MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 1449 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 63 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 263 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT ---------------------------------------- (0) Obligation: Rules: l0(b_16HAT0, rt_11HAT0, st_15HAT0, x_14HAT0) -> l1(b_16HATpost, rt_11HATpost, st_15HATpost, x_14HATpost) :|: x_14HAT0 = x_14HATpost && st_15HAT0 = st_15HATpost && rt_11HAT0 = rt_11HATpost && b_16HATpost = 1 && 1 <= x_14HAT0 l2(x, x1, x2, x3) -> l4(x4, x5, x6, x7) :|: x3 = x7 && x2 = x6 && x1 = x5 && x = x4 && 1 <= x3 l2(x8, x9, x10, x11) -> l4(x12, x13, x14, x15) :|: x11 = x15 && x10 = x14 && x9 = x13 && x8 = x12 && 1 + x11 <= 0 l4(x16, x17, x18, x19) -> l3(x20, x21, x22, x23) :|: x18 = x22 && x17 = x21 && x20 = 0 && x23 = -1 + x19 && x16 <= 1 && 1 <= x16 l1(x24, x25, x26, x27) -> l5(x28, x29, x30, x31) :|: x27 = x31 && x26 = x30 && x24 = x28 && x29 = x26 && x27 <= 0 && 0 <= x27 l1(x32, x33, x34, x35) -> l6(x36, x37, x38, x39) :|: x35 = x39 && x34 = x38 && x33 = x37 && x32 = x36 && 1 <= x35 l1(x40, x41, x42, x43) -> l6(x44, x45, x46, x47) :|: x43 = x47 && x42 = x46 && x41 = x45 && x40 = x44 && 1 + x43 <= 0 l6(x48, x49, x50, x51) -> l3(x52, x53, x54, x55) :|: x50 = x54 && x49 = x53 && x52 = 0 && x55 = -1 + x51 && x48 <= 1 && 1 <= x48 l7(x56, x57, x58, x59) -> l5(x60, x61, x62, x63) :|: x59 = x63 && x58 = x62 && x56 = x60 && x61 = x58 && x59 <= 0 && 0 <= x59 l7(x64, x65, x66, x67) -> l8(x68, x69, x70, x71) :|: x67 = x71 && x66 = x70 && x65 = x69 && x64 = x68 && 1 <= x67 l7(x72, x73, x74, x75) -> l8(x76, x77, x78, x79) :|: x75 = x79 && x74 = x78 && x73 = x77 && x72 = x76 && 1 + x75 <= 0 l8(x80, x81, x82, x83) -> l9(x84, x85, x86, x87) :|: x83 = x87 && x82 = x86 && x81 = x85 && x80 = x84 && 2 <= x80 l8(x88, x89, x90, x91) -> l9(x92, x93, x94, x95) :|: x91 = x95 && x90 = x94 && x89 = x93 && x88 = x92 && 1 + x88 <= 1 l9(x96, x97, x98, x99) -> l1(x100, x101, x102, x103) :|: x104 = 1 + x99 && x100 = 1 && x103 = -1 * x104 && x97 = x101 && x98 = x102 l3(x105, x106, x107, x108) -> l7(x109, x110, x111, x112) :|: x107 = x111 && x106 = x110 && x105 = x109 && x112 = -1 * x108 l10(x113, x114, x115, x116) -> l7(x117, x118, x119, x120) :|: x115 = x119 && x114 = x118 && x113 = x117 && x120 = -1 * x116 l11(x121, x122, x123, x124) -> l0(x125, x126, x127, x128) :|: x124 = x128 && x123 = x127 && x122 = x126 && x121 = x125 Start term: l11(b_16HAT0, rt_11HAT0, st_15HAT0, x_14HAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(b_16HAT0, rt_11HAT0, st_15HAT0, x_14HAT0) -> l1(b_16HATpost, rt_11HATpost, st_15HATpost, x_14HATpost) :|: x_14HAT0 = x_14HATpost && st_15HAT0 = st_15HATpost && rt_11HAT0 = rt_11HATpost && b_16HATpost = 1 && 1 <= x_14HAT0 l2(x, x1, x2, x3) -> l4(x4, x5, x6, x7) :|: x3 = x7 && x2 = x6 && x1 = x5 && x = x4 && 1 <= x3 l2(x8, x9, x10, x11) -> l4(x12, x13, x14, x15) :|: x11 = x15 && x10 = x14 && x9 = x13 && x8 = x12 && 1 + x11 <= 0 l4(x16, x17, x18, x19) -> l3(x20, x21, x22, x23) :|: x18 = x22 && x17 = x21 && x20 = 0 && x23 = -1 + x19 && x16 <= 1 && 1 <= x16 l1(x24, x25, x26, x27) -> l5(x28, x29, x30, x31) :|: x27 = x31 && x26 = x30 && x24 = x28 && x29 = x26 && x27 <= 0 && 0 <= x27 l1(x32, x33, x34, x35) -> l6(x36, x37, x38, x39) :|: x35 = x39 && x34 = x38 && x33 = x37 && x32 = x36 && 1 <= x35 l1(x40, x41, x42, x43) -> l6(x44, x45, x46, x47) :|: x43 = x47 && x42 = x46 && x41 = x45 && x40 = x44 && 1 + x43 <= 0 l6(x48, x49, x50, x51) -> l3(x52, x53, x54, x55) :|: x50 = x54 && x49 = x53 && x52 = 0 && x55 = -1 + x51 && x48 <= 1 && 1 <= x48 l7(x56, x57, x58, x59) -> l5(x60, x61, x62, x63) :|: x59 = x63 && x58 = x62 && x56 = x60 && x61 = x58 && x59 <= 0 && 0 <= x59 l7(x64, x65, x66, x67) -> l8(x68, x69, x70, x71) :|: x67 = x71 && x66 = x70 && x65 = x69 && x64 = x68 && 1 <= x67 l7(x72, x73, x74, x75) -> l8(x76, x77, x78, x79) :|: x75 = x79 && x74 = x78 && x73 = x77 && x72 = x76 && 1 + x75 <= 0 l8(x80, x81, x82, x83) -> l9(x84, x85, x86, x87) :|: x83 = x87 && x82 = x86 && x81 = x85 && x80 = x84 && 2 <= x80 l8(x88, x89, x90, x91) -> l9(x92, x93, x94, x95) :|: x91 = x95 && x90 = x94 && x89 = x93 && x88 = x92 && 1 + x88 <= 1 l9(x96, x97, x98, x99) -> l1(x100, x101, x102, x103) :|: x104 = 1 + x99 && x100 = 1 && x103 = -1 * x104 && x97 = x101 && x98 = x102 l3(x105, x106, x107, x108) -> l7(x109, x110, x111, x112) :|: x107 = x111 && x106 = x110 && x105 = x109 && x112 = -1 * x108 l10(x113, x114, x115, x116) -> l7(x117, x118, x119, x120) :|: x115 = x119 && x114 = x118 && x113 = x117 && x120 = -1 * x116 l11(x121, x122, x123, x124) -> l0(x125, x126, x127, x128) :|: x124 = x128 && x123 = x127 && x122 = x126 && x121 = x125 Start term: l11(b_16HAT0, rt_11HAT0, st_15HAT0, x_14HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(b_16HAT0, rt_11HAT0, st_15HAT0, x_14HAT0) -> l1(b_16HATpost, rt_11HATpost, st_15HATpost, x_14HATpost) :|: x_14HAT0 = x_14HATpost && st_15HAT0 = st_15HATpost && rt_11HAT0 = rt_11HATpost && b_16HATpost = 1 && 1 <= x_14HAT0 (2) l2(x, x1, x2, x3) -> l4(x4, x5, x6, x7) :|: x3 = x7 && x2 = x6 && x1 = x5 && x = x4 && 1 <= x3 (3) l2(x8, x9, x10, x11) -> l4(x12, x13, x14, x15) :|: x11 = x15 && x10 = x14 && x9 = x13 && x8 = x12 && 1 + x11 <= 0 (4) l4(x16, x17, x18, x19) -> l3(x20, x21, x22, x23) :|: x18 = x22 && x17 = x21 && x20 = 0 && x23 = -1 + x19 && x16 <= 1 && 1 <= x16 (5) l1(x24, x25, x26, x27) -> l5(x28, x29, x30, x31) :|: x27 = x31 && x26 = x30 && x24 = x28 && x29 = x26 && x27 <= 0 && 0 <= x27 (6) l1(x32, x33, x34, x35) -> l6(x36, x37, x38, x39) :|: x35 = x39 && x34 = x38 && x33 = x37 && x32 = x36 && 1 <= x35 (7) l1(x40, x41, x42, x43) -> l6(x44, x45, x46, x47) :|: x43 = x47 && x42 = x46 && x41 = x45 && x40 = x44 && 1 + x43 <= 0 (8) l6(x48, x49, x50, x51) -> l3(x52, x53, x54, x55) :|: x50 = x54 && x49 = x53 && x52 = 0 && x55 = -1 + x51 && x48 <= 1 && 1 <= x48 (9) l7(x56, x57, x58, x59) -> l5(x60, x61, x62, x63) :|: x59 = x63 && x58 = x62 && x56 = x60 && x61 = x58 && x59 <= 0 && 0 <= x59 (10) l7(x64, x65, x66, x67) -> l8(x68, x69, x70, x71) :|: x67 = x71 && x66 = x70 && x65 = x69 && x64 = x68 && 1 <= x67 (11) l7(x72, x73, x74, x75) -> l8(x76, x77, x78, x79) :|: x75 = x79 && x74 = x78 && x73 = x77 && x72 = x76 && 1 + x75 <= 0 (12) l8(x80, x81, x82, x83) -> l9(x84, x85, x86, x87) :|: x83 = x87 && x82 = x86 && x81 = x85 && x80 = x84 && 2 <= x80 (13) l8(x88, x89, x90, x91) -> l9(x92, x93, x94, x95) :|: x91 = x95 && x90 = x94 && x89 = x93 && x88 = x92 && 1 + x88 <= 1 (14) l9(x96, x97, x98, x99) -> l1(x100, x101, x102, x103) :|: x104 = 1 + x99 && x100 = 1 && x103 = -1 * x104 && x97 = x101 && x98 = x102 (15) l3(x105, x106, x107, x108) -> l7(x109, x110, x111, x112) :|: x107 = x111 && x106 = x110 && x105 = x109 && x112 = -1 * x108 (16) l10(x113, x114, x115, x116) -> l7(x117, x118, x119, x120) :|: x115 = x119 && x114 = x118 && x113 = x117 && x120 = -1 * x116 (17) l11(x121, x122, x123, x124) -> l0(x125, x126, x127, x128) :|: x124 = x128 && x123 = x127 && x122 = x126 && x121 = x125 Arcs: (1) -> (6) (2) -> (4) (3) -> (4) (4) -> (15) (6) -> (8) (7) -> (8) (8) -> (15) (10) -> (12), (13) (11) -> (12), (13) (12) -> (14) (13) -> (14) (14) -> (5), (6), (7) (15) -> (9), (10), (11) (16) -> (9), (10), (11) (17) -> (1) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l1(x32, x33, x34, x35) -> l6(x36, x37, x38, x39) :|: x35 = x39 && x34 = x38 && x33 = x37 && x32 = x36 && 1 <= x35 (2) l9(x96, x97, x98, x99) -> l1(x100, x101, x102, x103) :|: x104 = 1 + x99 && x100 = 1 && x103 = -1 * x104 && x97 = x101 && x98 = x102 (3) l8(x88, x89, x90, x91) -> l9(x92, x93, x94, x95) :|: x91 = x95 && x90 = x94 && x89 = x93 && x88 = x92 && 1 + x88 <= 1 (4) l8(x80, x81, x82, x83) -> l9(x84, x85, x86, x87) :|: x83 = x87 && x82 = x86 && x81 = x85 && x80 = x84 && 2 <= x80 (5) l7(x72, x73, x74, x75) -> l8(x76, x77, x78, x79) :|: x75 = x79 && x74 = x78 && x73 = x77 && x72 = x76 && 1 + x75 <= 0 (6) l7(x64, x65, x66, x67) -> l8(x68, x69, x70, x71) :|: x67 = x71 && x66 = x70 && x65 = x69 && x64 = x68 && 1 <= x67 (7) l3(x105, x106, x107, x108) -> l7(x109, x110, x111, x112) :|: x107 = x111 && x106 = x110 && x105 = x109 && x112 = -1 * x108 (8) l6(x48, x49, x50, x51) -> l3(x52, x53, x54, x55) :|: x50 = x54 && x49 = x53 && x52 = 0 && x55 = -1 + x51 && x48 <= 1 && 1 <= x48 (9) l1(x40, x41, x42, x43) -> l6(x44, x45, x46, x47) :|: x43 = x47 && x42 = x46 && x41 = x45 && x40 = x44 && 1 + x43 <= 0 Arcs: (1) -> (8) (2) -> (1), (9) (3) -> (2) (4) -> (2) (5) -> (3), (4) (6) -> (3), (4) (7) -> (5), (6) (8) -> (7) (9) -> (8) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l9(x96:0, x101:0, x102:0, x99:0) -> l3(0, x101:0, x102:0, -1 + -1 * (1 + x99:0)) :|: 0 < -1 * (1 + x99:0) l8(x88:0, x89:0, x90:0, x91:0) -> l9(x88:0, x89:0, x90:0, x91:0) :|: x88:0 < 1 l8(x80:0, x81:0, x82:0, x83:0) -> l9(x80:0, x81:0, x82:0, x83:0) :|: x80:0 > 1 l3(x105:0, x106:0, x107:0, x108:0) -> l8(x105:0, x106:0, x107:0, -1 * x108:0) :|: 0 > -1 * x108:0 l3(x, x1, x2, x3) -> l8(x, x1, x2, -1 * x3) :|: 0 < -1 * x3 l9(x4, x5, x6, x7) -> l3(0, x5, x6, -1 + -1 * (1 + x7)) :|: 0 > -1 * (1 + x7) ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l9(x1, x2, x3, x4) -> l9(x4) l8(x1, x2, x3, x4) -> l8(x1, x4) l3(x1, x2, x3, x4) -> l3(x1, x4) ---------------------------------------- (8) Obligation: Rules: l9(x99:0) -> l3(0, -1 + -1 * (1 + x99:0)) :|: 0 < -1 * (1 + x99:0) l8(x88:0, x91:0) -> l9(x91:0) :|: x88:0 < 1 l8(x80:0, x83:0) -> l9(x83:0) :|: x80:0 > 1 l3(x105:0, x108:0) -> l8(x105:0, -1 * x108:0) :|: 0 > -1 * x108:0 l3(x, x3) -> l8(x, -1 * x3) :|: 0 < -1 * x3 l9(x7) -> l3(0, -1 + -1 * (1 + x7)) :|: 0 > -1 * (1 + x7) ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l9(VARIABLE) l3(VARIABLE, INTEGER) l8(VARIABLE, VARIABLE) 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 - PolynomialOrderProcessor Rules: l9(x99:0) -> l3(c, c1) :|: c1 = -1 + -1 * (1 + x99:0) && c = 0 && 0 < -1 * (1 + x99:0) l8(x88:0, x91:0) -> l9(x91:0) :|: x88:0 < 1 l8(x80:0, x83:0) -> l9(x83:0) :|: x80:0 > 1 l3(x105:0, x108:0) -> l8(x105:0, c2) :|: c2 = -1 * x108:0 && 0 > -1 * x108:0 l3(x, x3) -> l8(x, c3) :|: c3 = -1 * x3 && 0 < -1 * x3 l9(x7) -> l3(c4, c5) :|: c5 = -1 + -1 * (1 + x7) && c4 = 0 && 0 > -1 * (1 + x7) Found the following polynomial interpretation: [l9(x)] = -3 - x [l3(x1, x2)] = -1 + x2 [l8(x3, x4)] = -3 - x4 The following rules are decreasing: l3(x105:0, x108:0) -> l8(x105:0, c2) :|: c2 = -1 * x108:0 && 0 > -1 * x108:0 l3(x, x3) -> l8(x, c3) :|: c3 = -1 * x3 && 0 < -1 * x3 The following rules are bounded: l3(x105:0, x108:0) -> l8(x105:0, c2) :|: c2 = -1 * x108:0 && 0 > -1 * x108:0 - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor Rules: l9(x99:0) -> l3(c, c1) :|: c1 = -1 + -1 * (1 + x99:0) && c = 0 && 0 < -1 * (1 + x99:0) l8(x88:0, x91:0) -> l9(x91:0) :|: x88:0 < 1 l8(x80:0, x83:0) -> l9(x83:0) :|: x80:0 > 1 l3(x, x3) -> l8(x, c3) :|: c3 = -1 * x3 && 0 < -1 * x3 l9(x7) -> l3(c4, c5) :|: c5 = -1 + -1 * (1 + x7) && c4 = 0 && 0 > -1 * (1 + x7) Found the following polynomial interpretation: [l9(x)] = -2 - x [l3(x1, x2)] = x2 [l8(x3, x4)] = -2 - x4 The following rules are decreasing: l3(x, x3) -> l8(x, c3) :|: c3 = -1 * x3 && 0 < -1 * x3 The following rules are bounded: l9(x99:0) -> l3(c, c1) :|: c1 = -1 + -1 * (1 + x99:0) && c = 0 && 0 < -1 * (1 + x99:0) - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - PolynomialOrderProcessor - IntTRS Rules: l9(x99:0) -> l3(c, c1) :|: c1 = -1 + -1 * (1 + x99:0) && c = 0 && 0 < -1 * (1 + x99:0) l8(x88:0, x91:0) -> l9(x91:0) :|: x88:0 < 1 l8(x80:0, x83:0) -> l9(x83:0) :|: x80:0 > 1 l9(x7) -> l3(c4, c5) :|: c5 = -1 + -1 * (1 + x7) && c4 = 0 && 0 > -1 * (1 + x7) Found the following polynomial interpretation: [l9(x)] = 0 [l3(x1, x2)] = c1*x1 [l8(x3, x4)] = 1 The following rules are decreasing: l8(x88:0, x91:0) -> l9(x91:0) :|: x88:0 < 1 l8(x80:0, x83:0) -> l9(x83:0) :|: x80:0 > 1 The following rules are bounded: l9(x99:0) -> l3(c, c1) :|: c1 = -1 + -1 * (1 + x99:0) && c = 0 && 0 < -1 * (1 + x99:0) l8(x88:0, x91:0) -> l9(x91:0) :|: x88:0 < 1 l8(x80:0, x83:0) -> l9(x83:0) :|: x80:0 > 1 l9(x7) -> l3(c4, c5) :|: c5 = -1 + -1 * (1 + x7) && c4 = 0 && 0 > -1 * (1 + x7) - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - PolynomialOrderProcessor - IntTRS - RankingReductionPairProof - IntTRS Rules: l9(x99:0) -> l3(c, c1) :|: c1 = -1 + -1 * (1 + x99:0) && c = 0 && 0 < -1 * (1 + x99:0) l9(x7) -> l3(c4, c5) :|: c5 = -1 + -1 * (1 + x7) && c4 = 0 && 0 > -1 * (1 + x7) Interpretation: [ l9 ] = 0 [ l3 ] = -1 The following rules are decreasing: l9(x99:0) -> l3(c, c1) :|: c1 = -1 + -1 * (1 + x99:0) && c = 0 && 0 < -1 * (1 + x99:0) l9(x7) -> l3(c4, c5) :|: c5 = -1 + -1 * (1 + x7) && c4 = 0 && 0 > -1 * (1 + x7) The following rules are bounded: l9(x99:0) -> l3(c, c1) :|: c1 = -1 + -1 * (1 + x99:0) && c = 0 && 0 < -1 * (1 + x99:0) l9(x7) -> l3(c4, c5) :|: c5 = -1 + -1 * (1 + x7) && c4 = 0 && 0 > -1 * (1 + x7) - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS - PolynomialOrderProcessor Rules: l8(x88:0, x91:0) -> l9(x91:0) :|: x88:0 < 1 l8(x80:0, x83:0) -> l9(x83:0) :|: x80:0 > 1 l3(x, x3) -> l8(x, c3) :|: c3 = -1 * x3 && 0 < -1 * x3 l9(x7) -> l3(c4, c5) :|: c5 = -1 + -1 * (1 + x7) && c4 = 0 && 0 > -1 * (1 + x7) Found the following polynomial interpretation: [l8(x, x1)] = x^2 [l9(x2)] = 0 [l3(x3, x4)] = x3^2 The following rules are decreasing: l8(x80:0, x83:0) -> l9(x83:0) :|: x80:0 > 1 The following rules are bounded: l8(x88:0, x91:0) -> l9(x91:0) :|: x88:0 < 1 l8(x80:0, x83:0) -> l9(x83:0) :|: x80:0 > 1 l3(x, x3) -> l8(x, c3) :|: c3 = -1 * x3 && 0 < -1 * x3 l9(x7) -> l3(c4, c5) :|: c5 = -1 + -1 * (1 + x7) && c4 = 0 && 0 > -1 * (1 + x7) - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS - PolynomialOrderProcessor - IntTRS Rules: l8(x88:0, x91:0) -> l9(x91:0) :|: x88:0 < 1 l3(x, x3) -> l8(x, c3) :|: c3 = -1 * x3 && 0 < -1 * x3 l9(x7) -> l3(c4, c5) :|: c5 = -1 + -1 * (1 + x7) && c4 = 0 && 0 > -1 * (1 + x7) ---------------------------------------- (10) Obligation: Rules: l8(x88:0, x91:0) -> l9(x91:0) :|: x88:0 < 1 l3(x, x3) -> l8(x, -1 * x3) :|: 0 < -1 * x3 l9(x7) -> l3(0, -1 + -1 * (1 + x7)) :|: 0 > -1 * (1 + x7) ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l8(x88:0, x91:0) -> l9(x91:0) :|: x88:0 < 1 (2) l3(x, x3) -> l8(x, -1 * x3) :|: 0 < -1 * x3 (3) l9(x7) -> l3(0, -1 + -1 * (1 + x7)) :|: 0 > -1 * (1 + x7) Arcs: (1) -> (3) (2) -> (1) (3) -> (2) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) l8(x88:0, x91:0) -> l9(x91:0) :|: x88:0 < 1 (2) l3(x, x3) -> l8(x, -1 * x3) :|: 0 < -1 * x3 (3) l9(x7) -> l3(0, -1 + -1 * (1 + x7)) :|: 0 > -1 * (1 + x7) Arcs: (1) -> (3) (2) -> (1) (3) -> (2) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: l3(x:0, x3:0) -> l3(0, -1 + -1 * (1 + -1 * x3:0)) :|: x:0 < 1 && 0 > -1 * (1 + -1 * x3:0) && 0 < -1 * x3:0