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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 8645 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 17 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 36 ms]
        (11) IntTRS
        (12) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 19 ms]
        (16) IRSwT
        (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (18) IRSwT
        (19) TempFilterProof [SOUND, 45 ms]
        (20) IntTRS
        (21) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (22) IntTRS
        (23) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (24) YES


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

(0)
Obligation:
Rules:
l0(Index2HAT0, Index7HAT0, Sorted5HAT0, Temp6HAT0, fact3HAT0, factorHAT0, i8HAT0) -> l1(Index2HATpost, Index7HATpost, Sorted5HATpost, Temp6HATpost, fact3HATpost, factorHATpost, i8HATpost) :|: factorHAT0 = factorHATpost && fact3HAT0 = fact3HATpost && Temp6HAT0 = Temp6HATpost && Index7HAT0 = Index7HATpost && Index2HAT0 = Index2HATpost && i8HATpost = 1 && Sorted5HATpost = 0 && 101 <= Index2HAT0
l0(x, x1, x2, x3, x4, x5, x6) -> l2(x7, x8, x9, x10, x11, x12, x13) :|: x6 = x13 && x5 = x12 && x4 = x11 && x3 = x10 && x2 = x9 && x1 = x8 && x7 = 1 + x && x <= 100
l2(x14, x15, x16, x17, x18, x19, x20) -> l0(x21, x22, x23, x24, x25, x26, x27) :|: x20 = x27 && x19 = x26 && x18 = x25 && x17 = x24 && x16 = x23 && x15 = x22 && x14 = x21
l3(x28, x29, x30, x31, x32, x33, x34) -> l4(x35, x36, x37, x38, x39, x40, x41) :|: x34 = x41 && x33 = x40 && x32 = x39 && x31 = x38 && x30 = x37 && x29 = x36 && x28 = x35
l5(x42, x43, x44, x45, x46, x47, x48) -> l3(x49, x50, x51, x52, x53, x54, x55) :|: x48 = x55 && x47 = x54 && x46 = x53 && x45 = x52 && x44 = x51 && x43 = x50 && x42 = x49
l6(x56, x57, x58, x59, x60, x61, x62) -> l7(x63, x64, x65, x66, x67, x68, x69) :|: x62 = x69 && x61 = x68 && x60 = x67 && x59 = x66 && x58 = x65 && x57 = x64 && x56 = x63
l7(x70, x71, x72, x73, x74, x75, x76) -> l1(x77, x78, x79, x80, x81, x82, x83) :|: x75 = x82 && x74 = x81 && x73 = x80 && x72 = x79 && x71 = x78 && x70 = x77 && x83 = 1 + x76 && 0 <= x72 && x72 <= 0
l7(x84, x85, x86, x87, x88, x89, x90) -> l5(x91, x92, x93, x94, x95, x96, x97) :|: x90 = x97 && x89 = x96 && x88 = x95 && x87 = x94 && x86 = x93 && x85 = x92 && x84 = x91 && 1 <= x86
l7(x98, x99, x100, x101, x102, x103, x104) -> l5(x105, x106, x107, x108, x109, x110, x111) :|: x104 = x111 && x103 = x110 && x102 = x109 && x101 = x108 && x100 = x107 && x99 = x106 && x98 = x105 && 1 + x100 <= 0
l8(x112, x113, x114, x115, x116, x117, x118) -> l9(x119, x120, x121, x122, x123, x124, x125) :|: x118 = x125 && x117 = x124 && x116 = x123 && x115 = x122 && x114 = x121 && x112 = x119 && x120 = 1 + x113
l1(x126, x127, x128, x129, x130, x131, x132) -> l10(x133, x134, x135, x136, x137, x138, x139) :|: x132 = x139 && x131 = x138 && x130 = x137 && x129 = x136 && x128 = x135 && x127 = x134 && x126 = x133
l11(x140, x141, x142, x143, x144, x145, x146) -> l8(x147, x148, x149, x150, x151, x152, x153) :|: x146 = x153 && x145 = x152 && x144 = x151 && x141 = x148 && x140 = x147 && x149 = 0 && x150 = x150
l11(x154, x155, x156, x157, x158, x159, x160) -> l8(x161, x162, x163, x164, x165, x166, x167) :|: x160 = x167 && x159 = x166 && x158 = x165 && x157 = x164 && x156 = x163 && x155 = x162 && x154 = x161
l12(x168, x169, x170, x171, x172, x173, x174) -> l11(x175, x176, x177, x178, x179, x180, x181) :|: x174 = x181 && x173 = x180 && x172 = x179 && x171 = x178 && x170 = x177 && x169 = x176 && x168 = x175 && x169 <= 100 - x174
l12(x182, x183, x184, x185, x186, x187, x188) -> l6(x189, x190, x191, x192, x193, x194, x195) :|: x188 = x195 && x187 = x194 && x186 = x193 && x185 = x192 && x184 = x191 && x183 = x190 && x182 = x189 && 101 - x188 <= x183
l13(x196, x197, x198, x199, x200, x201, x202) -> l6(x203, x204, x205, x206, x207, x208, x209) :|: x202 = x209 && x201 = x208 && x200 = x207 && x199 = x206 && x198 = x205 && x197 = x204 && x196 = x203 && 100 <= x197
l13(x210, x211, x212, x213, x214, x215, x216) -> l12(x217, x218, x219, x220, x221, x222, x223) :|: x216 = x223 && x215 = x222 && x214 = x221 && x213 = x220 && x212 = x219 && x211 = x218 && x210 = x217 && x211 <= 99
l9(x224, x225, x226, x227, x228, x229, x230) -> l13(x231, x232, x233, x234, x235, x236, x237) :|: x230 = x237 && x229 = x236 && x228 = x235 && x227 = x234 && x226 = x233 && x225 = x232 && x224 = x231
l10(x238, x239, x240, x241, x242, x243, x244) -> l3(x245, x246, x247, x248, x249, x250, x251) :|: x244 = x251 && x243 = x250 && x242 = x249 && x241 = x248 && x240 = x247 && x239 = x246 && x238 = x245 && 100 <= x244
l10(x252, x253, x254, x255, x256, x257, x258) -> l9(x259, x260, x261, x262, x263, x264, x265) :|: x258 = x265 && x257 = x264 && x256 = x263 && x255 = x262 && x252 = x259 && x260 = 1 && x261 = 1 && x258 <= 99
l14(x266, x267, x268, x269, x270, x271, x272) -> l2(x273, x274, x275, x276, x277, x278, x279) :|: x272 = x279 && x269 = x276 && x268 = x275 && x267 = x274 && x273 = 1 && x277 = x278 && x278 = -1
l15(x280, x281, x282, x283, x284, x285, x286) -> l14(x287, x288, x289, x290, x291, x292, x293) :|: x286 = x293 && x285 = x292 && x284 = x291 && x283 = x290 && x282 = x289 && x281 = x288 && x280 = x287
Start term: l15(Index2HAT0, Index7HAT0, Sorted5HAT0, Temp6HAT0, fact3HAT0, factorHAT0, i8HAT0)

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

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

(2)
Obligation:
Rules:
l0(Index2HAT0, Index7HAT0, Sorted5HAT0, Temp6HAT0, fact3HAT0, factorHAT0, i8HAT0) -> l1(Index2HATpost, Index7HATpost, Sorted5HATpost, Temp6HATpost, fact3HATpost, factorHATpost, i8HATpost) :|: factorHAT0 = factorHATpost && fact3HAT0 = fact3HATpost && Temp6HAT0 = Temp6HATpost && Index7HAT0 = Index7HATpost && Index2HAT0 = Index2HATpost && i8HATpost = 1 && Sorted5HATpost = 0 && 101 <= Index2HAT0
l0(x, x1, x2, x3, x4, x5, x6) -> l2(x7, x8, x9, x10, x11, x12, x13) :|: x6 = x13 && x5 = x12 && x4 = x11 && x3 = x10 && x2 = x9 && x1 = x8 && x7 = 1 + x && x <= 100
l2(x14, x15, x16, x17, x18, x19, x20) -> l0(x21, x22, x23, x24, x25, x26, x27) :|: x20 = x27 && x19 = x26 && x18 = x25 && x17 = x24 && x16 = x23 && x15 = x22 && x14 = x21
l3(x28, x29, x30, x31, x32, x33, x34) -> l4(x35, x36, x37, x38, x39, x40, x41) :|: x34 = x41 && x33 = x40 && x32 = x39 && x31 = x38 && x30 = x37 && x29 = x36 && x28 = x35
l5(x42, x43, x44, x45, x46, x47, x48) -> l3(x49, x50, x51, x52, x53, x54, x55) :|: x48 = x55 && x47 = x54 && x46 = x53 && x45 = x52 && x44 = x51 && x43 = x50 && x42 = x49
l6(x56, x57, x58, x59, x60, x61, x62) -> l7(x63, x64, x65, x66, x67, x68, x69) :|: x62 = x69 && x61 = x68 && x60 = x67 && x59 = x66 && x58 = x65 && x57 = x64 && x56 = x63
l7(x70, x71, x72, x73, x74, x75, x76) -> l1(x77, x78, x79, x80, x81, x82, x83) :|: x75 = x82 && x74 = x81 && x73 = x80 && x72 = x79 && x71 = x78 && x70 = x77 && x83 = 1 + x76 && 0 <= x72 && x72 <= 0
l7(x84, x85, x86, x87, x88, x89, x90) -> l5(x91, x92, x93, x94, x95, x96, x97) :|: x90 = x97 && x89 = x96 && x88 = x95 && x87 = x94 && x86 = x93 && x85 = x92 && x84 = x91 && 1 <= x86
l7(x98, x99, x100, x101, x102, x103, x104) -> l5(x105, x106, x107, x108, x109, x110, x111) :|: x104 = x111 && x103 = x110 && x102 = x109 && x101 = x108 && x100 = x107 && x99 = x106 && x98 = x105 && 1 + x100 <= 0
l8(x112, x113, x114, x115, x116, x117, x118) -> l9(x119, x120, x121, x122, x123, x124, x125) :|: x118 = x125 && x117 = x124 && x116 = x123 && x115 = x122 && x114 = x121 && x112 = x119 && x120 = 1 + x113
l1(x126, x127, x128, x129, x130, x131, x132) -> l10(x133, x134, x135, x136, x137, x138, x139) :|: x132 = x139 && x131 = x138 && x130 = x137 && x129 = x136 && x128 = x135 && x127 = x134 && x126 = x133
l11(x140, x141, x142, x143, x144, x145, x146) -> l8(x147, x148, x149, x150, x151, x152, x153) :|: x146 = x153 && x145 = x152 && x144 = x151 && x141 = x148 && x140 = x147 && x149 = 0 && x150 = x150
l11(x154, x155, x156, x157, x158, x159, x160) -> l8(x161, x162, x163, x164, x165, x166, x167) :|: x160 = x167 && x159 = x166 && x158 = x165 && x157 = x164 && x156 = x163 && x155 = x162 && x154 = x161
l12(x168, x169, x170, x171, x172, x173, x174) -> l11(x175, x176, x177, x178, x179, x180, x181) :|: x174 = x181 && x173 = x180 && x172 = x179 && x171 = x178 && x170 = x177 && x169 = x176 && x168 = x175 && x169 <= 100 - x174
l12(x182, x183, x184, x185, x186, x187, x188) -> l6(x189, x190, x191, x192, x193, x194, x195) :|: x188 = x195 && x187 = x194 && x186 = x193 && x185 = x192 && x184 = x191 && x183 = x190 && x182 = x189 && 101 - x188 <= x183
l13(x196, x197, x198, x199, x200, x201, x202) -> l6(x203, x204, x205, x206, x207, x208, x209) :|: x202 = x209 && x201 = x208 && x200 = x207 && x199 = x206 && x198 = x205 && x197 = x204 && x196 = x203 && 100 <= x197
l13(x210, x211, x212, x213, x214, x215, x216) -> l12(x217, x218, x219, x220, x221, x222, x223) :|: x216 = x223 && x215 = x222 && x214 = x221 && x213 = x220 && x212 = x219 && x211 = x218 && x210 = x217 && x211 <= 99
l9(x224, x225, x226, x227, x228, x229, x230) -> l13(x231, x232, x233, x234, x235, x236, x237) :|: x230 = x237 && x229 = x236 && x228 = x235 && x227 = x234 && x226 = x233 && x225 = x232 && x224 = x231
l10(x238, x239, x240, x241, x242, x243, x244) -> l3(x245, x246, x247, x248, x249, x250, x251) :|: x244 = x251 && x243 = x250 && x242 = x249 && x241 = x248 && x240 = x247 && x239 = x246 && x238 = x245 && 100 <= x244
l10(x252, x253, x254, x255, x256, x257, x258) -> l9(x259, x260, x261, x262, x263, x264, x265) :|: x258 = x265 && x257 = x264 && x256 = x263 && x255 = x262 && x252 = x259 && x260 = 1 && x261 = 1 && x258 <= 99
l14(x266, x267, x268, x269, x270, x271, x272) -> l2(x273, x274, x275, x276, x277, x278, x279) :|: x272 = x279 && x269 = x276 && x268 = x275 && x267 = x274 && x273 = 1 && x277 = x278 && x278 = -1
l15(x280, x281, x282, x283, x284, x285, x286) -> l14(x287, x288, x289, x290, x291, x292, x293) :|: x286 = x293 && x285 = x292 && x284 = x291 && x283 = x290 && x282 = x289 && x281 = x288 && x280 = x287
Start term: l15(Index2HAT0, Index7HAT0, Sorted5HAT0, Temp6HAT0, fact3HAT0, factorHAT0, i8HAT0)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(Index2HAT0, Index7HAT0, Sorted5HAT0, Temp6HAT0, fact3HAT0, factorHAT0, i8HAT0) -> l1(Index2HATpost, Index7HATpost, Sorted5HATpost, Temp6HATpost, fact3HATpost, factorHATpost, i8HATpost) :|: factorHAT0 = factorHATpost && fact3HAT0 = fact3HATpost && Temp6HAT0 = Temp6HATpost && Index7HAT0 = Index7HATpost && Index2HAT0 = Index2HATpost && i8HATpost = 1 && Sorted5HATpost = 0 && 101 <= Index2HAT0
(2) l0(x, x1, x2, x3, x4, x5, x6) -> l2(x7, x8, x9, x10, x11, x12, x13) :|: x6 = x13 && x5 = x12 && x4 = x11 && x3 = x10 && x2 = x9 && x1 = x8 && x7 = 1 + x && x <= 100
(3) l2(x14, x15, x16, x17, x18, x19, x20) -> l0(x21, x22, x23, x24, x25, x26, x27) :|: x20 = x27 && x19 = x26 && x18 = x25 && x17 = x24 && x16 = x23 && x15 = x22 && x14 = x21
(4) l3(x28, x29, x30, x31, x32, x33, x34) -> l4(x35, x36, x37, x38, x39, x40, x41) :|: x34 = x41 && x33 = x40 && x32 = x39 && x31 = x38 && x30 = x37 && x29 = x36 && x28 = x35
(5) l5(x42, x43, x44, x45, x46, x47, x48) -> l3(x49, x50, x51, x52, x53, x54, x55) :|: x48 = x55 && x47 = x54 && x46 = x53 && x45 = x52 && x44 = x51 && x43 = x50 && x42 = x49
(6) l6(x56, x57, x58, x59, x60, x61, x62) -> l7(x63, x64, x65, x66, x67, x68, x69) :|: x62 = x69 && x61 = x68 && x60 = x67 && x59 = x66 && x58 = x65 && x57 = x64 && x56 = x63
(7) l7(x70, x71, x72, x73, x74, x75, x76) -> l1(x77, x78, x79, x80, x81, x82, x83) :|: x75 = x82 && x74 = x81 && x73 = x80 && x72 = x79 && x71 = x78 && x70 = x77 && x83 = 1 + x76 && 0 <= x72 && x72 <= 0
(8) l7(x84, x85, x86, x87, x88, x89, x90) -> l5(x91, x92, x93, x94, x95, x96, x97) :|: x90 = x97 && x89 = x96 && x88 = x95 && x87 = x94 && x86 = x93 && x85 = x92 && x84 = x91 && 1 <= x86
(9) l7(x98, x99, x100, x101, x102, x103, x104) -> l5(x105, x106, x107, x108, x109, x110, x111) :|: x104 = x111 && x103 = x110 && x102 = x109 && x101 = x108 && x100 = x107 && x99 = x106 && x98 = x105 && 1 + x100 <= 0
(10) l8(x112, x113, x114, x115, x116, x117, x118) -> l9(x119, x120, x121, x122, x123, x124, x125) :|: x118 = x125 && x117 = x124 && x116 = x123 && x115 = x122 && x114 = x121 && x112 = x119 && x120 = 1 + x113
(11) l1(x126, x127, x128, x129, x130, x131, x132) -> l10(x133, x134, x135, x136, x137, x138, x139) :|: x132 = x139 && x131 = x138 && x130 = x137 && x129 = x136 && x128 = x135 && x127 = x134 && x126 = x133
(12) l11(x140, x141, x142, x143, x144, x145, x146) -> l8(x147, x148, x149, x150, x151, x152, x153) :|: x146 = x153 && x145 = x152 && x144 = x151 && x141 = x148 && x140 = x147 && x149 = 0 && x150 = x150
(13) l11(x154, x155, x156, x157, x158, x159, x160) -> l8(x161, x162, x163, x164, x165, x166, x167) :|: x160 = x167 && x159 = x166 && x158 = x165 && x157 = x164 && x156 = x163 && x155 = x162 && x154 = x161
(14) l12(x168, x169, x170, x171, x172, x173, x174) -> l11(x175, x176, x177, x178, x179, x180, x181) :|: x174 = x181 && x173 = x180 && x172 = x179 && x171 = x178 && x170 = x177 && x169 = x176 && x168 = x175 && x169 <= 100 - x174
(15) l12(x182, x183, x184, x185, x186, x187, x188) -> l6(x189, x190, x191, x192, x193, x194, x195) :|: x188 = x195 && x187 = x194 && x186 = x193 && x185 = x192 && x184 = x191 && x183 = x190 && x182 = x189 && 101 - x188 <= x183
(16) l13(x196, x197, x198, x199, x200, x201, x202) -> l6(x203, x204, x205, x206, x207, x208, x209) :|: x202 = x209 && x201 = x208 && x200 = x207 && x199 = x206 && x198 = x205 && x197 = x204 && x196 = x203 && 100 <= x197
(17) l13(x210, x211, x212, x213, x214, x215, x216) -> l12(x217, x218, x219, x220, x221, x222, x223) :|: x216 = x223 && x215 = x222 && x214 = x221 && x213 = x220 && x212 = x219 && x211 = x218 && x210 = x217 && x211 <= 99
(18) l9(x224, x225, x226, x227, x228, x229, x230) -> l13(x231, x232, x233, x234, x235, x236, x237) :|: x230 = x237 && x229 = x236 && x228 = x235 && x227 = x234 && x226 = x233 && x225 = x232 && x224 = x231
(19) l10(x238, x239, x240, x241, x242, x243, x244) -> l3(x245, x246, x247, x248, x249, x250, x251) :|: x244 = x251 && x243 = x250 && x242 = x249 && x241 = x248 && x240 = x247 && x239 = x246 && x238 = x245 && 100 <= x244
(20) l10(x252, x253, x254, x255, x256, x257, x258) -> l9(x259, x260, x261, x262, x263, x264, x265) :|: x258 = x265 && x257 = x264 && x256 = x263 && x255 = x262 && x252 = x259 && x260 = 1 && x261 = 1 && x258 <= 99
(21) l14(x266, x267, x268, x269, x270, x271, x272) -> l2(x273, x274, x275, x276, x277, x278, x279) :|: x272 = x279 && x269 = x276 && x268 = x275 && x267 = x274 && x273 = 1 && x277 = x278 && x278 = -1
(22) l15(x280, x281, x282, x283, x284, x285, x286) -> l14(x287, x288, x289, x290, x291, x292, x293) :|: x286 = x293 && x285 = x292 && x284 = x291 && x283 = x290 && x282 = x289 && x281 = x288 && x280 = x287

Arcs:
(1) -> (11)
(2) -> (3)
(3) -> (1), (2)
(5) -> (4)
(6) -> (7), (8), (9)
(7) -> (11)
(8) -> (5)
(9) -> (5)
(10) -> (18)
(11) -> (19), (20)
(12) -> (10)
(13) -> (10)
(14) -> (12), (13)
(15) -> (6)
(16) -> (6)
(17) -> (14), (15)
(18) -> (16), (17)
(19) -> (4)
(20) -> (18)
(21) -> (3)
(22) -> (21)

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) l0(x, x1, x2, x3, x4, x5, x6) -> l2(x7, x8, x9, x10, x11, x12, x13) :|: x6 = x13 && x5 = x12 && x4 = x11 && x3 = x10 && x2 = x9 && x1 = x8 && x7 = 1 + x && x <= 100
(2) l2(x14, x15, x16, x17, x18, x19, x20) -> l0(x21, x22, x23, x24, x25, x26, x27) :|: x20 = x27 && x19 = x26 && x18 = x25 && x17 = x24 && x16 = x23 && x15 = x22 && x14 = x21

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

This digraph is fully evaluated!

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

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

(7)
Obligation:
Rules:
l0(x:0, x1:0, x23:0, x10:0, x11:0, x12:0, x13:0) -> l0(1 + x:0, x1:0, x23:0, x10:0, x11:0, x12:0, x13:0) :|: x:0 < 101

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

(8) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:

   l0(x1, x2, x3, x4, x5, x6, x7) -> l0(x1)

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

(9)
Obligation:
Rules:
l0(x:0) -> l0(1 + x:0) :|: x:0 < 101

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

(10) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l0(INTEGER)
Replaced non-predefined constructor symbols by 0.
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(11)
Obligation:
Rules:
l0(x:0) -> l0(c) :|: c = 1 + x:0 && x:0 < 101

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(12) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l0 ] = -1*l0_1

The following rules are decreasing:
l0(x:0) -> l0(c) :|: c = 1 + x:0 && x:0 < 101

The following rules are bounded:
l0(x:0) -> l0(c) :|: c = 1 + x:0 && x:0 < 101


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(13)
YES

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(14)
Obligation:

Termination digraph:
Nodes:
(1) l1(x126, x127, x128, x129, x130, x131, x132) -> l10(x133, x134, x135, x136, x137, x138, x139) :|: x132 = x139 && x131 = x138 && x130 = x137 && x129 = x136 && x128 = x135 && x127 = x134 && x126 = x133
(2) l7(x70, x71, x72, x73, x74, x75, x76) -> l1(x77, x78, x79, x80, x81, x82, x83) :|: x75 = x82 && x74 = x81 && x73 = x80 && x72 = x79 && x71 = x78 && x70 = x77 && x83 = 1 + x76 && 0 <= x72 && x72 <= 0
(3) l6(x56, x57, x58, x59, x60, x61, x62) -> l7(x63, x64, x65, x66, x67, x68, x69) :|: x62 = x69 && x61 = x68 && x60 = x67 && x59 = x66 && x58 = x65 && x57 = x64 && x56 = x63
(4) l13(x196, x197, x198, x199, x200, x201, x202) -> l6(x203, x204, x205, x206, x207, x208, x209) :|: x202 = x209 && x201 = x208 && x200 = x207 && x199 = x206 && x198 = x205 && x197 = x204 && x196 = x203 && 100 <= x197
(5) l12(x182, x183, x184, x185, x186, x187, x188) -> l6(x189, x190, x191, x192, x193, x194, x195) :|: x188 = x195 && x187 = x194 && x186 = x193 && x185 = x192 && x184 = x191 && x183 = x190 && x182 = x189 && 101 - x188 <= x183
(6) l13(x210, x211, x212, x213, x214, x215, x216) -> l12(x217, x218, x219, x220, x221, x222, x223) :|: x216 = x223 && x215 = x222 && x214 = x221 && x213 = x220 && x212 = x219 && x211 = x218 && x210 = x217 && x211 <= 99
(7) l9(x224, x225, x226, x227, x228, x229, x230) -> l13(x231, x232, x233, x234, x235, x236, x237) :|: x230 = x237 && x229 = x236 && x228 = x235 && x227 = x234 && x226 = x233 && x225 = x232 && x224 = x231
(8) l10(x252, x253, x254, x255, x256, x257, x258) -> l9(x259, x260, x261, x262, x263, x264, x265) :|: x258 = x265 && x257 = x264 && x256 = x263 && x255 = x262 && x252 = x259 && x260 = 1 && x261 = 1 && x258 <= 99
(9) l8(x112, x113, x114, x115, x116, x117, x118) -> l9(x119, x120, x121, x122, x123, x124, x125) :|: x118 = x125 && x117 = x124 && x116 = x123 && x115 = x122 && x114 = x121 && x112 = x119 && x120 = 1 + x113
(10) l11(x154, x155, x156, x157, x158, x159, x160) -> l8(x161, x162, x163, x164, x165, x166, x167) :|: x160 = x167 && x159 = x166 && x158 = x165 && x157 = x164 && x156 = x163 && x155 = x162 && x154 = x161
(11) l11(x140, x141, x142, x143, x144, x145, x146) -> l8(x147, x148, x149, x150, x151, x152, x153) :|: x146 = x153 && x145 = x152 && x144 = x151 && x141 = x148 && x140 = x147 && x149 = 0 && x150 = x150
(12) l12(x168, x169, x170, x171, x172, x173, x174) -> l11(x175, x176, x177, x178, x179, x180, x181) :|: x174 = x181 && x173 = x180 && x172 = x179 && x171 = x178 && x170 = x177 && x169 = x176 && x168 = x175 && x169 <= 100 - x174

Arcs:
(1) -> (8)
(2) -> (1)
(3) -> (2)
(4) -> (3)
(5) -> (3)
(6) -> (5), (12)
(7) -> (4), (6)
(8) -> (7)
(9) -> (7)
(10) -> (9)
(11) -> (9)
(12) -> (10), (11)

This digraph is fully evaluated!

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(15) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(16)
Obligation:
Rules:
l9(x119:0, x162:0, x121:0, x122:0, x123:0, x124:0, x125:0) -> l9(x119:0, 1 + x162:0, x121:0, x122:0, x123:0, x124:0, x125:0) :|: x162:0 < 100 && x162:0 <= 100 - x125:0
l9(x133:0, x134:0, x135:0, x136:0, x137:0, x138:0, x209:0) -> l9(x133:0, 1, 1, x136:0, x137:0, x138:0, 1 + x209:0) :|: x135:0 < 1 && x134:0 > 99 && x209:0 < 99 && x135:0 > -1
l9(x, x1, x2, x3, x4, x5, x6) -> l9(x, 1 + x1, 0, x7, x4, x5, x6) :|: x1 < 100 && x1 <= 100 - x6
l9(x8, x9, x10, x11, x12, x13, x14) -> l9(x8, 1, 1, x11, x12, x13, 1 + x14) :|: x9 >= 101 - x14 && x9 < 100 && x10 < 1 && x14 < 99 && x10 > -1

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(17) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:

   l9(x1, x2, x3, x4, x5, x6, x7) -> l9(x2, x3, x7)

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(18)
Obligation:
Rules:
l9(x162:0, x121:0, x125:0) -> l9(1 + x162:0, x121:0, x125:0) :|: x162:0 < 100 && x162:0 <= 100 - x125:0
l9(x134:0, x135:0, x209:0) -> l9(1, 1, 1 + x209:0) :|: x135:0 < 1 && x134:0 > 99 && x209:0 < 99 && x135:0 > -1
l9(x1, x2, x6) -> l9(1 + x1, 0, x6) :|: x1 < 100 && x1 <= 100 - x6
l9(x9, x10, x14) -> l9(1, 1, 1 + x14) :|: x9 >= 101 - x14 && x9 < 100 && x10 < 1 && x14 < 99 && x10 > -1

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(19) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l9(VARIABLE, VARIABLE, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(20)
Obligation:
Rules:
l9(x162:0, x121:0, x125:0) -> l9(c, x121:0, x125:0) :|: c = 1 + x162:0 && (x162:0 < 100 && x162:0 <= 100 - x125:0)
l9(x134:0, x135:0, x209:0) -> l9(c1, c2, c3) :|: c3 = 1 + x209:0 && (c2 = 1 && c1 = 1) && (x135:0 < 1 && x134:0 > 99 && x209:0 < 99 && x135:0 > -1)
l9(x1, x2, x6) -> l9(c4, c5, x6) :|: c5 = 0 && c4 = 1 + x1 && (x1 < 100 && x1 <= 100 - x6)
l9(x9, x10, x14) -> l9(c6, c7, c8) :|: c8 = 1 + x14 && (c7 = 1 && c6 = 1) && (x9 >= 101 - x14 && x9 < 100 && x10 < 1 && x14 < 99 && x10 > -1)

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(21) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[l9(x, x1, x2)] = 98 - x2

The following rules are decreasing:
l9(x134:0, x135:0, x209:0) -> l9(c1, c2, c3) :|: c3 = 1 + x209:0 && (c2 = 1 && c1 = 1) && (x135:0 < 1 && x134:0 > 99 && x209:0 < 99 && x135:0 > -1)
l9(x9, x10, x14) -> l9(c6, c7, c8) :|: c8 = 1 + x14 && (c7 = 1 && c6 = 1) && (x9 >= 101 - x14 && x9 < 100 && x10 < 1 && x14 < 99 && x10 > -1)
The following rules are bounded:
l9(x134:0, x135:0, x209:0) -> l9(c1, c2, c3) :|: c3 = 1 + x209:0 && (c2 = 1 && c1 = 1) && (x135:0 < 1 && x134:0 > 99 && x209:0 < 99 && x135:0 > -1)
l9(x9, x10, x14) -> l9(c6, c7, c8) :|: c8 = 1 + x14 && (c7 = 1 && c6 = 1) && (x9 >= 101 - x14 && x9 < 100 && x10 < 1 && x14 < 99 && x10 > -1)

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(22)
Obligation:
Rules:
l9(x162:0, x121:0, x125:0) -> l9(c, x121:0, x125:0) :|: c = 1 + x162:0 && (x162:0 < 100 && x162:0 <= 100 - x125:0)
l9(x1, x2, x6) -> l9(c4, c5, x6) :|: c5 = 0 && c4 = 1 + x1 && (x1 < 100 && x1 <= 100 - x6)

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(23) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[l9(x, x1, x2)] = 99 - x

The following rules are decreasing:
l9(x162:0, x121:0, x125:0) -> l9(c, x121:0, x125:0) :|: c = 1 + x162:0 && (x162:0 < 100 && x162:0 <= 100 - x125:0)
l9(x1, x2, x6) -> l9(c4, c5, x6) :|: c5 = 0 && c4 = 1 + x1 && (x1 < 100 && x1 <= 100 - x6)
The following rules are bounded:
l9(x162:0, x121:0, x125:0) -> l9(c, x121:0, x125:0) :|: c = 1 + x162:0 && (x162:0 < 100 && x162:0 <= 100 - x125:0)
l9(x1, x2, x6) -> l9(c4, c5, x6) :|: c5 = 0 && c4 = 1 + x1 && (x1 < 100 && x1 <= 100 - x6)

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(24)
YES