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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 8016 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 8 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 29 ms]
        (11) IntTRS
        (12) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 4 ms]
        (16) IRSwT
        (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (18) IRSwT
        (19) TempFilterProof [SOUND, 8 ms]
        (20) IntTRS
        (21) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (22) YES
    (23) IRSwT
        (24) IntTRSCompressionProof [EQUIVALENT, 4 ms]
        (25) IRSwT
        (26) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (27) IRSwT
        (28) TempFilterProof [SOUND, 17 ms]
        (29) IntTRS
        (30) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (31) YES
    (32) IRSwT
        (33) IntTRSCompressionProof [EQUIVALENT, 10 ms]
        (34) IRSwT
        (35) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (36) IRSwT
        (37) TempFilterProof [SOUND, 8 ms]
        (38) IntTRS
        (39) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (40) YES
    (41) IRSwT
        (42) IntTRSCompressionProof [EQUIVALENT, 4 ms]
        (43) IRSwT
        (44) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (45) IRSwT
        (46) TempFilterProof [SOUND, 11 ms]
        (47) IntTRS
        (48) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (49) YES
    (50) IRSwT
        (51) IntTRSCompressionProof [EQUIVALENT, 2 ms]
        (52) IRSwT
        (53) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (54) IRSwT
        (55) TempFilterProof [SOUND, 7 ms]
        (56) IntTRS
        (57) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (58) YES


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

(0)
Obligation:
Rules:
l0(__const_50HAT0, i11HAT0, i13HAT0, i7HAT0, i9HAT0, iHAT0, tmpHAT0, tmp___0HAT0) -> l1(__const_50HATpost, i11HATpost, i13HATpost, i7HATpost, i9HATpost, iHATpost, tmpHATpost, tmp___0HATpost) :|: tmp___0HAT0 = tmp___0HATpost && tmpHAT0 = tmpHATpost && i9HAT0 = i9HATpost && i7HAT0 = i7HATpost && i13HAT0 = i13HATpost && i11HAT0 = i11HATpost && iHAT0 = iHATpost && __const_50HAT0 = __const_50HATpost
l2(x, x1, x2, x3, x4, x5, x6, x7) -> l3(x8, x9, x10, x11, x12, x13, x14, x15) :|: x7 = x15 && x6 = x14 && x4 = x12 && x3 = x11 && x2 = x10 && x1 = x9 && x5 = x13 && x = x8 && x <= x5
l2(x16, x17, x18, x19, x20, x21, x22, x23) -> l4(x24, x25, x26, x27, x28, x29, x30, x31) :|: x23 = x31 && x22 = x30 && x20 = x28 && x19 = x27 && x18 = x26 && x17 = x25 && x16 = x24 && x29 = 1 + x21 && 1 + x21 <= x16
l5(x32, x33, x34, x35, x36, x37, x38, x39) -> l6(x40, x41, x42, x43, x44, x45, x46, x47) :|: x39 = x47 && x38 = x46 && x36 = x44 && x35 = x43 && x34 = x42 && x33 = x41 && x37 = x45 && x32 = x40
l7(x48, x49, x50, x51, x52, x53, x54, x55) -> l4(x56, x57, x58, x59, x60, x61, x62, x63) :|: x55 = x63 && x54 = x62 && x52 = x60 && x51 = x59 && x50 = x58 && x49 = x57 && x48 = x56 && x61 = 0 && x48 <= x50
l7(x64, x65, x66, x67, x68, x69, x70, x71) -> l8(x72, x73, x74, x75, x76, x77, x78, x79) :|: x71 = x79 && x70 = x78 && x68 = x76 && x67 = x75 && x65 = x73 && x69 = x77 && x64 = x72 && x74 = 1 + x66 && 1 + x66 <= x64
l9(x80, x81, x82, x83, x84, x85, x86, x87) -> l10(x88, x89, x90, x91, x92, x93, x94, x95) :|: x87 = x95 && x86 = x94 && x84 = x92 && x83 = x91 && x82 = x90 && x81 = x89 && x85 = x93 && x80 = x88
l11(x96, x97, x98, x99, x100, x101, x102, x103) -> l8(x104, x105, x106, x107, x108, x109, x110, x111) :|: x96 <= x97 && x112 = 0 && x106 = 0 && x96 = x104 && x101 = x109 && x97 = x105 && x99 = x107 && x100 = x108 && x102 = x110 && x103 = x111
l11(x113, x114, x115, x116, x117, x118, x119, x120) -> l12(x121, x122, x123, x124, x125, x126, x127, x128) :|: x120 = x128 && x119 = x127 && x117 = x125 && x116 = x124 && x115 = x123 && x118 = x126 && x113 = x121 && x122 = 1 + x114 && 1 + x114 <= x113
l12(x129, x130, x131, x132, x133, x134, x135, x136) -> l11(x137, x138, x139, x140, x141, x142, x143, x144) :|: x136 = x144 && x135 = x143 && x133 = x141 && x132 = x140 && x131 = x139 && x130 = x138 && x134 = x142 && x129 = x137
l10(x145, x146, x147, x148, x149, x150, x151, x152) -> l12(x153, x154, x155, x156, x157, x158, x159, x160) :|: x145 <= x150 && x161 = 0 && x154 = 0 && x145 = x153 && x150 = x158 && x147 = x155 && x148 = x156 && x149 = x157 && x151 = x159 && x152 = x160
l10(x162, x163, x164, x165, x166, x167, x168, x169) -> l9(x170, x171, x172, x173, x174, x175, x176, x177) :|: x169 = x177 && x168 = x176 && x166 = x174 && x165 = x173 && x164 = x172 && x163 = x171 && x162 = x170 && x175 = 1 + x167 && 1 + x167 <= x162
l8(x178, x179, x180, x181, x182, x183, x184, x185) -> l7(x186, x187, x188, x189, x190, x191, x192, x193) :|: x185 = x193 && x184 = x192 && x182 = x190 && x181 = x189 && x180 = x188 && x179 = x187 && x183 = x191 && x178 = x186
l6(x194, x195, x196, x197, x198, x199, x200, x201) -> l9(x202, x203, x204, x205, x206, x207, x208, x209) :|: x201 = x209 && x200 = x208 && x198 = x206 && x197 = x205 && x196 = x204 && x195 = x203 && x194 = x202 && x207 = 0 && x194 <= x198
l6(x210, x211, x212, x213, x214, x215, x216, x217) -> l5(x218, x219, x220, x221, x222, x223, x224, x225) :|: x217 = x225 && x216 = x224 && x213 = x221 && x212 = x220 && x211 = x219 && x215 = x223 && x210 = x218 && x222 = 1 + x214 && 1 + x214 <= x210
l4(x226, x227, x228, x229, x230, x231, x232, x233) -> l2(x234, x235, x236, x237, x238, x239, x240, x241) :|: x233 = x241 && x232 = x240 && x230 = x238 && x229 = x237 && x228 = x236 && x227 = x235 && x231 = x239 && x226 = x234
l1(x242, x243, x244, x245, x246, x247, x248, x249) -> l5(x250, x251, x252, x253, x254, x255, x256, x257) :|: x242 <= x245 && x258 = 0 && x254 = 0 && x242 = x250 && x247 = x255 && x243 = x251 && x244 = x252 && x245 = x253 && x248 = x256 && x249 = x257
l1(x259, x260, x261, x262, x263, x264, x265, x266) -> l0(x267, x268, x269, x270, x271, x272, x273, x274) :|: x266 = x274 && x265 = x273 && x263 = x271 && x261 = x269 && x260 = x268 && x264 = x272 && x259 = x267 && x270 = 1 + x262 && 1 + x262 <= x259
l13(x275, x276, x277, x278, x279, x280, x281, x282) -> l0(x283, x284, x285, x286, x287, x288, x289, x290) :|: x288 = 0 && x289 = x289 && x290 = x290 && x291 = 0 && x286 = 0 && x275 = x283 && x276 = x284 && x277 = x285 && x279 = x287
l14(x292, x293, x294, x295, x296, x297, x298, x299) -> l13(x300, x301, x302, x303, x304, x305, x306, x307) :|: x299 = x307 && x298 = x306 && x296 = x304 && x295 = x303 && x294 = x302 && x293 = x301 && x297 = x305 && x292 = x300
Start term: l14(__const_50HAT0, i11HAT0, i13HAT0, i7HAT0, i9HAT0, iHAT0, tmpHAT0, tmp___0HAT0)

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

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

(2)
Obligation:
Rules:
l0(__const_50HAT0, i11HAT0, i13HAT0, i7HAT0, i9HAT0, iHAT0, tmpHAT0, tmp___0HAT0) -> l1(__const_50HATpost, i11HATpost, i13HATpost, i7HATpost, i9HATpost, iHATpost, tmpHATpost, tmp___0HATpost) :|: tmp___0HAT0 = tmp___0HATpost && tmpHAT0 = tmpHATpost && i9HAT0 = i9HATpost && i7HAT0 = i7HATpost && i13HAT0 = i13HATpost && i11HAT0 = i11HATpost && iHAT0 = iHATpost && __const_50HAT0 = __const_50HATpost
l2(x, x1, x2, x3, x4, x5, x6, x7) -> l3(x8, x9, x10, x11, x12, x13, x14, x15) :|: x7 = x15 && x6 = x14 && x4 = x12 && x3 = x11 && x2 = x10 && x1 = x9 && x5 = x13 && x = x8 && x <= x5
l2(x16, x17, x18, x19, x20, x21, x22, x23) -> l4(x24, x25, x26, x27, x28, x29, x30, x31) :|: x23 = x31 && x22 = x30 && x20 = x28 && x19 = x27 && x18 = x26 && x17 = x25 && x16 = x24 && x29 = 1 + x21 && 1 + x21 <= x16
l5(x32, x33, x34, x35, x36, x37, x38, x39) -> l6(x40, x41, x42, x43, x44, x45, x46, x47) :|: x39 = x47 && x38 = x46 && x36 = x44 && x35 = x43 && x34 = x42 && x33 = x41 && x37 = x45 && x32 = x40
l7(x48, x49, x50, x51, x52, x53, x54, x55) -> l4(x56, x57, x58, x59, x60, x61, x62, x63) :|: x55 = x63 && x54 = x62 && x52 = x60 && x51 = x59 && x50 = x58 && x49 = x57 && x48 = x56 && x61 = 0 && x48 <= x50
l7(x64, x65, x66, x67, x68, x69, x70, x71) -> l8(x72, x73, x74, x75, x76, x77, x78, x79) :|: x71 = x79 && x70 = x78 && x68 = x76 && x67 = x75 && x65 = x73 && x69 = x77 && x64 = x72 && x74 = 1 + x66 && 1 + x66 <= x64
l9(x80, x81, x82, x83, x84, x85, x86, x87) -> l10(x88, x89, x90, x91, x92, x93, x94, x95) :|: x87 = x95 && x86 = x94 && x84 = x92 && x83 = x91 && x82 = x90 && x81 = x89 && x85 = x93 && x80 = x88
l11(x96, x97, x98, x99, x100, x101, x102, x103) -> l8(x104, x105, x106, x107, x108, x109, x110, x111) :|: x96 <= x97 && x112 = 0 && x106 = 0 && x96 = x104 && x101 = x109 && x97 = x105 && x99 = x107 && x100 = x108 && x102 = x110 && x103 = x111
l11(x113, x114, x115, x116, x117, x118, x119, x120) -> l12(x121, x122, x123, x124, x125, x126, x127, x128) :|: x120 = x128 && x119 = x127 && x117 = x125 && x116 = x124 && x115 = x123 && x118 = x126 && x113 = x121 && x122 = 1 + x114 && 1 + x114 <= x113
l12(x129, x130, x131, x132, x133, x134, x135, x136) -> l11(x137, x138, x139, x140, x141, x142, x143, x144) :|: x136 = x144 && x135 = x143 && x133 = x141 && x132 = x140 && x131 = x139 && x130 = x138 && x134 = x142 && x129 = x137
l10(x145, x146, x147, x148, x149, x150, x151, x152) -> l12(x153, x154, x155, x156, x157, x158, x159, x160) :|: x145 <= x150 && x161 = 0 && x154 = 0 && x145 = x153 && x150 = x158 && x147 = x155 && x148 = x156 && x149 = x157 && x151 = x159 && x152 = x160
l10(x162, x163, x164, x165, x166, x167, x168, x169) -> l9(x170, x171, x172, x173, x174, x175, x176, x177) :|: x169 = x177 && x168 = x176 && x166 = x174 && x165 = x173 && x164 = x172 && x163 = x171 && x162 = x170 && x175 = 1 + x167 && 1 + x167 <= x162
l8(x178, x179, x180, x181, x182, x183, x184, x185) -> l7(x186, x187, x188, x189, x190, x191, x192, x193) :|: x185 = x193 && x184 = x192 && x182 = x190 && x181 = x189 && x180 = x188 && x179 = x187 && x183 = x191 && x178 = x186
l6(x194, x195, x196, x197, x198, x199, x200, x201) -> l9(x202, x203, x204, x205, x206, x207, x208, x209) :|: x201 = x209 && x200 = x208 && x198 = x206 && x197 = x205 && x196 = x204 && x195 = x203 && x194 = x202 && x207 = 0 && x194 <= x198
l6(x210, x211, x212, x213, x214, x215, x216, x217) -> l5(x218, x219, x220, x221, x222, x223, x224, x225) :|: x217 = x225 && x216 = x224 && x213 = x221 && x212 = x220 && x211 = x219 && x215 = x223 && x210 = x218 && x222 = 1 + x214 && 1 + x214 <= x210
l4(x226, x227, x228, x229, x230, x231, x232, x233) -> l2(x234, x235, x236, x237, x238, x239, x240, x241) :|: x233 = x241 && x232 = x240 && x230 = x238 && x229 = x237 && x228 = x236 && x227 = x235 && x231 = x239 && x226 = x234
l1(x242, x243, x244, x245, x246, x247, x248, x249) -> l5(x250, x251, x252, x253, x254, x255, x256, x257) :|: x242 <= x245 && x258 = 0 && x254 = 0 && x242 = x250 && x247 = x255 && x243 = x251 && x244 = x252 && x245 = x253 && x248 = x256 && x249 = x257
l1(x259, x260, x261, x262, x263, x264, x265, x266) -> l0(x267, x268, x269, x270, x271, x272, x273, x274) :|: x266 = x274 && x265 = x273 && x263 = x271 && x261 = x269 && x260 = x268 && x264 = x272 && x259 = x267 && x270 = 1 + x262 && 1 + x262 <= x259
l13(x275, x276, x277, x278, x279, x280, x281, x282) -> l0(x283, x284, x285, x286, x287, x288, x289, x290) :|: x288 = 0 && x289 = x289 && x290 = x290 && x291 = 0 && x286 = 0 && x275 = x283 && x276 = x284 && x277 = x285 && x279 = x287
l14(x292, x293, x294, x295, x296, x297, x298, x299) -> l13(x300, x301, x302, x303, x304, x305, x306, x307) :|: x299 = x307 && x298 = x306 && x296 = x304 && x295 = x303 && x294 = x302 && x293 = x301 && x297 = x305 && x292 = x300
Start term: l14(__const_50HAT0, i11HAT0, i13HAT0, i7HAT0, i9HAT0, iHAT0, tmpHAT0, tmp___0HAT0)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(__const_50HAT0, i11HAT0, i13HAT0, i7HAT0, i9HAT0, iHAT0, tmpHAT0, tmp___0HAT0) -> l1(__const_50HATpost, i11HATpost, i13HATpost, i7HATpost, i9HATpost, iHATpost, tmpHATpost, tmp___0HATpost) :|: tmp___0HAT0 = tmp___0HATpost && tmpHAT0 = tmpHATpost && i9HAT0 = i9HATpost && i7HAT0 = i7HATpost && i13HAT0 = i13HATpost && i11HAT0 = i11HATpost && iHAT0 = iHATpost && __const_50HAT0 = __const_50HATpost
(2) l2(x, x1, x2, x3, x4, x5, x6, x7) -> l3(x8, x9, x10, x11, x12, x13, x14, x15) :|: x7 = x15 && x6 = x14 && x4 = x12 && x3 = x11 && x2 = x10 && x1 = x9 && x5 = x13 && x = x8 && x <= x5
(3) l2(x16, x17, x18, x19, x20, x21, x22, x23) -> l4(x24, x25, x26, x27, x28, x29, x30, x31) :|: x23 = x31 && x22 = x30 && x20 = x28 && x19 = x27 && x18 = x26 && x17 = x25 && x16 = x24 && x29 = 1 + x21 && 1 + x21 <= x16
(4) l5(x32, x33, x34, x35, x36, x37, x38, x39) -> l6(x40, x41, x42, x43, x44, x45, x46, x47) :|: x39 = x47 && x38 = x46 && x36 = x44 && x35 = x43 && x34 = x42 && x33 = x41 && x37 = x45 && x32 = x40
(5) l7(x48, x49, x50, x51, x52, x53, x54, x55) -> l4(x56, x57, x58, x59, x60, x61, x62, x63) :|: x55 = x63 && x54 = x62 && x52 = x60 && x51 = x59 && x50 = x58 && x49 = x57 && x48 = x56 && x61 = 0 && x48 <= x50
(6) l7(x64, x65, x66, x67, x68, x69, x70, x71) -> l8(x72, x73, x74, x75, x76, x77, x78, x79) :|: x71 = x79 && x70 = x78 && x68 = x76 && x67 = x75 && x65 = x73 && x69 = x77 && x64 = x72 && x74 = 1 + x66 && 1 + x66 <= x64
(7) l9(x80, x81, x82, x83, x84, x85, x86, x87) -> l10(x88, x89, x90, x91, x92, x93, x94, x95) :|: x87 = x95 && x86 = x94 && x84 = x92 && x83 = x91 && x82 = x90 && x81 = x89 && x85 = x93 && x80 = x88
(8) l11(x96, x97, x98, x99, x100, x101, x102, x103) -> l8(x104, x105, x106, x107, x108, x109, x110, x111) :|: x96 <= x97 && x112 = 0 && x106 = 0 && x96 = x104 && x101 = x109 && x97 = x105 && x99 = x107 && x100 = x108 && x102 = x110 && x103 = x111
(9) l11(x113, x114, x115, x116, x117, x118, x119, x120) -> l12(x121, x122, x123, x124, x125, x126, x127, x128) :|: x120 = x128 && x119 = x127 && x117 = x125 && x116 = x124 && x115 = x123 && x118 = x126 && x113 = x121 && x122 = 1 + x114 && 1 + x114 <= x113
(10) l12(x129, x130, x131, x132, x133, x134, x135, x136) -> l11(x137, x138, x139, x140, x141, x142, x143, x144) :|: x136 = x144 && x135 = x143 && x133 = x141 && x132 = x140 && x131 = x139 && x130 = x138 && x134 = x142 && x129 = x137
(11) l10(x145, x146, x147, x148, x149, x150, x151, x152) -> l12(x153, x154, x155, x156, x157, x158, x159, x160) :|: x145 <= x150 && x161 = 0 && x154 = 0 && x145 = x153 && x150 = x158 && x147 = x155 && x148 = x156 && x149 = x157 && x151 = x159 && x152 = x160
(12) l10(x162, x163, x164, x165, x166, x167, x168, x169) -> l9(x170, x171, x172, x173, x174, x175, x176, x177) :|: x169 = x177 && x168 = x176 && x166 = x174 && x165 = x173 && x164 = x172 && x163 = x171 && x162 = x170 && x175 = 1 + x167 && 1 + x167 <= x162
(13) l8(x178, x179, x180, x181, x182, x183, x184, x185) -> l7(x186, x187, x188, x189, x190, x191, x192, x193) :|: x185 = x193 && x184 = x192 && x182 = x190 && x181 = x189 && x180 = x188 && x179 = x187 && x183 = x191 && x178 = x186
(14) l6(x194, x195, x196, x197, x198, x199, x200, x201) -> l9(x202, x203, x204, x205, x206, x207, x208, x209) :|: x201 = x209 && x200 = x208 && x198 = x206 && x197 = x205 && x196 = x204 && x195 = x203 && x194 = x202 && x207 = 0 && x194 <= x198
(15) l6(x210, x211, x212, x213, x214, x215, x216, x217) -> l5(x218, x219, x220, x221, x222, x223, x224, x225) :|: x217 = x225 && x216 = x224 && x213 = x221 && x212 = x220 && x211 = x219 && x215 = x223 && x210 = x218 && x222 = 1 + x214 && 1 + x214 <= x210
(16) l4(x226, x227, x228, x229, x230, x231, x232, x233) -> l2(x234, x235, x236, x237, x238, x239, x240, x241) :|: x233 = x241 && x232 = x240 && x230 = x238 && x229 = x237 && x228 = x236 && x227 = x235 && x231 = x239 && x226 = x234
(17) l1(x242, x243, x244, x245, x246, x247, x248, x249) -> l5(x250, x251, x252, x253, x254, x255, x256, x257) :|: x242 <= x245 && x258 = 0 && x254 = 0 && x242 = x250 && x247 = x255 && x243 = x251 && x244 = x252 && x245 = x253 && x248 = x256 && x249 = x257
(18) l1(x259, x260, x261, x262, x263, x264, x265, x266) -> l0(x267, x268, x269, x270, x271, x272, x273, x274) :|: x266 = x274 && x265 = x273 && x263 = x271 && x261 = x269 && x260 = x268 && x264 = x272 && x259 = x267 && x270 = 1 + x262 && 1 + x262 <= x259
(19) l13(x275, x276, x277, x278, x279, x280, x281, x282) -> l0(x283, x284, x285, x286, x287, x288, x289, x290) :|: x288 = 0 && x289 = x289 && x290 = x290 && x291 = 0 && x286 = 0 && x275 = x283 && x276 = x284 && x277 = x285 && x279 = x287
(20) l14(x292, x293, x294, x295, x296, x297, x298, x299) -> l13(x300, x301, x302, x303, x304, x305, x306, x307) :|: x299 = x307 && x298 = x306 && x296 = x304 && x295 = x303 && x294 = x302 && x293 = x301 && x297 = x305 && x292 = x300

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

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) l0(__const_50HAT0, i11HAT0, i13HAT0, i7HAT0, i9HAT0, iHAT0, tmpHAT0, tmp___0HAT0) -> l1(__const_50HATpost, i11HATpost, i13HATpost, i7HATpost, i9HATpost, iHATpost, tmpHATpost, tmp___0HATpost) :|: tmp___0HAT0 = tmp___0HATpost && tmpHAT0 = tmpHATpost && i9HAT0 = i9HATpost && i7HAT0 = i7HATpost && i13HAT0 = i13HATpost && i11HAT0 = i11HATpost && iHAT0 = iHATpost && __const_50HAT0 = __const_50HATpost
(2) l1(x259, x260, x261, x262, x263, x264, x265, x266) -> l0(x267, x268, x269, x270, x271, x272, x273, x274) :|: x266 = x274 && x265 = x273 && x263 = x271 && x261 = x269 && x260 = x268 && x264 = x272 && x259 = x267 && x270 = 1 + x262 && 1 + x262 <= x259

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

This digraph is fully evaluated!

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

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

(7)
Obligation:
Rules:
l0(__const_50HAT0:0, i11HAT0:0, i13HAT0:0, i7HAT0:0, i9HAT0:0, iHAT0:0, tmpHAT0:0, tmp___0HAT0:0) -> l0(__const_50HAT0:0, i11HAT0:0, i13HAT0:0, 1 + i7HAT0:0, i9HAT0:0, iHAT0:0, tmpHAT0:0, tmp___0HAT0:0) :|: __const_50HAT0:0 >= 1 + i7HAT0:0

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

(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, x8) -> l0(x1, x4)

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

(9)
Obligation:
Rules:
l0(__const_50HAT0:0, i7HAT0:0) -> l0(__const_50HAT0:0, 1 + i7HAT0:0) :|: __const_50HAT0:0 >= 1 + i7HAT0:0

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

(10) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l0(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(11)
Obligation:
Rules:
l0(__const_50HAT0:0, i7HAT0:0) -> l0(__const_50HAT0:0, c) :|: c = 1 + i7HAT0:0 && __const_50HAT0:0 >= 1 + i7HAT0:0

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

(12) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l0 ] = l0_1 + -1*l0_2

The following rules are decreasing:
l0(__const_50HAT0:0, i7HAT0:0) -> l0(__const_50HAT0:0, c) :|: c = 1 + i7HAT0:0 && __const_50HAT0:0 >= 1 + i7HAT0:0

The following rules are bounded:
l0(__const_50HAT0:0, i7HAT0:0) -> l0(__const_50HAT0:0, c) :|: c = 1 + i7HAT0:0 && __const_50HAT0:0 >= 1 + i7HAT0:0


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

(13)
YES

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

(14)
Obligation:

Termination digraph:
Nodes:
(1) l5(x32, x33, x34, x35, x36, x37, x38, x39) -> l6(x40, x41, x42, x43, x44, x45, x46, x47) :|: x39 = x47 && x38 = x46 && x36 = x44 && x35 = x43 && x34 = x42 && x33 = x41 && x37 = x45 && x32 = x40
(2) l6(x210, x211, x212, x213, x214, x215, x216, x217) -> l5(x218, x219, x220, x221, x222, x223, x224, x225) :|: x217 = x225 && x216 = x224 && x213 = x221 && x212 = x220 && x211 = x219 && x215 = x223 && x210 = x218 && x222 = 1 + x214 && 1 + x214 <= x210

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

This digraph is fully evaluated!

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

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

(16)
Obligation:
Rules:
l5(x218:0, x219:0, x220:0, x221:0, x36:0, x223:0, x224:0, x225:0) -> l5(x218:0, x219:0, x220:0, x221:0, 1 + x36:0, x223:0, x224:0, x225:0) :|: x218:0 >= 1 + x36:0

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

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

   l5(x1, x2, x3, x4, x5, x6, x7, x8) -> l5(x1, x5)

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

(18)
Obligation:
Rules:
l5(x218:0, x36:0) -> l5(x218:0, 1 + x36:0) :|: x218:0 >= 1 + x36:0

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

(19) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l5(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(20)
Obligation:
Rules:
l5(x218:0, x36:0) -> l5(x218:0, c) :|: c = 1 + x36:0 && x218:0 >= 1 + x36:0

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

(21) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l5 ] = l5_1 + -1*l5_2

The following rules are decreasing:
l5(x218:0, x36:0) -> l5(x218:0, c) :|: c = 1 + x36:0 && x218:0 >= 1 + x36:0

The following rules are bounded:
l5(x218:0, x36:0) -> l5(x218:0, c) :|: c = 1 + x36:0 && x218:0 >= 1 + x36:0


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

(22)
YES

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

(23)
Obligation:

Termination digraph:
Nodes:
(1) l9(x80, x81, x82, x83, x84, x85, x86, x87) -> l10(x88, x89, x90, x91, x92, x93, x94, x95) :|: x87 = x95 && x86 = x94 && x84 = x92 && x83 = x91 && x82 = x90 && x81 = x89 && x85 = x93 && x80 = x88
(2) l10(x162, x163, x164, x165, x166, x167, x168, x169) -> l9(x170, x171, x172, x173, x174, x175, x176, x177) :|: x169 = x177 && x168 = x176 && x166 = x174 && x165 = x173 && x164 = x172 && x163 = x171 && x162 = x170 && x175 = 1 + x167 && 1 + x167 <= x162

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

This digraph is fully evaluated!

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

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

(25)
Obligation:
Rules:
l9(x170:0, x171:0, x172:0, x173:0, x174:0, x85:0, x176:0, x177:0) -> l9(x170:0, x171:0, x172:0, x173:0, x174:0, 1 + x85:0, x176:0, x177:0) :|: x170:0 >= 1 + x85:0

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

(26) 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, x8) -> l9(x1, x6)

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

(27)
Obligation:
Rules:
l9(x170:0, x85:0) -> l9(x170:0, 1 + x85:0) :|: x170:0 >= 1 + x85:0

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

(28) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l9(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(29)
Obligation:
Rules:
l9(x170:0, x85:0) -> l9(x170:0, c) :|: c = 1 + x85:0 && x170:0 >= 1 + x85:0

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

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

The following rules are decreasing:
l9(x170:0, x85:0) -> l9(x170:0, c) :|: c = 1 + x85:0 && x170:0 >= 1 + x85:0
The following rules are bounded:
l9(x170:0, x85:0) -> l9(x170:0, c) :|: c = 1 + x85:0 && x170:0 >= 1 + x85:0

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

(31)
YES

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

(32)
Obligation:

Termination digraph:
Nodes:
(1) l12(x129, x130, x131, x132, x133, x134, x135, x136) -> l11(x137, x138, x139, x140, x141, x142, x143, x144) :|: x136 = x144 && x135 = x143 && x133 = x141 && x132 = x140 && x131 = x139 && x130 = x138 && x134 = x142 && x129 = x137
(2) l11(x113, x114, x115, x116, x117, x118, x119, x120) -> l12(x121, x122, x123, x124, x125, x126, x127, x128) :|: x120 = x128 && x119 = x127 && x117 = x125 && x116 = x124 && x115 = x123 && x118 = x126 && x113 = x121 && x122 = 1 + x114 && 1 + x114 <= x113

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

This digraph is fully evaluated!

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

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

(34)
Obligation:
Rules:
l12(x121:0, x130:0, x123:0, x124:0, x125:0, x126:0, x127:0, x128:0) -> l12(x121:0, 1 + x130:0, x123:0, x124:0, x125:0, x126:0, x127:0, x128:0) :|: x121:0 >= 1 + x130:0

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

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

   l12(x1, x2, x3, x4, x5, x6, x7, x8) -> l12(x1, x2)

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

(36)
Obligation:
Rules:
l12(x121:0, x130:0) -> l12(x121:0, 1 + x130:0) :|: x121:0 >= 1 + x130:0

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

(37) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l12(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(38)
Obligation:
Rules:
l12(x121:0, x130:0) -> l12(x121:0, c) :|: c = 1 + x130:0 && x121:0 >= 1 + x130:0

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

(39) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l12 ] = l12_1 + -1*l12_2

The following rules are decreasing:
l12(x121:0, x130:0) -> l12(x121:0, c) :|: c = 1 + x130:0 && x121:0 >= 1 + x130:0

The following rules are bounded:
l12(x121:0, x130:0) -> l12(x121:0, c) :|: c = 1 + x130:0 && x121:0 >= 1 + x130:0


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

(40)
YES

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

(41)
Obligation:

Termination digraph:
Nodes:
(1) l8(x178, x179, x180, x181, x182, x183, x184, x185) -> l7(x186, x187, x188, x189, x190, x191, x192, x193) :|: x185 = x193 && x184 = x192 && x182 = x190 && x181 = x189 && x180 = x188 && x179 = x187 && x183 = x191 && x178 = x186
(2) l7(x64, x65, x66, x67, x68, x69, x70, x71) -> l8(x72, x73, x74, x75, x76, x77, x78, x79) :|: x71 = x79 && x70 = x78 && x68 = x76 && x67 = x75 && x65 = x73 && x69 = x77 && x64 = x72 && x74 = 1 + x66 && 1 + x66 <= x64

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

This digraph is fully evaluated!

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

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

(43)
Obligation:
Rules:
l8(x178:0, x179:0, x180:0, x181:0, x182:0, x183:0, x184:0, x185:0) -> l8(x178:0, x179:0, 1 + x180:0, x181:0, x182:0, x183:0, x184:0, x185:0) :|: x178:0 >= 1 + x180:0

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

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

   l8(x1, x2, x3, x4, x5, x6, x7, x8) -> l8(x1, x3)

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

(45)
Obligation:
Rules:
l8(x178:0, x180:0) -> l8(x178:0, 1 + x180:0) :|: x178:0 >= 1 + x180:0

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

(46) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l8(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(47)
Obligation:
Rules:
l8(x178:0, x180:0) -> l8(x178:0, c) :|: c = 1 + x180:0 && x178:0 >= 1 + x180:0

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

(48) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l8 ] = l8_1 + -1*l8_2

The following rules are decreasing:
l8(x178:0, x180:0) -> l8(x178:0, c) :|: c = 1 + x180:0 && x178:0 >= 1 + x180:0

The following rules are bounded:
l8(x178:0, x180:0) -> l8(x178:0, c) :|: c = 1 + x180:0 && x178:0 >= 1 + x180:0


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

(49)
YES

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

(50)
Obligation:

Termination digraph:
Nodes:
(1) l4(x226, x227, x228, x229, x230, x231, x232, x233) -> l2(x234, x235, x236, x237, x238, x239, x240, x241) :|: x233 = x241 && x232 = x240 && x230 = x238 && x229 = x237 && x228 = x236 && x227 = x235 && x231 = x239 && x226 = x234
(2) l2(x16, x17, x18, x19, x20, x21, x22, x23) -> l4(x24, x25, x26, x27, x28, x29, x30, x31) :|: x23 = x31 && x22 = x30 && x20 = x28 && x19 = x27 && x18 = x26 && x17 = x25 && x16 = x24 && x29 = 1 + x21 && 1 + x21 <= x16

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

This digraph is fully evaluated!

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

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

(52)
Obligation:
Rules:
l4(x226:0, x227:0, x228:0, x229:0, x230:0, x231:0, x232:0, x233:0) -> l4(x226:0, x227:0, x228:0, x229:0, x230:0, 1 + x231:0, x232:0, x233:0) :|: x226:0 >= 1 + x231:0

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

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

   l4(x1, x2, x3, x4, x5, x6, x7, x8) -> l4(x1, x6)

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

(54)
Obligation:
Rules:
l4(x226:0, x231:0) -> l4(x226:0, 1 + x231:0) :|: x226:0 >= 1 + x231:0

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

(55) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l4(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(56)
Obligation:
Rules:
l4(x226:0, x231:0) -> l4(x226:0, c) :|: c = 1 + x231:0 && x226:0 >= 1 + x231:0

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

(57) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l4 ] = l4_1 + -1*l4_2

The following rules are decreasing:
l4(x226:0, x231:0) -> l4(x226:0, c) :|: c = 1 + x231:0 && x226:0 >= 1 + x231:0

The following rules are bounded:
l4(x226:0, x231:0) -> l4(x226:0, c) :|: c = 1 + x231:0 && x226:0 >= 1 + x231:0


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

(58)
YES