MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 2391 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 17 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 8704 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 80 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT ---------------------------------------- (0) Obligation: Rules: f1_0_main_Load(arg1, arg2, arg3, arg4) -> f490_0_loop_GT(arg1P, arg2P, arg3P, arg4P) :|: arg2 = arg3P && 0 = arg2P && 20 = arg1P && -1 <= arg2 - 1 && 0 <= arg1 - 1 f490_0_loop_GT(x, x1, x2, x3) -> f564_0_loop_NE(x4, x5, x6, x7) :|: x - 2 = x7 && x2 + 1 = x6 && x1 = x5 && x = x4 && x1 <= -1 && -1 <= x - 1 && x2 <= x - 1 && 0 <= x2 - 1 f490_0_loop_GT(x8, x9, x10, x11) -> f564_0_loop_NE(x12, x13, x14, x15) :|: x8 - 2 = x15 && x10 + 1 = x14 && x9 = x13 && x8 = x12 && 0 <= x9 - 1 && -1 <= x8 - 1 && x10 <= x8 - 1 && 0 <= x10 - 1 f490_0_loop_GT(x16, x17, x18, x19) -> f565_0_loop_NE(x20, x21, x22, x23) :|: x16 - 2 = x22 && x18 - 1 = x21 && x16 = x20 && 0 = x17 && x18 <= x16 - 1 && 0 <= x18 - 1 && -1 <= x16 - 1 f490_0_loop_GT(x24, x25, x26, x27) -> f573_0_loop_NE(x28, x29, x30, x31) :|: x24 - 2 = x30 && x24 - 1 = x29 && x24 = x28 && x24 = x26 && 0 <= x24 - 1 f564_0_loop_NE(x32, x33, x34, x35) -> f490_0_loop_GT(x36, x37, x38, x39) :|: x34 = x38 && x33 = x37 && x32 = x36 && x34 <= x35 - 1 f564_0_loop_NE(x40, x41, x42, x43) -> f490_0_loop_GT(x44, x45, x46, x47) :|: x42 = x46 && x41 = x45 && x40 = x44 && x43 <= x42 - 1 f565_0_loop_NE(x48, x49, x50, x51) -> f490_0_loop_GT(x52, x53, x54, x55) :|: x49 = x54 && 0 = x53 && x48 = x52 && x49 <= x50 - 1 f565_0_loop_NE(x56, x57, x58, x59) -> f490_0_loop_GT(x60, x61, x62, x63) :|: x57 = x62 && 0 = x61 && x56 = x60 && x58 <= x57 - 1 f573_0_loop_NE(x64, x65, x66, x67) -> f490_0_loop_GT(x68, x69, x70, x71) :|: x65 = x70 && 0 = x69 && x64 = x68 && x65 <= x66 - 1 f573_0_loop_NE(x72, x73, x74, x75) -> f490_0_loop_GT(x76, x77, x78, x79) :|: x73 = x78 && 0 = x77 && x72 = x76 && x74 <= x73 - 1 f490_0_loop_GT(x80, x81, x82, x83) -> f490_0_loop_GT(x84, x85, x86, x87) :|: 1 = x86 && 1 = x85 && x80 = x84 && 0 = x82 && x80 <= 2 && 0 <= x80 - 1 f490_0_loop_GT(x88, x89, x90, x91) -> f490_0_loop_GT(x92, x93, x94, x95) :|: 1 = x94 && 1 = x93 && x88 = x92 && 0 = x90 && 3 <= x88 - 1 f564_0_loop_NE(x96, x97, x98, x99) -> f490_0_loop_GT(x100, x101, x102, x103) :|: x98 = x102 && x97 = x101 && x96 - 1 = x100 && x98 = x99 f490_0_loop_GT(x104, x105, x106, x107) -> f490_0_loop_GT(x108, x109, x110, x111) :|: -1 = x110 && 0 = x109 && 0 = x108 && 0 = x106 && 0 = x104 f565_0_loop_NE(x112, x113, x114, x115) -> f490_0_loop_GT(x116, x117, x118, x119) :|: x113 = x118 && 0 = x117 && x112 - 1 = x116 && x113 = x114 f573_0_loop_NE(x120, x121, x122, x123) -> f490_0_loop_GT(x124, x125, x126, x127) :|: x121 = x126 && 0 = x125 && x120 - 1 = x124 && x121 = x122 f490_0_loop_GT(x128, x129, x130, x131) -> f490_0_loop_GT(x132, x133, x134, x135) :|: 1 = x134 && 1 = x133 && 2 = x132 && 0 = x130 && 3 = x128 __init(x136, x137, x138, x139) -> f1_0_main_Load(x140, x141, x142, x143) :|: 0 <= 0 Start term: __init(arg1, arg2, arg3, arg4) ---------------------------------------- (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, arg4) -> f490_0_loop_GT(arg1P, arg2P, arg3P, arg4P) :|: arg2 = arg3P && 0 = arg2P && 20 = arg1P && -1 <= arg2 - 1 && 0 <= arg1 - 1 f490_0_loop_GT(x, x1, x2, x3) -> f564_0_loop_NE(x4, x5, x6, x7) :|: x - 2 = x7 && x2 + 1 = x6 && x1 = x5 && x = x4 && x1 <= -1 && -1 <= x - 1 && x2 <= x - 1 && 0 <= x2 - 1 f490_0_loop_GT(x8, x9, x10, x11) -> f564_0_loop_NE(x12, x13, x14, x15) :|: x8 - 2 = x15 && x10 + 1 = x14 && x9 = x13 && x8 = x12 && 0 <= x9 - 1 && -1 <= x8 - 1 && x10 <= x8 - 1 && 0 <= x10 - 1 f490_0_loop_GT(x16, x17, x18, x19) -> f565_0_loop_NE(x20, x21, x22, x23) :|: x16 - 2 = x22 && x18 - 1 = x21 && x16 = x20 && 0 = x17 && x18 <= x16 - 1 && 0 <= x18 - 1 && -1 <= x16 - 1 f490_0_loop_GT(x24, x25, x26, x27) -> f573_0_loop_NE(x28, x29, x30, x31) :|: x24 - 2 = x30 && x24 - 1 = x29 && x24 = x28 && x24 = x26 && 0 <= x24 - 1 f564_0_loop_NE(x32, x33, x34, x35) -> f490_0_loop_GT(x36, x37, x38, x39) :|: x34 = x38 && x33 = x37 && x32 = x36 && x34 <= x35 - 1 f564_0_loop_NE(x40, x41, x42, x43) -> f490_0_loop_GT(x44, x45, x46, x47) :|: x42 = x46 && x41 = x45 && x40 = x44 && x43 <= x42 - 1 f565_0_loop_NE(x48, x49, x50, x51) -> f490_0_loop_GT(x52, x53, x54, x55) :|: x49 = x54 && 0 = x53 && x48 = x52 && x49 <= x50 - 1 f565_0_loop_NE(x56, x57, x58, x59) -> f490_0_loop_GT(x60, x61, x62, x63) :|: x57 = x62 && 0 = x61 && x56 = x60 && x58 <= x57 - 1 f573_0_loop_NE(x64, x65, x66, x67) -> f490_0_loop_GT(x68, x69, x70, x71) :|: x65 = x70 && 0 = x69 && x64 = x68 && x65 <= x66 - 1 f573_0_loop_NE(x72, x73, x74, x75) -> f490_0_loop_GT(x76, x77, x78, x79) :|: x73 = x78 && 0 = x77 && x72 = x76 && x74 <= x73 - 1 f490_0_loop_GT(x80, x81, x82, x83) -> f490_0_loop_GT(x84, x85, x86, x87) :|: 1 = x86 && 1 = x85 && x80 = x84 && 0 = x82 && x80 <= 2 && 0 <= x80 - 1 f490_0_loop_GT(x88, x89, x90, x91) -> f490_0_loop_GT(x92, x93, x94, x95) :|: 1 = x94 && 1 = x93 && x88 = x92 && 0 = x90 && 3 <= x88 - 1 f564_0_loop_NE(x96, x97, x98, x99) -> f490_0_loop_GT(x100, x101, x102, x103) :|: x98 = x102 && x97 = x101 && x96 - 1 = x100 && x98 = x99 f490_0_loop_GT(x104, x105, x106, x107) -> f490_0_loop_GT(x108, x109, x110, x111) :|: -1 = x110 && 0 = x109 && 0 = x108 && 0 = x106 && 0 = x104 f565_0_loop_NE(x112, x113, x114, x115) -> f490_0_loop_GT(x116, x117, x118, x119) :|: x113 = x118 && 0 = x117 && x112 - 1 = x116 && x113 = x114 f573_0_loop_NE(x120, x121, x122, x123) -> f490_0_loop_GT(x124, x125, x126, x127) :|: x121 = x126 && 0 = x125 && x120 - 1 = x124 && x121 = x122 f490_0_loop_GT(x128, x129, x130, x131) -> f490_0_loop_GT(x132, x133, x134, x135) :|: 1 = x134 && 1 = x133 && 2 = x132 && 0 = x130 && 3 = x128 __init(x136, x137, x138, x139) -> f1_0_main_Load(x140, x141, x142, x143) :|: 0 <= 0 Start term: __init(arg1, arg2, arg3, arg4) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f1_0_main_Load(arg1, arg2, arg3, arg4) -> f490_0_loop_GT(arg1P, arg2P, arg3P, arg4P) :|: arg2 = arg3P && 0 = arg2P && 20 = arg1P && -1 <= arg2 - 1 && 0 <= arg1 - 1 (2) f490_0_loop_GT(x, x1, x2, x3) -> f564_0_loop_NE(x4, x5, x6, x7) :|: x - 2 = x7 && x2 + 1 = x6 && x1 = x5 && x = x4 && x1 <= -1 && -1 <= x - 1 && x2 <= x - 1 && 0 <= x2 - 1 (3) f490_0_loop_GT(x8, x9, x10, x11) -> f564_0_loop_NE(x12, x13, x14, x15) :|: x8 - 2 = x15 && x10 + 1 = x14 && x9 = x13 && x8 = x12 && 0 <= x9 - 1 && -1 <= x8 - 1 && x10 <= x8 - 1 && 0 <= x10 - 1 (4) f490_0_loop_GT(x16, x17, x18, x19) -> f565_0_loop_NE(x20, x21, x22, x23) :|: x16 - 2 = x22 && x18 - 1 = x21 && x16 = x20 && 0 = x17 && x18 <= x16 - 1 && 0 <= x18 - 1 && -1 <= x16 - 1 (5) f490_0_loop_GT(x24, x25, x26, x27) -> f573_0_loop_NE(x28, x29, x30, x31) :|: x24 - 2 = x30 && x24 - 1 = x29 && x24 = x28 && x24 = x26 && 0 <= x24 - 1 (6) f564_0_loop_NE(x32, x33, x34, x35) -> f490_0_loop_GT(x36, x37, x38, x39) :|: x34 = x38 && x33 = x37 && x32 = x36 && x34 <= x35 - 1 (7) f564_0_loop_NE(x40, x41, x42, x43) -> f490_0_loop_GT(x44, x45, x46, x47) :|: x42 = x46 && x41 = x45 && x40 = x44 && x43 <= x42 - 1 (8) f565_0_loop_NE(x48, x49, x50, x51) -> f490_0_loop_GT(x52, x53, x54, x55) :|: x49 = x54 && 0 = x53 && x48 = x52 && x49 <= x50 - 1 (9) f565_0_loop_NE(x56, x57, x58, x59) -> f490_0_loop_GT(x60, x61, x62, x63) :|: x57 = x62 && 0 = x61 && x56 = x60 && x58 <= x57 - 1 (10) f573_0_loop_NE(x64, x65, x66, x67) -> f490_0_loop_GT(x68, x69, x70, x71) :|: x65 = x70 && 0 = x69 && x64 = x68 && x65 <= x66 - 1 (11) f573_0_loop_NE(x72, x73, x74, x75) -> f490_0_loop_GT(x76, x77, x78, x79) :|: x73 = x78 && 0 = x77 && x72 = x76 && x74 <= x73 - 1 (12) f490_0_loop_GT(x80, x81, x82, x83) -> f490_0_loop_GT(x84, x85, x86, x87) :|: 1 = x86 && 1 = x85 && x80 = x84 && 0 = x82 && x80 <= 2 && 0 <= x80 - 1 (13) f490_0_loop_GT(x88, x89, x90, x91) -> f490_0_loop_GT(x92, x93, x94, x95) :|: 1 = x94 && 1 = x93 && x88 = x92 && 0 = x90 && 3 <= x88 - 1 (14) f564_0_loop_NE(x96, x97, x98, x99) -> f490_0_loop_GT(x100, x101, x102, x103) :|: x98 = x102 && x97 = x101 && x96 - 1 = x100 && x98 = x99 (15) f490_0_loop_GT(x104, x105, x106, x107) -> f490_0_loop_GT(x108, x109, x110, x111) :|: -1 = x110 && 0 = x109 && 0 = x108 && 0 = x106 && 0 = x104 (16) f565_0_loop_NE(x112, x113, x114, x115) -> f490_0_loop_GT(x116, x117, x118, x119) :|: x113 = x118 && 0 = x117 && x112 - 1 = x116 && x113 = x114 (17) f573_0_loop_NE(x120, x121, x122, x123) -> f490_0_loop_GT(x124, x125, x126, x127) :|: x121 = x126 && 0 = x125 && x120 - 1 = x124 && x121 = x122 (18) f490_0_loop_GT(x128, x129, x130, x131) -> f490_0_loop_GT(x132, x133, x134, x135) :|: 1 = x134 && 1 = x133 && 2 = x132 && 0 = x130 && 3 = x128 (19) __init(x136, x137, x138, x139) -> f1_0_main_Load(x140, x141, x142, x143) :|: 0 <= 0 Arcs: (1) -> (4), (5), (13) (2) -> (6), (7), (14) (3) -> (6), (7), (14) (4) -> (8), (16) (5) -> (11) (6) -> (2), (3), (4), (5), (12), (13), (15), (18) (7) -> (2), (3), (4), (5), (12), (13), (15), (18) (8) -> (4), (5), (12), (13), (15), (18) (9) -> (4), (5), (12), (13), (15), (18) (10) -> (4), (5), (12), (13), (15), (18) (11) -> (4), (5), (12), (13), (15), (18) (12) -> (3), (5) (13) -> (3) (14) -> (2), (3), (4), (5), (12), (13), (15), (18) (16) -> (4), (5), (12), (13), (15), (18) (17) -> (4), (5), (12), (13), (15), (18) (18) -> (3) (19) -> (1) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) f490_0_loop_GT(x16, x17, x18, x19) -> f565_0_loop_NE(x20, x21, x22, x23) :|: x16 - 2 = x22 && x18 - 1 = x21 && x16 = x20 && 0 = x17 && x18 <= x16 - 1 && 0 <= x18 - 1 && -1 <= x16 - 1 (2) f564_0_loop_NE(x32, x33, x34, x35) -> f490_0_loop_GT(x36, x37, x38, x39) :|: x34 = x38 && x33 = x37 && x32 = x36 && x34 <= x35 - 1 (3) f490_0_loop_GT(x, x1, x2, x3) -> f564_0_loop_NE(x4, x5, x6, x7) :|: x - 2 = x7 && x2 + 1 = x6 && x1 = x5 && x = x4 && x1 <= -1 && -1 <= x - 1 && x2 <= x - 1 && 0 <= x2 - 1 (4) f564_0_loop_NE(x40, x41, x42, x43) -> f490_0_loop_GT(x44, x45, x46, x47) :|: x42 = x46 && x41 = x45 && x40 = x44 && x43 <= x42 - 1 (5) f490_0_loop_GT(x8, x9, x10, x11) -> f564_0_loop_NE(x12, x13, x14, x15) :|: x8 - 2 = x15 && x10 + 1 = x14 && x9 = x13 && x8 = x12 && 0 <= x9 - 1 && -1 <= x8 - 1 && x10 <= x8 - 1 && 0 <= x10 - 1 (6) f490_0_loop_GT(x128, x129, x130, x131) -> f490_0_loop_GT(x132, x133, x134, x135) :|: 1 = x134 && 1 = x133 && 2 = x132 && 0 = x130 && 3 = x128 (7) f490_0_loop_GT(x88, x89, x90, x91) -> f490_0_loop_GT(x92, x93, x94, x95) :|: 1 = x94 && 1 = x93 && x88 = x92 && 0 = x90 && 3 <= x88 - 1 (8) f490_0_loop_GT(x80, x81, x82, x83) -> f490_0_loop_GT(x84, x85, x86, x87) :|: 1 = x86 && 1 = x85 && x80 = x84 && 0 = x82 && x80 <= 2 && 0 <= x80 - 1 (9) f573_0_loop_NE(x72, x73, x74, x75) -> f490_0_loop_GT(x76, x77, x78, x79) :|: x73 = x78 && 0 = x77 && x72 = x76 && x74 <= x73 - 1 (10) f490_0_loop_GT(x24, x25, x26, x27) -> f573_0_loop_NE(x28, x29, x30, x31) :|: x24 - 2 = x30 && x24 - 1 = x29 && x24 = x28 && x24 = x26 && 0 <= x24 - 1 (11) f565_0_loop_NE(x112, x113, x114, x115) -> f490_0_loop_GT(x116, x117, x118, x119) :|: x113 = x118 && 0 = x117 && x112 - 1 = x116 && x113 = x114 (12) f564_0_loop_NE(x96, x97, x98, x99) -> f490_0_loop_GT(x100, x101, x102, x103) :|: x98 = x102 && x97 = x101 && x96 - 1 = x100 && x98 = x99 (13) f565_0_loop_NE(x48, x49, x50, x51) -> f490_0_loop_GT(x52, x53, x54, x55) :|: x49 = x54 && 0 = x53 && x48 = x52 && x49 <= x50 - 1 Arcs: (1) -> (11), (13) (2) -> (1), (3), (5), (6), (7), (8), (10) (3) -> (2), (4), (12) (4) -> (1), (3), (5), (6), (7), (8), (10) (5) -> (2), (4), (12) (6) -> (5) (7) -> (5) (8) -> (5), (10) (9) -> (1), (6), (7), (8), (10) (10) -> (9) (11) -> (1), (6), (7), (8), (10) (12) -> (1), (3), (5), (6), (7), (8), (10) (13) -> (1), (6), (7), (8), (10) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: f564_0_loop_NE(x40:0, x41:0, x42:0, x43:0) -> f490_0_loop_GT(x40:0, x41:0, x42:0, x47:0) :|: x43:0 <= x42:0 - 1 f490_0_loop_GT(x12:0, x13:0, x10:0, x11:0) -> f564_0_loop_NE(x12:0, x13:0, x10:0 + 1, x12:0 - 2) :|: x12:0 - 1 >= x10:0 && x10:0 > 0 && x13:0 > 0 && x12:0 > -1 f490_0_loop_GT(x16:0, cons_0, x18:0, x19:0) -> f490_0_loop_GT(x16:0 - 1, 0, x16:0 - 2, x119:0) :|: x18:0 > 0 && x16:0 > -1 && x18:0 - 1 = x16:0 - 2 && x18:0 <= x16:0 - 1 && cons_0 = 0 f490_0_loop_GT(x24:0, x25:0, x24:0, x27:0) -> f490_0_loop_GT(x24:0, 0, x24:0 - 1, x79:0) :|: x24:0 > 0 f490_0_loop_GT(x, x1, x2, x3) -> f490_0_loop_GT(2, 1, 1, x4) :|: TRUE && x = 3 && x2 = 0 f490_0_loop_GT(x5, x6, x7, x8) -> f490_0_loop_GT(x5, 1, 1, x9) :|: x5 > 3 && x7 = 0 f564_0_loop_NE(x96:0, x101:0, x102:0, x102:0) -> f490_0_loop_GT(x96:0 - 1, x101:0, x102:0, x103:0) :|: TRUE f490_0_loop_GT(x10, x11, x12, x13) -> f490_0_loop_GT(x10, 1, 1, x14) :|: x10 > 0 && x10 < 3 && x12 = 0 f490_0_loop_GT(x15, x16, x17, x18) -> f490_0_loop_GT(x15, 0, x17 - 1, x19) :|: x17 - 1 <= x15 - 3 && x15 > -1 && x17 <= x15 - 1 && x17 > 0 && x16 = 0 f564_0_loop_NE(x32:0, x33:0, x34:0, x35:0) -> f490_0_loop_GT(x32:0, x33:0, x34:0, x39:0) :|: x35:0 - 1 >= x34:0 f490_0_loop_GT(x4:0, x1:0, x2:0, x3:0) -> f564_0_loop_NE(x4:0, x1:0, x2:0 + 1, x4:0 - 2) :|: x4:0 - 1 >= x2:0 && x2:0 > 0 && x1:0 < 0 && x4:0 > -1 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f490_0_loop_GT(x1, x2, x3, x4) -> f490_0_loop_GT(x1, x2, x3) ---------------------------------------- (8) Obligation: Rules: f564_0_loop_NE(x40:0, x41:0, x42:0, x43:0) -> f490_0_loop_GT(x40:0, x41:0, x42:0) :|: x43:0 <= x42:0 - 1 f490_0_loop_GT(x12:0, x13:0, x10:0) -> f564_0_loop_NE(x12:0, x13:0, x10:0 + 1, x12:0 - 2) :|: x12:0 - 1 >= x10:0 && x10:0 > 0 && x13:0 > 0 && x12:0 > -1 f490_0_loop_GT(x16:0, cons_0, x18:0) -> f490_0_loop_GT(x16:0 - 1, 0, x16:0 - 2) :|: x18:0 > 0 && x16:0 > -1 && x18:0 - 1 = x16:0 - 2 && x18:0 <= x16:0 - 1 && cons_0 = 0 f490_0_loop_GT(x24:0, x25:0, x24:0) -> f490_0_loop_GT(x24:0, 0, x24:0 - 1) :|: x24:0 > 0 f490_0_loop_GT(x, x1, x2) -> f490_0_loop_GT(2, 1, 1) :|: TRUE && x = 3 && x2 = 0 f490_0_loop_GT(x5, x6, x7) -> f490_0_loop_GT(x5, 1, 1) :|: x5 > 3 && x7 = 0 f564_0_loop_NE(x96:0, x101:0, x102:0, x102:0) -> f490_0_loop_GT(x96:0 - 1, x101:0, x102:0) :|: TRUE f490_0_loop_GT(x10, x11, x12) -> f490_0_loop_GT(x10, 1, 1) :|: x10 > 0 && x10 < 3 && x12 = 0 f490_0_loop_GT(x15, x16, x17) -> f490_0_loop_GT(x15, 0, x17 - 1) :|: x17 - 1 <= x15 - 3 && x15 > -1 && x17 <= x15 - 1 && x17 > 0 && x16 = 0 f564_0_loop_NE(x32:0, x33:0, x34:0, x35:0) -> f490_0_loop_GT(x32:0, x33:0, x34:0) :|: x35:0 - 1 >= x34:0 f490_0_loop_GT(x4:0, x1:0, x2:0) -> f564_0_loop_NE(x4:0, x1:0, x2:0 + 1, x4:0 - 2) :|: x4:0 - 1 >= x2:0 && x2:0 > 0 && x1:0 < 0 && x4:0 > -1 ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f564_0_loop_NE(VARIABLE, VARIABLE, VARIABLE, VARIABLE) f490_0_loop_GT(VARIABLE, 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: f564_0_loop_NE(x40:0, x41:0, x42:0, x43:0) -> f490_0_loop_GT(x40:0, x41:0, x42:0) :|: x43:0 <= x42:0 - 1 f490_0_loop_GT(x12:0, x13:0, x10:0) -> f564_0_loop_NE(x12:0, x13:0, c, c1) :|: c1 = x12:0 - 2 && c = x10:0 + 1 && (x12:0 - 1 >= x10:0 && x10:0 > 0 && x13:0 > 0 && x12:0 > -1) f490_0_loop_GT(x16:0, c2, x18:0) -> f490_0_loop_GT(c3, c4, c5) :|: c5 = x16:0 - 2 && (c4 = 0 && (c3 = x16:0 - 1 && c2 = 0)) && (x18:0 > 0 && x16:0 > -1 && x18:0 - 1 = x16:0 - 2 && x18:0 <= x16:0 - 1 && cons_0 = 0) f490_0_loop_GT(x24:0, x25:0, x24:0) -> f490_0_loop_GT(x24:0, c6, c7) :|: c7 = x24:0 - 1 && c6 = 0 && x24:0 > 0 f490_0_loop_GT(c8, x1, c9) -> f490_0_loop_GT(c10, c11, c12) :|: c12 = 1 && (c11 = 1 && (c10 = 2 && (c9 = 0 && c8 = 3))) && (TRUE && x = 3 && x2 = 0) f490_0_loop_GT(x5, x6, c13) -> f490_0_loop_GT(x5, c14, c15) :|: c15 = 1 && (c14 = 1 && c13 = 0) && (x5 > 3 && x7 = 0) f564_0_loop_NE(x96:0, x101:0, x102:0, x102:0) -> f490_0_loop_GT(c16, x101:0, x102:0) :|: c16 = x96:0 - 1 && TRUE f490_0_loop_GT(x10, x11, c17) -> f490_0_loop_GT(x10, c18, c19) :|: c19 = 1 && (c18 = 1 && c17 = 0) && (x10 > 0 && x10 < 3 && x12 = 0) f490_0_loop_GT(x15, c20, x17) -> f490_0_loop_GT(x15, c21, c22) :|: c22 = x17 - 1 && (c21 = 0 && c20 = 0) && (x17 - 1 <= x15 - 3 && x15 > -1 && x17 <= x15 - 1 && x17 > 0 && x16 = 0) f564_0_loop_NE(x32:0, x33:0, x34:0, x35:0) -> f490_0_loop_GT(x32:0, x33:0, x34:0) :|: x35:0 - 1 >= x34:0 f490_0_loop_GT(x4:0, x1:0, x2:0) -> f564_0_loop_NE(x4:0, x1:0, c23, c24) :|: c24 = x4:0 - 2 && c23 = x2:0 + 1 && (x4:0 - 1 >= x2:0 && x2:0 > 0 && x1:0 < 0 && x4:0 > -1) Found the following polynomial interpretation: [f564_0_loop_NE(x, x1, x2, x3)] = -4 + x [f490_0_loop_GT(x4, x5, x6)] = -4 + x4 The following rules are decreasing: f490_0_loop_GT(x16:0, c2, x18:0) -> f490_0_loop_GT(c3, c4, c5) :|: c5 = x16:0 - 2 && (c4 = 0 && (c3 = x16:0 - 1 && c2 = 0)) && (x18:0 > 0 && x16:0 > -1 && x18:0 - 1 = x16:0 - 2 && x18:0 <= x16:0 - 1 && cons_0 = 0) f490_0_loop_GT(c8, x1, c9) -> f490_0_loop_GT(c10, c11, c12) :|: c12 = 1 && (c11 = 1 && (c10 = 2 && (c9 = 0 && c8 = 3))) && (TRUE && x = 3 && x2 = 0) f564_0_loop_NE(x96:0, x101:0, x102:0, x102:0) -> f490_0_loop_GT(c16, x101:0, x102:0) :|: c16 = x96:0 - 1 && TRUE The following rules are bounded: f490_0_loop_GT(x5, x6, c13) -> f490_0_loop_GT(x5, c14, c15) :|: c15 = 1 && (c14 = 1 && c13 = 0) && (x5 > 3 && x7 = 0) - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS Rules: f564_0_loop_NE(x40:0, x41:0, x42:0, x43:0) -> f490_0_loop_GT(x40:0, x41:0, x42:0) :|: x43:0 <= x42:0 - 1 f490_0_loop_GT(x12:0, x13:0, x10:0) -> f564_0_loop_NE(x12:0, x13:0, c, c1) :|: c1 = x12:0 - 2 && c = x10:0 + 1 && (x12:0 - 1 >= x10:0 && x10:0 > 0 && x13:0 > 0 && x12:0 > -1) f490_0_loop_GT(x24:0, x25:0, x24:0) -> f490_0_loop_GT(x24:0, c6, c7) :|: c7 = x24:0 - 1 && c6 = 0 && x24:0 > 0 f490_0_loop_GT(x5, x6, c13) -> f490_0_loop_GT(x5, c14, c15) :|: c15 = 1 && (c14 = 1 && c13 = 0) && (x5 > 3 && x7 = 0) f490_0_loop_GT(x10, x11, c17) -> f490_0_loop_GT(x10, c18, c19) :|: c19 = 1 && (c18 = 1 && c17 = 0) && (x10 > 0 && x10 < 3 && x12 = 0) f490_0_loop_GT(x15, c20, x17) -> f490_0_loop_GT(x15, c21, c22) :|: c22 = x17 - 1 && (c21 = 0 && c20 = 0) && (x17 - 1 <= x15 - 3 && x15 > -1 && x17 <= x15 - 1 && x17 > 0 && x16 = 0) f564_0_loop_NE(x32:0, x33:0, x34:0, x35:0) -> f490_0_loop_GT(x32:0, x33:0, x34:0) :|: x35:0 - 1 >= x34:0 f490_0_loop_GT(x4:0, x1:0, x2:0) -> f564_0_loop_NE(x4:0, x1:0, c23, c24) :|: c24 = x4:0 - 2 && c23 = x2:0 + 1 && (x4:0 - 1 >= x2:0 && x2:0 > 0 && x1:0 < 0 && x4:0 > -1) - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS - PolynomialOrderProcessor Rules: f564_0_loop_NE(x40:0, x41:0, x42:0, x43:0) -> f490_0_loop_GT(x40:0, x41:0, x42:0) :|: x43:0 <= x42:0 - 1 f490_0_loop_GT(x12:0, x13:0, x10:0) -> f564_0_loop_NE(x12:0, x13:0, c, c1) :|: c1 = x12:0 - 2 && c = x10:0 + 1 && (x12:0 - 1 >= x10:0 && x10:0 > 0 && x13:0 > 0 && x12:0 > -1) f490_0_loop_GT(x16:0, c2, x18:0) -> f490_0_loop_GT(c3, c4, c5) :|: c5 = x16:0 - 2 && (c4 = 0 && (c3 = x16:0 - 1 && c2 = 0)) && (x18:0 > 0 && x16:0 > -1 && x18:0 - 1 = x16:0 - 2 && x18:0 <= x16:0 - 1 && cons_0 = 0) f490_0_loop_GT(x24:0, x25:0, x24:0) -> f490_0_loop_GT(x24:0, c6, c7) :|: c7 = x24:0 - 1 && c6 = 0 && x24:0 > 0 f490_0_loop_GT(c8, x1, c9) -> f490_0_loop_GT(c10, c11, c12) :|: c12 = 1 && (c11 = 1 && (c10 = 2 && (c9 = 0 && c8 = 3))) && (TRUE && x = 3 && x2 = 0) f564_0_loop_NE(x96:0, x101:0, x102:0, x102:0) -> f490_0_loop_GT(c16, x101:0, x102:0) :|: c16 = x96:0 - 1 && TRUE f490_0_loop_GT(x10, x11, c17) -> f490_0_loop_GT(x10, c18, c19) :|: c19 = 1 && (c18 = 1 && c17 = 0) && (x10 > 0 && x10 < 3 && x12 = 0) f490_0_loop_GT(x15, c20, x17) -> f490_0_loop_GT(x15, c21, c22) :|: c22 = x17 - 1 && (c21 = 0 && c20 = 0) && (x17 - 1 <= x15 - 3 && x15 > -1 && x17 <= x15 - 1 && x17 > 0 && x16 = 0) f564_0_loop_NE(x32:0, x33:0, x34:0, x35:0) -> f490_0_loop_GT(x32:0, x33:0, x34:0) :|: x35:0 - 1 >= x34:0 f490_0_loop_GT(x4:0, x1:0, x2:0) -> f564_0_loop_NE(x4:0, x1:0, c23, c24) :|: c24 = x4:0 - 2 && c23 = x2:0 + 1 && (x4:0 - 1 >= x2:0 && x2:0 > 0 && x1:0 < 0 && x4:0 > -1) Found the following polynomial interpretation: [f564_0_loop_NE(x, x1, x2, x3)] = -3 + x [f490_0_loop_GT(x4, x5, x6)] = -3 + x4 The following rules are decreasing: f490_0_loop_GT(x16:0, c2, x18:0) -> f490_0_loop_GT(c3, c4, c5) :|: c5 = x16:0 - 2 && (c4 = 0 && (c3 = x16:0 - 1 && c2 = 0)) && (x18:0 > 0 && x16:0 > -1 && x18:0 - 1 = x16:0 - 2 && x18:0 <= x16:0 - 1 && cons_0 = 0) f490_0_loop_GT(c8, x1, c9) -> f490_0_loop_GT(c10, c11, c12) :|: c12 = 1 && (c11 = 1 && (c10 = 2 && (c9 = 0 && c8 = 3))) && (TRUE && x = 3 && x2 = 0) f564_0_loop_NE(x96:0, x101:0, x102:0, x102:0) -> f490_0_loop_GT(c16, x101:0, x102:0) :|: c16 = x96:0 - 1 && TRUE The following rules are bounded: f490_0_loop_GT(c8, x1, c9) -> f490_0_loop_GT(c10, c11, c12) :|: c12 = 1 && (c11 = 1 && (c10 = 2 && (c9 = 0 && c8 = 3))) && (TRUE && x = 3 && x2 = 0) f490_0_loop_GT(x15, c20, x17) -> f490_0_loop_GT(x15, c21, c22) :|: c22 = x17 - 1 && (c21 = 0 && c20 = 0) && (x17 - 1 <= x15 - 3 && x15 > -1 && x17 <= x15 - 1 && x17 > 0 && x16 = 0) - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS Rules: f564_0_loop_NE(x40:0, x41:0, x42:0, x43:0) -> f490_0_loop_GT(x40:0, x41:0, x42:0) :|: x43:0 <= x42:0 - 1 f490_0_loop_GT(x12:0, x13:0, x10:0) -> f564_0_loop_NE(x12:0, x13:0, c, c1) :|: c1 = x12:0 - 2 && c = x10:0 + 1 && (x12:0 - 1 >= x10:0 && x10:0 > 0 && x13:0 > 0 && x12:0 > -1) f490_0_loop_GT(x24:0, x25:0, x24:0) -> f490_0_loop_GT(x24:0, c6, c7) :|: c7 = x24:0 - 1 && c6 = 0 && x24:0 > 0 f490_0_loop_GT(x10, x11, c17) -> f490_0_loop_GT(x10, c18, c19) :|: c19 = 1 && (c18 = 1 && c17 = 0) && (x10 > 0 && x10 < 3 && x12 = 0) f490_0_loop_GT(x15, c20, x17) -> f490_0_loop_GT(x15, c21, c22) :|: c22 = x17 - 1 && (c21 = 0 && c20 = 0) && (x17 - 1 <= x15 - 3 && x15 > -1 && x17 <= x15 - 1 && x17 > 0 && x16 = 0) f564_0_loop_NE(x32:0, x33:0, x34:0, x35:0) -> f490_0_loop_GT(x32:0, x33:0, x34:0) :|: x35:0 - 1 >= x34:0 f490_0_loop_GT(x4:0, x1:0, x2:0) -> f564_0_loop_NE(x4:0, x1:0, c23, c24) :|: c24 = x4:0 - 2 && c23 = x2:0 + 1 && (x4:0 - 1 >= x2:0 && x2:0 > 0 && x1:0 < 0 && x4:0 > -1) - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS - PolynomialOrderProcessor Rules: f564_0_loop_NE(x40:0, x41:0, x42:0, x43:0) -> f490_0_loop_GT(x40:0, x41:0, x42:0) :|: x43:0 <= x42:0 - 1 f490_0_loop_GT(x12:0, x13:0, x10:0) -> f564_0_loop_NE(x12:0, x13:0, c, c1) :|: c1 = x12:0 - 2 && c = x10:0 + 1 && (x12:0 - 1 >= x10:0 && x10:0 > 0 && x13:0 > 0 && x12:0 > -1) f490_0_loop_GT(x16:0, c2, x18:0) -> f490_0_loop_GT(c3, c4, c5) :|: c5 = x16:0 - 2 && (c4 = 0 && (c3 = x16:0 - 1 && c2 = 0)) && (x18:0 > 0 && x16:0 > -1 && x18:0 - 1 = x16:0 - 2 && x18:0 <= x16:0 - 1 && cons_0 = 0) f490_0_loop_GT(x24:0, x25:0, x24:0) -> f490_0_loop_GT(x24:0, c6, c7) :|: c7 = x24:0 - 1 && c6 = 0 && x24:0 > 0 f564_0_loop_NE(x96:0, x101:0, x102:0, x102:0) -> f490_0_loop_GT(c16, x101:0, x102:0) :|: c16 = x96:0 - 1 && TRUE f490_0_loop_GT(x10, x11, c17) -> f490_0_loop_GT(x10, c18, c19) :|: c19 = 1 && (c18 = 1 && c17 = 0) && (x10 > 0 && x10 < 3 && x12 = 0) f564_0_loop_NE(x32:0, x33:0, x34:0, x35:0) -> f490_0_loop_GT(x32:0, x33:0, x34:0) :|: x35:0 - 1 >= x34:0 f490_0_loop_GT(x4:0, x1:0, x2:0) -> f564_0_loop_NE(x4:0, x1:0, c23, c24) :|: c24 = x4:0 - 2 && c23 = x2:0 + 1 && (x4:0 - 1 >= x2:0 && x2:0 > 0 && x1:0 < 0 && x4:0 > -1) Found the following polynomial interpretation: [f564_0_loop_NE(x, x1, x2, x3)] = -1 + x [f490_0_loop_GT(x4, x5, x6)] = -1 + x4 The following rules are decreasing: f490_0_loop_GT(x16:0, c2, x18:0) -> f490_0_loop_GT(c3, c4, c5) :|: c5 = x16:0 - 2 && (c4 = 0 && (c3 = x16:0 - 1 && c2 = 0)) && (x18:0 > 0 && x16:0 > -1 && x18:0 - 1 = x16:0 - 2 && x18:0 <= x16:0 - 1 && cons_0 = 0) f564_0_loop_NE(x96:0, x101:0, x102:0, x102:0) -> f490_0_loop_GT(c16, x101:0, x102:0) :|: c16 = x96:0 - 1 && TRUE The following rules are bounded: f490_0_loop_GT(x12:0, x13:0, x10:0) -> f564_0_loop_NE(x12:0, x13:0, c, c1) :|: c1 = x12:0 - 2 && c = x10:0 + 1 && (x12:0 - 1 >= x10:0 && x10:0 > 0 && x13:0 > 0 && x12:0 > -1) f490_0_loop_GT(x16:0, c2, x18:0) -> f490_0_loop_GT(c3, c4, c5) :|: c5 = x16:0 - 2 && (c4 = 0 && (c3 = x16:0 - 1 && c2 = 0)) && (x18:0 > 0 && x16:0 > -1 && x18:0 - 1 = x16:0 - 2 && x18:0 <= x16:0 - 1 && cons_0 = 0) f490_0_loop_GT(x24:0, x25:0, x24:0) -> f490_0_loop_GT(x24:0, c6, c7) :|: c7 = x24:0 - 1 && c6 = 0 && x24:0 > 0 f490_0_loop_GT(x10, x11, c17) -> f490_0_loop_GT(x10, c18, c19) :|: c19 = 1 && (c18 = 1 && c17 = 0) && (x10 > 0 && x10 < 3 && x12 = 0) f490_0_loop_GT(x4:0, x1:0, x2:0) -> f564_0_loop_NE(x4:0, x1:0, c23, c24) :|: c24 = x4:0 - 2 && c23 = x2:0 + 1 && (x4:0 - 1 >= x2:0 && x2:0 > 0 && x1:0 < 0 && x4:0 > -1) - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS Rules: f564_0_loop_NE(x40:0, x41:0, x42:0, x43:0) -> f490_0_loop_GT(x40:0, x41:0, x42:0) :|: x43:0 <= x42:0 - 1 f490_0_loop_GT(x12:0, x13:0, x10:0) -> f564_0_loop_NE(x12:0, x13:0, c, c1) :|: c1 = x12:0 - 2 && c = x10:0 + 1 && (x12:0 - 1 >= x10:0 && x10:0 > 0 && x13:0 > 0 && x12:0 > -1) f490_0_loop_GT(x24:0, x25:0, x24:0) -> f490_0_loop_GT(x24:0, c6, c7) :|: c7 = x24:0 - 1 && c6 = 0 && x24:0 > 0 f490_0_loop_GT(x10, x11, c17) -> f490_0_loop_GT(x10, c18, c19) :|: c19 = 1 && (c18 = 1 && c17 = 0) && (x10 > 0 && x10 < 3 && x12 = 0) f564_0_loop_NE(x32:0, x33:0, x34:0, x35:0) -> f490_0_loop_GT(x32:0, x33:0, x34:0) :|: x35:0 - 1 >= x34:0 f490_0_loop_GT(x4:0, x1:0, x2:0) -> f564_0_loop_NE(x4:0, x1:0, c23, c24) :|: c24 = x4:0 - 2 && c23 = x2:0 + 1 && (x4:0 - 1 >= x2:0 && x2:0 > 0 && x1:0 < 0 && x4:0 > -1) - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS - RankingReductionPairProof Rules: f564_0_loop_NE(x40:0, x41:0, x42:0, x43:0) -> f490_0_loop_GT(x40:0, x41:0, x42:0) :|: x43:0 <= x42:0 - 1 f564_0_loop_NE(x96:0, x101:0, x102:0, x102:0) -> f490_0_loop_GT(c16, x101:0, x102:0) :|: c16 = x96:0 - 1 && TRUE f564_0_loop_NE(x32:0, x33:0, x34:0, x35:0) -> f490_0_loop_GT(x32:0, x33:0, x34:0) :|: x35:0 - 1 >= x34:0 Interpretation: [ f564_0_loop_NE ] = 1 [ f490_0_loop_GT ] = 0 The following rules are decreasing: f564_0_loop_NE(x40:0, x41:0, x42:0, x43:0) -> f490_0_loop_GT(x40:0, x41:0, x42:0) :|: x43:0 <= x42:0 - 1 f564_0_loop_NE(x96:0, x101:0, x102:0, x102:0) -> f490_0_loop_GT(c16, x101:0, x102:0) :|: c16 = x96:0 - 1 && TRUE f564_0_loop_NE(x32:0, x33:0, x34:0, x35:0) -> f490_0_loop_GT(x32:0, x33:0, x34:0) :|: x35:0 - 1 >= x34:0 The following rules are bounded: f564_0_loop_NE(x40:0, x41:0, x42:0, x43:0) -> f490_0_loop_GT(x40:0, x41:0, x42:0) :|: x43:0 <= x42:0 - 1 f564_0_loop_NE(x96:0, x101:0, x102:0, x102:0) -> f490_0_loop_GT(c16, x101:0, x102:0) :|: c16 = x96:0 - 1 && TRUE f564_0_loop_NE(x32:0, x33:0, x34:0, x35:0) -> f490_0_loop_GT(x32:0, x33:0, x34:0) :|: x35:0 - 1 >= x34:0 ---------------------------------------- (10) Obligation: Rules: f564_0_loop_NE(x40:0, x41:0, x42:0, x43:0) -> f490_0_loop_GT(x40:0, x41:0, x42:0) :|: x43:0 <= x42:0 - 1 f490_0_loop_GT(x12:0, x13:0, x10:0) -> f564_0_loop_NE(x12:0, x13:0, x10:0 + 1, x12:0 - 2) :|: x12:0 - 1 >= x10:0 && x10:0 > 0 && x13:0 > 0 && x12:0 > -1 f490_0_loop_GT(x24:0, x25:0, x24:0) -> f490_0_loop_GT(x24:0, 0, x24:0 - 1) :|: x24:0 > 0 f490_0_loop_GT(x10, x11, x12) -> f490_0_loop_GT(x10, 1, 1) :|: x10 > 0 && x10 < 3 && x12 = 0 f564_0_loop_NE(x32:0, x33:0, x34:0, x35:0) -> f490_0_loop_GT(x32:0, x33:0, x34:0) :|: x35:0 - 1 >= x34:0 f490_0_loop_GT(x4:0, x1:0, x2:0) -> f564_0_loop_NE(x4:0, x1:0, x2:0 + 1, x4:0 - 2) :|: x4:0 - 1 >= x2:0 && x2:0 > 0 && x1:0 < 0 && x4:0 > -1 f490_0_loop_GT(x15, x16, x17) -> f490_0_loop_GT(x15, 0, x17 - 1) :|: x17 - 1 <= x15 - 3 && x15 > -1 && x17 <= x15 - 1 && x17 > 0 && x16 = 0 f490_0_loop_GT(x5, x6, x7) -> f490_0_loop_GT(x5, 1, 1) :|: x5 > 3 && x7 = 0 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f564_0_loop_NE(x40:0, x41:0, x42:0, x43:0) -> f490_0_loop_GT(x40:0, x41:0, x42:0) :|: x43:0 <= x42:0 - 1 (2) f490_0_loop_GT(x12:0, x13:0, x10:0) -> f564_0_loop_NE(x12:0, x13:0, x10:0 + 1, x12:0 - 2) :|: x12:0 - 1 >= x10:0 && x10:0 > 0 && x13:0 > 0 && x12:0 > -1 (3) f490_0_loop_GT(x24:0, x25:0, x24:0) -> f490_0_loop_GT(x24:0, 0, x24:0 - 1) :|: x24:0 > 0 (4) f490_0_loop_GT(x10, x11, x12) -> f490_0_loop_GT(x10, 1, 1) :|: x10 > 0 && x10 < 3 && x12 = 0 (5) f564_0_loop_NE(x32:0, x33:0, x34:0, x35:0) -> f490_0_loop_GT(x32:0, x33:0, x34:0) :|: x35:0 - 1 >= x34:0 (6) f490_0_loop_GT(x4:0, x1:0, x2:0) -> f564_0_loop_NE(x4:0, x1:0, x2:0 + 1, x4:0 - 2) :|: x4:0 - 1 >= x2:0 && x2:0 > 0 && x1:0 < 0 && x4:0 > -1 (7) f490_0_loop_GT(x15, x16, x17) -> f490_0_loop_GT(x15, 0, x17 - 1) :|: x17 - 1 <= x15 - 3 && x15 > -1 && x17 <= x15 - 1 && x17 > 0 && x16 = 0 (8) f490_0_loop_GT(x5, x6, x7) -> f490_0_loop_GT(x5, 1, 1) :|: x5 > 3 && x7 = 0 Arcs: (1) -> (2), (3), (4), (6), (7), (8) (2) -> (1), (5) (3) -> (4) (4) -> (2), (3) (5) -> (2), (3), (4), (6), (7), (8) (6) -> (1), (5) (7) -> (7), (8) (8) -> (2) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) f564_0_loop_NE(x40:0, x41:0, x42:0, x43:0) -> f490_0_loop_GT(x40:0, x41:0, x42:0) :|: x43:0 <= x42:0 - 1 (2) f490_0_loop_GT(x12:0, x13:0, x10:0) -> f564_0_loop_NE(x12:0, x13:0, x10:0 + 1, x12:0 - 2) :|: x12:0 - 1 >= x10:0 && x10:0 > 0 && x13:0 > 0 && x12:0 > -1 (3) f490_0_loop_GT(x5, x6, x7) -> f490_0_loop_GT(x5, 1, 1) :|: x5 > 3 && x7 = 0 (4) f490_0_loop_GT(x15, x16, x17) -> f490_0_loop_GT(x15, 0, x17 - 1) :|: x17 - 1 <= x15 - 3 && x15 > -1 && x17 <= x15 - 1 && x17 > 0 && x16 = 0 (5) f490_0_loop_GT(x10, x11, x12) -> f490_0_loop_GT(x10, 1, 1) :|: x10 > 0 && x10 < 3 && x12 = 0 (6) f490_0_loop_GT(x24:0, x25:0, x24:0) -> f490_0_loop_GT(x24:0, 0, x24:0 - 1) :|: x24:0 > 0 (7) f564_0_loop_NE(x32:0, x33:0, x34:0, x35:0) -> f490_0_loop_GT(x32:0, x33:0, x34:0) :|: x35:0 - 1 >= x34:0 (8) f490_0_loop_GT(x4:0, x1:0, x2:0) -> f564_0_loop_NE(x4:0, x1:0, x2:0 + 1, x4:0 - 2) :|: x4:0 - 1 >= x2:0 && x2:0 > 0 && x1:0 < 0 && x4:0 > -1 Arcs: (1) -> (2), (3), (4), (5), (6), (8) (2) -> (1), (7) (3) -> (2) (4) -> (3), (4) (5) -> (2), (6) (6) -> (5) (7) -> (2), (3), (4), (5), (6), (8) (8) -> (1), (7) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: f490_0_loop_GT(x15:0, cons_0, x17:0) -> f490_0_loop_GT(x15:0, 0, x17:0 - 1) :|: x17:0 <= x15:0 - 1 && x17:0 > 0 && x15:0 > -1 && x17:0 - 1 <= x15:0 - 3 && cons_0 = 0 f490_0_loop_GT(x, x1, x2) -> f490_0_loop_GT(x, 1, 1) :|: x > 0 && x < 3 && x2 = 0 f490_0_loop_GT(x24:0:0, x25:0:0, x24:0:0) -> f490_0_loop_GT(x24:0:0, 0, x24:0:0 - 1) :|: x24:0:0 > 0 f490_0_loop_GT(x3, x4, x5) -> f490_0_loop_GT(x3, 1, 1) :|: x3 > 3 && x5 = 0 f490_0_loop_GT(x4:0:0, x1:0:0, x2:0:0) -> f564_0_loop_NE(x4:0:0, x1:0:0, x2:0:0 + 1, x4:0:0 - 2) :|: x1:0:0 < 0 && x4:0:0 > -1 && x2:0:0 > 0 && x4:0:0 - 1 >= x2:0:0 f564_0_loop_NE(x32:0:0, x33:0:0, x34:0:0, x35:0:0) -> f490_0_loop_GT(x32:0:0, x33:0:0, x34:0:0) :|: x35:0:0 - 1 >= x34:0:0 f564_0_loop_NE(x40:0:0, x41:0:0, x42:0:0, x43:0:0) -> f490_0_loop_GT(x40:0:0, x41:0:0, x42:0:0) :|: x43:0:0 <= x42:0:0 - 1 f490_0_loop_GT(x12:0:0, x13:0:0, x10:0:0) -> f564_0_loop_NE(x12:0:0, x13:0:0, x10:0:0 + 1, x12:0:0 - 2) :|: x13:0:0 > 0 && x12:0:0 > -1 && x10:0:0 > 0 && x12:0:0 - 1 >= x10:0:0