NO proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be disproven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof [EQUIVALENT, 584 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 0 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) FilterProof [EQUIVALENT, 0 ms] (10) IntTRS (11) IntTRSPeriodicNontermProof [COMPLETE, 7 ms] (12) NO ---------------------------------------- (0) Obligation: Rules: l0(Result_4HAT0, cnt_15HAT0, cnt_20HAT0, lt_7HAT0, lt_8HAT0, lt_9HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, cnt_15HATpost, cnt_20HATpost, lt_7HATpost, lt_8HATpost, lt_9HATpost, x_5HATpost, y_6HATpost) :|: lt_9HAT0 = lt_9HATpost && lt_8HAT0 = lt_8HATpost && lt_7HAT0 = lt_7HATpost && cnt_20HAT0 = cnt_20HATpost && cnt_15HAT0 = cnt_15HATpost && Result_4HAT0 = Result_4HATpost && x_5HATpost = x_5HATpost && y_6HATpost = y_6HATpost l1(x, x1, x2, x3, x4, x5, x6, x7) -> l2(x8, x9, x10, x11, x12, x13, x14, x15) :|: x16 = x1 && x17 = x2 && x16 <= x17 && x17 <= x16 && x12 = x12 && x13 = x13 && x8 = x8 && x1 = x9 && x2 = x10 && x3 = x11 && x6 = x14 && x7 = x15 l1(x18, x19, x20, x21, x22, x23, x24, x25) -> l4(x26, x27, x28, x29, x30, x31, x32, x33) :|: x25 = x33 && x24 = x32 && x21 = x29 && x20 = x28 && x19 = x27 && x18 = x26 && x31 = x20 && x30 = x19 l4(x34, x35, x36, x37, x38, x39, x40, x41) -> l5(x42, x43, x44, x45, x46, x47, x48, x49) :|: x41 = x49 && x40 = x48 && x39 = x47 && x38 = x46 && x37 = x45 && x36 = x44 && x35 = x43 && x34 = x42 && 1 + x38 <= x39 l4(x50, x51, x52, x53, x54, x55, x56, x57) -> l5(x58, x59, x60, x61, x62, x63, x64, x65) :|: x57 = x65 && x56 = x64 && x55 = x63 && x54 = x62 && x53 = x61 && x52 = x60 && x51 = x59 && x50 = x58 && 1 + x55 <= x54 l5(x66, x67, x68, x69, x70, x71, x72, x73) -> l3(x74, x75, x76, x77, x78, x79, x80, x81) :|: x78 = x78 && x79 = x79 && x82 = x67 && x77 = x77 && x66 = x74 && x67 = x75 && x68 = x76 && x72 = x80 && x73 = x81 l3(x83, x84, x85, x86, x87, x88, x89, x90) -> l1(x91, x92, x93, x94, x95, x96, x97, x98) :|: x90 = x98 && x89 = x97 && x88 = x96 && x87 = x95 && x86 = x94 && x85 = x93 && x84 = x92 && x83 = x91 l6(x99, x100, x101, x102, x103, x104, x105, x106) -> l0(x107, x108, x109, x110, x111, x112, x113, x114) :|: x106 = x114 && x105 = x113 && x104 = x112 && x103 = x111 && x102 = x110 && x101 = x109 && x100 = x108 && x99 = x107 Start term: l6(Result_4HAT0, cnt_15HAT0, cnt_20HAT0, lt_7HAT0, lt_8HAT0, lt_9HAT0, 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, cnt_15HAT0, cnt_20HAT0, lt_7HAT0, lt_8HAT0, lt_9HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, cnt_15HATpost, cnt_20HATpost, lt_7HATpost, lt_8HATpost, lt_9HATpost, x_5HATpost, y_6HATpost) :|: lt_9HAT0 = lt_9HATpost && lt_8HAT0 = lt_8HATpost && lt_7HAT0 = lt_7HATpost && cnt_20HAT0 = cnt_20HATpost && cnt_15HAT0 = cnt_15HATpost && Result_4HAT0 = Result_4HATpost && x_5HATpost = x_5HATpost && y_6HATpost = y_6HATpost l1(x, x1, x2, x3, x4, x5, x6, x7) -> l2(x8, x9, x10, x11, x12, x13, x14, x15) :|: x16 = x1 && x17 = x2 && x16 <= x17 && x17 <= x16 && x12 = x12 && x13 = x13 && x8 = x8 && x1 = x9 && x2 = x10 && x3 = x11 && x6 = x14 && x7 = x15 l1(x18, x19, x20, x21, x22, x23, x24, x25) -> l4(x26, x27, x28, x29, x30, x31, x32, x33) :|: x25 = x33 && x24 = x32 && x21 = x29 && x20 = x28 && x19 = x27 && x18 = x26 && x31 = x20 && x30 = x19 l4(x34, x35, x36, x37, x38, x39, x40, x41) -> l5(x42, x43, x44, x45, x46, x47, x48, x49) :|: x41 = x49 && x40 = x48 && x39 = x47 && x38 = x46 && x37 = x45 && x36 = x44 && x35 = x43 && x34 = x42 && 1 + x38 <= x39 l4(x50, x51, x52, x53, x54, x55, x56, x57) -> l5(x58, x59, x60, x61, x62, x63, x64, x65) :|: x57 = x65 && x56 = x64 && x55 = x63 && x54 = x62 && x53 = x61 && x52 = x60 && x51 = x59 && x50 = x58 && 1 + x55 <= x54 l5(x66, x67, x68, x69, x70, x71, x72, x73) -> l3(x74, x75, x76, x77, x78, x79, x80, x81) :|: x78 = x78 && x79 = x79 && x82 = x67 && x77 = x77 && x66 = x74 && x67 = x75 && x68 = x76 && x72 = x80 && x73 = x81 l3(x83, x84, x85, x86, x87, x88, x89, x90) -> l1(x91, x92, x93, x94, x95, x96, x97, x98) :|: x90 = x98 && x89 = x97 && x88 = x96 && x87 = x95 && x86 = x94 && x85 = x93 && x84 = x92 && x83 = x91 l6(x99, x100, x101, x102, x103, x104, x105, x106) -> l0(x107, x108, x109, x110, x111, x112, x113, x114) :|: x106 = x114 && x105 = x113 && x104 = x112 && x103 = x111 && x102 = x110 && x101 = x109 && x100 = x108 && x99 = x107 Start term: l6(Result_4HAT0, cnt_15HAT0, cnt_20HAT0, lt_7HAT0, lt_8HAT0, lt_9HAT0, x_5HAT0, y_6HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(Result_4HAT0, cnt_15HAT0, cnt_20HAT0, lt_7HAT0, lt_8HAT0, lt_9HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, cnt_15HATpost, cnt_20HATpost, lt_7HATpost, lt_8HATpost, lt_9HATpost, x_5HATpost, y_6HATpost) :|: lt_9HAT0 = lt_9HATpost && lt_8HAT0 = lt_8HATpost && lt_7HAT0 = lt_7HATpost && cnt_20HAT0 = cnt_20HATpost && cnt_15HAT0 = cnt_15HATpost && Result_4HAT0 = Result_4HATpost && x_5HATpost = x_5HATpost && y_6HATpost = y_6HATpost (2) l1(x, x1, x2, x3, x4, x5, x6, x7) -> l2(x8, x9, x10, x11, x12, x13, x14, x15) :|: x16 = x1 && x17 = x2 && x16 <= x17 && x17 <= x16 && x12 = x12 && x13 = x13 && x8 = x8 && x1 = x9 && x2 = x10 && x3 = x11 && x6 = x14 && x7 = x15 (3) l1(x18, x19, x20, x21, x22, x23, x24, x25) -> l4(x26, x27, x28, x29, x30, x31, x32, x33) :|: x25 = x33 && x24 = x32 && x21 = x29 && x20 = x28 && x19 = x27 && x18 = x26 && x31 = x20 && x30 = x19 (4) l4(x34, x35, x36, x37, x38, x39, x40, x41) -> l5(x42, x43, x44, x45, x46, x47, x48, x49) :|: x41 = x49 && x40 = x48 && x39 = x47 && x38 = x46 && x37 = x45 && x36 = x44 && x35 = x43 && x34 = x42 && 1 + x38 <= x39 (5) l4(x50, x51, x52, x53, x54, x55, x56, x57) -> l5(x58, x59, x60, x61, x62, x63, x64, x65) :|: x57 = x65 && x56 = x64 && x55 = x63 && x54 = x62 && x53 = x61 && x52 = x60 && x51 = x59 && x50 = x58 && 1 + x55 <= x54 (6) l5(x66, x67, x68, x69, x70, x71, x72, x73) -> l3(x74, x75, x76, x77, x78, x79, x80, x81) :|: x78 = x78 && x79 = x79 && x82 = x67 && x77 = x77 && x66 = x74 && x67 = x75 && x68 = x76 && x72 = x80 && x73 = x81 (7) l3(x83, x84, x85, x86, x87, x88, x89, x90) -> l1(x91, x92, x93, x94, x95, x96, x97, x98) :|: x90 = x98 && x89 = x97 && x88 = x96 && x87 = x95 && x86 = x94 && x85 = x93 && x84 = x92 && x83 = x91 (8) l6(x99, x100, x101, x102, x103, x104, x105, x106) -> l0(x107, x108, x109, x110, x111, x112, x113, x114) :|: x106 = x114 && x105 = x113 && x104 = x112 && x103 = x111 && x102 = x110 && x101 = x109 && x100 = x108 && x99 = x107 Arcs: (1) -> (2), (3) (3) -> (4), (5) (4) -> (6) (5) -> (6) (6) -> (7) (7) -> (2), (3) (8) -> (1) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l1(x18, x19, x20, x21, x22, x23, x24, x25) -> l4(x26, x27, x28, x29, x30, x31, x32, x33) :|: x25 = x33 && x24 = x32 && x21 = x29 && x20 = x28 && x19 = x27 && x18 = x26 && x31 = x20 && x30 = x19 (2) l3(x83, x84, x85, x86, x87, x88, x89, x90) -> l1(x91, x92, x93, x94, x95, x96, x97, x98) :|: x90 = x98 && x89 = x97 && x88 = x96 && x87 = x95 && x86 = x94 && x85 = x93 && x84 = x92 && x83 = x91 (3) l5(x66, x67, x68, x69, x70, x71, x72, x73) -> l3(x74, x75, x76, x77, x78, x79, x80, x81) :|: x78 = x78 && x79 = x79 && x82 = x67 && x77 = x77 && x66 = x74 && x67 = x75 && x68 = x76 && x72 = x80 && x73 = x81 (4) l4(x50, x51, x52, x53, x54, x55, x56, x57) -> l5(x58, x59, x60, x61, x62, x63, x64, x65) :|: x57 = x65 && x56 = x64 && x55 = x63 && x54 = x62 && x53 = x61 && x52 = x60 && x51 = x59 && x50 = x58 && 1 + x55 <= x54 (5) l4(x34, x35, x36, x37, x38, x39, x40, x41) -> l5(x42, x43, x44, x45, x46, x47, x48, x49) :|: x41 = x49 && x40 = x48 && x39 = x47 && x38 = x46 && x37 = x45 && x36 = x44 && x35 = x43 && x34 = x42 && 1 + x38 <= x39 Arcs: (1) -> (4), (5) (2) -> (1) (3) -> (2) (4) -> (3) (5) -> (3) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l5(x26:0, x27:0, x28:0, x69:0, x70:0, x71:0, x32:0, x33:0) -> l5(x26:0, x27:0, x28:0, x29:0, x27:0, x28:0, x32:0, x33:0) :|: x27:0 >= 1 + x28:0 l5(x, x1, x2, x3, x4, x5, x6, x7) -> l5(x, x1, x2, x8, x1, x2, x6, x7) :|: x2 >= 1 + x1 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l5(x1, x2, x3, x4, x5, x6, x7, x8) -> l5(x2, x3) ---------------------------------------- (8) Obligation: Rules: l5(x27:0, x28:0) -> l5(x27:0, x28:0) :|: x27:0 >= 1 + x28:0 l5(x1, x2) -> l5(x1, x2) :|: x2 >= 1 + x1 ---------------------------------------- (9) FilterProof (EQUIVALENT) Used the following sort dictionary for filtering: l5(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (10) Obligation: Rules: l5(x27:0, x28:0) -> l5(x27:0, x28:0) :|: x27:0 >= 1 + x28:0 l5(x1, x2) -> l5(x1, x2) :|: x2 >= 1 + x1 ---------------------------------------- (11) IntTRSPeriodicNontermProof (COMPLETE) Normalized system to the following form: f(pc, x27:0, x28:0) -> f(1, x27:0, x28:0) :|: pc = 1 && x27:0 >= 1 + x28:0 f(pc, x1, x2) -> f(1, x1, x2) :|: pc = 1 && x2 >= 1 + x1 Witness term starting non-terminating reduction: f(1, -1, 7) ---------------------------------------- (12) NO