NO
proof of prog.inttrs
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given IRSwT could be disproven:

(0) IRSwT
(1) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(2) IRSwT
(3) IRSwTTerminationDigraphProof [EQUIVALENT, 6878 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IRSwT
(7) FilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) IntTRSPeriodicNontermProof [COMPLETE, 0 ms]
(10) NO


----------------------------------------

(0)
Obligation:
Rules:
l0(___rho_2_HAT0, ___rho_3_HAT0, ___rho_4_HAT0, ___rho_5_HAT0, a22HAT0, curtimeHAT0, got_SIGHUPHAT0, last_copy_timeHAT0, tt1HAT0, wakendHAT0) -> l1(___rho_2_HATpost, ___rho_3_HATpost, ___rho_4_HATpost, ___rho_5_HATpost, a22HATpost, curtimeHATpost, got_SIGHUPHATpost, last_copy_timeHATpost, tt1HATpost, wakendHATpost) :|: wakendHAT0 = wakendHATpost && tt1HAT0 = tt1HATpost && last_copy_timeHAT0 = last_copy_timeHATpost && got_SIGHUPHAT0 = got_SIGHUPHATpost && curtimeHAT0 = curtimeHATpost && a22HAT0 = a22HATpost && ___rho_5_HAT0 = ___rho_5_HATpost && ___rho_4_HAT0 = ___rho_4_HATpost && ___rho_3_HAT0 = ___rho_3_HATpost && ___rho_2_HAT0 = ___rho_2_HATpost && got_SIGHUPHAT0 <= 0
l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l2(x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) :|: x9 = x19 && x7 = x17 && x5 = x15 && x3 = x13 && x2 = x12 && x = x10 && x18 = x11 && x11 = x11 && x14 = 1 && x16 = 0 && 1 <= x6
l3(x20, x21, x22, x23, x24, x25, x26, x27, x28, x29) -> l4(x30, x31, x32, x33, x34, x35, x36, x37, x38, x39) :|: x29 = x39 && x28 = x38 && x27 = x37 && x26 = x36 && x25 = x35 && x24 = x34 && x23 = x33 && x22 = x32 && x21 = x31 && x20 = x30
l5(x40, x41, x42, x43, x44, x45, x46, x47, x48, x49) -> l6(x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) :|: x49 = x59 && x48 = x58 && x47 = x57 && x46 = x56 && x45 = x55 && x44 = x54 && x43 = x53 && x42 = x52 && x41 = x51 && x40 = x50
l7(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69) -> l5(x70, x71, x72, x73, x74, x75, x76, x77, x78, x79) :|: x69 = x79 && x68 = x78 && x67 = x77 && x66 = x76 && x65 = x75 && x64 = x74 && x62 = x72 && x61 = x71 && x60 = x70 && x73 = x73
l8(x80, x81, x82, x83, x84, x85, x86, x87, x88, x89) -> l7(x90, x91, x92, x93, x94, x95, x96, x97, x98, x99) :|: x89 = x99 && x88 = x98 && x87 = x97 && x86 = x96 && x85 = x95 && x84 = x94 && x83 = x93 && x82 = x92 && x81 = x91 && x80 = x90 && 1 + x85 - x87 <= 1000
l8(x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) -> l7(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x108 = x118 && x107 = x117 && x106 = x116 && x105 = x115 && x104 = x114 && x103 = x113 && x102 = x112 && x101 = x111 && x100 = x110 && x119 = 1 && 1000 <= x105 - x107
l9(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129) -> l7(x130, x131, x132, x133, x134, x135, x136, x137, x138, x139) :|: x129 = x139 && x128 = x138 && x127 = x137 && x126 = x136 && x125 = x135 && x124 = x134 && x123 = x133 && x122 = x132 && x121 = x131 && x120 = x130 && 1 <= x129
l9(x140, x141, x142, x143, x144, x145, x146, x147, x148, x149) -> l8(x150, x151, x152, x153, x154, x155, x156, x157, x158, x159) :|: x149 = x159 && x148 = x158 && x147 = x157 && x146 = x156 && x144 = x154 && x143 = x153 && x142 = x152 && x141 = x151 && x140 = x150 && x155 = x155 && x149 <= 0
l6(x160, x161, x162, x163, x164, x165, x166, x167, x168, x169) -> l10(x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x169 = x179 && x168 = x178 && x167 = x177 && x166 = x176 && x165 = x175 && x164 = x174 && x163 = x173 && x162 = x172 && x161 = x171 && x160 = x170
l10(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189) -> l6(x190, x191, x192, x193, x194, x195, x196, x197, x198, x199) :|: x189 = x199 && x188 = x198 && x187 = x197 && x186 = x196 && x185 = x195 && x184 = x194 && x183 = x193 && x182 = x192 && x181 = x191 && x180 = x190
l1(x200, x201, x202, x203, x204, x205, x206, x207, x208, x209) -> l9(x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) :|: x209 = x219 && x208 = x218 && x207 = x217 && x206 = x216 && x205 = x215 && x204 = x214 && x203 = x213 && x202 = x212 && x201 = x211 && x200 = x210 && x209 <= 0
l1(x220, x221, x222, x223, x224, x225, x226, x227, x228, x229) -> l9(x230, x231, x232, x233, x234, x235, x236, x237, x238, x239) :|: x228 = x238 && x226 = x236 && x225 = x235 && x224 = x234 && x223 = x233 && x221 = x231 && x220 = x230 && x237 = x232 && x232 = x232 && x239 = 0 && 1 <= x229
l2(x240, x241, x242, x243, x244, x245, x246, x247, x248, x249) -> l1(x250, x251, x252, x253, x254, x255, x256, x257, x258, x259) :|: x249 = x259 && x248 = x258 && x247 = x257 && x246 = x256 && x245 = x255 && x244 = x254 && x243 = x253 && x242 = x252 && x241 = x251 && x240 = x250 && 1 <= x248
l2(x260, x261, x262, x263, x264, x265, x266, x267, x268, x269) -> l5(x270, x271, x272, x273, x274, x275, x276, x277, x278, x279) :|: x269 = x279 && x268 = x278 && x267 = x277 && x266 = x276 && x265 = x275 && x264 = x274 && x263 = x273 && x262 = x272 && x261 = x271 && x260 = x270 && x268 <= 0
l11(x280, x281, x282, x283, x284, x285, x286, x287, x288, x289) -> l0(x290, x291, x292, x293, x294, x295, x296, x297, x298, x299) :|: x300 = 1 && x290 = x290 && x296 = x290 && x299 = 1 && x281 = x291 && x282 = x292 && x283 = x293 && x284 = x294 && x285 = x295 && x287 = x297 && x288 = x298
l12(x301, x302, x303, x304, x305, x306, x307, x308, x309, x310) -> l11(x311, x312, x313, x314, x315, x316, x317, x318, x319, x320) :|: x310 = x320 && x309 = x319 && x308 = x318 && x307 = x317 && x306 = x316 && x305 = x315 && x304 = x314 && x303 = x313 && x302 = x312 && x301 = x311
Start term: l12(___rho_2_HAT0, ___rho_3_HAT0, ___rho_4_HAT0, ___rho_5_HAT0, a22HAT0, curtimeHAT0, got_SIGHUPHAT0, last_copy_timeHAT0, tt1HAT0, wakendHAT0)

----------------------------------------

(1) IRSFormatTransformerProof (EQUIVALENT)
Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
----------------------------------------

(2)
Obligation:
Rules:
l0(___rho_2_HAT0, ___rho_3_HAT0, ___rho_4_HAT0, ___rho_5_HAT0, a22HAT0, curtimeHAT0, got_SIGHUPHAT0, last_copy_timeHAT0, tt1HAT0, wakendHAT0) -> l1(___rho_2_HATpost, ___rho_3_HATpost, ___rho_4_HATpost, ___rho_5_HATpost, a22HATpost, curtimeHATpost, got_SIGHUPHATpost, last_copy_timeHATpost, tt1HATpost, wakendHATpost) :|: wakendHAT0 = wakendHATpost && tt1HAT0 = tt1HATpost && last_copy_timeHAT0 = last_copy_timeHATpost && got_SIGHUPHAT0 = got_SIGHUPHATpost && curtimeHAT0 = curtimeHATpost && a22HAT0 = a22HATpost && ___rho_5_HAT0 = ___rho_5_HATpost && ___rho_4_HAT0 = ___rho_4_HATpost && ___rho_3_HAT0 = ___rho_3_HATpost && ___rho_2_HAT0 = ___rho_2_HATpost && got_SIGHUPHAT0 <= 0
l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l2(x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) :|: x9 = x19 && x7 = x17 && x5 = x15 && x3 = x13 && x2 = x12 && x = x10 && x18 = x11 && x11 = x11 && x14 = 1 && x16 = 0 && 1 <= x6
l3(x20, x21, x22, x23, x24, x25, x26, x27, x28, x29) -> l4(x30, x31, x32, x33, x34, x35, x36, x37, x38, x39) :|: x29 = x39 && x28 = x38 && x27 = x37 && x26 = x36 && x25 = x35 && x24 = x34 && x23 = x33 && x22 = x32 && x21 = x31 && x20 = x30
l5(x40, x41, x42, x43, x44, x45, x46, x47, x48, x49) -> l6(x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) :|: x49 = x59 && x48 = x58 && x47 = x57 && x46 = x56 && x45 = x55 && x44 = x54 && x43 = x53 && x42 = x52 && x41 = x51 && x40 = x50
l7(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69) -> l5(x70, x71, x72, x73, x74, x75, x76, x77, x78, x79) :|: x69 = x79 && x68 = x78 && x67 = x77 && x66 = x76 && x65 = x75 && x64 = x74 && x62 = x72 && x61 = x71 && x60 = x70 && x73 = x73
l8(x80, x81, x82, x83, x84, x85, x86, x87, x88, x89) -> l7(x90, x91, x92, x93, x94, x95, x96, x97, x98, x99) :|: x89 = x99 && x88 = x98 && x87 = x97 && x86 = x96 && x85 = x95 && x84 = x94 && x83 = x93 && x82 = x92 && x81 = x91 && x80 = x90 && 1 + x85 - x87 <= 1000
l8(x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) -> l7(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x108 = x118 && x107 = x117 && x106 = x116 && x105 = x115 && x104 = x114 && x103 = x113 && x102 = x112 && x101 = x111 && x100 = x110 && x119 = 1 && 1000 <= x105 - x107
l9(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129) -> l7(x130, x131, x132, x133, x134, x135, x136, x137, x138, x139) :|: x129 = x139 && x128 = x138 && x127 = x137 && x126 = x136 && x125 = x135 && x124 = x134 && x123 = x133 && x122 = x132 && x121 = x131 && x120 = x130 && 1 <= x129
l9(x140, x141, x142, x143, x144, x145, x146, x147, x148, x149) -> l8(x150, x151, x152, x153, x154, x155, x156, x157, x158, x159) :|: x149 = x159 && x148 = x158 && x147 = x157 && x146 = x156 && x144 = x154 && x143 = x153 && x142 = x152 && x141 = x151 && x140 = x150 && x155 = x155 && x149 <= 0
l6(x160, x161, x162, x163, x164, x165, x166, x167, x168, x169) -> l10(x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x169 = x179 && x168 = x178 && x167 = x177 && x166 = x176 && x165 = x175 && x164 = x174 && x163 = x173 && x162 = x172 && x161 = x171 && x160 = x170
l10(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189) -> l6(x190, x191, x192, x193, x194, x195, x196, x197, x198, x199) :|: x189 = x199 && x188 = x198 && x187 = x197 && x186 = x196 && x185 = x195 && x184 = x194 && x183 = x193 && x182 = x192 && x181 = x191 && x180 = x190
l1(x200, x201, x202, x203, x204, x205, x206, x207, x208, x209) -> l9(x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) :|: x209 = x219 && x208 = x218 && x207 = x217 && x206 = x216 && x205 = x215 && x204 = x214 && x203 = x213 && x202 = x212 && x201 = x211 && x200 = x210 && x209 <= 0
l1(x220, x221, x222, x223, x224, x225, x226, x227, x228, x229) -> l9(x230, x231, x232, x233, x234, x235, x236, x237, x238, x239) :|: x228 = x238 && x226 = x236 && x225 = x235 && x224 = x234 && x223 = x233 && x221 = x231 && x220 = x230 && x237 = x232 && x232 = x232 && x239 = 0 && 1 <= x229
l2(x240, x241, x242, x243, x244, x245, x246, x247, x248, x249) -> l1(x250, x251, x252, x253, x254, x255, x256, x257, x258, x259) :|: x249 = x259 && x248 = x258 && x247 = x257 && x246 = x256 && x245 = x255 && x244 = x254 && x243 = x253 && x242 = x252 && x241 = x251 && x240 = x250 && 1 <= x248
l2(x260, x261, x262, x263, x264, x265, x266, x267, x268, x269) -> l5(x270, x271, x272, x273, x274, x275, x276, x277, x278, x279) :|: x269 = x279 && x268 = x278 && x267 = x277 && x266 = x276 && x265 = x275 && x264 = x274 && x263 = x273 && x262 = x272 && x261 = x271 && x260 = x270 && x268 <= 0
l11(x280, x281, x282, x283, x284, x285, x286, x287, x288, x289) -> l0(x290, x291, x292, x293, x294, x295, x296, x297, x298, x299) :|: x300 = 1 && x290 = x290 && x296 = x290 && x299 = 1 && x281 = x291 && x282 = x292 && x283 = x293 && x284 = x294 && x285 = x295 && x287 = x297 && x288 = x298
l12(x301, x302, x303, x304, x305, x306, x307, x308, x309, x310) -> l11(x311, x312, x313, x314, x315, x316, x317, x318, x319, x320) :|: x310 = x320 && x309 = x319 && x308 = x318 && x307 = x317 && x306 = x316 && x305 = x315 && x304 = x314 && x303 = x313 && x302 = x312 && x301 = x311
Start term: l12(___rho_2_HAT0, ___rho_3_HAT0, ___rho_4_HAT0, ___rho_5_HAT0, a22HAT0, curtimeHAT0, got_SIGHUPHAT0, last_copy_timeHAT0, tt1HAT0, wakendHAT0)

----------------------------------------

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(___rho_2_HAT0, ___rho_3_HAT0, ___rho_4_HAT0, ___rho_5_HAT0, a22HAT0, curtimeHAT0, got_SIGHUPHAT0, last_copy_timeHAT0, tt1HAT0, wakendHAT0) -> l1(___rho_2_HATpost, ___rho_3_HATpost, ___rho_4_HATpost, ___rho_5_HATpost, a22HATpost, curtimeHATpost, got_SIGHUPHATpost, last_copy_timeHATpost, tt1HATpost, wakendHATpost) :|: wakendHAT0 = wakendHATpost && tt1HAT0 = tt1HATpost && last_copy_timeHAT0 = last_copy_timeHATpost && got_SIGHUPHAT0 = got_SIGHUPHATpost && curtimeHAT0 = curtimeHATpost && a22HAT0 = a22HATpost && ___rho_5_HAT0 = ___rho_5_HATpost && ___rho_4_HAT0 = ___rho_4_HATpost && ___rho_3_HAT0 = ___rho_3_HATpost && ___rho_2_HAT0 = ___rho_2_HATpost && got_SIGHUPHAT0 <= 0
(2) l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l2(x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) :|: x9 = x19 && x7 = x17 && x5 = x15 && x3 = x13 && x2 = x12 && x = x10 && x18 = x11 && x11 = x11 && x14 = 1 && x16 = 0 && 1 <= x6
(3) l3(x20, x21, x22, x23, x24, x25, x26, x27, x28, x29) -> l4(x30, x31, x32, x33, x34, x35, x36, x37, x38, x39) :|: x29 = x39 && x28 = x38 && x27 = x37 && x26 = x36 && x25 = x35 && x24 = x34 && x23 = x33 && x22 = x32 && x21 = x31 && x20 = x30
(4) l5(x40, x41, x42, x43, x44, x45, x46, x47, x48, x49) -> l6(x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) :|: x49 = x59 && x48 = x58 && x47 = x57 && x46 = x56 && x45 = x55 && x44 = x54 && x43 = x53 && x42 = x52 && x41 = x51 && x40 = x50
(5) l7(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69) -> l5(x70, x71, x72, x73, x74, x75, x76, x77, x78, x79) :|: x69 = x79 && x68 = x78 && x67 = x77 && x66 = x76 && x65 = x75 && x64 = x74 && x62 = x72 && x61 = x71 && x60 = x70 && x73 = x73
(6) l8(x80, x81, x82, x83, x84, x85, x86, x87, x88, x89) -> l7(x90, x91, x92, x93, x94, x95, x96, x97, x98, x99) :|: x89 = x99 && x88 = x98 && x87 = x97 && x86 = x96 && x85 = x95 && x84 = x94 && x83 = x93 && x82 = x92 && x81 = x91 && x80 = x90 && 1 + x85 - x87 <= 1000
(7) l8(x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) -> l7(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x108 = x118 && x107 = x117 && x106 = x116 && x105 = x115 && x104 = x114 && x103 = x113 && x102 = x112 && x101 = x111 && x100 = x110 && x119 = 1 && 1000 <= x105 - x107
(8) l9(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129) -> l7(x130, x131, x132, x133, x134, x135, x136, x137, x138, x139) :|: x129 = x139 && x128 = x138 && x127 = x137 && x126 = x136 && x125 = x135 && x124 = x134 && x123 = x133 && x122 = x132 && x121 = x131 && x120 = x130 && 1 <= x129
(9) l9(x140, x141, x142, x143, x144, x145, x146, x147, x148, x149) -> l8(x150, x151, x152, x153, x154, x155, x156, x157, x158, x159) :|: x149 = x159 && x148 = x158 && x147 = x157 && x146 = x156 && x144 = x154 && x143 = x153 && x142 = x152 && x141 = x151 && x140 = x150 && x155 = x155 && x149 <= 0
(10) l6(x160, x161, x162, x163, x164, x165, x166, x167, x168, x169) -> l10(x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x169 = x179 && x168 = x178 && x167 = x177 && x166 = x176 && x165 = x175 && x164 = x174 && x163 = x173 && x162 = x172 && x161 = x171 && x160 = x170
(11) l10(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189) -> l6(x190, x191, x192, x193, x194, x195, x196, x197, x198, x199) :|: x189 = x199 && x188 = x198 && x187 = x197 && x186 = x196 && x185 = x195 && x184 = x194 && x183 = x193 && x182 = x192 && x181 = x191 && x180 = x190
(12) l1(x200, x201, x202, x203, x204, x205, x206, x207, x208, x209) -> l9(x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) :|: x209 = x219 && x208 = x218 && x207 = x217 && x206 = x216 && x205 = x215 && x204 = x214 && x203 = x213 && x202 = x212 && x201 = x211 && x200 = x210 && x209 <= 0
(13) l1(x220, x221, x222, x223, x224, x225, x226, x227, x228, x229) -> l9(x230, x231, x232, x233, x234, x235, x236, x237, x238, x239) :|: x228 = x238 && x226 = x236 && x225 = x235 && x224 = x234 && x223 = x233 && x221 = x231 && x220 = x230 && x237 = x232 && x232 = x232 && x239 = 0 && 1 <= x229
(14) l2(x240, x241, x242, x243, x244, x245, x246, x247, x248, x249) -> l1(x250, x251, x252, x253, x254, x255, x256, x257, x258, x259) :|: x249 = x259 && x248 = x258 && x247 = x257 && x246 = x256 && x245 = x255 && x244 = x254 && x243 = x253 && x242 = x252 && x241 = x251 && x240 = x250 && 1 <= x248
(15) l2(x260, x261, x262, x263, x264, x265, x266, x267, x268, x269) -> l5(x270, x271, x272, x273, x274, x275, x276, x277, x278, x279) :|: x269 = x279 && x268 = x278 && x267 = x277 && x266 = x276 && x265 = x275 && x264 = x274 && x263 = x273 && x262 = x272 && x261 = x271 && x260 = x270 && x268 <= 0
(16) l11(x280, x281, x282, x283, x284, x285, x286, x287, x288, x289) -> l0(x290, x291, x292, x293, x294, x295, x296, x297, x298, x299) :|: x300 = 1 && x290 = x290 && x296 = x290 && x299 = 1 && x281 = x291 && x282 = x292 && x283 = x293 && x284 = x294 && x285 = x295 && x287 = x297 && x288 = x298
(17) l12(x301, x302, x303, x304, x305, x306, x307, x308, x309, x310) -> l11(x311, x312, x313, x314, x315, x316, x317, x318, x319, x320) :|: x310 = x320 && x309 = x319 && x308 = x318 && x307 = x317 && x306 = x316 && x305 = x315 && x304 = x314 && x303 = x313 && x302 = x312 && x301 = x311

Arcs:
(1) -> (12), (13)
(2) -> (14), (15)
(4) -> (10)
(5) -> (4)
(6) -> (5)
(7) -> (5)
(8) -> (5)
(9) -> (6), (7)
(10) -> (11)
(11) -> (10)
(12) -> (9)
(13) -> (9)
(14) -> (12), (13)
(15) -> (4)
(16) -> (1), (2)
(17) -> (16)

This digraph is fully evaluated!
----------------------------------------

(4)
Obligation:

Termination digraph:
Nodes:
(1) l6(x160, x161, x162, x163, x164, x165, x166, x167, x168, x169) -> l10(x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x169 = x179 && x168 = x178 && x167 = x177 && x166 = x176 && x165 = x175 && x164 = x174 && x163 = x173 && x162 = x172 && x161 = x171 && x160 = x170
(2) l10(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189) -> l6(x190, x191, x192, x193, x194, x195, x196, x197, x198, x199) :|: x189 = x199 && x188 = x198 && x187 = x197 && x186 = x196 && x185 = x195 && x184 = x194 && x183 = x193 && x182 = x192 && x181 = x191 && x180 = x190

Arcs:
(1) -> (2)
(2) -> (1)

This digraph is fully evaluated!

----------------------------------------

(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
----------------------------------------

(6)
Obligation:
Rules:
l6(x160:0, x161:0, x162:0, x163:0, x164:0, x165:0, x166:0, x167:0, x168:0, x169:0) -> l6(x160:0, x161:0, x162:0, x163:0, x164:0, x165:0, x166:0, x167:0, x168:0, x169:0) :|: TRUE

----------------------------------------

(7) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
l6(VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(8)
Obligation:
Rules:
l6(x160:0, x161:0, x162:0, x163:0, x164:0, x165:0, x166:0, x167:0, x168:0, x169:0) -> l6(x160:0, x161:0, x162:0, x163:0, x164:0, x165:0, x166:0, x167:0, x168:0, x169:0) :|: TRUE

----------------------------------------

(9) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x160:0, x161:0, x162:0, x163:0, x164:0, x165:0, x166:0, x167:0, x168:0, x169:0) -> f(1, x160:0, x161:0, x162:0, x163:0, x164:0, x165:0, x166:0, x167:0, x168:0, x169:0) :|: pc = 1 && TRUE
Witness term starting non-terminating reduction: f(1, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8)
----------------------------------------

(10)
NO