YES proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be proven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof [EQUIVALENT, 5085 ms] (4) AND (5) IRSwT (6) IntTRSCompressionProof [EQUIVALENT, 4 ms] (7) IRSwT (8) TempFilterProof [SOUND, 30 ms] (9) IntTRS (10) RankingReductionPairProof [EQUIVALENT, 0 ms] (11) IntTRS (12) RankingReductionPairProof [EQUIVALENT, 0 ms] (13) YES (14) IRSwT (15) IntTRSCompressionProof [EQUIVALENT, 16 ms] (16) IRSwT (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (18) IRSwT (19) TempFilterProof [SOUND, 11 ms] (20) IntTRS (21) RankingReductionPairProof [EQUIVALENT, 0 ms] (22) YES (23) IRSwT (24) IntTRSCompressionProof [EQUIVALENT, 1 ms] (25) IRSwT (26) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (27) IRSwT (28) TempFilterProof [SOUND, 16 ms] (29) IntTRS (30) RankingReductionPairProof [EQUIVALENT, 0 ms] (31) YES (32) IRSwT (33) IntTRSCompressionProof [EQUIVALENT, 1 ms] (34) IRSwT (35) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (36) IRSwT (37) TempFilterProof [SOUND, 6 ms] (38) IntTRS (39) RankingReductionPairProof [EQUIVALENT, 0 ms] (40) YES (41) IRSwT (42) IntTRSCompressionProof [EQUIVALENT, 7 ms] (43) IRSwT (44) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (45) IRSwT (46) TempFilterProof [SOUND, 11 ms] (47) IntTRS (48) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (49) YES (50) IRSwT (51) IntTRSCompressionProof [EQUIVALENT, 2 ms] (52) IRSwT (53) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (54) IRSwT (55) TempFilterProof [SOUND, 9 ms] (56) IntTRS (57) RankingReductionPairProof [EQUIVALENT, 0 ms] (58) YES (59) IRSwT (60) IntTRSCompressionProof [EQUIVALENT, 1 ms] (61) IRSwT (62) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (63) IRSwT (64) TempFilterProof [SOUND, 14 ms] (65) IntTRS (66) RankingReductionPairProof [EQUIVALENT, 0 ms] (67) YES (68) IRSwT (69) IntTRSCompressionProof [EQUIVALENT, 1 ms] (70) IRSwT (71) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (72) IRSwT (73) TempFilterProof [SOUND, 7 ms] (74) IntTRS (75) RankingReductionPairProof [EQUIVALENT, 0 ms] (76) YES (77) IRSwT (78) IntTRSCompressionProof [EQUIVALENT, 0 ms] (79) IRSwT (80) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (81) IRSwT (82) TempFilterProof [SOUND, 6 ms] (83) IntTRS (84) RankingReductionPairProof [EQUIVALENT, 0 ms] (85) YES (86) IRSwT (87) IntTRSCompressionProof [EQUIVALENT, 0 ms] (88) IRSwT (89) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (90) IRSwT (91) TempFilterProof [SOUND, 9 ms] (92) IntTRS (93) RankingReductionPairProof [EQUIVALENT, 0 ms] (94) YES (95) IRSwT (96) IntTRSCompressionProof [EQUIVALENT, 0 ms] (97) IRSwT (98) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (99) IRSwT (100) TempFilterProof [SOUND, 7 ms] (101) IntTRS (102) RankingReductionPairProof [EQUIVALENT, 0 ms] (103) YES (104) IRSwT (105) IntTRSCompressionProof [EQUIVALENT, 0 ms] (106) IRSwT (107) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (108) IRSwT (109) TempFilterProof [SOUND, 11 ms] (110) IntTRS (111) RankingReductionPairProof [EQUIVALENT, 0 ms] (112) YES (113) IRSwT (114) IntTRSCompressionProof [EQUIVALENT, 0 ms] (115) IRSwT (116) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (117) IRSwT (118) TempFilterProof [SOUND, 8 ms] (119) IntTRS (120) RankingReductionPairProof [EQUIVALENT, 0 ms] (121) YES ---------------------------------------- (0) Obligation: Rules: f1_0_main_Load(arg1, arg2, arg3) -> f31_0_main_Cmp(arg1P, arg2P, arg3P) :|: arg2 = arg1P && -1 <= arg2 - 1 && 0 <= arg1 - 1 f31_0_main_Cmp(x, x1, x2) -> f43_0_main_GE(x3, x4, x5) :|: x = x5 && x = x4 && x = x3 f43_0_main_GE(x6, x7, x8) -> f31_0_main_Cmp(x9, x10, x11) :|: x6 - 1 = x9 && x7 = x8 && 99 <= x7 - 1 && 0 <= x6 - 1 f43_0_main_GE(x12, x13, x14) -> f43_0_main_GE(x15, x16, x17) :|: x13 + 1 = x17 && x13 + 1 = x16 && x12 = x15 && x13 = x14 && x13 <= 99 && 0 <= x13 - 1 f43_0_main_GE(x18, x19, x20) -> f64_0_test_LE(x21, x22, x23) :|: x19 = x23 && x19 = x22 && x19 = x21 && x19 = x20 && x19 <= 99 && 0 <= x19 - 1 f64_0_test_LE(x24, x25, x26) -> f64_0_test_LE(x27, x28, x29) :|: x25 - 1 = x29 && x25 - 1 = x28 && x24 = x27 && x25 = x26 && 0 <= x25 - 1 f64_0_test_LE(x30, x31, x32) -> f78_0_test_LE(x33, x34, x35) :|: x30 = x35 && x30 = x34 && x30 = x33 && 0 = x32 && 0 = x31 f78_0_test_LE(x36, x37, x38) -> f78_0_test_LE(x39, x40, x41) :|: x37 - 1 = x41 && x37 - 1 = x40 && x36 = x39 && x37 = x38 && 0 <= x37 - 1 f78_0_test_LE(x42, x43, x44) -> f92_0_test_LE(x45, x46, x47) :|: x42 = x47 && x42 = x46 && x42 = x45 && 0 = x44 && 0 = x43 f92_0_test_LE(x48, x49, x50) -> f92_0_test_LE(x51, x52, x53) :|: x49 - 1 = x53 && x49 - 1 = x52 && x48 = x51 && x49 = x50 && 0 <= x49 - 1 f92_0_test_LE(x54, x55, x56) -> f106_0_test_LE(x57, x58, x59) :|: x54 = x59 && x54 = x58 && x54 = x57 && 0 = x56 && 0 = x55 f106_0_test_LE(x60, x61, x62) -> f106_0_test_LE(x63, x64, x65) :|: x61 - 1 = x65 && x61 - 1 = x64 && x60 = x63 && x61 = x62 && 0 <= x61 - 1 f106_0_test_LE(x66, x67, x68) -> f120_0_test_LE(x69, x70, x71) :|: x66 = x71 && x66 = x70 && x66 = x69 && 0 = x68 && 0 = x67 f120_0_test_LE(x72, x73, x74) -> f120_0_test_LE(x75, x76, x77) :|: x73 - 1 = x77 && x73 - 1 = x76 && x72 = x75 && x73 = x74 && 0 <= x73 - 1 f120_0_test_LE(x78, x79, x80) -> f134_0_test_LE(x81, x82, x83) :|: x78 = x83 && x78 = x82 && x78 = x81 && 0 = x80 && 0 = x79 f134_0_test_LE(x84, x85, x86) -> f134_0_test_LE(x87, x88, x89) :|: x85 - 1 = x89 && x85 - 1 = x88 && x84 = x87 && x85 = x86 && 0 <= x85 - 1 f134_0_test_LE(x90, x91, x92) -> f148_0_test_LE(x93, x94, x95) :|: x90 = x95 && x90 = x94 && x90 = x93 && 0 = x92 && 0 = x91 f148_0_test_LE(x96, x97, x98) -> f148_0_test_LE(x99, x100, x101) :|: x97 - 1 = x101 && x97 - 1 = x100 && x96 = x99 && x97 = x98 && 0 <= x97 - 1 f148_0_test_LE(x102, x103, x104) -> f162_0_test_LE(x105, x106, x107) :|: x102 = x107 && x102 = x106 && x102 = x105 && 0 = x104 && 0 = x103 f162_0_test_LE(x108, x109, x110) -> f162_0_test_LE(x111, x112, x113) :|: x109 - 1 = x113 && x109 - 1 = x112 && x108 = x111 && x109 = x110 && 0 <= x109 - 1 f162_0_test_LE(x114, x115, x116) -> f176_0_test_LE(x117, x118, x119) :|: x114 = x119 && x114 = x118 && x114 = x117 && 0 = x116 && 0 = x115 f176_0_test_LE(x120, x121, x122) -> f176_0_test_LE(x123, x124, x125) :|: x121 - 1 = x125 && x121 - 1 = x124 && x120 = x123 && x121 = x122 && 0 <= x121 - 1 f176_0_test_LE(x126, x127, x128) -> f190_0_test_LE(x129, x130, x131) :|: x126 = x131 && x126 = x130 && x126 = x129 && 0 = x128 && 0 = x127 f190_0_test_LE(x132, x133, x134) -> f190_0_test_LE(x135, x136, x137) :|: x133 - 1 = x137 && x133 - 1 = x136 && x132 = x135 && x133 = x134 && 0 <= x133 - 1 f190_0_test_LE(x138, x139, x140) -> f204_0_test_LE(x141, x142, x143) :|: x138 = x143 && x138 = x142 && x138 = x141 && 0 = x140 && 0 = x139 f204_0_test_LE(x144, x145, x146) -> f204_0_test_LE(x147, x148, x149) :|: x145 - 1 = x149 && x145 - 1 = x148 && x144 = x147 && x145 = x146 && 0 <= x145 - 1 f204_0_test_LE(x150, x151, x152) -> f218_0_test_LE(x153, x154, x155) :|: x150 = x153 && 0 = x152 && 0 = x151 f218_0_test_LE(x156, x157, x158) -> f218_0_test_LE(x159, x160, x161) :|: x156 - 1 = x159 && 0 <= x156 - 1 __init(x162, x163, x164) -> f1_0_main_Load(x165, x166, x167) :|: 0 <= 0 Start term: __init(arg1, arg2, arg3) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: f1_0_main_Load(arg1, arg2, arg3) -> f31_0_main_Cmp(arg1P, arg2P, arg3P) :|: arg2 = arg1P && -1 <= arg2 - 1 && 0 <= arg1 - 1 f31_0_main_Cmp(x, x1, x2) -> f43_0_main_GE(x3, x4, x5) :|: x = x5 && x = x4 && x = x3 f43_0_main_GE(x6, x7, x8) -> f31_0_main_Cmp(x9, x10, x11) :|: x6 - 1 = x9 && x7 = x8 && 99 <= x7 - 1 && 0 <= x6 - 1 f43_0_main_GE(x12, x13, x14) -> f43_0_main_GE(x15, x16, x17) :|: x13 + 1 = x17 && x13 + 1 = x16 && x12 = x15 && x13 = x14 && x13 <= 99 && 0 <= x13 - 1 f43_0_main_GE(x18, x19, x20) -> f64_0_test_LE(x21, x22, x23) :|: x19 = x23 && x19 = x22 && x19 = x21 && x19 = x20 && x19 <= 99 && 0 <= x19 - 1 f64_0_test_LE(x24, x25, x26) -> f64_0_test_LE(x27, x28, x29) :|: x25 - 1 = x29 && x25 - 1 = x28 && x24 = x27 && x25 = x26 && 0 <= x25 - 1 f64_0_test_LE(x30, x31, x32) -> f78_0_test_LE(x33, x34, x35) :|: x30 = x35 && x30 = x34 && x30 = x33 && 0 = x32 && 0 = x31 f78_0_test_LE(x36, x37, x38) -> f78_0_test_LE(x39, x40, x41) :|: x37 - 1 = x41 && x37 - 1 = x40 && x36 = x39 && x37 = x38 && 0 <= x37 - 1 f78_0_test_LE(x42, x43, x44) -> f92_0_test_LE(x45, x46, x47) :|: x42 = x47 && x42 = x46 && x42 = x45 && 0 = x44 && 0 = x43 f92_0_test_LE(x48, x49, x50) -> f92_0_test_LE(x51, x52, x53) :|: x49 - 1 = x53 && x49 - 1 = x52 && x48 = x51 && x49 = x50 && 0 <= x49 - 1 f92_0_test_LE(x54, x55, x56) -> f106_0_test_LE(x57, x58, x59) :|: x54 = x59 && x54 = x58 && x54 = x57 && 0 = x56 && 0 = x55 f106_0_test_LE(x60, x61, x62) -> f106_0_test_LE(x63, x64, x65) :|: x61 - 1 = x65 && x61 - 1 = x64 && x60 = x63 && x61 = x62 && 0 <= x61 - 1 f106_0_test_LE(x66, x67, x68) -> f120_0_test_LE(x69, x70, x71) :|: x66 = x71 && x66 = x70 && x66 = x69 && 0 = x68 && 0 = x67 f120_0_test_LE(x72, x73, x74) -> f120_0_test_LE(x75, x76, x77) :|: x73 - 1 = x77 && x73 - 1 = x76 && x72 = x75 && x73 = x74 && 0 <= x73 - 1 f120_0_test_LE(x78, x79, x80) -> f134_0_test_LE(x81, x82, x83) :|: x78 = x83 && x78 = x82 && x78 = x81 && 0 = x80 && 0 = x79 f134_0_test_LE(x84, x85, x86) -> f134_0_test_LE(x87, x88, x89) :|: x85 - 1 = x89 && x85 - 1 = x88 && x84 = x87 && x85 = x86 && 0 <= x85 - 1 f134_0_test_LE(x90, x91, x92) -> f148_0_test_LE(x93, x94, x95) :|: x90 = x95 && x90 = x94 && x90 = x93 && 0 = x92 && 0 = x91 f148_0_test_LE(x96, x97, x98) -> f148_0_test_LE(x99, x100, x101) :|: x97 - 1 = x101 && x97 - 1 = x100 && x96 = x99 && x97 = x98 && 0 <= x97 - 1 f148_0_test_LE(x102, x103, x104) -> f162_0_test_LE(x105, x106, x107) :|: x102 = x107 && x102 = x106 && x102 = x105 && 0 = x104 && 0 = x103 f162_0_test_LE(x108, x109, x110) -> f162_0_test_LE(x111, x112, x113) :|: x109 - 1 = x113 && x109 - 1 = x112 && x108 = x111 && x109 = x110 && 0 <= x109 - 1 f162_0_test_LE(x114, x115, x116) -> f176_0_test_LE(x117, x118, x119) :|: x114 = x119 && x114 = x118 && x114 = x117 && 0 = x116 && 0 = x115 f176_0_test_LE(x120, x121, x122) -> f176_0_test_LE(x123, x124, x125) :|: x121 - 1 = x125 && x121 - 1 = x124 && x120 = x123 && x121 = x122 && 0 <= x121 - 1 f176_0_test_LE(x126, x127, x128) -> f190_0_test_LE(x129, x130, x131) :|: x126 = x131 && x126 = x130 && x126 = x129 && 0 = x128 && 0 = x127 f190_0_test_LE(x132, x133, x134) -> f190_0_test_LE(x135, x136, x137) :|: x133 - 1 = x137 && x133 - 1 = x136 && x132 = x135 && x133 = x134 && 0 <= x133 - 1 f190_0_test_LE(x138, x139, x140) -> f204_0_test_LE(x141, x142, x143) :|: x138 = x143 && x138 = x142 && x138 = x141 && 0 = x140 && 0 = x139 f204_0_test_LE(x144, x145, x146) -> f204_0_test_LE(x147, x148, x149) :|: x145 - 1 = x149 && x145 - 1 = x148 && x144 = x147 && x145 = x146 && 0 <= x145 - 1 f204_0_test_LE(x150, x151, x152) -> f218_0_test_LE(x153, x154, x155) :|: x150 = x153 && 0 = x152 && 0 = x151 f218_0_test_LE(x156, x157, x158) -> f218_0_test_LE(x159, x160, x161) :|: x156 - 1 = x159 && 0 <= x156 - 1 __init(x162, x163, x164) -> f1_0_main_Load(x165, x166, x167) :|: 0 <= 0 Start term: __init(arg1, arg2, arg3) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f1_0_main_Load(arg1, arg2, arg3) -> f31_0_main_Cmp(arg1P, arg2P, arg3P) :|: arg2 = arg1P && -1 <= arg2 - 1 && 0 <= arg1 - 1 (2) f31_0_main_Cmp(x, x1, x2) -> f43_0_main_GE(x3, x4, x5) :|: x = x5 && x = x4 && x = x3 (3) f43_0_main_GE(x6, x7, x8) -> f31_0_main_Cmp(x9, x10, x11) :|: x6 - 1 = x9 && x7 = x8 && 99 <= x7 - 1 && 0 <= x6 - 1 (4) f43_0_main_GE(x12, x13, x14) -> f43_0_main_GE(x15, x16, x17) :|: x13 + 1 = x17 && x13 + 1 = x16 && x12 = x15 && x13 = x14 && x13 <= 99 && 0 <= x13 - 1 (5) f43_0_main_GE(x18, x19, x20) -> f64_0_test_LE(x21, x22, x23) :|: x19 = x23 && x19 = x22 && x19 = x21 && x19 = x20 && x19 <= 99 && 0 <= x19 - 1 (6) f64_0_test_LE(x24, x25, x26) -> f64_0_test_LE(x27, x28, x29) :|: x25 - 1 = x29 && x25 - 1 = x28 && x24 = x27 && x25 = x26 && 0 <= x25 - 1 (7) f64_0_test_LE(x30, x31, x32) -> f78_0_test_LE(x33, x34, x35) :|: x30 = x35 && x30 = x34 && x30 = x33 && 0 = x32 && 0 = x31 (8) f78_0_test_LE(x36, x37, x38) -> f78_0_test_LE(x39, x40, x41) :|: x37 - 1 = x41 && x37 - 1 = x40 && x36 = x39 && x37 = x38 && 0 <= x37 - 1 (9) f78_0_test_LE(x42, x43, x44) -> f92_0_test_LE(x45, x46, x47) :|: x42 = x47 && x42 = x46 && x42 = x45 && 0 = x44 && 0 = x43 (10) f92_0_test_LE(x48, x49, x50) -> f92_0_test_LE(x51, x52, x53) :|: x49 - 1 = x53 && x49 - 1 = x52 && x48 = x51 && x49 = x50 && 0 <= x49 - 1 (11) f92_0_test_LE(x54, x55, x56) -> f106_0_test_LE(x57, x58, x59) :|: x54 = x59 && x54 = x58 && x54 = x57 && 0 = x56 && 0 = x55 (12) f106_0_test_LE(x60, x61, x62) -> f106_0_test_LE(x63, x64, x65) :|: x61 - 1 = x65 && x61 - 1 = x64 && x60 = x63 && x61 = x62 && 0 <= x61 - 1 (13) f106_0_test_LE(x66, x67, x68) -> f120_0_test_LE(x69, x70, x71) :|: x66 = x71 && x66 = x70 && x66 = x69 && 0 = x68 && 0 = x67 (14) f120_0_test_LE(x72, x73, x74) -> f120_0_test_LE(x75, x76, x77) :|: x73 - 1 = x77 && x73 - 1 = x76 && x72 = x75 && x73 = x74 && 0 <= x73 - 1 (15) f120_0_test_LE(x78, x79, x80) -> f134_0_test_LE(x81, x82, x83) :|: x78 = x83 && x78 = x82 && x78 = x81 && 0 = x80 && 0 = x79 (16) f134_0_test_LE(x84, x85, x86) -> f134_0_test_LE(x87, x88, x89) :|: x85 - 1 = x89 && x85 - 1 = x88 && x84 = x87 && x85 = x86 && 0 <= x85 - 1 (17) f134_0_test_LE(x90, x91, x92) -> f148_0_test_LE(x93, x94, x95) :|: x90 = x95 && x90 = x94 && x90 = x93 && 0 = x92 && 0 = x91 (18) f148_0_test_LE(x96, x97, x98) -> f148_0_test_LE(x99, x100, x101) :|: x97 - 1 = x101 && x97 - 1 = x100 && x96 = x99 && x97 = x98 && 0 <= x97 - 1 (19) f148_0_test_LE(x102, x103, x104) -> f162_0_test_LE(x105, x106, x107) :|: x102 = x107 && x102 = x106 && x102 = x105 && 0 = x104 && 0 = x103 (20) f162_0_test_LE(x108, x109, x110) -> f162_0_test_LE(x111, x112, x113) :|: x109 - 1 = x113 && x109 - 1 = x112 && x108 = x111 && x109 = x110 && 0 <= x109 - 1 (21) f162_0_test_LE(x114, x115, x116) -> f176_0_test_LE(x117, x118, x119) :|: x114 = x119 && x114 = x118 && x114 = x117 && 0 = x116 && 0 = x115 (22) f176_0_test_LE(x120, x121, x122) -> f176_0_test_LE(x123, x124, x125) :|: x121 - 1 = x125 && x121 - 1 = x124 && x120 = x123 && x121 = x122 && 0 <= x121 - 1 (23) f176_0_test_LE(x126, x127, x128) -> f190_0_test_LE(x129, x130, x131) :|: x126 = x131 && x126 = x130 && x126 = x129 && 0 = x128 && 0 = x127 (24) f190_0_test_LE(x132, x133, x134) -> f190_0_test_LE(x135, x136, x137) :|: x133 - 1 = x137 && x133 - 1 = x136 && x132 = x135 && x133 = x134 && 0 <= x133 - 1 (25) f190_0_test_LE(x138, x139, x140) -> f204_0_test_LE(x141, x142, x143) :|: x138 = x143 && x138 = x142 && x138 = x141 && 0 = x140 && 0 = x139 (26) f204_0_test_LE(x144, x145, x146) -> f204_0_test_LE(x147, x148, x149) :|: x145 - 1 = x149 && x145 - 1 = x148 && x144 = x147 && x145 = x146 && 0 <= x145 - 1 (27) f204_0_test_LE(x150, x151, x152) -> f218_0_test_LE(x153, x154, x155) :|: x150 = x153 && 0 = x152 && 0 = x151 (28) f218_0_test_LE(x156, x157, x158) -> f218_0_test_LE(x159, x160, x161) :|: x156 - 1 = x159 && 0 <= x156 - 1 (29) __init(x162, x163, x164) -> f1_0_main_Load(x165, x166, x167) :|: 0 <= 0 Arcs: (1) -> (2) (2) -> (3), (4), (5) (3) -> (2) (4) -> (3), (4), (5) (5) -> (6) (6) -> (6), (7) (7) -> (8), (9) (8) -> (8), (9) (9) -> (10), (11) (10) -> (10), (11) (11) -> (12), (13) (12) -> (12), (13) (13) -> (14), (15) (14) -> (14), (15) (15) -> (16), (17) (16) -> (16), (17) (17) -> (18), (19) (18) -> (18), (19) (19) -> (20), (21) (20) -> (20), (21) (21) -> (22), (23) (22) -> (22), (23) (23) -> (24), (25) (24) -> (24), (25) (25) -> (26), (27) (26) -> (26), (27) (27) -> (28) (28) -> (28) (29) -> (1) This digraph is fully evaluated! ---------------------------------------- (4) Complex Obligation (AND) ---------------------------------------- (5) Obligation: Termination digraph: Nodes: (1) f31_0_main_Cmp(x, x1, x2) -> f43_0_main_GE(x3, x4, x5) :|: x = x5 && x = x4 && x = x3 (2) f43_0_main_GE(x6, x7, x8) -> f31_0_main_Cmp(x9, x10, x11) :|: x6 - 1 = x9 && x7 = x8 && 99 <= x7 - 1 && 0 <= x6 - 1 (3) f43_0_main_GE(x12, x13, x14) -> f43_0_main_GE(x15, x16, x17) :|: x13 + 1 = x17 && x13 + 1 = x16 && x12 = x15 && x13 = x14 && x13 <= 99 && 0 <= x13 - 1 Arcs: (1) -> (2), (3) (2) -> (1) (3) -> (2), (3) This digraph is fully evaluated! ---------------------------------------- (6) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (7) Obligation: Rules: f43_0_main_GE(x12:0, x13:0, x13:0) -> f43_0_main_GE(x12:0, x13:0 + 1, x13:0 + 1) :|: x13:0 > 0 && x13:0 < 100 f43_0_main_GE(x6:0, x7:0, x7:0) -> f43_0_main_GE(x6:0 - 1, x6:0 - 1, x6:0 - 1) :|: x6:0 > 0 && x7:0 > 99 ---------------------------------------- (8) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f43_0_main_GE(VARIABLE, INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (9) Obligation: Rules: f43_0_main_GE(x12:0, x13:0, x13:0) -> f43_0_main_GE(x12:0, c, c1) :|: c1 = x13:0 + 1 && c = x13:0 + 1 && (x13:0 > 0 && x13:0 < 100) f43_0_main_GE(x6:0, x7:0, x7:0) -> f43_0_main_GE(c2, c3, c4) :|: c4 = x6:0 - 1 && (c3 = x6:0 - 1 && c2 = x6:0 - 1) && (x6:0 > 0 && x7:0 > 99) ---------------------------------------- (10) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f43_0_main_GE ] = 2*f43_0_main_GE_1 + 1 The following rules are decreasing: f43_0_main_GE(x6:0, x7:0, x7:0) -> f43_0_main_GE(c2, c3, c4) :|: c4 = x6:0 - 1 && (c3 = x6:0 - 1 && c2 = x6:0 - 1) && (x6:0 > 0 && x7:0 > 99) The following rules are bounded: f43_0_main_GE(x6:0, x7:0, x7:0) -> f43_0_main_GE(c2, c3, c4) :|: c4 = x6:0 - 1 && (c3 = x6:0 - 1 && c2 = x6:0 - 1) && (x6:0 > 0 && x7:0 > 99) ---------------------------------------- (11) Obligation: Rules: f43_0_main_GE(x12:0, x13:0, x13:0) -> f43_0_main_GE(x12:0, c, c1) :|: c1 = x13:0 + 1 && c = x13:0 + 1 && (x13:0 > 0 && x13:0 < 100) ---------------------------------------- (12) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f43_0_main_GE ] = -1*f43_0_main_GE_3 The following rules are decreasing: f43_0_main_GE(x12:0, x13:0, x13:0) -> f43_0_main_GE(x12:0, c, c1) :|: c1 = x13:0 + 1 && c = x13:0 + 1 && (x13:0 > 0 && x13:0 < 100) The following rules are bounded: f43_0_main_GE(x12:0, x13:0, x13:0) -> f43_0_main_GE(x12:0, c, c1) :|: c1 = x13:0 + 1 && c = x13:0 + 1 && (x13:0 > 0 && x13:0 < 100) ---------------------------------------- (13) YES ---------------------------------------- (14) Obligation: Termination digraph: Nodes: (1) f64_0_test_LE(x24, x25, x26) -> f64_0_test_LE(x27, x28, x29) :|: x25 - 1 = x29 && x25 - 1 = x28 && x24 = x27 && x25 = x26 && 0 <= x25 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (15) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (16) Obligation: Rules: f64_0_test_LE(x24:0, x25:0, x25:0) -> f64_0_test_LE(x24:0, x25:0 - 1, x25:0 - 1) :|: x25:0 > 0 ---------------------------------------- (17) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f64_0_test_LE(x1, x2, x3) -> f64_0_test_LE(x2, x3) ---------------------------------------- (18) Obligation: Rules: f64_0_test_LE(x25:0, x25:0) -> f64_0_test_LE(x25:0 - 1, x25:0 - 1) :|: x25:0 > 0 ---------------------------------------- (19) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f64_0_test_LE(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (20) Obligation: Rules: f64_0_test_LE(x25:0, x25:0) -> f64_0_test_LE(c, c1) :|: c1 = x25:0 - 1 && c = x25:0 - 1 && x25:0 > 0 ---------------------------------------- (21) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f64_0_test_LE ] = f64_0_test_LE_2 The following rules are decreasing: f64_0_test_LE(x25:0, x25:0) -> f64_0_test_LE(c, c1) :|: c1 = x25:0 - 1 && c = x25:0 - 1 && x25:0 > 0 The following rules are bounded: f64_0_test_LE(x25:0, x25:0) -> f64_0_test_LE(c, c1) :|: c1 = x25:0 - 1 && c = x25:0 - 1 && x25:0 > 0 ---------------------------------------- (22) YES ---------------------------------------- (23) Obligation: Termination digraph: Nodes: (1) f78_0_test_LE(x36, x37, x38) -> f78_0_test_LE(x39, x40, x41) :|: x37 - 1 = x41 && x37 - 1 = x40 && x36 = x39 && x37 = x38 && 0 <= x37 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (24) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (25) Obligation: Rules: f78_0_test_LE(x36:0, x37:0, x37:0) -> f78_0_test_LE(x36:0, x37:0 - 1, x37:0 - 1) :|: x37:0 > 0 ---------------------------------------- (26) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f78_0_test_LE(x1, x2, x3) -> f78_0_test_LE(x2, x3) ---------------------------------------- (27) Obligation: Rules: f78_0_test_LE(x37:0, x37:0) -> f78_0_test_LE(x37:0 - 1, x37:0 - 1) :|: x37:0 > 0 ---------------------------------------- (28) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f78_0_test_LE(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (29) Obligation: Rules: f78_0_test_LE(x37:0, x37:0) -> f78_0_test_LE(c, c1) :|: c1 = x37:0 - 1 && c = x37:0 - 1 && x37:0 > 0 ---------------------------------------- (30) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f78_0_test_LE ] = f78_0_test_LE_2 The following rules are decreasing: f78_0_test_LE(x37:0, x37:0) -> f78_0_test_LE(c, c1) :|: c1 = x37:0 - 1 && c = x37:0 - 1 && x37:0 > 0 The following rules are bounded: f78_0_test_LE(x37:0, x37:0) -> f78_0_test_LE(c, c1) :|: c1 = x37:0 - 1 && c = x37:0 - 1 && x37:0 > 0 ---------------------------------------- (31) YES ---------------------------------------- (32) Obligation: Termination digraph: Nodes: (1) f92_0_test_LE(x48, x49, x50) -> f92_0_test_LE(x51, x52, x53) :|: x49 - 1 = x53 && x49 - 1 = x52 && x48 = x51 && x49 = x50 && 0 <= x49 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (33) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (34) Obligation: Rules: f92_0_test_LE(x48:0, x49:0, x49:0) -> f92_0_test_LE(x48:0, x49:0 - 1, x49:0 - 1) :|: x49:0 > 0 ---------------------------------------- (35) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f92_0_test_LE(x1, x2, x3) -> f92_0_test_LE(x2, x3) ---------------------------------------- (36) Obligation: Rules: f92_0_test_LE(x49:0, x49:0) -> f92_0_test_LE(x49:0 - 1, x49:0 - 1) :|: x49:0 > 0 ---------------------------------------- (37) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f92_0_test_LE(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (38) Obligation: Rules: f92_0_test_LE(x49:0, x49:0) -> f92_0_test_LE(c, c1) :|: c1 = x49:0 - 1 && c = x49:0 - 1 && x49:0 > 0 ---------------------------------------- (39) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f92_0_test_LE ] = f92_0_test_LE_2 The following rules are decreasing: f92_0_test_LE(x49:0, x49:0) -> f92_0_test_LE(c, c1) :|: c1 = x49:0 - 1 && c = x49:0 - 1 && x49:0 > 0 The following rules are bounded: f92_0_test_LE(x49:0, x49:0) -> f92_0_test_LE(c, c1) :|: c1 = x49:0 - 1 && c = x49:0 - 1 && x49:0 > 0 ---------------------------------------- (40) YES ---------------------------------------- (41) Obligation: Termination digraph: Nodes: (1) f106_0_test_LE(x60, x61, x62) -> f106_0_test_LE(x63, x64, x65) :|: x61 - 1 = x65 && x61 - 1 = x64 && x60 = x63 && x61 = x62 && 0 <= x61 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (42) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (43) Obligation: Rules: f106_0_test_LE(x60:0, x61:0, x61:0) -> f106_0_test_LE(x60:0, x61:0 - 1, x61:0 - 1) :|: x61:0 > 0 ---------------------------------------- (44) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f106_0_test_LE(x1, x2, x3) -> f106_0_test_LE(x2, x3) ---------------------------------------- (45) Obligation: Rules: f106_0_test_LE(x61:0, x61:0) -> f106_0_test_LE(x61:0 - 1, x61:0 - 1) :|: x61:0 > 0 ---------------------------------------- (46) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f106_0_test_LE(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (47) Obligation: Rules: f106_0_test_LE(x61:0, x61:0) -> f106_0_test_LE(c, c1) :|: c1 = x61:0 - 1 && c = x61:0 - 1 && x61:0 > 0 ---------------------------------------- (48) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f106_0_test_LE(x, x1)] = x1 The following rules are decreasing: f106_0_test_LE(x61:0, x61:0) -> f106_0_test_LE(c, c1) :|: c1 = x61:0 - 1 && c = x61:0 - 1 && x61:0 > 0 The following rules are bounded: f106_0_test_LE(x61:0, x61:0) -> f106_0_test_LE(c, c1) :|: c1 = x61:0 - 1 && c = x61:0 - 1 && x61:0 > 0 ---------------------------------------- (49) YES ---------------------------------------- (50) Obligation: Termination digraph: Nodes: (1) f120_0_test_LE(x72, x73, x74) -> f120_0_test_LE(x75, x76, x77) :|: x73 - 1 = x77 && x73 - 1 = x76 && x72 = x75 && x73 = x74 && 0 <= x73 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (51) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (52) Obligation: Rules: f120_0_test_LE(x72:0, x73:0, x73:0) -> f120_0_test_LE(x72:0, x73:0 - 1, x73:0 - 1) :|: x73:0 > 0 ---------------------------------------- (53) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f120_0_test_LE(x1, x2, x3) -> f120_0_test_LE(x2, x3) ---------------------------------------- (54) Obligation: Rules: f120_0_test_LE(x73:0, x73:0) -> f120_0_test_LE(x73:0 - 1, x73:0 - 1) :|: x73:0 > 0 ---------------------------------------- (55) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f120_0_test_LE(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (56) Obligation: Rules: f120_0_test_LE(x73:0, x73:0) -> f120_0_test_LE(c, c1) :|: c1 = x73:0 - 1 && c = x73:0 - 1 && x73:0 > 0 ---------------------------------------- (57) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f120_0_test_LE ] = f120_0_test_LE_2 The following rules are decreasing: f120_0_test_LE(x73:0, x73:0) -> f120_0_test_LE(c, c1) :|: c1 = x73:0 - 1 && c = x73:0 - 1 && x73:0 > 0 The following rules are bounded: f120_0_test_LE(x73:0, x73:0) -> f120_0_test_LE(c, c1) :|: c1 = x73:0 - 1 && c = x73:0 - 1 && x73:0 > 0 ---------------------------------------- (58) YES ---------------------------------------- (59) Obligation: Termination digraph: Nodes: (1) f134_0_test_LE(x84, x85, x86) -> f134_0_test_LE(x87, x88, x89) :|: x85 - 1 = x89 && x85 - 1 = x88 && x84 = x87 && x85 = x86 && 0 <= x85 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (60) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (61) Obligation: Rules: f134_0_test_LE(x84:0, x85:0, x85:0) -> f134_0_test_LE(x84:0, x85:0 - 1, x85:0 - 1) :|: x85:0 > 0 ---------------------------------------- (62) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f134_0_test_LE(x1, x2, x3) -> f134_0_test_LE(x2, x3) ---------------------------------------- (63) Obligation: Rules: f134_0_test_LE(x85:0, x85:0) -> f134_0_test_LE(x85:0 - 1, x85:0 - 1) :|: x85:0 > 0 ---------------------------------------- (64) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f134_0_test_LE(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (65) Obligation: Rules: f134_0_test_LE(x85:0, x85:0) -> f134_0_test_LE(c, c1) :|: c1 = x85:0 - 1 && c = x85:0 - 1 && x85:0 > 0 ---------------------------------------- (66) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f134_0_test_LE ] = f134_0_test_LE_2 The following rules are decreasing: f134_0_test_LE(x85:0, x85:0) -> f134_0_test_LE(c, c1) :|: c1 = x85:0 - 1 && c = x85:0 - 1 && x85:0 > 0 The following rules are bounded: f134_0_test_LE(x85:0, x85:0) -> f134_0_test_LE(c, c1) :|: c1 = x85:0 - 1 && c = x85:0 - 1 && x85:0 > 0 ---------------------------------------- (67) YES ---------------------------------------- (68) Obligation: Termination digraph: Nodes: (1) f148_0_test_LE(x96, x97, x98) -> f148_0_test_LE(x99, x100, x101) :|: x97 - 1 = x101 && x97 - 1 = x100 && x96 = x99 && x97 = x98 && 0 <= x97 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (69) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (70) Obligation: Rules: f148_0_test_LE(x96:0, x97:0, x97:0) -> f148_0_test_LE(x96:0, x97:0 - 1, x97:0 - 1) :|: x97:0 > 0 ---------------------------------------- (71) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f148_0_test_LE(x1, x2, x3) -> f148_0_test_LE(x2, x3) ---------------------------------------- (72) Obligation: Rules: f148_0_test_LE(x97:0, x97:0) -> f148_0_test_LE(x97:0 - 1, x97:0 - 1) :|: x97:0 > 0 ---------------------------------------- (73) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f148_0_test_LE(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (74) Obligation: Rules: f148_0_test_LE(x97:0, x97:0) -> f148_0_test_LE(c, c1) :|: c1 = x97:0 - 1 && c = x97:0 - 1 && x97:0 > 0 ---------------------------------------- (75) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f148_0_test_LE ] = f148_0_test_LE_2 The following rules are decreasing: f148_0_test_LE(x97:0, x97:0) -> f148_0_test_LE(c, c1) :|: c1 = x97:0 - 1 && c = x97:0 - 1 && x97:0 > 0 The following rules are bounded: f148_0_test_LE(x97:0, x97:0) -> f148_0_test_LE(c, c1) :|: c1 = x97:0 - 1 && c = x97:0 - 1 && x97:0 > 0 ---------------------------------------- (76) YES ---------------------------------------- (77) Obligation: Termination digraph: Nodes: (1) f162_0_test_LE(x108, x109, x110) -> f162_0_test_LE(x111, x112, x113) :|: x109 - 1 = x113 && x109 - 1 = x112 && x108 = x111 && x109 = x110 && 0 <= x109 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (78) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (79) Obligation: Rules: f162_0_test_LE(x108:0, x109:0, x109:0) -> f162_0_test_LE(x108:0, x109:0 - 1, x109:0 - 1) :|: x109:0 > 0 ---------------------------------------- (80) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f162_0_test_LE(x1, x2, x3) -> f162_0_test_LE(x2, x3) ---------------------------------------- (81) Obligation: Rules: f162_0_test_LE(x109:0, x109:0) -> f162_0_test_LE(x109:0 - 1, x109:0 - 1) :|: x109:0 > 0 ---------------------------------------- (82) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f162_0_test_LE(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (83) Obligation: Rules: f162_0_test_LE(x109:0, x109:0) -> f162_0_test_LE(c, c1) :|: c1 = x109:0 - 1 && c = x109:0 - 1 && x109:0 > 0 ---------------------------------------- (84) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f162_0_test_LE ] = f162_0_test_LE_2 The following rules are decreasing: f162_0_test_LE(x109:0, x109:0) -> f162_0_test_LE(c, c1) :|: c1 = x109:0 - 1 && c = x109:0 - 1 && x109:0 > 0 The following rules are bounded: f162_0_test_LE(x109:0, x109:0) -> f162_0_test_LE(c, c1) :|: c1 = x109:0 - 1 && c = x109:0 - 1 && x109:0 > 0 ---------------------------------------- (85) YES ---------------------------------------- (86) Obligation: Termination digraph: Nodes: (1) f176_0_test_LE(x120, x121, x122) -> f176_0_test_LE(x123, x124, x125) :|: x121 - 1 = x125 && x121 - 1 = x124 && x120 = x123 && x121 = x122 && 0 <= x121 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (87) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (88) Obligation: Rules: f176_0_test_LE(x120:0, x121:0, x121:0) -> f176_0_test_LE(x120:0, x121:0 - 1, x121:0 - 1) :|: x121:0 > 0 ---------------------------------------- (89) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f176_0_test_LE(x1, x2, x3) -> f176_0_test_LE(x2, x3) ---------------------------------------- (90) Obligation: Rules: f176_0_test_LE(x121:0, x121:0) -> f176_0_test_LE(x121:0 - 1, x121:0 - 1) :|: x121:0 > 0 ---------------------------------------- (91) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f176_0_test_LE(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (92) Obligation: Rules: f176_0_test_LE(x121:0, x121:0) -> f176_0_test_LE(c, c1) :|: c1 = x121:0 - 1 && c = x121:0 - 1 && x121:0 > 0 ---------------------------------------- (93) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f176_0_test_LE ] = f176_0_test_LE_2 The following rules are decreasing: f176_0_test_LE(x121:0, x121:0) -> f176_0_test_LE(c, c1) :|: c1 = x121:0 - 1 && c = x121:0 - 1 && x121:0 > 0 The following rules are bounded: f176_0_test_LE(x121:0, x121:0) -> f176_0_test_LE(c, c1) :|: c1 = x121:0 - 1 && c = x121:0 - 1 && x121:0 > 0 ---------------------------------------- (94) YES ---------------------------------------- (95) Obligation: Termination digraph: Nodes: (1) f190_0_test_LE(x132, x133, x134) -> f190_0_test_LE(x135, x136, x137) :|: x133 - 1 = x137 && x133 - 1 = x136 && x132 = x135 && x133 = x134 && 0 <= x133 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (96) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (97) Obligation: Rules: f190_0_test_LE(x132:0, x133:0, x133:0) -> f190_0_test_LE(x132:0, x133:0 - 1, x133:0 - 1) :|: x133:0 > 0 ---------------------------------------- (98) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f190_0_test_LE(x1, x2, x3) -> f190_0_test_LE(x2, x3) ---------------------------------------- (99) Obligation: Rules: f190_0_test_LE(x133:0, x133:0) -> f190_0_test_LE(x133:0 - 1, x133:0 - 1) :|: x133:0 > 0 ---------------------------------------- (100) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f190_0_test_LE(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (101) Obligation: Rules: f190_0_test_LE(x133:0, x133:0) -> f190_0_test_LE(c, c1) :|: c1 = x133:0 - 1 && c = x133:0 - 1 && x133:0 > 0 ---------------------------------------- (102) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f190_0_test_LE ] = f190_0_test_LE_2 The following rules are decreasing: f190_0_test_LE(x133:0, x133:0) -> f190_0_test_LE(c, c1) :|: c1 = x133:0 - 1 && c = x133:0 - 1 && x133:0 > 0 The following rules are bounded: f190_0_test_LE(x133:0, x133:0) -> f190_0_test_LE(c, c1) :|: c1 = x133:0 - 1 && c = x133:0 - 1 && x133:0 > 0 ---------------------------------------- (103) YES ---------------------------------------- (104) Obligation: Termination digraph: Nodes: (1) f204_0_test_LE(x144, x145, x146) -> f204_0_test_LE(x147, x148, x149) :|: x145 - 1 = x149 && x145 - 1 = x148 && x144 = x147 && x145 = x146 && 0 <= x145 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (105) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (106) Obligation: Rules: f204_0_test_LE(x144:0, x145:0, x145:0) -> f204_0_test_LE(x144:0, x145:0 - 1, x145:0 - 1) :|: x145:0 > 0 ---------------------------------------- (107) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f204_0_test_LE(x1, x2, x3) -> f204_0_test_LE(x2, x3) ---------------------------------------- (108) Obligation: Rules: f204_0_test_LE(x145:0, x145:0) -> f204_0_test_LE(x145:0 - 1, x145:0 - 1) :|: x145:0 > 0 ---------------------------------------- (109) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f204_0_test_LE(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (110) Obligation: Rules: f204_0_test_LE(x145:0, x145:0) -> f204_0_test_LE(c, c1) :|: c1 = x145:0 - 1 && c = x145:0 - 1 && x145:0 > 0 ---------------------------------------- (111) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f204_0_test_LE ] = f204_0_test_LE_2 The following rules are decreasing: f204_0_test_LE(x145:0, x145:0) -> f204_0_test_LE(c, c1) :|: c1 = x145:0 - 1 && c = x145:0 - 1 && x145:0 > 0 The following rules are bounded: f204_0_test_LE(x145:0, x145:0) -> f204_0_test_LE(c, c1) :|: c1 = x145:0 - 1 && c = x145:0 - 1 && x145:0 > 0 ---------------------------------------- (112) YES ---------------------------------------- (113) Obligation: Termination digraph: Nodes: (1) f218_0_test_LE(x156, x157, x158) -> f218_0_test_LE(x159, x160, x161) :|: x156 - 1 = x159 && 0 <= x156 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (114) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (115) Obligation: Rules: f218_0_test_LE(x156:0, x157:0, x158:0) -> f218_0_test_LE(x156:0 - 1, x160:0, x161:0) :|: x156:0 > 0 ---------------------------------------- (116) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f218_0_test_LE(x1, x2, x3) -> f218_0_test_LE(x1) ---------------------------------------- (117) Obligation: Rules: f218_0_test_LE(x156:0) -> f218_0_test_LE(x156:0 - 1) :|: x156:0 > 0 ---------------------------------------- (118) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f218_0_test_LE(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (119) Obligation: Rules: f218_0_test_LE(x156:0) -> f218_0_test_LE(c) :|: c = x156:0 - 1 && x156:0 > 0 ---------------------------------------- (120) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f218_0_test_LE ] = f218_0_test_LE_1 The following rules are decreasing: f218_0_test_LE(x156:0) -> f218_0_test_LE(c) :|: c = x156:0 - 1 && x156:0 > 0 The following rules are bounded: f218_0_test_LE(x156:0) -> f218_0_test_LE(c) :|: c = x156:0 - 1 && x156:0 > 0 ---------------------------------------- (121) YES