x3) -> l3(x4, x5, x6, x7) :|: x3 = x7 && x2 = x6 && x1 = x5 && x = x4 && 0 <= x2 && x2 <= 0 l2(x8, x9, x10, x11) -> l0(x12, x13, x14, x15) :|: x11 = x15 && x10 = x14 && x9 = x13 && x8 = x12 && 1 <= x10 l2(x16, x17, x18, x19) -> l0(x20, x21, x22, x23) :|: x19 = x23 && x18 = x22 && x17 = x21 && x16 = x20 && 1 + x18 <= 0 l1(x24, x25, x26, x27) -> l2(x28, x29, x30, x31) :|: x27 = x31 && x26 = x30 && x25 = x29 && x24 = x28 l4(x32, x33, x34, x35) -> l5(x36, x37, x38, x39) :|: x35 = x39 && x34 = x38 && x33 = x37 && x32 = x36 l3(x40, x41, x42, x43) -> l4(x44, x45, x46, x47) :|: x43 = x47 && x42 = x46 && x41 = x45 && x40 = x44 && 1 + x41 <= x40 l3(x48, x49, x50, x51) -> l4(x52, x53, x54, x55) :|: x51 = x55 && x50 = x54 && x49 = x53 && x48 = x52 && 1 + x48 <= x49 l3(x56, x57, x58, x59) -> l4(x60, x61, x62, x63) :|: x59 = x63 && x58 = x62 && x57 = x61 && x56 = x60 && x57 <= x56 && x56 <= x57 l6(x64, x65, x66, x67) -> l1(x68, x69, x70, x71) :|: x65 = x69 && x64 = x68 && x71 = x65 && x70 = x64 l7(x72, x73, x74, x75) -> l6(x76, x77, x78, x79) :|: x75 = x79 && x74 = x78 && x73 = x77 && x72 = x76 Start term: l7(iHAT0, jHAT0, xHAT0, yHAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(iHAT0, jHAT0, xHAT0, yHAT0) -> l1(iHATpost, jHATpost, xHATpost, yHATpost) :|: jHAT0 = jHATpost && iHAT0 = iHATpost && yHATpost = -1 + yHAT0 && xHATpost = -1 + xHAT0 (2) l2(x, x1, x2, x3) -> l3(x4, x5, x6, x7) :|: x3 = x7 && x2 = x6 && x1 = x5 && x = x4 && 0 <= x2 && x2 <= 0 (3) l2(x8, x9, x10, x11) -> l0(x12, x13, x14, x15) :|: x11 = x15 && x10 = x14 && x9 = x13 && x8 = x12 && 1 <= x10 (4) l2(x16, x17, x18, x19) -> l0(x20, x21, x22, x23) :|: x19 = x23 && x18 = x22 && x17 = x21 && x16 = x20 && 1 + x18 <= 0 (5) l1(x24, x25, x26, x27) -> l2(x28, x29, x30, x31) :|: x27 = x31 && x26 = x30 && x25 = x29 && x24 = x28 (6) l4(x32, x33, x34, x35) -> l5(x36, x37, x38, x39) :|: x35 = x39 && x34 = x38 && x33 = x37 && x32 = x36 (7) l3(x40, x41, x42, x43) -> l4(x44, x45, x46, x47) :|: x43 = x47 && x42 = x46 && x41 = x45 && x40 = x44 && 1 + x41 <= x40 (8) l3(x48, x49, x50, x51) -> l4(x52, x53, x54, x55) :|: x51 = x55 && x50 = x54 && x49 = x53 && x48 = x52 && 1 + x48 <= x49 (9) l3(x56, x57, x58, x59) -> l4(x60, x61, x62, x63) :|: x59 = x63 && x58 = x62 && x57 = x61 && x56 = x60 && x57 <= x56 && x56 <= x57 (10) l6(x64, x65, x66, x67) -> l1(x68, x69, x70, x71) :|: x65 = x69 && x64 = x68 && x71 = x65 && x70 = x64 (11) l7(x72, x73, x74, x75) -> l6(x76, x77, x78, x79) :|: x75 = x79 && x74 = x78 && x73 = x77 && x72 = x76 Arcs: (1) -> (5) (2) -> (7), (8), (9) (3) -> (1) (4) -> (1) (5) -> (2), (3), (4) (7) -> (6) (8) -> (6) (9) -> (6) (10) -> (5) (11) -> (10) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l0(iHAT0, jHAT0, xHAT0, yHAT0) -> l1(iHATpost, jHATpost, xHATpost, yHATpost) :|: jHAT0 = jHATpost && iHAT0 = iHATpost && yHATpost = -1 + yHAT0 && xHATpost = -1 + xHAT0 (2) l2(x16, x17, x18, x19) -> l0(x20, x21, x22, x23) :|: x19 = x23 && x18 = x22 && x17 = x21 && x16 = x20 && 1 + x18 <= 0 (3) l2(x8, x9, x10, x11) -> l0(x12, x13, x14, x15) :|: x11 = x15 && x10 = x14 && x9 = x13 && x8 = x12 && 1 <= x10 (4) l1(x24, x25, x26, x27) -> l2(x28, x29, x30, x31) :|: x27 = x31 && x26 = x30 && x25 = x29 && x24 = x28 Arcs: (1) -> (4) (2) -> (1) (3) -> (1) (4) -> (2), (3) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l2(iHATpost:0, jHATpost:0, x10:0, x11:0) -> l2(iHATpost:0, jHATpost:0, -1 + x10:0, -1 + x11:0) :|: x10:0 > 0 l2(x, x1, x2, x3) -> l2(x, x1, -1 + x2, -1 + x3) :|: x2 < 0 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l2(x1, x2, x3, x4) -> l2(x3) ---------------------------------------- (8) Obligation: Rules: l2(x10:0) -> l2(-1 + x10:0) :|: x10:0 > 0 l2(x2) -> l2(-1 + x2) :|: x2 < 0 ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l2(INTEGER) Replaced non-predefined constructor symbols by 0.The following proof was generated: # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IntTRS could not be shown: - IntTRS - RankingReductionPairProof Rules: l2(x10:0) -> l2(c) :|: c = -1 + x10:0 && x10:0 > 0 l2(x2) -> l2(c1) :|: c1 = -1 + x2 && x2 < 0 Interpretation: [ l2 ] = l2_1 + 1 The following rules are decreasing: l2(x10:0) -> l2(c) :|: c = -1 + x10:0 && x10:0 > 0 l2(x2) -> l2(c1) :|: c1 = -1 + x2 && x2 < 0 The following rules are bounded: l2(x10:0) -> l2(c) :|: c = -1 + x10:0 && x10:0 > 0 - IntTRS - RankingReductionPairProof - IntTRS Rules: l2(x2) -> l2(c1) :|: c1 = -1 + x2 && x2 < 0 ---------------------------------------- (10) Obligation: Rules: l2(x2) -> l2(-1 + x2) :|: x2 < 0 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l2(x2) -> l2(-1 + x2) :|: x2 < 0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) l2(x2) -> l2(-1 + x2) :|: x2 < 0 Arcs: (1) -> (1) This digraph is fully evaluated!