MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 6138 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 0 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 10.2 s] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 71 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT ---------------------------------------- (0) Obligation: Rules: f1_0_main_Load(arg1, arg2, arg3, arg4, arg5) -> f887_0_loop_aux_GT(arg1P, arg2P, arg3P, arg4P, arg5P) :|: arg2 + 15 = arg3P && 0 = arg2P && 20 = arg1P && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg2 <= arg2 + 15 - 1 f887_0_loop_aux_GT(x, x1, x2, x3, x4) -> f961_0_loop_aux_NE(x5, x6, x7, x8, x9) :|: x - 2 = x9 && x2 + 1 = x8 && x1 = x7 && x = x6 && x2 = x5 && x1 <= -1 && -1 <= x - 1 && x2 <= x - 1 && 0 <= x2 - 1 f887_0_loop_aux_GT(x10, x11, x12, x13, x14) -> f961_0_loop_aux_NE(x15, x16, x17, x18, x19) :|: x10 - 2 = x19 && x12 + 1 = x18 && x11 = x17 && x10 = x16 && x12 = x15 && 0 <= x11 - 1 && -1 <= x10 - 1 && x12 <= x10 - 1 && 0 <= x12 - 1 f887_0_loop_aux_GT(x20, x21, x22, x23, x24) -> f962_0_loop_aux_NE(x25, x26, x27, x28, x29) :|: x20 - 2 = x28 && x22 - 1 = x27 && x20 = x26 && x22 = x25 && 0 = x21 && x22 <= x20 - 1 && 0 <= x22 - 1 && -1 <= x20 - 1 f887_0_loop_aux_GT(x30, x31, x32, x33, x34) -> f970_0_loop_aux_NE(x35, x36, x37, x38, x39) :|: x30 - 2 = x37 && x30 - 1 = x36 && x30 = x35 && x30 = x32 && 0 <= x30 - 1 f961_0_loop_aux_NE(x40, x41, x42, x43, x44) -> f887_0_loop_aux_GT(x45, x46, x47, x48, x49) :|: x43 = x47 && x42 = x46 && x41 = x45 && x43 <= x44 - 1 && x40 <= x41 - 1 && 1 <= x43 - 1 && 0 <= x40 - 1 f961_0_loop_aux_NE(x50, x51, x52, x53, x54) -> f887_0_loop_aux_GT(x55, x56, x57, x58, x59) :|: x53 = x57 && x52 = x56 && x51 = x55 && x53 <= x54 - 1 && x51 <= x50 - 1 && 1 <= x53 - 1 && 0 <= x50 - 1 f961_0_loop_aux_NE(x60, x61, x62, x63, x64) -> f887_0_loop_aux_GT(x65, x66, x67, x68, x69) :|: x63 = x67 && x62 = x66 && x61 = x65 && x64 <= x63 - 1 && x60 <= x61 - 1 && 1 <= x63 - 1 && 0 <= x60 - 1 f961_0_loop_aux_NE(x70, x71, x72, x73, x74) -> f887_0_loop_aux_GT(x75, x76, x77, x78, x79) :|: x73 = x77 && x72 = x76 && x71 = x75 && x74 <= x73 - 1 && x71 <= x70 - 1 && 1 <= x73 - 1 && 0 <= x70 - 1 f962_0_loop_aux_NE(x80, x81, x82, x83, x84) -> f887_0_loop_aux_GT(x85, x86, x87, x88, x89) :|: x82 = x87 && 0 = x86 && x81 = x85 && x82 <= x83 - 1 && x80 <= x81 - 1 && 0 <= x80 - 1 f962_0_loop_aux_NE(x90, x91, x92, x93, x94) -> f887_0_loop_aux_GT(x95, x96, x97, x98, x99) :|: x92 = x97 && 0 = x96 && x91 = x95 && x92 <= x93 - 1 && x91 <= x90 - 1 && 0 <= x90 - 1 f962_0_loop_aux_NE(x100, x101, x102, x103, x104) -> f887_0_loop_aux_GT(x105, x106, x107, x108, x109) :|: x102 = x107 && 0 = x106 && x101 = x105 && x103 <= x102 - 1 && x100 <= x101 - 1 && 0 <= x100 - 1 f962_0_loop_aux_NE(x110, x111, x112, x113, x114) -> f887_0_loop_aux_GT(x115, x116, x117, x118, x119) :|: x112 = x117 && 0 = x116 && x111 = x115 && x113 <= x112 - 1 && x111 <= x110 - 1 && 0 <= x110 - 1 f961_0_loop_aux_NE(x120, x121, x122, x123, x124) -> f887_0_loop_aux_GT(x125, x126, x127, x128, x129) :|: x123 = x127 && x122 = x126 && x121 - 1 = x125 && x123 = x124 && x123 <= x121 - 1 && 0 <= x120 - 1 f962_0_loop_aux_NE(x130, x131, x132, x133, x134) -> f887_0_loop_aux_GT(x135, x136, x137, x138, x139) :|: x132 = x137 && 0 = x136 && x131 - 1 = x135 && x132 = x133 && x132 <= x131 - 1 && 0 <= x130 - 1 f970_0_loop_aux_NE(x140, x141, x142, x143, x144) -> f887_0_loop_aux_GT(x145, x146, x147, x148, x149) :|: x141 = x147 && 0 = x146 && x140 = x145 && x141 <= x142 - 1 f970_0_loop_aux_NE(x150, x151, x152, x153, x154) -> f887_0_loop_aux_GT(x155, x156, x157, x158, x159) :|: x151 = x157 && 0 = x156 && x150 = x155 && x152 <= x151 - 1 f887_0_loop_aux_GT(x160, x161, x162, x163, x164) -> f887_0_loop_aux_GT(x165, x166, x167, x168, x169) :|: 1 = x167 && 1 = x166 && x160 = x165 && 0 = x162 && x160 <= 2 && 0 <= x160 - 1 f887_0_loop_aux_GT(x170, x171, x172, x173, x174) -> f887_0_loop_aux_GT(x175, x176, x177, x178, x179) :|: 1 = x177 && 1 = x176 && x170 = x175 && 0 = x172 && 3 <= x170 - 1 f970_0_loop_aux_NE(x180, x181, x182, x183, x184) -> f887_0_loop_aux_GT(x185, x186, x187, x188, x189) :|: x181 = x187 && 0 = x186 && x180 - 1 = x185 && x181 = x182 && x181 <= x180 - 1 && x181 <= x180 - 1 f887_0_loop_aux_GT(x190, x191, x192, x193, x194) -> f887_0_loop_aux_GT(x195, x196, x197, x198, x199) :|: 1 = x197 && 1 = x196 && 2 = x195 && 0 = x192 && 3 = x190 f887_0_loop_aux_GT(x200, x201, x202, x203, x204) -> f887_0_loop_aux_GT(x205, x206, x207, x208, x209) :|: -1 = x207 && 0 = x206 && 0 = x205 && 0 = x202 && 0 = x200 __init(x210, x211, x212, x213, x214) -> f1_0_main_Load(x215, x216, x217, x218, x219) :|: 0 <= 0 Start term: __init(arg1, arg2, arg3, arg4, arg5) ---------------------------------------- (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, arg5) -> f887_0_loop_aux_GT(arg1P, arg2P, arg3P, arg4P, arg5P) :|: arg2 + 15 = arg3P && 0 = arg2P && 20 = arg1P && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg2 <= arg2 + 15 - 1 f887_0_loop_aux_GT(x, x1, x2, x3, x4) -> f961_0_loop_aux_NE(x5, x6, x7, x8, x9) :|: x - 2 = x9 && x2 + 1 = x8 && x1 = x7 && x = x6 && x2 = x5 && x1 <= -1 && -1 <= x - 1 && x2 <= x - 1 && 0 <= x2 - 1 f887_0_loop_aux_GT(x10, x11, x12, x13, x14) -> f961_0_loop_aux_NE(x15, x16, x17, x18, x19) :|: x10 - 2 = x19 && x12 + 1 = x18 && x11 = x17 && x10 = x16 && x12 = x15 && 0 <= x11 - 1 && -1 <= x10 - 1 && x12 <= x10 - 1 && 0 <= x12 - 1 f887_0_loop_aux_GT(x20, x21, x22, x23, x24) -> f962_0_loop_aux_NE(x25, x26, x27, x28, x29) :|: x20 - 2 = x28 && x22 - 1 = x27 && x20 = x26 && x22 = x25 && 0 = x21 && x22 <= x20 - 1 && 0 <= x22 - 1 && -1 <= x20 - 1 f887_0_loop_aux_GT(x30, x31, x32, x33, x34) -> f970_0_loop_aux_NE(x35, x36, x37, x38, x39) :|: x30 - 2 = x37 && x30 - 1 = x36 && x30 = x35 && x30 = x32 && 0 <= x30 - 1 f961_0_loop_aux_NE(x40, x41, x42, x43, x44) -> f887_0_loop_aux_GT(x45, x46, x47, x48, x49) :|: x43 = x47 && x42 = x46 && x41 = x45 && x43 <= x44 - 1 && x40 <= x41 - 1 && 1 <= x43 - 1 && 0 <= x40 - 1 f961_0_loop_aux_NE(x50, x51, x52, x53, x54) -> f887_0_loop_aux_GT(x55, x56, x57, x58, x59) :|: x53 = x57 && x52 = x56 && x51 = x55 && x53 <= x54 - 1 && x51 <= x50 - 1 && 1 <= x53 - 1 && 0 <= x50 - 1 f961_0_loop_aux_NE(x60, x61, x62, x63, x64) -> f887_0_loop_aux_GT(x65, x66, x67, x68, x69) :|: x63 = x67 && x62 = x66 && x61 = x65 && x64 <= x63 - 1 && x60 <= x61 - 1 && 1 <= x63 - 1 && 0 <= x60 - 1 f961_0_loop_aux_NE(x70, x71, x72, x73, x74) -> f887_0_loop_aux_GT(x75, x76, x77, x78, x79) :|: x73 = x77 && x72 = x76 && x71 = x75 && x74 <= x73 - 1 && x71 <= x70 - 1 && 1 <= x73 - 1 && 0 <= x70 - 1 f962_0_loop_aux_NE(x80, x81, x82, x83, x84) -> f887_0_loop_aux_GT(x85, x86, x87, x88, x89) :|: x82 = x87 && 0 = x86 && x81 = x85 && x82 <= x83 - 1 && x80 <= x81 - 1 && 0 <= x80 - 1 f962_0_loop_aux_NE(x90, x91, x92, x93, x94) -> f887_0_loop_aux_GT(x95, x96, x97, x98, x99) :|: x92 = x97 && 0 = x96 && x91 = x95 && x92 <= x93 - 1 && x91 <= x90 - 1 && 0 <= x90 - 1 f962_0_loop_aux_NE(x100, x101, x102, x103, x104) -> f887_0_loop_aux_GT(x105, x106, x107, x108, x109) :|: x102 = x107 && 0 = x106 && x101 = x105 && x103 <= x102 - 1 && x100 <= x101 - 1 && 0 <= x100 - 1 f962_0_loop_aux_NE(x110, x111, x112, x113, x114) -> f887_0_loop_aux_GT(x115, x116, x117, x118, x119) :|: x112 = x117 && 0 = x116 && x111 = x115 && x113 <= x112 - 1 && x111 <= x110 - 1 && 0 <= x110 - 1 f961_0_loop_aux_NE(x120, x121, x122, x123, x124) -> f887_0_loop_aux_GT(x125, x126, x127, x128, x129) :|: x123 = x127 && x122 = x126 && x121 - 1 = x125 && x123 = x124 && x123 <= x121 - 1 && 0 <= x120 - 1 f962_0_loop_aux_NE(x130, x131, x132, x133, x134) -> f887_0_loop_aux_GT(x135, x136, x137, x138, x139) :|: x132 = x137 && 0 = x136 && x131 - 1 = x135 && x132 = x133 && x132 <= x131 - 1 && 0 <= x130 - 1 f970_0_loop_aux_NE(x140, x141, x142, x143, x144) -> f887_0_loop_aux_GT(x145, x146, x147, x148, x149) :|: x141 = x147 && 0 = x146 && x140 = x145 && x141 <= x142 - 1 f970_0_loop_aux_NE(x150, x151, x152, x153, x154) -> f887_0_loop_aux_GT(x155, x156, x157, x158, x159) :|: x151 = x157 && 0 = x156 && x150 = x155 && x152 <= x151 - 1 f887_0_loop_aux_GT(x160, x161, x162, x163, x164) -> f887_0_loop_aux_GT(x165, x166, x167, x168, x169) :|: 1 = x167 && 1 = x166 && x160 = x165 && 0 = x162 && x160 <= 2 && 0 <= x160 - 1 f887_0_loop_aux_GT(x170, x171, x172, x173, x174) -> f887_0_loop_aux_GT(x175, x176, x177, x178, x179) :|: 1 = x177 && 1 = x176 && x170 = x175 && 0 = x172 && 3 <= x170 - 1 f970_0_loop_aux_NE(x180, x181, x182, x183, x184) -> f887_0_loop_aux_GT(x185, x186, x187, x188, x189) :|: x181 = x187 && 0 = x186 && x180 - 1 = x185 && x181 = x182 && x181 <= x180 - 1 && x181 <= x180 - 1 f887_0_loop_aux_GT(x190, x191, x192, x193, x194) -> f887_0_loop_aux_GT(x195, x196, x197, x198, x199) :|: 1 = x197 && 1 = x196 && 2 = x195 && 0 = x192 && 3 = x190 f887_0_loop_aux_GT(x200, x201, x202, x203, x204) -> f887_0_loop_aux_GT(x205, x206, x207, x208, x209) :|: -1 = x207 && 0 = x206 && 0 = x205 && 0 = x202 && 0 = x200 __init(x210, x211, x212, x213, x214) -> f1_0_main_Load(x215, x216, x217, x218, x219) :|: 0 <= 0 Start term: __init(arg1, arg2, arg3, arg4, arg5) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f1_0_main_Load(arg1, arg2, arg3, arg4, arg5) -> f887_0_loop_aux_GT(arg1P, arg2P, arg3P, arg4P, arg5P) :|: arg2 + 15 = arg3P && 0 = arg2P && 20 = arg1P && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg2 <= arg2 + 15 - 1 (2) f887_0_loop_aux_GT(x, x1, x2, x3, x4) -> f961_0_loop_aux_NE(x5, x6, x7, x8, x9) :|: x - 2 = x9 && x2 + 1 = x8 && x1 = x7 && x = x6 && x2 = x5 && x1 <= -1 && -1 <= x - 1 && x2 <= x - 1 && 0 <= x2 - 1 (3) f887_0_loop_aux_GT(x10, x11, x12, x13, x14) -> f961_0_loop_aux_NE(x15, x16, x17, x18, x19) :|: x10 - 2 = x19 && x12 + 1 = x18 && x11 = x17 && x10 = x16 && x12 = x15 && 0 <= x11 - 1 && -1 <= x10 - 1 && x12 <= x10 - 1 && 0 <= x12 - 1 (4) f887_0_loop_aux_GT(x20, x21, x22, x23, x24) -> f962_0_loop_aux_NE(x25, x26, x27, x28, x29) :|: x20 - 2 = x28 && x22 - 1 = x27 && x20 = x26 && x22 = x25 && 0 = x21 && x22 <= x20 - 1 && 0 <= x22 - 1 && -1 <= x20 - 1 (5) f887_0_loop_aux_GT(x30, x31, x32, x33, x34) -> f970_0_loop_aux_NE(x35, x36, x37, x38, x39) :|: x30 - 2 = x37 && x30 - 1 = x36 && x30 = x35 && x30 = x32 && 0 <= x30 - 1 (6) f961_0_loop_aux_NE(x40, x41, x42, x43, x44) -> f887_0_loop_aux_GT(x45, x46, x47, x48, x49) :|: x43 = x47 && x42 = x46 && x41 = x45 && x43 <= x44 - 1 && x40 <= x41 - 1 && 1 <= x43 - 1 && 0 <= x40 - 1 (7) f961_0_loop_aux_NE(x50, x51, x52, x53, x54) -> f887_0_loop_aux_GT(x55, x56, x57, x58, x59) :|: x53 = x57 && x52 = x56 && x51 = x55 && x53 <= x54 - 1 && x51 <= x50 - 1 && 1 <= x53 - 1 && 0 <= x50 - 1 (8) f961_0_loop_aux_NE(x60, x61, x62, x63, x64) -> f887_0_loop_aux_GT(x65, x66, x67, x68, x69) :|: x63 = x67 && x62 = x66 && x61 = x65 && x64 <= x63 - 1 && x60 <= x61 - 1 && 1 <= x63 - 1 && 0 <= x60 - 1 (9) f961_0_loop_aux_NE(x70, x71, x72, x73, x74) -> f887_0_loop_aux_GT(x75, x76, x77, x78, x79) :|: x73 = x77 && x72 = x76 && x71 = x75 && x74 <= x73 - 1 && x71 <= x70 - 1 && 1 <= x73 - 1 && 0 <= x70 - 1 (10) f962_0_loop_aux_NE(x80, x81, x82, x83, x84) -> f887_0_loop_aux_GT(x85, x86, x87, x88, x89) :|: x82 = x87 && 0 = x86 && x81 = x85 && x82 <= x83 - 1 && x80 <= x81 - 1 && 0 <= x80 - 1 (11) f962_0_loop_aux_NE(x90, x91, x92, x93, x94) -> f887_0_loop_aux_GT(x95, x96, x97, x98, x99) :|: x92 = x97 && 0 = x96 && x91 = x95 && x92 <= x93 - 1 && x91 <= x90 - 1 && 0 <= x90 - 1 (12) f962_0_loop_aux_NE(x100, x101, x102, x103, x104) -> f887_0_loop_aux_GT(x105, x106, x107, x108, x109) :|: x102 = x107 && 0 = x106 && x101 = x105 && x103 <= x102 - 1 && x100 <= x101 - 1 && 0 <= x100 - 1 (13) f962_0_loop_aux_NE(x110, x111, x112, x113, x114) -> f887_0_loop_aux_GT(x115, x116, x117, x118, x119) :|: x112 = x117 && 0 = x116 && x111 = x115 && x113 <= x112 - 1 && x111 <= x110 - 1 && 0 <= x110 - 1 (14) f961_0_loop_aux_NE(x120, x121, x122, x123, x124) -> f887_0_loop_aux_GT(x125, x126, x127, x128, x129) :|: x123 = x127 && x122 = x126 && x121 - 1 = x125 && x123 = x124 && x123 <= x121 - 1 && 0 <= x120 - 1 (15) f962_0_loop_aux_NE(x130, x131, x132, x133, x134) -> f887_0_loop_aux_GT(x135, x136, x137, x138, x139) :|: x132 = x137 && 0 = x136 && x131 - 1 = x135 && x132 = x133 && x132 <= x131 - 1 && 0 <= x130 - 1 (16) f970_0_loop_aux_NE(x140, x141, x142, x143, x144) -> f887_0_loop_aux_GT(x145, x146, x147, x148, x149) :|: x141 = x147 && 0 = x146 && x140 = x145 && x141 <= x142 - 1 (17) f970_0_loop_aux_NE(x150, x151, x152, x153, x154) -> f887_0_loop_aux_GT(x155, x156, x157, x158, x159) :|: x151 = x157 && 0 = x156 && x150 = x155 && x152 <= x151 - 1 (18) f887_0_loop_aux_GT(x160, x161, x162, x163, x164) -> f887_0_loop_aux_GT(x165, x166, x167, x168, x169) :|: 1 = x167 && 1 = x166 && x160 = x165 && 0 = x162 && x160 <= 2 && 0 <= x160 - 1 (19) f887_0_loop_aux_GT(x170, x171, x172, x173, x174) -> f887_0_loop_aux_GT(x175, x176, x177, x178, x179) :|: 1 = x177 && 1 = x176 && x170 = x175 && 0 = x172 && 3 <= x170 - 1 (20) f970_0_loop_aux_NE(x180, x181, x182, x183, x184) -> f887_0_loop_aux_GT(x185, x186, x187, x188, x189) :|: x181 = x187 && 0 = x186 && x180 - 1 = x185 && x181 = x182 && x181 <= x180 - 1 && x181 <= x180 - 1 (21) f887_0_loop_aux_GT(x190, x191, x192, x193, x194) -> f887_0_loop_aux_GT(x195, x196, x197, x198, x199) :|: 1 = x197 && 1 = x196 && 2 = x195 && 0 = x192 && 3 = x190 (22) f887_0_loop_aux_GT(x200, x201, x202, x203, x204) -> f887_0_loop_aux_GT(x205, x206, x207, x208, x209) :|: -1 = x207 && 0 = x206 && 0 = x205 && 0 = x202 && 0 = x200 (23) __init(x210, x211, x212, x213, x214) -> f1_0_main_Load(x215, x216, x217, x218, x219) :|: 0 <= 0 Arcs: (1) -> (4), (5) (2) -> (6), (8), (14) (3) -> (6), (8), (14) (4) -> (10), (15) (5) -> (17) (6) -> (2), (3), (4), (5) (7) -> (2), (3), (4), (5) (8) -> (2), (3), (4), (5) (9) -> (2), (3), (4), (5) (10) -> (4), (5), (18), (19), (21) (11) -> (4), (5), (18), (19), (21), (22) (12) -> (4), (5), (18), (19), (21) (13) -> (4), (5), (18), (19), (21), (22) (14) -> (2), (3), (4), (5), (18), (19), (21), (22) (15) -> (4), (5), (18), (19), (21), (22) (16) -> (4), (5), (18), (19), (21), (22) (17) -> (4), (5), (18), (19), (21), (22) (18) -> (3), (5) (19) -> (3) (20) -> (4), (5), (18), (19), (21), (22) (21) -> (3) (23) -> (1) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) f887_0_loop_aux_GT(x20, x21, x22, x23, x24) -> f962_0_loop_aux_NE(x25, x26, x27, x28, x29) :|: x20 - 2 = x28 && x22 - 1 = x27 && x20 = x26 && x22 = x25 && 0 = x21 && x22 <= x20 - 1 && 0 <= x22 - 1 && -1 <= x20 - 1 (2) f961_0_loop_aux_NE(x40, x41, x42, x43, x44) -> f887_0_loop_aux_GT(x45, x46, x47, x48, x49) :|: x43 = x47 && x42 = x46 && x41 = x45 && x43 <= x44 - 1 && x40 <= x41 - 1 && 1 <= x43 - 1 && 0 <= x40 - 1 (3) f887_0_loop_aux_GT(x, x1, x2, x3, x4) -> f961_0_loop_aux_NE(x5, x6, x7, x8, x9) :|: x - 2 = x9 && x2 + 1 = x8 && x1 = x7 && x = x6 && x2 = x5 && x1 <= -1 && -1 <= x - 1 && x2 <= x - 1 && 0 <= x2 - 1 (4) f961_0_loop_aux_NE(x60, x61, x62, x63, x64) -> f887_0_loop_aux_GT(x65, x66, x67, x68, x69) :|: x63 = x67 && x62 = x66 && x61 = x65 && x64 <= x63 - 1 && x60 <= x61 - 1 && 1 <= x63 - 1 && 0 <= x60 - 1 (5) f887_0_loop_aux_GT(x10, x11, x12, x13, x14) -> f961_0_loop_aux_NE(x15, x16, x17, x18, x19) :|: x10 - 2 = x19 && x12 + 1 = x18 && x11 = x17 && x10 = x16 && x12 = x15 && 0 <= x11 - 1 && -1 <= x10 - 1 && x12 <= x10 - 1 && 0 <= x12 - 1 (6) f887_0_loop_aux_GT(x190, x191, x192, x193, x194) -> f887_0_loop_aux_GT(x195, x196, x197, x198, x199) :|: 1 = x197 && 1 = x196 && 2 = x195 && 0 = x192 && 3 = x190 (7) f887_0_loop_aux_GT(x170, x171, x172, x173, x174) -> f887_0_loop_aux_GT(x175, x176, x177, x178, x179) :|: 1 = x177 && 1 = x176 && x170 = x175 && 0 = x172 && 3 <= x170 - 1 (8) f887_0_loop_aux_GT(x160, x161, x162, x163, x164) -> f887_0_loop_aux_GT(x165, x166, x167, x168, x169) :|: 1 = x167 && 1 = x166 && x160 = x165 && 0 = x162 && x160 <= 2 && 0 <= x160 - 1 (9) f970_0_loop_aux_NE(x150, x151, x152, x153, x154) -> f887_0_loop_aux_GT(x155, x156, x157, x158, x159) :|: x151 = x157 && 0 = x156 && x150 = x155 && x152 <= x151 - 1 (10) f887_0_loop_aux_GT(x30, x31, x32, x33, x34) -> f970_0_loop_aux_NE(x35, x36, x37, x38, x39) :|: x30 - 2 = x37 && x30 - 1 = x36 && x30 = x35 && x30 = x32 && 0 <= x30 - 1 (11) f962_0_loop_aux_NE(x130, x131, x132, x133, x134) -> f887_0_loop_aux_GT(x135, x136, x137, x138, x139) :|: x132 = x137 && 0 = x136 && x131 - 1 = x135 && x132 = x133 && x132 <= x131 - 1 && 0 <= x130 - 1 (12) f962_0_loop_aux_NE(x80, x81, x82, x83, x84) -> f887_0_loop_aux_GT(x85, x86, x87, x88, x89) :|: x82 = x87 && 0 = x86 && x81 = x85 && x82 <= x83 - 1 && x80 <= x81 - 1 && 0 <= x80 - 1 (13) f961_0_loop_aux_NE(x120, x121, x122, x123, x124) -> f887_0_loop_aux_GT(x125, x126, x127, x128, x129) :|: x123 = x127 && x122 = x126 && x121 - 1 = x125 && x123 = x124 && x123 <= x121 - 1 && 0 <= x120 - 1 Arcs: (1) -> (11), (12) (2) -> (1), (3), (5), (10) (3) -> (2), (4), (13) (4) -> (1), (3), (5), (10) (5) -> (2), (4), (13) (6) -> (5) (7) -> (5) (8) -> (5), (10) (9) -> (1), (6), (7), (8), (10) (10) -> (9) (11) -> (1), (6), (7), (8), (10) (12) -> (1), (6), (7), (8), (10) (13) -> (1), (3), (5), (6), (7), (8), (10) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: f887_0_loop_aux_GT(x155:0, x31:0, x155:0, x33:0, x34:0) -> f887_0_loop_aux_GT(x155:0, 0, x155:0 - 1, x158:0, x159:0) :|: x155:0 > 0 f887_0_loop_aux_GT(x20:0, cons_0, x22:0, x23:0, x24:0) -> f887_0_loop_aux_GT(x20:0 - 1, 0, x20:0 - 2, x138:0, x139:0) :|: x20:0 > -1 && x22:0 > 0 && x20:0 - 2 <= x20:0 - 1 && x22:0 - 1 = x20:0 - 2 && x22:0 <= x20:0 - 1 && cons_0 = 0 f887_0_loop_aux_GT(x6:0, x1:0, x2:0, x3:0, x4:0) -> f961_0_loop_aux_NE(x2:0, x6:0, x1:0, x2:0 + 1, x6:0 - 2) :|: x6:0 - 1 >= x2:0 && x2:0 > 0 && x1:0 < 0 && x6:0 > -1 f887_0_loop_aux_GT(x, x1, x2, x3, x4) -> f887_0_loop_aux_GT(x, 1, 1, x5, x6) :|: x > 0 && x < 3 && x2 = 0 f887_0_loop_aux_GT(x10:0, x11:0, x12:0, x13:0, x14:0) -> f961_0_loop_aux_NE(x12:0, x10:0, x11:0, x12:0 + 1, x10:0 - 2) :|: x12:0 <= x10:0 - 1 && x12:0 > 0 && x11:0 > 0 && x10:0 > -1 f961_0_loop_aux_NE(x40:0, x41:0, x42:0, x43:0, x44:0) -> f887_0_loop_aux_GT(x41:0, x42:0, x43:0, x48:0, x49:0) :|: x43:0 > 1 && x40:0 > 0 && x44:0 - 1 >= x43:0 && x41:0 - 1 >= x40:0 f961_0_loop_aux_NE(x60:0, x61:0, x62:0, x63:0, x64:0) -> f887_0_loop_aux_GT(x61:0, x62:0, x63:0, x68:0, x69:0) :|: x63:0 > 1 && x60:0 > 0 && x64:0 <= x63:0 - 1 && x61:0 - 1 >= x60:0 f887_0_loop_aux_GT(x7, x8, x9, x10, x11) -> f887_0_loop_aux_GT(x7, 0, x9 - 1, x12, x13) :|: x7 > -1 && x9 > 0 && x9 - 1 <= x7 - 3 && x9 <= x7 - 1 && x8 = 0 f887_0_loop_aux_GT(x14, x15, x16, x17, x18) -> f887_0_loop_aux_GT(2, 1, 1, x19, x20) :|: TRUE && x14 = 3 && x16 = 0 f887_0_loop_aux_GT(x21, x22, x23, x24, x25) -> f887_0_loop_aux_GT(x21, 1, 1, x26, x27) :|: x21 > 3 && x23 = 0 f961_0_loop_aux_NE(x120:0, x121:0, x122:0, x123:0, x123:0) -> f887_0_loop_aux_GT(x121:0 - 1, x122:0, x123:0, x128:0, x129:0) :|: x120:0 > 0 && x123:0 <= x121:0 - 1 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f887_0_loop_aux_GT(x1, x2, x3, x4, x5) -> f887_0_loop_aux_GT(x1, x2, x3) ---------------------------------------- (8) Obligation: Rules: f887_0_loop_aux_GT(x155:0, x31:0, x155:0) -> f887_0_loop_aux_GT(x155:0, 0, x155:0 - 1) :|: x155:0 > 0 f887_0_loop_aux_GT(x20:0, cons_0, x22:0) -> f887_0_loop_aux_GT(x20:0 - 1, 0, x20:0 - 2) :|: x20:0 > -1 && x22:0 > 0 && x20:0 - 2 <= x20:0 - 1 && x22:0 - 1 = x20:0 - 2 && x22:0 <= x20:0 - 1 && cons_0 = 0 f887_0_loop_aux_GT(x6:0, x1:0, x2:0) -> f961_0_loop_aux_NE(x2:0, x6:0, x1:0, x2:0 + 1, x6:0 - 2) :|: x6:0 - 1 >= x2:0 && x2:0 > 0 && x1:0 < 0 && x6:0 > -1 f887_0_loop_aux_GT(x, x1, x2) -> f887_0_loop_aux_GT(x, 1, 1) :|: x > 0 && x < 3 && x2 = 0 f887_0_loop_aux_GT(x10:0, x11:0, x12:0) -> f961_0_loop_aux_NE(x12:0, x10:0, x11:0, x12:0 + 1, x10:0 - 2) :|: x12:0 <= x10:0 - 1 && x12:0 > 0 && x11:0 > 0 && x10:0 > -1 f961_0_loop_aux_NE(x40:0, x41:0, x42:0, x43:0, x44:0) -> f887_0_loop_aux_GT(x41:0, x42:0, x43:0) :|: x43:0 > 1 && x40:0 > 0 && x44:0 - 1 >= x43:0 && x41:0 - 1 >= x40:0 f961_0_loop_aux_NE(x60:0, x61:0, x62:0, x63:0, x64:0) -> f887_0_loop_aux_GT(x61:0, x62:0, x63:0) :|: x63:0 > 1 && x60:0 > 0 && x64:0 <= x63:0 - 1 && x61:0 - 1 >= x60:0 f887_0_loop_aux_GT(x7, x8, x9) -> f887_0_loop_aux_GT(x7, 0, x9 - 1) :|: x7 > -1 && x9 > 0 && x9 - 1 <= x7 - 3 && x9 <= x7 - 1 && x8 = 0 f887_0_loop_aux_GT(x14, x15, x16) -> f887_0_loop_aux_GT(2, 1, 1) :|: TRUE && x14 = 3 && x16 = 0 f887_0_loop_aux_GT(x21, x22, x23) -> f887_0_loop_aux_GT(x21, 1, 1) :|: x21 > 3 && x23 = 0 f961_0_loop_aux_NE(x120:0, x121:0, x122:0, x123:0, x123:0) -> f887_0_loop_aux_GT(x121:0 - 1, x122:0, x123:0) :|: x120:0 > 0 && x123:0 <= x121:0 - 1 ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f887_0_loop_aux_GT(VARIABLE, VARIABLE, VARIABLE) f961_0_loop_aux_NE(INTEGER, INTEGER, VARIABLE, INTEGER, INTEGER) 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: f887_0_loop_aux_GT(x155:0, x31:0, x155:0) -> f887_0_loop_aux_GT(x155:0, c, c1) :|: c1 = x155:0 - 1 && c = 0 && x155:0 > 0 f887_0_loop_aux_GT(x20:0, c2, x22:0) -> f887_0_loop_aux_GT(c3, c4, c5) :|: c5 = x20:0 - 2 && (c4 = 0 && (c3 = x20:0 - 1 && c2 = 0)) && (x20:0 > -1 && x22:0 > 0 && x20:0 - 2 <= x20:0 - 1 && x22:0 - 1 = x20:0 - 2 && x22:0 <= x20:0 - 1 && cons_0 = 0) f887_0_loop_aux_GT(x6:0, x1:0, x2:0) -> f961_0_loop_aux_NE(x2:0, x6:0, x1:0, c6, c7) :|: c7 = x6:0 - 2 && c6 = x2:0 + 1 && (x6:0 - 1 >= x2:0 && x2:0 > 0 && x1:0 < 0 && x6:0 > -1) f887_0_loop_aux_GT(x, x1, c8) -> f887_0_loop_aux_GT(x, c9, c10) :|: c10 = 1 && (c9 = 1 && c8 = 0) && (x > 0 && x < 3 && x2 = 0) f887_0_loop_aux_GT(x10:0, x11:0, x12:0) -> f961_0_loop_aux_NE(x12:0, x10:0, x11:0, c11, c12) :|: c12 = x10:0 - 2 && c11 = x12:0 + 1 && (x12:0 <= x10:0 - 1 && x12:0 > 0 && x11:0 > 0 && x10:0 > -1) f961_0_loop_aux_NE(x40:0, x41:0, x42:0, x43:0, x44:0) -> f887_0_loop_aux_GT(x41:0, x42:0, x43:0) :|: x43:0 > 1 && x40:0 > 0 && x44:0 - 1 >= x43:0 && x41:0 - 1 >= x40:0 f961_0_loop_aux_NE(x60:0, x61:0, x62:0, x63:0, x64:0) -> f887_0_loop_aux_GT(x61:0, x62:0, x63:0) :|: x63:0 > 1 && x60:0 > 0 && x64:0 <= x63:0 - 1 && x61:0 - 1 >= x60:0 f887_0_loop_aux_GT(x7, c13, x9) -> f887_0_loop_aux_GT(x7, c14, c15) :|: c15 = x9 - 1 && (c14 = 0 && c13 = 0) && (x7 > -1 && x9 > 0 && x9 - 1 <= x7 - 3 && x9 <= x7 - 1 && x8 = 0) f887_0_loop_aux_GT(c16, x15, c17) -> f887_0_loop_aux_GT(c18, c19, c20) :|: c20 = 1 && (c19 = 1 && (c18 = 2 && (c17 = 0 && c16 = 3))) && (TRUE && x14 = 3 && x16 = 0) f887_0_loop_aux_GT(x21, x22, c21) -> f887_0_loop_aux_GT(x21, c22, c23) :|: c23 = 1 && (c22 = 1 && c21 = 0) && (x21 > 3 && x23 = 0) f961_0_loop_aux_NE(x120:0, x121:0, x122:0, x123:0, x123:0) -> f887_0_loop_aux_GT(c24, x122:0, x123:0) :|: c24 = x121:0 - 1 && (x120:0 > 0 && x123:0 <= x121:0 - 1) Found the following polynomial interpretation: [f887_0_loop_aux_GT(x, x1, x2)] = -4 + x [f961_0_loop_aux_NE(x3, x4, x5, x6, x7)] = -4 + x4 The following rules are decreasing: f887_0_loop_aux_GT(x20:0, c2, x22:0) -> f887_0_loop_aux_GT(c3, c4, c5) :|: c5 = x20:0 - 2 && (c4 = 0 && (c3 = x20:0 - 1 && c2 = 0)) && (x20:0 > -1 && x22:0 > 0 && x20:0 - 2 <= x20:0 - 1 && x22:0 - 1 = x20:0 - 2 && x22:0 <= x20:0 - 1 && cons_0 = 0) f887_0_loop_aux_GT(c16, x15, c17) -> f887_0_loop_aux_GT(c18, c19, c20) :|: c20 = 1 && (c19 = 1 && (c18 = 2 && (c17 = 0 && c16 = 3))) && (TRUE && x14 = 3 && x16 = 0) f961_0_loop_aux_NE(x120:0, x121:0, x122:0, x123:0, x123:0) -> f887_0_loop_aux_GT(c24, x122:0, x123:0) :|: c24 = x121:0 - 1 && (x120:0 > 0 && x123:0 <= x121:0 - 1) The following rules are bounded: f887_0_loop_aux_GT(x21, x22, c21) -> f887_0_loop_aux_GT(x21, c22, c23) :|: c23 = 1 && (c22 = 1 && c21 = 0) && (x21 > 3 && x23 = 0) - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS Rules: f887_0_loop_aux_GT(x155:0, x31:0, x155:0) -> f887_0_loop_aux_GT(x155:0, c, c1) :|: c1 = x155:0 - 1 && c = 0 && x155:0 > 0 f887_0_loop_aux_GT(x6:0, x1:0, x2:0) -> f961_0_loop_aux_NE(x2:0, x6:0, x1:0, c6, c7) :|: c7 = x6:0 - 2 && c6 = x2:0 + 1 && (x6:0 - 1 >= x2:0 && x2:0 > 0 && x1:0 < 0 && x6:0 > -1) f887_0_loop_aux_GT(x, x1, c8) -> f887_0_loop_aux_GT(x, c9, c10) :|: c10 = 1 && (c9 = 1 && c8 = 0) && (x > 0 && x < 3 && x2 = 0) f887_0_loop_aux_GT(x10:0, x11:0, x12:0) -> f961_0_loop_aux_NE(x12:0, x10:0, x11:0, c11, c12) :|: c12 = x10:0 - 2 && c11 = x12:0 + 1 && (x12:0 <= x10:0 - 1 && x12:0 > 0 && x11:0 > 0 && x10:0 > -1) f961_0_loop_aux_NE(x40:0, x41:0, x42:0, x43:0, x44:0) -> f887_0_loop_aux_GT(x41:0, x42:0, x43:0) :|: x43:0 > 1 && x40:0 > 0 && x44:0 - 1 >= x43:0 && x41:0 - 1 >= x40:0 f961_0_loop_aux_NE(x60:0, x61:0, x62:0, x63:0, x64:0) -> f887_0_loop_aux_GT(x61:0, x62:0, x63:0) :|: x63:0 > 1 && x60:0 > 0 && x64:0 <= x63:0 - 1 && x61:0 - 1 >= x60:0 f887_0_loop_aux_GT(x7, c13, x9) -> f887_0_loop_aux_GT(x7, c14, c15) :|: c15 = x9 - 1 && (c14 = 0 && c13 = 0) && (x7 > -1 && x9 > 0 && x9 - 1 <= x7 - 3 && x9 <= x7 - 1 && x8 = 0) f887_0_loop_aux_GT(x21, x22, c21) -> f887_0_loop_aux_GT(x21, c22, c23) :|: c23 = 1 && (c22 = 1 && c21 = 0) && (x21 > 3 && x23 = 0) - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS - PolynomialOrderProcessor Rules: f887_0_loop_aux_GT(x155:0, x31:0, x155:0) -> f887_0_loop_aux_GT(x155:0, c, c1) :|: c1 = x155:0 - 1 && c = 0 && x155:0 > 0 f887_0_loop_aux_GT(x20:0, c2, x22:0) -> f887_0_loop_aux_GT(c3, c4, c5) :|: c5 = x20:0 - 2 && (c4 = 0 && (c3 = x20:0 - 1 && c2 = 0)) && (x20:0 > -1 && x22:0 > 0 && x20:0 - 2 <= x20:0 - 1 && x22:0 - 1 = x20:0 - 2 && x22:0 <= x20:0 - 1 && cons_0 = 0) f887_0_loop_aux_GT(x6:0, x1:0, x2:0) -> f961_0_loop_aux_NE(x2:0, x6:0, x1:0, c6, c7) :|: c7 = x6:0 - 2 && c6 = x2:0 + 1 && (x6:0 - 1 >= x2:0 && x2:0 > 0 && x1:0 < 0 && x6:0 > -1) f887_0_loop_aux_GT(x, x1, c8) -> f887_0_loop_aux_GT(x, c9, c10) :|: c10 = 1 && (c9 = 1 && c8 = 0) && (x > 0 && x < 3 && x2 = 0) f887_0_loop_aux_GT(x10:0, x11:0, x12:0) -> f961_0_loop_aux_NE(x12:0, x10:0, x11:0, c11, c12) :|: c12 = x10:0 - 2 && c11 = x12:0 + 1 && (x12:0 <= x10:0 - 1 && x12:0 > 0 && x11:0 > 0 && x10:0 > -1) f961_0_loop_aux_NE(x40:0, x41:0, x42:0, x43:0, x44:0) -> f887_0_loop_aux_GT(x41:0, x42:0, x43:0) :|: x43:0 > 1 && x40:0 > 0 && x44:0 - 1 >= x43:0 && x41:0 - 1 >= x40:0 f961_0_loop_aux_NE(x60:0, x61:0, x62:0, x63:0, x64:0) -> f887_0_loop_aux_GT(x61:0, x62:0, x63:0) :|: x63:0 > 1 && x60:0 > 0 && x64:0 <= x63:0 - 1 && x61:0 - 1 >= x60:0 f887_0_loop_aux_GT(x7, c13, x9) -> f887_0_loop_aux_GT(x7, c14, c15) :|: c15 = x9 - 1 && (c14 = 0 && c13 = 0) && (x7 > -1 && x9 > 0 && x9 - 1 <= x7 - 3 && x9 <= x7 - 1 && x8 = 0) f887_0_loop_aux_GT(c16, x15, c17) -> f887_0_loop_aux_GT(c18, c19, c20) :|: c20 = 1 && (c19 = 1 && (c18 = 2 && (c17 = 0 && c16 = 3))) && (TRUE && x14 = 3 && x16 = 0) f961_0_loop_aux_NE(x120:0, x121:0, x122:0, x123:0, x123:0) -> f887_0_loop_aux_GT(c24, x122:0, x123:0) :|: c24 = x121:0 - 1 && (x120:0 > 0 && x123:0 <= x121:0 - 1) Found the following polynomial interpretation: [f887_0_loop_aux_GT(x, x1, x2)] = -2 + x [f961_0_loop_aux_NE(x3, x4, x5, x6, x7)] = -2 + x4 The following rules are decreasing: f887_0_loop_aux_GT(x20:0, c2, x22:0) -> f887_0_loop_aux_GT(c3, c4, c5) :|: c5 = x20:0 - 2 && (c4 = 0 && (c3 = x20:0 - 1 && c2 = 0)) && (x20:0 > -1 && x22:0 > 0 && x20:0 - 2 <= x20:0 - 1 && x22:0 - 1 = x20:0 - 2 && x22:0 <= x20:0 - 1 && cons_0 = 0) f887_0_loop_aux_GT(c16, x15, c17) -> f887_0_loop_aux_GT(c18, c19, c20) :|: c20 = 1 && (c19 = 1 && (c18 = 2 && (c17 = 0 && c16 = 3))) && (TRUE && x14 = 3 && x16 = 0) f961_0_loop_aux_NE(x120:0, x121:0, x122:0, x123:0, x123:0) -> f887_0_loop_aux_GT(c24, x122:0, x123:0) :|: c24 = x121:0 - 1 && (x120:0 > 0 && x123:0 <= x121:0 - 1) The following rules are bounded: f887_0_loop_aux_GT(x20:0, c2, x22:0) -> f887_0_loop_aux_GT(c3, c4, c5) :|: c5 = x20:0 - 2 && (c4 = 0 && (c3 = x20:0 - 1 && c2 = 0)) && (x20:0 > -1 && x22:0 > 0 && x20:0 - 2 <= x20:0 - 1 && x22:0 - 1 = x20:0 - 2 && x22:0 <= x20:0 - 1 && cons_0 = 0) f887_0_loop_aux_GT(x6:0, x1:0, x2:0) -> f961_0_loop_aux_NE(x2:0, x6:0, x1:0, c6, c7) :|: c7 = x6:0 - 2 && c6 = x2:0 + 1 && (x6:0 - 1 >= x2:0 && x2:0 > 0 && x1:0 < 0 && x6:0 > -1) f887_0_loop_aux_GT(x10:0, x11:0, x12:0) -> f961_0_loop_aux_NE(x12:0, x10:0, x11:0, c11, c12) :|: c12 = x10:0 - 2 && c11 = x12:0 + 1 && (x12:0 <= x10:0 - 1 && x12:0 > 0 && x11:0 > 0 && x10:0 > -1) f961_0_loop_aux_NE(x40:0, x41:0, x42:0, x43:0, x44:0) -> f887_0_loop_aux_GT(x41:0, x42:0, x43:0) :|: x43:0 > 1 && x40:0 > 0 && x44:0 - 1 >= x43:0 && x41:0 - 1 >= x40:0 f961_0_loop_aux_NE(x60:0, x61:0, x62:0, x63:0, x64:0) -> f887_0_loop_aux_GT(x61:0, x62:0, x63:0) :|: x63:0 > 1 && x60:0 > 0 && x64:0 <= x63:0 - 1 && x61:0 - 1 >= x60:0 f887_0_loop_aux_GT(x7, c13, x9) -> f887_0_loop_aux_GT(x7, c14, c15) :|: c15 = x9 - 1 && (c14 = 0 && c13 = 0) && (x7 > -1 && x9 > 0 && x9 - 1 <= x7 - 3 && x9 <= x7 - 1 && x8 = 0) f887_0_loop_aux_GT(c16, x15, c17) -> f887_0_loop_aux_GT(c18, c19, c20) :|: c20 = 1 && (c19 = 1 && (c18 = 2 && (c17 = 0 && c16 = 3))) && (TRUE && x14 = 3 && x16 = 0) - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS Rules: f887_0_loop_aux_GT(x155:0, x31:0, x155:0) -> f887_0_loop_aux_GT(x155:0, c, c1) :|: c1 = x155:0 - 1 && c = 0 && x155:0 > 0 f887_0_loop_aux_GT(x6:0, x1:0, x2:0) -> f961_0_loop_aux_NE(x2:0, x6:0, x1:0, c6, c7) :|: c7 = x6:0 - 2 && c6 = x2:0 + 1 && (x6:0 - 1 >= x2:0 && x2:0 > 0 && x1:0 < 0 && x6:0 > -1) f887_0_loop_aux_GT(x, x1, c8) -> f887_0_loop_aux_GT(x, c9, c10) :|: c10 = 1 && (c9 = 1 && c8 = 0) && (x > 0 && x < 3 && x2 = 0) f887_0_loop_aux_GT(x10:0, x11:0, x12:0) -> f961_0_loop_aux_NE(x12:0, x10:0, x11:0, c11, c12) :|: c12 = x10:0 - 2 && c11 = x12:0 + 1 && (x12:0 <= x10:0 - 1 && x12:0 > 0 && x11:0 > 0 && x10:0 > -1) f961_0_loop_aux_NE(x40:0, x41:0, x42:0, x43:0, x44:0) -> f887_0_loop_aux_GT(x41:0, x42:0, x43:0) :|: x43:0 > 1 && x40:0 > 0 && x44:0 - 1 >= x43:0 && x41:0 - 1 >= x40:0 f961_0_loop_aux_NE(x60:0, x61:0, x62:0, x63:0, x64:0) -> f887_0_loop_aux_GT(x61:0, x62:0, x63:0) :|: x63:0 > 1 && x60:0 > 0 && x64:0 <= x63:0 - 1 && x61:0 - 1 >= x60:0 f887_0_loop_aux_GT(x7, c13, x9) -> f887_0_loop_aux_GT(x7, c14, c15) :|: c15 = x9 - 1 && (c14 = 0 && c13 = 0) && (x7 > -1 && x9 > 0 && x9 - 1 <= x7 - 3 && x9 <= x7 - 1 && x8 = 0) - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS - RankingReductionPairProof Rules: f887_0_loop_aux_GT(x155:0, x31:0, x155:0) -> f887_0_loop_aux_GT(x155:0, c, c1) :|: c1 = x155:0 - 1 && c = 0 && x155:0 > 0 f887_0_loop_aux_GT(x, x1, c8) -> f887_0_loop_aux_GT(x, c9, c10) :|: c10 = 1 && (c9 = 1 && c8 = 0) && (x > 0 && x < 3 && x2 = 0) f961_0_loop_aux_NE(x120:0, x121:0, x122:0, x123:0, x123:0) -> f887_0_loop_aux_GT(c24, x122:0, x123:0) :|: c24 = x121:0 - 1 && (x120:0 > 0 && x123:0 <= x121:0 - 1) Interpretation: [ f887_0_loop_aux_GT ] = 0 [ f961_0_loop_aux_NE ] = 1 The following rules are decreasing: f961_0_loop_aux_NE(x120:0, x121:0, x122:0, x123:0, x123:0) -> f887_0_loop_aux_GT(c24, x122:0, x123:0) :|: c24 = x121:0 - 1 && (x120:0 > 0 && x123:0 <= x121:0 - 1) The following rules are bounded: f887_0_loop_aux_GT(x155:0, x31:0, x155:0) -> f887_0_loop_aux_GT(x155:0, c, c1) :|: c1 = x155:0 - 1 && c = 0 && x155:0 > 0 f887_0_loop_aux_GT(x, x1, c8) -> f887_0_loop_aux_GT(x, c9, c10) :|: c10 = 1 && (c9 = 1 && c8 = 0) && (x > 0 && x < 3 && x2 = 0) f961_0_loop_aux_NE(x120:0, x121:0, x122:0, x123:0, x123:0) -> f887_0_loop_aux_GT(c24, x122:0, x123:0) :|: c24 = x121:0 - 1 && (x120:0 > 0 && x123:0 <= x121:0 - 1) - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS - RankingReductionPairProof - IntTRS Rules: f887_0_loop_aux_GT(x155:0, x31:0, x155:0) -> f887_0_loop_aux_GT(x155:0, c, c1) :|: c1 = x155:0 - 1 && c = 0 && x155:0 > 0 f887_0_loop_aux_GT(x, x1, c8) -> f887_0_loop_aux_GT(x, c9, c10) :|: c10 = 1 && (c9 = 1 && c8 = 0) && (x > 0 && x < 3 && x2 = 0) ---------------------------------------- (10) Obligation: Rules: f887_0_loop_aux_GT(x155:0, x31:0, x155:0) -> f887_0_loop_aux_GT(x155:0, 0, x155:0 - 1) :|: x155:0 > 0 f887_0_loop_aux_GT(x, x1, x2) -> f887_0_loop_aux_GT(x, 1, 1) :|: x > 0 && x < 3 && x2 = 0 f887_0_loop_aux_GT(x6:0, x1:0, x2:0) -> f961_0_loop_aux_NE(x2:0, x6:0, x1:0, x2:0 + 1, x6:0 - 2) :|: x6:0 - 1 >= x2:0 && x2:0 > 0 && x1:0 < 0 && x6:0 > -1 f887_0_loop_aux_GT(x10:0, x11:0, x12:0) -> f961_0_loop_aux_NE(x12:0, x10:0, x11:0, x12:0 + 1, x10:0 - 2) :|: x12:0 <= x10:0 - 1 && x12:0 > 0 && x11:0 > 0 && x10:0 > -1 f961_0_loop_aux_NE(x40:0, x41:0, x42:0, x43:0, x44:0) -> f887_0_loop_aux_GT(x41:0, x42:0, x43:0) :|: x43:0 > 1 && x40:0 > 0 && x44:0 - 1 >= x43:0 && x41:0 - 1 >= x40:0 f961_0_loop_aux_NE(x60:0, x61:0, x62:0, x63:0, x64:0) -> f887_0_loop_aux_GT(x61:0, x62:0, x63:0) :|: x63:0 > 1 && x60:0 > 0 && x64:0 <= x63:0 - 1 && x61:0 - 1 >= x60:0 f887_0_loop_aux_GT(x7, x8, x9) -> f887_0_loop_aux_GT(x7, 0, x9 - 1) :|: x7 > -1 && x9 > 0 && x9 - 1 <= x7 - 3 && x9 <= x7 - 1 && x8 = 0 f887_0_loop_aux_GT(x21, x22, x23) -> f887_0_loop_aux_GT(x21, 1, 1) :|: x21 > 3 && x23 = 0 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f887_0_loop_aux_GT(x155:0, x31:0, x155:0) -> f887_0_loop_aux_GT(x155:0, 0, x155:0 - 1) :|: x155:0 > 0 (2) f887_0_loop_aux_GT(x, x1, x2) -> f887_0_loop_aux_GT(x, 1, 1) :|: x > 0 && x < 3 && x2 = 0 (3) f887_0_loop_aux_GT(x6:0, x1:0, x2:0) -> f961_0_loop_aux_NE(x2:0, x6:0, x1:0, x2:0 + 1, x6:0 - 2) :|: x6:0 - 1 >= x2:0 && x2:0 > 0 && x1:0 < 0 && x6:0 > -1 (4) f887_0_loop_aux_GT(x10:0, x11:0, x12:0) -> f961_0_loop_aux_NE(x12:0, x10:0, x11:0, x12:0 + 1, x10:0 - 2) :|: x12:0 <= x10:0 - 1 && x12:0 > 0 && x11:0 > 0 && x10:0 > -1 (5) f961_0_loop_aux_NE(x40:0, x41:0, x42:0, x43:0, x44:0) -> f887_0_loop_aux_GT(x41:0, x42:0, x43:0) :|: x43:0 > 1 && x40:0 > 0 && x44:0 - 1 >= x43:0 && x41:0 - 1 >= x40:0 (6) f961_0_loop_aux_NE(x60:0, x61:0, x62:0, x63:0, x64:0) -> f887_0_loop_aux_GT(x61:0, x62:0, x63:0) :|: x63:0 > 1 && x60:0 > 0 && x64:0 <= x63:0 - 1 && x61:0 - 1 >= x60:0 (7) f887_0_loop_aux_GT(x7, x8, x9) -> f887_0_loop_aux_GT(x7, 0, x9 - 1) :|: x7 > -1 && x9 > 0 && x9 - 1 <= x7 - 3 && x9 <= x7 - 1 && x8 = 0 (8) f887_0_loop_aux_GT(x21, x22, x23) -> f887_0_loop_aux_GT(x21, 1, 1) :|: x21 > 3 && x23 = 0 Arcs: (1) -> (2) (2) -> (1), (4) (3) -> (5), (6) (4) -> (5), (6) (5) -> (1), (3), (4), (7) (6) -> (1), (3), (4), (7) (7) -> (7), (8) (8) -> (4) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) f887_0_loop_aux_GT(x155:0, x31:0, x155:0) -> f887_0_loop_aux_GT(x155:0, 0, x155:0 - 1) :|: x155:0 > 0 (2) f961_0_loop_aux_NE(x40:0, x41:0, x42:0, x43:0, x44:0) -> f887_0_loop_aux_GT(x41:0, x42:0, x43:0) :|: x43:0 > 1 && x40:0 > 0 && x44:0 - 1 >= x43:0 && x41:0 - 1 >= x40:0 (3) f887_0_loop_aux_GT(x6:0, x1:0, x2:0) -> f961_0_loop_aux_NE(x2:0, x6:0, x1:0, x2:0 + 1, x6:0 - 2) :|: x6:0 - 1 >= x2:0 && x2:0 > 0 && x1:0 < 0 && x6:0 > -1 (4) f961_0_loop_aux_NE(x60:0, x61:0, x62:0, x63:0, x64:0) -> f887_0_loop_aux_GT(x61:0, x62:0, x63:0) :|: x63:0 > 1 && x60:0 > 0 && x64:0 <= x63:0 - 1 && x61:0 - 1 >= x60:0 (5) f887_0_loop_aux_GT(x10:0, x11:0, x12:0) -> f961_0_loop_aux_NE(x12:0, x10:0, x11:0, x12:0 + 1, x10:0 - 2) :|: x12:0 <= x10:0 - 1 && x12:0 > 0 && x11:0 > 0 && x10:0 > -1 (6) f887_0_loop_aux_GT(x21, x22, x23) -> f887_0_loop_aux_GT(x21, 1, 1) :|: x21 > 3 && x23 = 0 (7) f887_0_loop_aux_GT(x7, x8, x9) -> f887_0_loop_aux_GT(x7, 0, x9 - 1) :|: x7 > -1 && x9 > 0 && x9 - 1 <= x7 - 3 && x9 <= x7 - 1 && x8 = 0 (8) f887_0_loop_aux_GT(x, x1, x2) -> f887_0_loop_aux_GT(x, 1, 1) :|: x > 0 && x < 3 && x2 = 0 Arcs: (1) -> (8) (2) -> (1), (3), (5), (7) (3) -> (2), (4) (4) -> (1), (3), (5), (7) (5) -> (2), (4) (6) -> (5) (7) -> (6), (7) (8) -> (1), (5) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: f887_0_loop_aux_GT(x155:0:0, x31:0:0, x155:0:0) -> f887_0_loop_aux_GT(x155:0:0, 0, x155:0:0 - 1) :|: x155:0:0 > 0 f887_0_loop_aux_GT(x7:0, cons_0, x9:0) -> f887_0_loop_aux_GT(x7:0, 0, x9:0 - 1) :|: x9:0 - 1 <= x7:0 - 3 && x9:0 <= x7:0 - 1 && x9:0 > 0 && x7:0 > -1 && cons_0 = 0 f961_0_loop_aux_NE(x40:0:0, x41:0:0, x42:0:0, x43:0:0, x44:0:0) -> f887_0_loop_aux_GT(x41:0:0, x42:0:0, x43:0:0) :|: x44:0:0 - 1 >= x43:0:0 && x41:0:0 - 1 >= x40:0:0 && x40:0:0 > 0 && x43:0:0 > 1 f961_0_loop_aux_NE(x60:0:0, x61:0:0, x62:0:0, x63:0:0, x64:0:0) -> f887_0_loop_aux_GT(x61:0:0, x62:0:0, x63:0:0) :|: x64:0:0 <= x63:0:0 - 1 && x61:0:0 - 1 >= x60:0:0 && x60:0:0 > 0 && x63:0:0 > 1 f887_0_loop_aux_GT(x, x1, x2) -> f887_0_loop_aux_GT(x, 1, 1) :|: x > 3 && x2 = 0 f887_0_loop_aux_GT(x3, x4, x5) -> f887_0_loop_aux_GT(x3, 1, 1) :|: x3 > 0 && x3 < 3 && x5 = 0 f887_0_loop_aux_GT(x6:0:0, x1:0:0, x2:0:0) -> f961_0_loop_aux_NE(x2:0:0, x6:0:0, x1:0:0, x2:0:0 + 1, x6:0:0 - 2) :|: x1:0:0 < 0 && x6:0:0 > -1 && x2:0:0 > 0 && x6:0:0 - 1 >= x2:0:0 f887_0_loop_aux_GT(x10:0:0, x11:0:0, x12:0:0) -> f961_0_loop_aux_NE(x12:0:0, x10:0:0, x11:0:0, x12:0:0 + 1, x10:0:0 - 2) :|: x11:0:0 > 0 && x10:0:0 > -1 && x12:0:0 > 0 && x12:0:0 <= x10:0:0 - 1