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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 2456 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 86 ms]
(6) IRSwT
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) TempFilterProof [SOUND, 72 ms]
(10) IntTRS
(11) PolynomialOrderProcessor [EQUIVALENT, 28 ms]
(12) IntTRS
(13) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(14) YES


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

(0)
Obligation:
Rules:
l0(acc12HAT0, acc_length11HAT0, coef_len210HAT0, coef_len6HAT0, i8HAT0, in_len4HAT0, j9HAT0, scale7HAT0) -> l1(acc12HATpost, acc_length11HATpost, coef_len210HATpost, coef_len6HATpost, i8HATpost, in_len4HATpost, j9HATpost, scale7HATpost) :|: scale7HAT0 = scale7HATpost && j9HAT0 = j9HATpost && in_len4HAT0 = in_len4HATpost && i8HAT0 = i8HATpost && coef_len6HAT0 = coef_len6HATpost && coef_len210HAT0 = coef_len210HATpost && acc_length11HAT0 = acc_length11HATpost && acc12HAT0 = acc12HATpost
l2(x, x1, x2, x3, x4, x5, x6, x7) -> l0(x8, x9, x10, x11, x12, x13, x14, x15) :|: x7 = x15 && x6 = x14 && x5 = x13 && x4 = x12 && x3 = x11 && x2 = x10 && x1 = x9 && x = x8 && x3 <= x1
l2(x16, x17, x18, x19, x20, x21, x22, x23) -> l0(x24, x25, x26, x27, x28, x29, x30, x31) :|: x23 = x31 && x22 = x30 && x21 = x29 && x20 = x28 && x19 = x27 && x18 = x26 && x16 = x24 && x25 = 1 + x17 && 1 + x17 <= x19
l1(x32, x33, x34, x35, x36, x37, x38, x39) -> l3(x40, x41, x42, x43, x44, x45, x46, x47) :|: x39 = x47 && x38 = x46 && x37 = x45 && x35 = x43 && x34 = x42 && x33 = x41 && x32 = x40 && x44 = 1 + x36
l4(x48, x49, x50, x51, x52, x53, x54, x55) -> l2(x56, x57, x58, x59, x60, x61, x62, x63) :|: x55 = x63 && x54 = x62 && x53 = x61 && x52 = x60 && x51 = x59 && x50 = x58 && x49 = x57 && x48 = x56
l4(x64, x65, x66, x67, x68, x69, x70, x71) -> l1(x72, x73, x74, x75, x76, x77, x78, x79) :|: x71 = x79 && x70 = x78 && x69 = x77 && x68 = x76 && x67 = x75 && x66 = x74 && x64 = x72 && x73 = -1 + x65
l3(x80, x81, x82, x83, x84, x85, x86, x87) -> l5(x88, x89, x90, x91, x92, x93, x94, x95) :|: x87 = x95 && x86 = x94 && x85 = x93 && x84 = x92 && x83 = x91 && x82 = x90 && x81 = x89 && x80 = x88
l6(x96, x97, x98, x99, x100, x101, x102, x103) -> l4(x104, x105, x106, x107, x108, x109, x110, x111) :|: x103 = x111 && x102 = x110 && x101 = x109 && x100 = x108 && x99 = x107 && x98 = x106 && x97 = x105 && x96 = x104 && x97 <= x102
l6(x112, x113, x114, x115, x116, x117, x118, x119) -> l7(x120, x121, x122, x123, x124, x125, x126, x127) :|: x119 = x127 && x117 = x125 && x116 = x124 && x115 = x123 && x114 = x122 && x113 = x121 && x126 = 1 + x118 && x120 = x120 && 1 + x118 <= x113
l7(x128, x129, x130, x131, x132, x133, x134, x135) -> l6(x136, x137, x138, x139, x140, x141, x142, x143) :|: x135 = x143 && x134 = x142 && x133 = x141 && x132 = x140 && x131 = x139 && x130 = x138 && x129 = x137 && x128 = x136
l5(x144, x145, x146, x147, x148, x149, x150, x151) -> l8(x152, x153, x154, x155, x156, x157, x158, x159) :|: x151 = x159 && x150 = x158 && x149 = x157 && x148 = x156 && x147 = x155 && x146 = x154 && x145 = x153 && x144 = x152 && x149 <= x148
l5(x160, x161, x162, x163, x164, x165, x166, x167) -> l7(x168, x169, x170, x171, x172, x173, x174, x175) :|: x167 = x175 && x165 = x173 && x164 = x172 && x163 = x171 && x162 = x170 && x161 = x169 && x174 = 1 && x168 = x168 && 1 + x164 <= x165
l9(x176, x177, x178, x179, x180, x181, x182, x183) -> l3(x184, x185, x186, x187, x188, x189, x190, x191) :|: x182 = x190 && x176 = x184 && x188 = 0 && x185 = x186 && x186 = x186 && x191 = 285 && x187 = 35 && x189 = 10
l10(x192, x193, x194, x195, x196, x197, x198, x199) -> l9(x200, x201, x202, x203, x204, x205, x206, x207) :|: x199 = x207 && x198 = x206 && x197 = x205 && x196 = x204 && x195 = x203 && x194 = x202 && x193 = x201 && x192 = x200
Start term: l10(acc12HAT0, acc_length11HAT0, coef_len210HAT0, coef_len6HAT0, i8HAT0, in_len4HAT0, j9HAT0, scale7HAT0)

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

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

(2)
Obligation:
Rules:
l0(acc12HAT0, acc_length11HAT0, coef_len210HAT0, coef_len6HAT0, i8HAT0, in_len4HAT0, j9HAT0, scale7HAT0) -> l1(acc12HATpost, acc_length11HATpost, coef_len210HATpost, coef_len6HATpost, i8HATpost, in_len4HATpost, j9HATpost, scale7HATpost) :|: scale7HAT0 = scale7HATpost && j9HAT0 = j9HATpost && in_len4HAT0 = in_len4HATpost && i8HAT0 = i8HATpost && coef_len6HAT0 = coef_len6HATpost && coef_len210HAT0 = coef_len210HATpost && acc_length11HAT0 = acc_length11HATpost && acc12HAT0 = acc12HATpost
l2(x, x1, x2, x3, x4, x5, x6, x7) -> l0(x8, x9, x10, x11, x12, x13, x14, x15) :|: x7 = x15 && x6 = x14 && x5 = x13 && x4 = x12 && x3 = x11 && x2 = x10 && x1 = x9 && x = x8 && x3 <= x1
l2(x16, x17, x18, x19, x20, x21, x22, x23) -> l0(x24, x25, x26, x27, x28, x29, x30, x31) :|: x23 = x31 && x22 = x30 && x21 = x29 && x20 = x28 && x19 = x27 && x18 = x26 && x16 = x24 && x25 = 1 + x17 && 1 + x17 <= x19
l1(x32, x33, x34, x35, x36, x37, x38, x39) -> l3(x40, x41, x42, x43, x44, x45, x46, x47) :|: x39 = x47 && x38 = x46 && x37 = x45 && x35 = x43 && x34 = x42 && x33 = x41 && x32 = x40 && x44 = 1 + x36
l4(x48, x49, x50, x51, x52, x53, x54, x55) -> l2(x56, x57, x58, x59, x60, x61, x62, x63) :|: x55 = x63 && x54 = x62 && x53 = x61 && x52 = x60 && x51 = x59 && x50 = x58 && x49 = x57 && x48 = x56
l4(x64, x65, x66, x67, x68, x69, x70, x71) -> l1(x72, x73, x74, x75, x76, x77, x78, x79) :|: x71 = x79 && x70 = x78 && x69 = x77 && x68 = x76 && x67 = x75 && x66 = x74 && x64 = x72 && x73 = -1 + x65
l3(x80, x81, x82, x83, x84, x85, x86, x87) -> l5(x88, x89, x90, x91, x92, x93, x94, x95) :|: x87 = x95 && x86 = x94 && x85 = x93 && x84 = x92 && x83 = x91 && x82 = x90 && x81 = x89 && x80 = x88
l6(x96, x97, x98, x99, x100, x101, x102, x103) -> l4(x104, x105, x106, x107, x108, x109, x110, x111) :|: x103 = x111 && x102 = x110 && x101 = x109 && x100 = x108 && x99 = x107 && x98 = x106 && x97 = x105 && x96 = x104 && x97 <= x102
l6(x112, x113, x114, x115, x116, x117, x118, x119) -> l7(x120, x121, x122, x123, x124, x125, x126, x127) :|: x119 = x127 && x117 = x125 && x116 = x124 && x115 = x123 && x114 = x122 && x113 = x121 && x126 = 1 + x118 && x120 = x120 && 1 + x118 <= x113
l7(x128, x129, x130, x131, x132, x133, x134, x135) -> l6(x136, x137, x138, x139, x140, x141, x142, x143) :|: x135 = x143 && x134 = x142 && x133 = x141 && x132 = x140 && x131 = x139 && x130 = x138 && x129 = x137 && x128 = x136
l5(x144, x145, x146, x147, x148, x149, x150, x151) -> l8(x152, x153, x154, x155, x156, x157, x158, x159) :|: x151 = x159 && x150 = x158 && x149 = x157 && x148 = x156 && x147 = x155 && x146 = x154 && x145 = x153 && x144 = x152 && x149 <= x148
l5(x160, x161, x162, x163, x164, x165, x166, x167) -> l7(x168, x169, x170, x171, x172, x173, x174, x175) :|: x167 = x175 && x165 = x173 && x164 = x172 && x163 = x171 && x162 = x170 && x161 = x169 && x174 = 1 && x168 = x168 && 1 + x164 <= x165
l9(x176, x177, x178, x179, x180, x181, x182, x183) -> l3(x184, x185, x186, x187, x188, x189, x190, x191) :|: x182 = x190 && x176 = x184 && x188 = 0 && x185 = x186 && x186 = x186 && x191 = 285 && x187 = 35 && x189 = 10
l10(x192, x193, x194, x195, x196, x197, x198, x199) -> l9(x200, x201, x202, x203, x204, x205, x206, x207) :|: x199 = x207 && x198 = x206 && x197 = x205 && x196 = x204 && x195 = x203 && x194 = x202 && x193 = x201 && x192 = x200
Start term: l10(acc12HAT0, acc_length11HAT0, coef_len210HAT0, coef_len6HAT0, i8HAT0, in_len4HAT0, j9HAT0, scale7HAT0)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(acc12HAT0, acc_length11HAT0, coef_len210HAT0, coef_len6HAT0, i8HAT0, in_len4HAT0, j9HAT0, scale7HAT0) -> l1(acc12HATpost, acc_length11HATpost, coef_len210HATpost, coef_len6HATpost, i8HATpost, in_len4HATpost, j9HATpost, scale7HATpost) :|: scale7HAT0 = scale7HATpost && j9HAT0 = j9HATpost && in_len4HAT0 = in_len4HATpost && i8HAT0 = i8HATpost && coef_len6HAT0 = coef_len6HATpost && coef_len210HAT0 = coef_len210HATpost && acc_length11HAT0 = acc_length11HATpost && acc12HAT0 = acc12HATpost
(2) l2(x, x1, x2, x3, x4, x5, x6, x7) -> l0(x8, x9, x10, x11, x12, x13, x14, x15) :|: x7 = x15 && x6 = x14 && x5 = x13 && x4 = x12 && x3 = x11 && x2 = x10 && x1 = x9 && x = x8 && x3 <= x1
(3) l2(x16, x17, x18, x19, x20, x21, x22, x23) -> l0(x24, x25, x26, x27, x28, x29, x30, x31) :|: x23 = x31 && x22 = x30 && x21 = x29 && x20 = x28 && x19 = x27 && x18 = x26 && x16 = x24 && x25 = 1 + x17 && 1 + x17 <= x19
(4) l1(x32, x33, x34, x35, x36, x37, x38, x39) -> l3(x40, x41, x42, x43, x44, x45, x46, x47) :|: x39 = x47 && x38 = x46 && x37 = x45 && x35 = x43 && x34 = x42 && x33 = x41 && x32 = x40 && x44 = 1 + x36
(5) l4(x48, x49, x50, x51, x52, x53, x54, x55) -> l2(x56, x57, x58, x59, x60, x61, x62, x63) :|: x55 = x63 && x54 = x62 && x53 = x61 && x52 = x60 && x51 = x59 && x50 = x58 && x49 = x57 && x48 = x56
(6) l4(x64, x65, x66, x67, x68, x69, x70, x71) -> l1(x72, x73, x74, x75, x76, x77, x78, x79) :|: x71 = x79 && x70 = x78 && x69 = x77 && x68 = x76 && x67 = x75 && x66 = x74 && x64 = x72 && x73 = -1 + x65
(7) l3(x80, x81, x82, x83, x84, x85, x86, x87) -> l5(x88, x89, x90, x91, x92, x93, x94, x95) :|: x87 = x95 && x86 = x94 && x85 = x93 && x84 = x92 && x83 = x91 && x82 = x90 && x81 = x89 && x80 = x88
(8) l6(x96, x97, x98, x99, x100, x101, x102, x103) -> l4(x104, x105, x106, x107, x108, x109, x110, x111) :|: x103 = x111 && x102 = x110 && x101 = x109 && x100 = x108 && x99 = x107 && x98 = x106 && x97 = x105 && x96 = x104 && x97 <= x102
(9) l6(x112, x113, x114, x115, x116, x117, x118, x119) -> l7(x120, x121, x122, x123, x124, x125, x126, x127) :|: x119 = x127 && x117 = x125 && x116 = x124 && x115 = x123 && x114 = x122 && x113 = x121 && x126 = 1 + x118 && x120 = x120 && 1 + x118 <= x113
(10) l7(x128, x129, x130, x131, x132, x133, x134, x135) -> l6(x136, x137, x138, x139, x140, x141, x142, x143) :|: x135 = x143 && x134 = x142 && x133 = x141 && x132 = x140 && x131 = x139 && x130 = x138 && x129 = x137 && x128 = x136
(11) l5(x144, x145, x146, x147, x148, x149, x150, x151) -> l8(x152, x153, x154, x155, x156, x157, x158, x159) :|: x151 = x159 && x150 = x158 && x149 = x157 && x148 = x156 && x147 = x155 && x146 = x154 && x145 = x153 && x144 = x152 && x149 <= x148
(12) l5(x160, x161, x162, x163, x164, x165, x166, x167) -> l7(x168, x169, x170, x171, x172, x173, x174, x175) :|: x167 = x175 && x165 = x173 && x164 = x172 && x163 = x171 && x162 = x170 && x161 = x169 && x174 = 1 && x168 = x168 && 1 + x164 <= x165
(13) l9(x176, x177, x178, x179, x180, x181, x182, x183) -> l3(x184, x185, x186, x187, x188, x189, x190, x191) :|: x182 = x190 && x176 = x184 && x188 = 0 && x185 = x186 && x186 = x186 && x191 = 285 && x187 = 35 && x189 = 10
(14) l10(x192, x193, x194, x195, x196, x197, x198, x199) -> l9(x200, x201, x202, x203, x204, x205, x206, x207) :|: x199 = x207 && x198 = x206 && x197 = x205 && x196 = x204 && x195 = x203 && x194 = x202 && x193 = x201 && x192 = x200

Arcs:
(1) -> (4)
(2) -> (1)
(3) -> (1)
(4) -> (7)
(5) -> (2), (3)
(6) -> (4)
(7) -> (11), (12)
(8) -> (5), (6)
(9) -> (10)
(10) -> (8), (9)
(12) -> (10)
(13) -> (7)
(14) -> (13)

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

(4)
Obligation:

Termination digraph:
Nodes:
(1) l0(acc12HAT0, acc_length11HAT0, coef_len210HAT0, coef_len6HAT0, i8HAT0, in_len4HAT0, j9HAT0, scale7HAT0) -> l1(acc12HATpost, acc_length11HATpost, coef_len210HATpost, coef_len6HATpost, i8HATpost, in_len4HATpost, j9HATpost, scale7HATpost) :|: scale7HAT0 = scale7HATpost && j9HAT0 = j9HATpost && in_len4HAT0 = in_len4HATpost && i8HAT0 = i8HATpost && coef_len6HAT0 = coef_len6HATpost && coef_len210HAT0 = coef_len210HATpost && acc_length11HAT0 = acc_length11HATpost && acc12HAT0 = acc12HATpost
(2) l2(x16, x17, x18, x19, x20, x21, x22, x23) -> l0(x24, x25, x26, x27, x28, x29, x30, x31) :|: x23 = x31 && x22 = x30 && x21 = x29 && x20 = x28 && x19 = x27 && x18 = x26 && x16 = x24 && x25 = 1 + x17 && 1 + x17 <= x19
(3) l2(x, x1, x2, x3, x4, x5, x6, x7) -> l0(x8, x9, x10, x11, x12, x13, x14, x15) :|: x7 = x15 && x6 = x14 && x5 = x13 && x4 = x12 && x3 = x11 && x2 = x10 && x1 = x9 && x = x8 && x3 <= x1
(4) l4(x48, x49, x50, x51, x52, x53, x54, x55) -> l2(x56, x57, x58, x59, x60, x61, x62, x63) :|: x55 = x63 && x54 = x62 && x53 = x61 && x52 = x60 && x51 = x59 && x50 = x58 && x49 = x57 && x48 = x56
(5) l6(x96, x97, x98, x99, x100, x101, x102, x103) -> l4(x104, x105, x106, x107, x108, x109, x110, x111) :|: x103 = x111 && x102 = x110 && x101 = x109 && x100 = x108 && x99 = x107 && x98 = x106 && x97 = x105 && x96 = x104 && x97 <= x102
(6) l7(x128, x129, x130, x131, x132, x133, x134, x135) -> l6(x136, x137, x138, x139, x140, x141, x142, x143) :|: x135 = x143 && x134 = x142 && x133 = x141 && x132 = x140 && x131 = x139 && x130 = x138 && x129 = x137 && x128 = x136
(7) l5(x160, x161, x162, x163, x164, x165, x166, x167) -> l7(x168, x169, x170, x171, x172, x173, x174, x175) :|: x167 = x175 && x165 = x173 && x164 = x172 && x163 = x171 && x162 = x170 && x161 = x169 && x174 = 1 && x168 = x168 && 1 + x164 <= x165
(8) l3(x80, x81, x82, x83, x84, x85, x86, x87) -> l5(x88, x89, x90, x91, x92, x93, x94, x95) :|: x87 = x95 && x86 = x94 && x85 = x93 && x84 = x92 && x83 = x91 && x82 = x90 && x81 = x89 && x80 = x88
(9) l1(x32, x33, x34, x35, x36, x37, x38, x39) -> l3(x40, x41, x42, x43, x44, x45, x46, x47) :|: x39 = x47 && x38 = x46 && x37 = x45 && x35 = x43 && x34 = x42 && x33 = x41 && x32 = x40 && x44 = 1 + x36
(10) l4(x64, x65, x66, x67, x68, x69, x70, x71) -> l1(x72, x73, x74, x75, x76, x77, x78, x79) :|: x71 = x79 && x70 = x78 && x69 = x77 && x68 = x76 && x67 = x75 && x66 = x74 && x64 = x72 && x73 = -1 + x65
(11) l6(x112, x113, x114, x115, x116, x117, x118, x119) -> l7(x120, x121, x122, x123, x124, x125, x126, x127) :|: x119 = x127 && x117 = x125 && x116 = x124 && x115 = x123 && x114 = x122 && x113 = x121 && x126 = 1 + x118 && x120 = x120 && 1 + x118 <= x113

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

This digraph is fully evaluated!

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

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

(6)
Obligation:
Rules:
l7(x104:0, x105:0, x106:0, x107:0, x108:0, x109:0, x110:0, x111:0) -> l7(x168:0, -1 + x105:0, x106:0, x107:0, 1 + x108:0, x109:0, 1, x111:0) :|: x109:0 >= 1 + (1 + x108:0) && x110:0 >= x105:0
l7(x128:0, x121:0, x122:0, x123:0, x124:0, x125:0, x134:0, x127:0) -> l7(x120:0, x121:0, x122:0, x123:0, x124:0, x125:0, 1 + x134:0, x127:0) :|: x121:0 >= 1 + x134:0
l7(x, x1, x2, x3, x4, x5, x6, x7) -> l7(x8, 1 + x1, x2, x3, 1 + x4, x5, 1, x7) :|: x1 <= x6 && x3 >= 1 + x1 && x5 >= 1 + (1 + x4)
l7(x9, x10, x11, x12, x13, x14, x15, x16) -> l7(x17, x10, x11, x12, 1 + x13, x14, 1, x16) :|: x15 >= x10 && x12 <= x10 && x14 >= 1 + (1 + x13)

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

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

   l7(x1, x2, x3, x4, x5, x6, x7, x8) -> l7(x2, x4, x5, x6, x7)

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

(8)
Obligation:
Rules:
l7(x105:0, x107:0, x108:0, x109:0, x110:0) -> l7(-1 + x105:0, x107:0, 1 + x108:0, x109:0, 1) :|: x109:0 >= 1 + (1 + x108:0) && x110:0 >= x105:0
l7(x121:0, x123:0, x124:0, x125:0, x134:0) -> l7(x121:0, x123:0, x124:0, x125:0, 1 + x134:0) :|: x121:0 >= 1 + x134:0
l7(x1, x3, x4, x5, x6) -> l7(1 + x1, x3, 1 + x4, x5, 1) :|: x1 <= x6 && x3 >= 1 + x1 && x5 >= 1 + (1 + x4)
l7(x10, x12, x13, x14, x15) -> l7(x10, x12, 1 + x13, x14, 1) :|: x15 >= x10 && x12 <= x10 && x14 >= 1 + (1 + x13)

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

(9) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l7(INTEGER, VARIABLE, VARIABLE, VARIABLE, VARIABLE)
Replaced non-predefined constructor symbols by 0.
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(10)
Obligation:
Rules:
l7(x105:0, x107:0, x108:0, x109:0, x110:0) -> l7(c, x107:0, c1, x109:0, c2) :|: c2 = 1 && (c1 = 1 + x108:0 && c = -1 + x105:0) && (x109:0 >= 1 + (1 + x108:0) && x110:0 >= x105:0)
l7(x121:0, x123:0, x124:0, x125:0, x134:0) -> l7(x121:0, x123:0, x124:0, x125:0, c3) :|: c3 = 1 + x134:0 && x121:0 >= 1 + x134:0
l7(x1, x3, x4, x5, x6) -> l7(c4, x3, c5, x5, c6) :|: c6 = 1 && (c5 = 1 + x4 && c4 = 1 + x1) && (x1 <= x6 && x3 >= 1 + x1 && x5 >= 1 + (1 + x4))
l7(x10, x12, x13, x14, x15) -> l7(x10, x12, c7, x14, c8) :|: c8 = 1 && c7 = 1 + x13 && (x15 >= x10 && x12 <= x10 && x14 >= 1 + (1 + x13))

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(11) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[l7(x, x1, x2, x3, x4)] = -1 - x2 + x3

The following rules are decreasing:
l7(x105:0, x107:0, x108:0, x109:0, x110:0) -> l7(c, x107:0, c1, x109:0, c2) :|: c2 = 1 && (c1 = 1 + x108:0 && c = -1 + x105:0) && (x109:0 >= 1 + (1 + x108:0) && x110:0 >= x105:0)
l7(x1, x3, x4, x5, x6) -> l7(c4, x3, c5, x5, c6) :|: c6 = 1 && (c5 = 1 + x4 && c4 = 1 + x1) && (x1 <= x6 && x3 >= 1 + x1 && x5 >= 1 + (1 + x4))
l7(x10, x12, x13, x14, x15) -> l7(x10, x12, c7, x14, c8) :|: c8 = 1 && c7 = 1 + x13 && (x15 >= x10 && x12 <= x10 && x14 >= 1 + (1 + x13))
The following rules are bounded:
l7(x105:0, x107:0, x108:0, x109:0, x110:0) -> l7(c, x107:0, c1, x109:0, c2) :|: c2 = 1 && (c1 = 1 + x108:0 && c = -1 + x105:0) && (x109:0 >= 1 + (1 + x108:0) && x110:0 >= x105:0)
l7(x1, x3, x4, x5, x6) -> l7(c4, x3, c5, x5, c6) :|: c6 = 1 && (c5 = 1 + x4 && c4 = 1 + x1) && (x1 <= x6 && x3 >= 1 + x1 && x5 >= 1 + (1 + x4))
l7(x10, x12, x13, x14, x15) -> l7(x10, x12, c7, x14, c8) :|: c8 = 1 && c7 = 1 + x13 && (x15 >= x10 && x12 <= x10 && x14 >= 1 + (1 + x13))

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(12)
Obligation:
Rules:
l7(x121:0, x123:0, x124:0, x125:0, x134:0) -> l7(x121:0, x123:0, x124:0, x125:0, c3) :|: c3 = 1 + x134:0 && x121:0 >= 1 + x134:0

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(13) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[l7(x, x1, x2, x3, x4)] = x - x4

The following rules are decreasing:
l7(x121:0, x123:0, x124:0, x125:0, x134:0) -> l7(x121:0, x123:0, x124:0, x125:0, c3) :|: c3 = 1 + x134:0 && x121:0 >= 1 + x134:0
The following rules are bounded:
l7(x121:0, x123:0, x124:0, x125:0, x134:0) -> l7(x121:0, x123:0, x124:0, x125:0, c3) :|: c3 = 1 + x134:0 && x121:0 >= 1 + x134:0

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(14)
YES