MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 377 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 1 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 90 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT ---------------------------------------- (0) Obligation: Rules: l0(Result_4HAT0, __disjvr_0HAT0, tmp_7HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, __disjvr_0HATpost, tmp_7HATpost, x_5HATpost, y_6HATpost) :|: y_6HAT0 = y_6HATpost && x_5HAT0 = x_5HATpost && tmp_7HAT0 = tmp_7HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && Result_4HATpost = Result_4HATpost && -1 * x_5HAT0 + y_6HAT0 <= 0 l0(x, x1, x2, x3, x4) -> l2(x5, x6, x7, x8, x9) :|: x4 = x9 && x3 = x8 && x1 = x6 && x = x5 && 0 <= x7 && x7 <= 0 && x7 = x7 && 0 <= -1 - x3 + x4 l2(x10, x11, x12, x13, x14) -> l0(x15, x16, x17, x18, x19) :|: x14 = x19 && x13 = x18 && x12 = x17 && x11 = x16 && x10 = x15 l0(x20, x21, x22, x23, x24) -> l4(x25, x26, x27, x28, x29) :|: x24 = x29 && x23 = x28 && x21 = x26 && x20 = x25 && x27 = x27 && 0 <= -1 - x23 + x24 l4(x30, x31, x32, x33, x34) -> l5(x35, x36, x37, x38, x39) :|: x34 = x39 && x33 = x38 && x32 = x37 && x31 = x36 && x30 = x35 && x36 = x31 l5(x40, x41, x42, x43, x44) -> l3(x45, x46, x47, x48, x49) :|: x44 = x49 && x42 = x47 && x41 = x46 && x40 = x45 && x48 = 1 + x43 l3(x50, x51, x52, x53, x54) -> l0(x55, x56, x57, x58, x59) :|: x54 = x59 && x53 = x58 && x52 = x57 && x51 = x56 && x50 = x55 l6(x60, x61, x62, x63, x64) -> l0(x65, x66, x67, x68, x69) :|: x64 = x69 && x63 = x68 && x62 = x67 && x61 = x66 && x60 = x65 l7(x70, x71, x72, x73, x74) -> l6(x75, x76, x77, x78, x79) :|: x74 = x79 && x73 = x78 && x72 = x77 && x71 = x76 && x70 = x75 Start term: l7(Result_4HAT0, __disjvr_0HAT0, tmp_7HAT0, x_5HAT0, y_6HAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(Result_4HAT0, __disjvr_0HAT0, tmp_7HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, __disjvr_0HATpost, tmp_7HATpost, x_5HATpost, y_6HATpost) :|: y_6HAT0 = y_6HATpost && x_5HAT0 = x_5HATpost && tmp_7HAT0 = tmp_7HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && Result_4HATpost = Result_4HATpost && -1 * x_5HAT0 + y_6HAT0 <= 0 l0(x, x1, x2, x3, x4) -> l2(x5, x6, x7, x8, x9) :|: x4 = x9 && x3 = x8 && x1 = x6 && x = x5 && 0 <= x7 && x7 <= 0 && x7 = x7 && 0 <= -1 - x3 + x4 l2(x10, x11, x12, x13, x14) -> l0(x15, x16, x17, x18, x19) :|: x14 = x19 && x13 = x18 && x12 = x17 && x11 = x16 && x10 = x15 l0(x20, x21, x22, x23, x24) -> l4(x25, x26, x27, x28, x29) :|: x24 = x29 && x23 = x28 && x21 = x26 && x20 = x25 && x27 = x27 && 0 <= -1 - x23 + x24 l4(x30, x31, x32, x33, x34) -> l5(x35, x36, x37, x38, x39) :|: x34 = x39 && x33 = x38 && x32 = x37 && x31 = x36 && x30 = x35 && x36 = x31 l5(x40, x41, x42, x43, x44) -> l3(x45, x46, x47, x48, x49) :|: x44 = x49 && x42 = x47 && x41 = x46 && x40 = x45 && x48 = 1 + x43 l3(x50, x51, x52, x53, x54) -> l0(x55, x56, x57, x58, x59) :|: x54 = x59 && x53 = x58 && x52 = x57 && x51 = x56 && x50 = x55 l6(x60, x61, x62, x63, x64) -> l0(x65, x66, x67, x68, x69) :|: x64 = x69 && x63 = x68 && x62 = x67 && x61 = x66 && x60 = x65 l7(x70, x71, x72, x73, x74) -> l6(x75, x76, x77, x78, x79) :|: x74 = x79 && x73 = x78 && x72 = x77 && x71 = x76 && x70 = x75 Start term: l7(Result_4HAT0, __disjvr_0HAT0, tmp_7HAT0, x_5HAT0, y_6HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(Result_4HAT0, __disjvr_0HAT0, tmp_7HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, __disjvr_0HATpost, tmp_7HATpost, x_5HATpost, y_6HATpost) :|: y_6HAT0 = y_6HATpost && x_5HAT0 = x_5HATpost && tmp_7HAT0 = tmp_7HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && Result_4HATpost = Result_4HATpost && -1 * x_5HAT0 + y_6HAT0 <= 0 (2) l0(x, x1, x2, x3, x4) -> l2(x5, x6, x7, x8, x9) :|: x4 = x9 && x3 = x8 && x1 = x6 && x = x5 && 0 <= x7 && x7 <= 0 && x7 = x7 && 0 <= -1 - x3 + x4 (3) l2(x10, x11, x12, x13, x14) -> l0(x15, x16, x17, x18, x19) :|: x14 = x19 && x13 = x18 && x12 = x17 && x11 = x16 && x10 = x15 (4) l0(x20, x21, x22, x23, x24) -> l4(x25, x26, x27, x28, x29) :|: x24 = x29 && x23 = x28 && x21 = x26 && x20 = x25 && x27 = x27 && 0 <= -1 - x23 + x24 (5) l4(x30, x31, x32, x33, x34) -> l5(x35, x36, x37, x38, x39) :|: x34 = x39 && x33 = x38 && x32 = x37 && x31 = x36 && x30 = x35 && x36 = x31 (6) l5(x40, x41, x42, x43, x44) -> l3(x45, x46, x47, x48, x49) :|: x44 = x49 && x42 = x47 && x41 = x46 && x40 = x45 && x48 = 1 + x43 (7) l3(x50, x51, x52, x53, x54) -> l0(x55, x56, x57, x58, x59) :|: x54 = x59 && x53 = x58 && x52 = x57 && x51 = x56 && x50 = x55 (8) l6(x60, x61, x62, x63, x64) -> l0(x65, x66, x67, x68, x69) :|: x64 = x69 && x63 = x68 && x62 = x67 && x61 = x66 && x60 = x65 (9) l7(x70, x71, x72, x73, x74) -> l6(x75, x76, x77, x78, x79) :|: x74 = x79 && x73 = x78 && x72 = x77 && x71 = x76 && x70 = x75 Arcs: (2) -> (3) (3) -> (1), (2), (4) (4) -> (5) (5) -> (6) (6) -> (7) (7) -> (1), (2), (4) (8) -> (1), (2), (4) (9) -> (8) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l0(x, x1, x2, x3, x4) -> l2(x5, x6, x7, x8, x9) :|: x4 = x9 && x3 = x8 && x1 = x6 && x = x5 && 0 <= x7 && x7 <= 0 && x7 = x7 && 0 <= -1 - x3 + x4 (2) l3(x50, x51, x52, x53, x54) -> l0(x55, x56, x57, x58, x59) :|: x54 = x59 && x53 = x58 && x52 = x57 && x51 = x56 && x50 = x55 (3) l5(x40, x41, x42, x43, x44) -> l3(x45, x46, x47, x48, x49) :|: x44 = x49 && x42 = x47 && x41 = x46 && x40 = x45 && x48 = 1 + x43 (4) l4(x30, x31, x32, x33, x34) -> l5(x35, x36, x37, x38, x39) :|: x34 = x39 && x33 = x38 && x32 = x37 && x31 = x36 && x30 = x35 && x36 = x31 (5) l0(x20, x21, x22, x23, x24) -> l4(x25, x26, x27, x28, x29) :|: x24 = x29 && x23 = x28 && x21 = x26 && x20 = x25 && x27 = x27 && 0 <= -1 - x23 + x24 (6) l2(x10, x11, x12, x13, x14) -> l0(x15, x16, x17, x18, x19) :|: x14 = x19 && x13 = x18 && x12 = x17 && x11 = x16 && x10 = x15 Arcs: (1) -> (6) (2) -> (1), (5) (3) -> (2) (4) -> (3) (5) -> (4) (6) -> (1), (5) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l0(x15:0, x16:0, x2:0, x18:0, x19:0) -> l0(x15:0, x16:0, x17:0, x18:0, x19:0) :|: x17:0 < 1 && x17:0 > -1 && 0 <= -1 - x18:0 + x19:0 l0(x20:0, x21:0, x22:0, x23:0, x24:0) -> l0(x20:0, x21:0, x27:0, 1 + x23:0, x24:0) :|: 0 <= -1 - x23:0 + x24:0 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l0(x1, x2, x3, x4, x5) -> l0(x4, x5) ---------------------------------------- (8) Obligation: Rules: l0(x18:0, x19:0) -> l0(x18:0, x19:0) :|: x17:0 < 1 && x17:0 > -1 && 0 <= -1 - x18:0 + x19:0 l0(x23:0, x24:0) -> l0(1 + x23:0, x24:0) :|: 0 <= -1 - x23:0 + x24:0 ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l0(INTEGER, 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: l0(x18:0, x19:0) -> l0(x18:0, x19:0) :|: x17:0 < 1 && x17:0 > -1 && 0 <= -1 - x18:0 + x19:0 l0(x23:0, x24:0) -> l0(c, x24:0) :|: c = 1 + x23:0 && 0 <= -1 - x23:0 + x24:0 Interpretation: [ l0 ] = -1*l0_1 + l0_2 The following rules are decreasing: l0(x23:0, x24:0) -> l0(c, x24:0) :|: c = 1 + x23:0 && 0 <= -1 - x23:0 + x24:0 The following rules are bounded: l0(x18:0, x19:0) -> l0(x18:0, x19:0) :|: x17:0 < 1 && x17:0 > -1 && 0 <= -1 - x18:0 + x19:0 l0(x23:0, x24:0) -> l0(c, x24:0) :|: c = 1 + x23:0 && 0 <= -1 - x23:0 + x24:0 - IntTRS - RankingReductionPairProof - IntTRS Rules: l0(x18:0, x19:0) -> l0(x18:0, x19:0) :|: x17:0 < 1 && x17:0 > -1 && 0 <= -1 - x18:0 + x19:0 ---------------------------------------- (10) Obligation: Rules: l0(x18:0, x19:0) -> l0(x18:0, x19:0) :|: x17:0 < 1 && x17:0 > -1 && 0 <= -1 - x18:0 + x19:0 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(x18:0, x19:0) -> l0(x18:0, x19:0) :|: x17:0 < 1 && x17:0 > -1 && 0 <= -1 - x18:0 + x19:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) l0(x18:0, x19:0) -> l0(x18:0, x19:0) :|: x17:0 < 1 && x17:0 > -1 && 0 <= -1 - x18:0 + x19:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: l0(x18:0:0, x19:0:0) -> l0(x18:0:0, x19:0:0) :|: x17:0:0 < 1 && x17:0:0 > -1 && 0 <= -1 - x18:0:0 + x19:0:0