NO proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be disproven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 858 ms] (4) AND (5) IRSwT (6) IntTRSCompressionProof [EQUIVALENT, 0 ms] (7) IRSwT (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (9) IRSwT (10) TempFilterProof [SOUND, 14 ms] (11) IntTRS (12) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (13) YES (14) IRSwT (15) IntTRSCompressionProof [EQUIVALENT, 0 ms] (16) IRSwT (17) FilterProof [EQUIVALENT, 0 ms] (18) IntTRS (19) IntTRSPeriodicNontermProof [COMPLETE, 0 ms] (20) NO (21) IRSwT (22) IntTRSCompressionProof [EQUIVALENT, 0 ms] (23) IRSwT (24) FilterProof [EQUIVALENT, 0 ms] (25) IntTRS (26) IntTRSPeriodicNontermProof [COMPLETE, 0 ms] (27) NO ---------------------------------------- (0) Obligation: Rules: l0(i5HAT0, length4HAT0, sHAT0, tmpHAT0, tmp___08HAT0) -> l1(i5HATpost, length4HATpost, sHATpost, tmpHATpost, tmp___08HATpost) :|: tmp___08HAT0 = tmp___08HATpost && tmpHAT0 = tmpHATpost && sHAT0 = sHATpost && length4HAT0 = length4HATpost && i5HAT0 = i5HATpost && length4HAT0 <= i5HAT0 l0(x, x1, x2, x3, x4) -> l2(x5, x6, x7, x8, x9) :|: x3 = x8 && x2 = x7 && x1 = x6 && x5 = 1 + x && x9 = x9 && 1 + x <= x1 l2(x10, x11, x12, x13, x14) -> l0(x15, x16, x17, x18, x19) :|: x14 = x19 && x13 = x18 && x12 = x17 && x11 = x16 && x10 = x15 l3(x20, x21, x22, x23, x24) -> l4(x25, x26, x27, x28, x29) :|: x24 = x29 && x23 = x28 && x22 = x27 && x21 = x26 && x20 = x25 l5(x30, x31, x32, x33, x34) -> l3(x35, x36, x37, x38, x39) :|: x34 = x39 && x33 = x38 && x32 = x37 && x31 = x36 && x30 = x35 l5(x40, x41, x42, x43, x44) -> l6(x45, x46, x47, x48, x49) :|: x44 = x49 && x43 = x48 && x42 = x47 && x41 = x46 && x40 = x45 l1(x50, x51, x52, x53, x54) -> l7(x55, x56, x57, x58, x59) :|: x54 = x59 && x53 = x58 && x52 = x57 && x51 = x56 && x50 = x55 l8(x60, x61, x62, x63, x64) -> l1(x65, x66, x67, x68, x69) :|: x64 = x69 && x63 = x68 && x62 = x67 && x61 = x66 && x60 = x65 l7(x70, x71, x72, x73, x74) -> l8(x75, x76, x77, x78, x79) :|: x74 = x79 && x73 = x78 && x72 = x77 && x71 = x76 && x70 = x75 l7(x80, x81, x82, x83, x84) -> l4(x85, x86, x87, x88, x89) :|: x84 = x89 && x83 = x88 && x82 = x87 && x81 = x86 && x80 = x85 l4(x90, x91, x92, x93, x94) -> l5(x95, x96, x97, x98, x99) :|: x94 = x99 && x93 = x98 && x92 = x97 && x91 = x96 && x90 = x95 l9(x100, x101, x102, x103, x104) -> l2(x105, x106, x107, x108, x109) :|: x104 = x109 && x105 = 0 && x106 = x107 && x107 = x108 && x108 = x108 l10(x110, x111, x112, x113, x114) -> l9(x115, x116, x117, x118, x119) :|: x114 = x119 && x113 = x118 && x112 = x117 && x111 = x116 && x110 = x115 Start term: l10(i5HAT0, length4HAT0, sHAT0, tmpHAT0, tmp___08HAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(i5HAT0, length4HAT0, sHAT0, tmpHAT0, tmp___08HAT0) -> l1(i5HATpost, length4HATpost, sHATpost, tmpHATpost, tmp___08HATpost) :|: tmp___08HAT0 = tmp___08HATpost && tmpHAT0 = tmpHATpost && sHAT0 = sHATpost && length4HAT0 = length4HATpost && i5HAT0 = i5HATpost && length4HAT0 <= i5HAT0 l0(x, x1, x2, x3, x4) -> l2(x5, x6, x7, x8, x9) :|: x3 = x8 && x2 = x7 && x1 = x6 && x5 = 1 + x && x9 = x9 && 1 + x <= x1 l2(x10, x11, x12, x13, x14) -> l0(x15, x16, x17, x18, x19) :|: x14 = x19 && x13 = x18 && x12 = x17 && x11 = x16 && x10 = x15 l3(x20, x21, x22, x23, x24) -> l4(x25, x26, x27, x28, x29) :|: x24 = x29 && x23 = x28 && x22 = x27 && x21 = x26 && x20 = x25 l5(x30, x31, x32, x33, x34) -> l3(x35, x36, x37, x38, x39) :|: x34 = x39 && x33 = x38 && x32 = x37 && x31 = x36 && x30 = x35 l5(x40, x41, x42, x43, x44) -> l6(x45, x46, x47, x48, x49) :|: x44 = x49 && x43 = x48 && x42 = x47 && x41 = x46 && x40 = x45 l1(x50, x51, x52, x53, x54) -> l7(x55, x56, x57, x58, x59) :|: x54 = x59 && x53 = x58 && x52 = x57 && x51 = x56 && x50 = x55 l8(x60, x61, x62, x63, x64) -> l1(x65, x66, x67, x68, x69) :|: x64 = x69 && x63 = x68 && x62 = x67 && x61 = x66 && x60 = x65 l7(x70, x71, x72, x73, x74) -> l8(x75, x76, x77, x78, x79) :|: x74 = x79 && x73 = x78 && x72 = x77 && x71 = x76 && x70 = x75 l7(x80, x81, x82, x83, x84) -> l4(x85, x86, x87, x88, x89) :|: x84 = x89 && x83 = x88 && x82 = x87 && x81 = x86 && x80 = x85 l4(x90, x91, x92, x93, x94) -> l5(x95, x96, x97, x98, x99) :|: x94 = x99 && x93 = x98 && x92 = x97 && x91 = x96 && x90 = x95 l9(x100, x101, x102, x103, x104) -> l2(x105, x106, x107, x108, x109) :|: x104 = x109 && x105 = 0 && x106 = x107 && x107 = x108 && x108 = x108 l10(x110, x111, x112, x113, x114) -> l9(x115, x116, x117, x118, x119) :|: x114 = x119 && x113 = x118 && x112 = x117 && x111 = x116 && x110 = x115 Start term: l10(i5HAT0, length4HAT0, sHAT0, tmpHAT0, tmp___08HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(i5HAT0, length4HAT0, sHAT0, tmpHAT0, tmp___08HAT0) -> l1(i5HATpost, length4HATpost, sHATpost, tmpHATpost, tmp___08HATpost) :|: tmp___08HAT0 = tmp___08HATpost && tmpHAT0 = tmpHATpost && sHAT0 = sHATpost && length4HAT0 = length4HATpost && i5HAT0 = i5HATpost && length4HAT0 <= i5HAT0 (2) l0(x, x1, x2, x3, x4) -> l2(x5, x6, x7, x8, x9) :|: x3 = x8 && x2 = x7 && x1 = x6 && x5 = 1 + x && x9 = x9 && 1 + x <= x1 (3) l2(x10, x11, x12, x13, x14) -> l0(x15, x16, x17, x18, x19) :|: x14 = x19 && x13 = x18 && x12 = x17 && x11 = x16 && x10 = x15 (4) l3(x20, x21, x22, x23, x24) -> l4(x25, x26, x27, x28, x29) :|: x24 = x29 && x23 = x28 && x22 = x27 && x21 = x26 && x20 = x25 (5) l5(x30, x31, x32, x33, x34) -> l3(x35, x36, x37, x38, x39) :|: x34 = x39 && x33 = x38 && x32 = x37 && x31 = x36 && x30 = x35 (6) l5(x40, x41, x42, x43, x44) -> l6(x45, x46, x47, x48, x49) :|: x44 = x49 && x43 = x48 && x42 = x47 && x41 = x46 && x40 = x45 (7) l1(x50, x51, x52, x53, x54) -> l7(x55, x56, x57, x58, x59) :|: x54 = x59 && x53 = x58 && x52 = x57 && x51 = x56 && x50 = x55 (8) l8(x60, x61, x62, x63, x64) -> l1(x65, x66, x67, x68, x69) :|: x64 = x69 && x63 = x68 && x62 = x67 && x61 = x66 && x60 = x65 (9) l7(x70, x71, x72, x73, x74) -> l8(x75, x76, x77, x78, x79) :|: x74 = x79 && x73 = x78 && x72 = x77 && x71 = x76 && x70 = x75 (10) l7(x80, x81, x82, x83, x84) -> l4(x85, x86, x87, x88, x89) :|: x84 = x89 && x83 = x88 && x82 = x87 && x81 = x86 && x80 = x85 (11) l4(x90, x91, x92, x93, x94) -> l5(x95, x96, x97, x98, x99) :|: x94 = x99 && x93 = x98 && x92 = x97 && x91 = x96 && x90 = x95 (12) l9(x100, x101, x102, x103, x104) -> l2(x105, x106, x107, x108, x109) :|: x104 = x109 && x105 = 0 && x106 = x107 && x107 = x108 && x108 = x108 (13) l10(x110, x111, x112, x113, x114) -> l9(x115, x116, x117, x118, x119) :|: x114 = x119 && x113 = x118 && x112 = x117 && x111 = x116 && x110 = x115 Arcs: (1) -> (7) (2) -> (3) (3) -> (1), (2) (4) -> (11) (5) -> (4) (7) -> (9), (10) (8) -> (7) (9) -> (8) (10) -> (11) (11) -> (5), (6) (12) -> (3) (13) -> (12) This digraph is fully evaluated! ---------------------------------------- (4) Complex Obligation (AND) ---------------------------------------- (5) Obligation: Termination digraph: Nodes: (1) l0(x, x1, x2, x3, x4) -> l2(x5, x6, x7, x8, x9) :|: x3 = x8 && x2 = x7 && x1 = x6 && x5 = 1 + x && x9 = x9 && 1 + x <= x1 (2) l2(x10, x11, x12, x13, x14) -> l0(x15, x16, x17, x18, x19) :|: x14 = x19 && x13 = x18 && x12 = x17 && x11 = x16 && x10 = x15 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (6) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (7) Obligation: Rules: l0(x:0, x16:0, x17:0, x18:0, x4:0) -> l0(1 + x:0, x16:0, x17:0, x18:0, x19:0) :|: x16:0 >= 1 + x:0 ---------------------------------------- (8) 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(x1, x2) ---------------------------------------- (9) Obligation: Rules: l0(x:0, x16:0) -> l0(1 + x:0, x16:0) :|: x16:0 >= 1 + x:0 ---------------------------------------- (10) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l0(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (11) Obligation: Rules: l0(x:0, x16:0) -> l0(c, x16:0) :|: c = 1 + x:0 && x16:0 >= 1 + x:0 ---------------------------------------- (12) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l0(x, x1)] = -x + x1 The following rules are decreasing: l0(x:0, x16:0) -> l0(c, x16:0) :|: c = 1 + x:0 && x16:0 >= 1 + x:0 The following rules are bounded: l0(x:0, x16:0) -> l0(c, x16:0) :|: c = 1 + x:0 && x16:0 >= 1 + x:0 ---------------------------------------- (13) YES ---------------------------------------- (14) Obligation: Termination digraph: Nodes: (1) l1(x50, x51, x52, x53, x54) -> l7(x55, x56, x57, x58, x59) :|: x54 = x59 && x53 = x58 && x52 = x57 && x51 = x56 && x50 = x55 (2) l8(x60, x61, x62, x63, x64) -> l1(x65, x66, x67, x68, x69) :|: x64 = x69 && x63 = x68 && x62 = x67 && x61 = x66 && x60 = x65 (3) l7(x70, x71, x72, x73, x74) -> l8(x75, x76, x77, x78, x79) :|: x74 = x79 && x73 = x78 && x72 = x77 && x71 = x76 && x70 = x75 Arcs: (1) -> (3) (2) -> (1) (3) -> (2) This digraph is fully evaluated! ---------------------------------------- (15) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (16) Obligation: Rules: l8(x55:0, x56:0, x57:0, x58:0, x59:0) -> l8(x55:0, x56:0, x57:0, x58:0, x59:0) :|: TRUE ---------------------------------------- (17) FilterProof (EQUIVALENT) Used the following sort dictionary for filtering: l8(VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (18) Obligation: Rules: l8(x55:0, x56:0, x57:0, x58:0, x59:0) -> l8(x55:0, x56:0, x57:0, x58:0, x59:0) :|: TRUE ---------------------------------------- (19) IntTRSPeriodicNontermProof (COMPLETE) Normalized system to the following form: f(pc, x55:0, x56:0, x57:0, x58:0, x59:0) -> f(1, x55:0, x56:0, x57:0, x58:0, x59:0) :|: pc = 1 && TRUE Witness term starting non-terminating reduction: f(1, -8, -8, -8, -8, -8) ---------------------------------------- (20) NO ---------------------------------------- (21) Obligation: Termination digraph: Nodes: (1) l4(x90, x91, x92, x93, x94) -> l5(x95, x96, x97, x98, x99) :|: x94 = x99 && x93 = x98 && x92 = x97 && x91 = x96 && x90 = x95 (2) l3(x20, x21, x22, x23, x24) -> l4(x25, x26, x27, x28, x29) :|: x24 = x29 && x23 = x28 && x22 = x27 && x21 = x26 && x20 = x25 (3) l5(x30, x31, x32, x33, x34) -> l3(x35, x36, x37, x38, x39) :|: x34 = x39 && x33 = x38 && x32 = x37 && x31 = x36 && x30 = x35 Arcs: (1) -> (3) (2) -> (1) (3) -> (2) This digraph is fully evaluated! ---------------------------------------- (22) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (23) Obligation: Rules: l3(x20:0, x21:0, x22:0, x23:0, x24:0) -> l3(x20:0, x21:0, x22:0, x23:0, x24:0) :|: TRUE ---------------------------------------- (24) FilterProof (EQUIVALENT) Used the following sort dictionary for filtering: l3(VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (25) Obligation: Rules: l3(x20:0, x21:0, x22:0, x23:0, x24:0) -> l3(x20:0, x21:0, x22:0, x23:0, x24:0) :|: TRUE ---------------------------------------- (26) IntTRSPeriodicNontermProof (COMPLETE) Normalized system to the following form: f(pc, x20:0, x21:0, x22:0, x23:0, x24:0) -> f(1, x20:0, x21:0, x22:0, x23:0, x24:0) :|: pc = 1 && TRUE Witness term starting non-terminating reduction: f(1, -8, -8, -8, -8, -8) ---------------------------------------- (27) NO