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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 2260 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 84 ms]
        (11) IntTRS
        (12) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (13) IntTRS
        (14) RankingReductionPairProof [EQUIVALENT, 9 ms]
        (15) YES
    (16) IRSwT
        (17) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (18) IRSwT
        (19) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (20) IRSwT
        (21) TempFilterProof [SOUND, 36 ms]
        (22) IntTRS
        (23) PolynomialOrderProcessor [EQUIVALENT, 5 ms]
        (24) YES
    (25) IRSwT
        (26) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (27) IRSwT
        (28) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (29) IRSwT
        (30) TempFilterProof [SOUND, 13 ms]
        (31) IntTRS
        (32) PolynomialOrderProcessor [EQUIVALENT, 5 ms]
        (33) YES


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

(0)
Obligation:
Rules:
f1_0_main_ConstantStackPush(arg1, arg2, arg3, arg4) -> f626_0_main_GE(arg1P, arg2P, arg3P, arg4P) :|: arg2 = arg3P && 0 = arg2P && 0 <= arg1P - 1 && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg1P <= arg1
f626_0_main_GE(x, x1, x2, x3) -> f675_0_main_InvokeMethod(x4, x5, x6, x7) :|: x1 <= x2 - 1 && 0 <= x2 - 1 && -1 <= x9 - 1 && x4 <= x && 0 <= x - 1 && 0 <= x4 - 1 && x1 = x5 && x2 = x7
f626_0_main_GE(x10, x11, x12, x13) -> f60_0_power_GT(x14, x15, x16, x17) :|: x12 = x14 && 0 <= x10 - 1 && -1 <= x15 - 1 && 0 <= x12 - 1 && x11 <= x12 - 1
f626_0_main_GE(x18, x19, x20, x22) -> f675_0_main_InvokeMethod(x23, x24, x25, x26) :|: x20 = x26 && 1 = x25 && x19 = x24 && 0 <= x23 - 1 && 0 <= x18 - 1 && x23 <= x18 && 0 <= x20 - 1 && x19 <= x20 - 1
f626_0_main_GE(x27, x28, x29, x30) -> f675_0_main_InvokeMethod(x31, x32, x33, x34) :|: x28 <= x29 - 1 && 0 <= x29 - 1 && -1 <= x35 - 1 && x31 <= x27 && 0 <= x27 - 1 && 0 <= x31 - 1 && x28 = x32 && x29 = x33 && x29 = x34
f675_0_main_InvokeMethod(x37, x38, x39, x40) -> f712_0_main_ArrayAccess(x41, x42, x43, x44) :|: x40 = x43 && x38 = x42 && 0 <= x41 - 1 && 0 <= x37 - 1 && x41 <= x37 && 0 <= x39 - 1 && 0 <= x40 - 1
f712_0_main_ArrayAccess(x46, x47, x48, x49) -> f60_0_power_GT(x50, x51, x52, x53) :|: x48 = x50 && 0 <= x46 - 1 && x47 <= x48 - 1 && -1 <= x51 - 1 && 0 <= x48 - 1
f712_0_main_ArrayAccess(x54, x55, x56, x57) -> f753_0_main_InvokeMethod(x58, x59, x60, x61) :|: 0 <= x56 - 1 && -1 <= x62 - 1 && x55 <= x56 - 1 && x58 <= x54 && 0 <= x54 - 1 && 0 <= x58 - 1 && x55 = x59 && x56 = x61
f712_0_main_ArrayAccess(x63, x64, x65, x66) -> f753_0_main_InvokeMethod(x67, x68, x70, x71) :|: x65 = x71 && 1 = x70 && x64 = x68 && 0 <= x67 - 1 && 0 <= x63 - 1 && x67 <= x63 && 0 <= x65 - 1 && x64 <= x65 - 1
f712_0_main_ArrayAccess(x72, x73, x74, x75) -> f753_0_main_InvokeMethod(x76, x77, x78, x79) :|: 0 <= x74 - 1 && -1 <= x80 - 1 && x73 <= x74 - 1 && x76 <= x72 && 0 <= x72 - 1 && 0 <= x76 - 1 && x73 = x77 && x74 = x78 && x74 = x79
f753_0_main_InvokeMethod(x81, x82, x83, x84) -> f626_0_main_GE(x85, x86, x87, x88) :|: x84 = x87 && x82 + 1 = x86 && 1 = x83 && 0 <= x85 - 1 && 0 <= x81 - 1 && 0 <= x84 - 1 && x85 <= x81
f753_0_main_InvokeMethod(x89, x90, x91, x92) -> f626_0_main_GE(x93, x94, x95, x96) :|: x92 = x95 && x90 + 1 = x94 && 0 <= x93 - 1 && 0 <= x89 - 1 && x93 <= x89 && 0 <= x92 - 1 && 0 <= x91 - 1
f60_0_power_GT(x97, x98, x99, x100) -> f60_0_power_GT'(x101, x102, x103, x104) :|: 0 <= x97 - 1 && 1 <= x98 - 1 && 1 <= x97 * x97 && 0 <= x105 - 1 && x105 <= x98 - 1 && x97 = x101 && x98 = x102
f60_0_power_GT'(x106, x107, x108, x109) -> f60_0_power_GT(x110, x111, x112, x113) :|: x106 * x106 = x110 && 0 <= x107 - 2 * x111 && x107 - 2 * x111 <= 1 && 0 <= x111 - 1 && x111 <= x107 - 1 && 1 <= x106 * x106 && 1 <= x107 - 1 && 0 <= x106 - 1
f675_0_main_InvokeMethod(x114, x115, x116, x117) -> f116_0_even_NE(x118, x119, x120, x121) :|: x116 = x118 && 0 <= x114 - 1 && 0 <= x117 - 1 && 0 <= x116 - 1
f753_0_main_InvokeMethod(x122, x123, x124, x125) -> f168_0_odd_NE(x126, x127, x128, x129) :|: x124 = x126 && 0 <= x122 - 1 && 0 <= x125 - 1 && 0 <= x124 - 1
f116_0_even_NE(x130, x131, x132, x133) -> f168_0_odd_NE(x134, x135, x136, x137) :|: x130 - 1 = x134 && x130 - 1 <= x130 - 1 && 1 <= x130 - 1
f168_0_odd_NE(x138, x139, x140, x141) -> f116_0_even_NE(x142, x143, x144, x145) :|: x138 - 1 = x142 && x138 - 1 <= x138 - 1 && 1 <= x138 - 1
__init(x146, x147, x148, x149) -> f1_0_main_ConstantStackPush(x150, x151, x152, x153) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4)

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

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

(2)
Obligation:
Rules:
f1_0_main_ConstantStackPush(arg1, arg2, arg3, arg4) -> f626_0_main_GE(arg1P, arg2P, arg3P, arg4P) :|: arg2 = arg3P && 0 = arg2P && 0 <= arg1P - 1 && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg1P <= arg1
f626_0_main_GE(x, x1, x2, x3) -> f675_0_main_InvokeMethod(x4, x5, x6, x7) :|: x1 <= x2 - 1 && 0 <= x2 - 1 && -1 <= x9 - 1 && x4 <= x && 0 <= x - 1 && 0 <= x4 - 1 && x1 = x5 && x2 = x7
f626_0_main_GE(x10, x11, x12, x13) -> f60_0_power_GT(x14, x15, x16, x17) :|: x12 = x14 && 0 <= x10 - 1 && -1 <= x15 - 1 && 0 <= x12 - 1 && x11 <= x12 - 1
f626_0_main_GE(x18, x19, x20, x22) -> f675_0_main_InvokeMethod(x23, x24, x25, x26) :|: x20 = x26 && 1 = x25 && x19 = x24 && 0 <= x23 - 1 && 0 <= x18 - 1 && x23 <= x18 && 0 <= x20 - 1 && x19 <= x20 - 1
f626_0_main_GE(x27, x28, x29, x30) -> f675_0_main_InvokeMethod(x31, x32, x33, x34) :|: x28 <= x29 - 1 && 0 <= x29 - 1 && -1 <= x35 - 1 && x31 <= x27 && 0 <= x27 - 1 && 0 <= x31 - 1 && x28 = x32 && x29 = x33 && x29 = x34
f675_0_main_InvokeMethod(x37, x38, x39, x40) -> f712_0_main_ArrayAccess(x41, x42, x43, x44) :|: x40 = x43 && x38 = x42 && 0 <= x41 - 1 && 0 <= x37 - 1 && x41 <= x37 && 0 <= x39 - 1 && 0 <= x40 - 1
f712_0_main_ArrayAccess(x46, x47, x48, x49) -> f60_0_power_GT(x50, x51, x52, x53) :|: x48 = x50 && 0 <= x46 - 1 && x47 <= x48 - 1 && -1 <= x51 - 1 && 0 <= x48 - 1
f712_0_main_ArrayAccess(x54, x55, x56, x57) -> f753_0_main_InvokeMethod(x58, x59, x60, x61) :|: 0 <= x56 - 1 && -1 <= x62 - 1 && x55 <= x56 - 1 && x58 <= x54 && 0 <= x54 - 1 && 0 <= x58 - 1 && x55 = x59 && x56 = x61
f712_0_main_ArrayAccess(x63, x64, x65, x66) -> f753_0_main_InvokeMethod(x67, x68, x70, x71) :|: x65 = x71 && 1 = x70 && x64 = x68 && 0 <= x67 - 1 && 0 <= x63 - 1 && x67 <= x63 && 0 <= x65 - 1 && x64 <= x65 - 1
f712_0_main_ArrayAccess(x72, x73, x74, x75) -> f753_0_main_InvokeMethod(x76, x77, x78, x79) :|: 0 <= x74 - 1 && -1 <= x80 - 1 && x73 <= x74 - 1 && x76 <= x72 && 0 <= x72 - 1 && 0 <= x76 - 1 && x73 = x77 && x74 = x78 && x74 = x79
f753_0_main_InvokeMethod(x81, x82, x83, x84) -> f626_0_main_GE(x85, x86, x87, x88) :|: x84 = x87 && x82 + 1 = x86 && 1 = x83 && 0 <= x85 - 1 && 0 <= x81 - 1 && 0 <= x84 - 1 && x85 <= x81
f753_0_main_InvokeMethod(x89, x90, x91, x92) -> f626_0_main_GE(x93, x94, x95, x96) :|: x92 = x95 && x90 + 1 = x94 && 0 <= x93 - 1 && 0 <= x89 - 1 && x93 <= x89 && 0 <= x92 - 1 && 0 <= x91 - 1
f60_0_power_GT(x97, x98, x99, x100) -> f60_0_power_GT'(x101, x102, x103, x104) :|: 0 <= x97 - 1 && 1 <= x98 - 1 && 1 <= x97 * x97 && 0 <= x105 - 1 && x105 <= x98 - 1 && x97 = x101 && x98 = x102
f60_0_power_GT'(x106, x107, x108, x109) -> f60_0_power_GT(x110, x111, x112, x113) :|: x106 * x106 = x110 && 0 <= x107 - 2 * x111 && x107 - 2 * x111 <= 1 && 0 <= x111 - 1 && x111 <= x107 - 1 && 1 <= x106 * x106 && 1 <= x107 - 1 && 0 <= x106 - 1
f675_0_main_InvokeMethod(x114, x115, x116, x117) -> f116_0_even_NE(x118, x119, x120, x121) :|: x116 = x118 && 0 <= x114 - 1 && 0 <= x117 - 1 && 0 <= x116 - 1
f753_0_main_InvokeMethod(x122, x123, x124, x125) -> f168_0_odd_NE(x126, x127, x128, x129) :|: x124 = x126 && 0 <= x122 - 1 && 0 <= x125 - 1 && 0 <= x124 - 1
f116_0_even_NE(x130, x131, x132, x133) -> f168_0_odd_NE(x134, x135, x136, x137) :|: x130 - 1 = x134 && x130 - 1 <= x130 - 1 && 1 <= x130 - 1
f168_0_odd_NE(x138, x139, x140, x141) -> f116_0_even_NE(x142, x143, x144, x145) :|: x138 - 1 = x142 && x138 - 1 <= x138 - 1 && 1 <= x138 - 1
__init(x146, x147, x148, x149) -> f1_0_main_ConstantStackPush(x150, x151, x152, x153) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_ConstantStackPush(arg1, arg2, arg3, arg4) -> f626_0_main_GE(arg1P, arg2P, arg3P, arg4P) :|: arg2 = arg3P && 0 = arg2P && 0 <= arg1P - 1 && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg1P <= arg1
(2) f626_0_main_GE(x, x1, x2, x3) -> f675_0_main_InvokeMethod(x4, x5, x6, x7) :|: x1 <= x2 - 1 && 0 <= x2 - 1 && -1 <= x9 - 1 && x4 <= x && 0 <= x - 1 && 0 <= x4 - 1 && x1 = x5 && x2 = x7
(3) f626_0_main_GE(x10, x11, x12, x13) -> f60_0_power_GT(x14, x15, x16, x17) :|: x12 = x14 && 0 <= x10 - 1 && -1 <= x15 - 1 && 0 <= x12 - 1 && x11 <= x12 - 1
(4) f626_0_main_GE(x18, x19, x20, x22) -> f675_0_main_InvokeMethod(x23, x24, x25, x26) :|: x20 = x26 && 1 = x25 && x19 = x24 && 0 <= x23 - 1 && 0 <= x18 - 1 && x23 <= x18 && 0 <= x20 - 1 && x19 <= x20 - 1
(5) f626_0_main_GE(x27, x28, x29, x30) -> f675_0_main_InvokeMethod(x31, x32, x33, x34) :|: x28 <= x29 - 1 && 0 <= x29 - 1 && -1 <= x35 - 1 && x31 <= x27 && 0 <= x27 - 1 && 0 <= x31 - 1 && x28 = x32 && x29 = x33 && x29 = x34
(6) f675_0_main_InvokeMethod(x37, x38, x39, x40) -> f712_0_main_ArrayAccess(x41, x42, x43, x44) :|: x40 = x43 && x38 = x42 && 0 <= x41 - 1 && 0 <= x37 - 1 && x41 <= x37 && 0 <= x39 - 1 && 0 <= x40 - 1
(7) f712_0_main_ArrayAccess(x46, x47, x48, x49) -> f60_0_power_GT(x50, x51, x52, x53) :|: x48 = x50 && 0 <= x46 - 1 && x47 <= x48 - 1 && -1 <= x51 - 1 && 0 <= x48 - 1
(8) f712_0_main_ArrayAccess(x54, x55, x56, x57) -> f753_0_main_InvokeMethod(x58, x59, x60, x61) :|: 0 <= x56 - 1 && -1 <= x62 - 1 && x55 <= x56 - 1 && x58 <= x54 && 0 <= x54 - 1 && 0 <= x58 - 1 && x55 = x59 && x56 = x61
(9) f712_0_main_ArrayAccess(x63, x64, x65, x66) -> f753_0_main_InvokeMethod(x67, x68, x70, x71) :|: x65 = x71 && 1 = x70 && x64 = x68 && 0 <= x67 - 1 && 0 <= x63 - 1 && x67 <= x63 && 0 <= x65 - 1 && x64 <= x65 - 1
(10) f712_0_main_ArrayAccess(x72, x73, x74, x75) -> f753_0_main_InvokeMethod(x76, x77, x78, x79) :|: 0 <= x74 - 1 && -1 <= x80 - 1 && x73 <= x74 - 1 && x76 <= x72 && 0 <= x72 - 1 && 0 <= x76 - 1 && x73 = x77 && x74 = x78 && x74 = x79
(11) f753_0_main_InvokeMethod(x81, x82, x83, x84) -> f626_0_main_GE(x85, x86, x87, x88) :|: x84 = x87 && x82 + 1 = x86 && 1 = x83 && 0 <= x85 - 1 && 0 <= x81 - 1 && 0 <= x84 - 1 && x85 <= x81
(12) f753_0_main_InvokeMethod(x89, x90, x91, x92) -> f626_0_main_GE(x93, x94, x95, x96) :|: x92 = x95 && x90 + 1 = x94 && 0 <= x93 - 1 && 0 <= x89 - 1 && x93 <= x89 && 0 <= x92 - 1 && 0 <= x91 - 1
(13) f60_0_power_GT(x97, x98, x99, x100) -> f60_0_power_GT'(x101, x102, x103, x104) :|: 0 <= x97 - 1 && 1 <= x98 - 1 && 1 <= x97 * x97 && 0 <= x105 - 1 && x105 <= x98 - 1 && x97 = x101 && x98 = x102
(14) f60_0_power_GT'(x106, x107, x108, x109) -> f60_0_power_GT(x110, x111, x112, x113) :|: x106 * x106 = x110 && 0 <= x107 - 2 * x111 && x107 - 2 * x111 <= 1 && 0 <= x111 - 1 && x111 <= x107 - 1 && 1 <= x106 * x106 && 1 <= x107 - 1 && 0 <= x106 - 1
(15) f675_0_main_InvokeMethod(x114, x115, x116, x117) -> f116_0_even_NE(x118, x119, x120, x121) :|: x116 = x118 && 0 <= x114 - 1 && 0 <= x117 - 1 && 0 <= x116 - 1
(16) f753_0_main_InvokeMethod(x122, x123, x124, x125) -> f168_0_odd_NE(x126, x127, x128, x129) :|: x124 = x126 && 0 <= x122 - 1 && 0 <= x125 - 1 && 0 <= x124 - 1
(17) f116_0_even_NE(x130, x131, x132, x133) -> f168_0_odd_NE(x134, x135, x136, x137) :|: x130 - 1 = x134 && x130 - 1 <= x130 - 1 && 1 <= x130 - 1
(18) f168_0_odd_NE(x138, x139, x140, x141) -> f116_0_even_NE(x142, x143, x144, x145) :|: x138 - 1 = x142 && x138 - 1 <= x138 - 1 && 1 <= x138 - 1
(19) __init(x146, x147, x148, x149) -> f1_0_main_ConstantStackPush(x150, x151, x152, x153) :|: 0 <= 0

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

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) f626_0_main_GE(x, x1, x2, x3) -> f675_0_main_InvokeMethod(x4, x5, x6, x7) :|: x1 <= x2 - 1 && 0 <= x2 - 1 && -1 <= x9 - 1 && x4 <= x && 0 <= x - 1 && 0 <= x4 - 1 && x1 = x5 && x2 = x7
(2) f753_0_main_InvokeMethod(x81, x82, x83, x84) -> f626_0_main_GE(x85, x86, x87, x88) :|: x84 = x87 && x82 + 1 = x86 && 1 = x83 && 0 <= x85 - 1 && 0 <= x81 - 1 && 0 <= x84 - 1 && x85 <= x81
(3) f712_0_main_ArrayAccess(x54, x55, x56, x57) -> f753_0_main_InvokeMethod(x58, x59, x60, x61) :|: 0 <= x56 - 1 && -1 <= x62 - 1 && x55 <= x56 - 1 && x58 <= x54 && 0 <= x54 - 1 && 0 <= x58 - 1 && x55 = x59 && x56 = x61
(4) f675_0_main_InvokeMethod(x37, x38, x39, x40) -> f712_0_main_ArrayAccess(x41, x42, x43, x44) :|: x40 = x43 && x38 = x42 && 0 <= x41 - 1 && 0 <= x37 - 1 && x41 <= x37 && 0 <= x39 - 1 && 0 <= x40 - 1
(5) f626_0_main_GE(x27, x28, x29, x30) -> f675_0_main_InvokeMethod(x31, x32, x33, x34) :|: x28 <= x29 - 1 && 0 <= x29 - 1 && -1 <= x35 - 1 && x31 <= x27 && 0 <= x27 - 1 && 0 <= x31 - 1 && x28 = x32 && x29 = x33 && x29 = x34
(6) f626_0_main_GE(x18, x19, x20, x22) -> f675_0_main_InvokeMethod(x23, x24, x25, x26) :|: x20 = x26 && 1 = x25 && x19 = x24 && 0 <= x23 - 1 && 0 <= x18 - 1 && x23 <= x18 && 0 <= x20 - 1 && x19 <= x20 - 1
(7) f753_0_main_InvokeMethod(x89, x90, x91, x92) -> f626_0_main_GE(x93, x94, x95, x96) :|: x92 = x95 && x90 + 1 = x94 && 0 <= x93 - 1 && 0 <= x89 - 1 && x93 <= x89 && 0 <= x92 - 1 && 0 <= x91 - 1
(8) f712_0_main_ArrayAccess(x72, x73, x74, x75) -> f753_0_main_InvokeMethod(x76, x77, x78, x79) :|: 0 <= x74 - 1 && -1 <= x80 - 1 && x73 <= x74 - 1 && x76 <= x72 && 0 <= x72 - 1 && 0 <= x76 - 1 && x73 = x77 && x74 = x78 && x74 = x79
(9) f712_0_main_ArrayAccess(x63, x64, x65, x66) -> f753_0_main_InvokeMethod(x67, x68, x70, x71) :|: x65 = x71 && 1 = x70 && x64 = x68 && 0 <= x67 - 1 && 0 <= x63 - 1 && x67 <= x63 && 0 <= x65 - 1 && x64 <= x65 - 1

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

This digraph is fully evaluated!

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

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

(7)
Obligation:
Rules:
f626_0_main_GE(x18:0, x19:0, x20:0, x22:0) -> f712_0_main_ArrayAccess(x41:0, x19:0, x20:0, x44:0) :|: x20:0 - 1 >= x19:0 && x20:0 > 0 && x23:0 <= x18:0 && x41:0 <= x23:0 && x18:0 > 0 && x41:0 > 0 && x23:0 > 0
f753_0_main_InvokeMethod(x81:0, x82:0, cons_1, x84:0) -> f626_0_main_GE(x85:0, x82:0 + 1, x84:0, x88:0) :|: x84:0 > 0 && x85:0 <= x81:0 && x85:0 > 0 && x81:0 > 0 && cons_1 = 1
f712_0_main_ArrayAccess(x72:0, x73:0, x74:0, x75:0) -> f753_0_main_InvokeMethod(x76:0, x73:0, x74:0, x74:0) :|: x72:0 > 0 && x76:0 > 0 && x76:0 <= x72:0 && x74:0 - 1 >= x73:0 && x80:0 > -1 && x74:0 > 0
f712_0_main_ArrayAccess(x54:0, x55:0, x56:0, x57:0) -> f753_0_main_InvokeMethod(x58:0, x55:0, x60:0, x56:0) :|: x54:0 > 0 && x58:0 > 0 && x58:0 <= x54:0 && x56:0 - 1 >= x55:0 && x62:0 > -1 && x56:0 > 0
f626_0_main_GE(x, x1, x2, x3) -> f712_0_main_ArrayAccess(x4, x1, x2, x5) :|: x6 > 0 && x7 >= x4 && x > 0 && x7 > 0 && x >= x7 && x4 > 0 && x8 > -1 && x2 > 0 && x2 - 1 >= x1
f626_0_main_GE(x9, x10, x11, x12) -> f712_0_main_ArrayAccess(x13, x10, x11, x14) :|: x13 <= x15 && x15 > 0 && x9 > 0 && x13 > 0 && x15 <= x9 && x16 > -1 && x11 > 0 && x11 - 1 >= x10
f712_0_main_ArrayAccess(x63:0, x64:0, x65:0, x66:0) -> f753_0_main_InvokeMethod(x67:0, x64:0, 1, x65:0) :|: x65:0 > 0 && x65:0 - 1 >= x64:0 && x67:0 <= x63:0 && x67:0 > 0 && x63:0 > 0
f753_0_main_InvokeMethod(x89:0, x90:0, x91:0, x92:0) -> f626_0_main_GE(x93:0, x90:0 + 1, x92:0, x96:0) :|: x92:0 > 0 && x91:0 > 0 && x93:0 <= x89:0 && x93:0 > 0 && x89:0 > 0

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

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

   f626_0_main_GE(x1, x2, x3, x4) -> f626_0_main_GE(x1, x2, x3)
   f712_0_main_ArrayAccess(x1, x2, x3, x4) -> f712_0_main_ArrayAccess(x1, x2, x3)

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

(9)
Obligation:
Rules:
f626_0_main_GE(x18:0, x19:0, x20:0) -> f712_0_main_ArrayAccess(x41:0, x19:0, x20:0) :|: x20:0 - 1 >= x19:0 && x20:0 > 0 && x23:0 <= x18:0 && x41:0 <= x23:0 && x18:0 > 0 && x41:0 > 0 && x23:0 > 0
f753_0_main_InvokeMethod(x81:0, x82:0, cons_1, x84:0) -> f626_0_main_GE(x85:0, x82:0 + 1, x84:0) :|: x84:0 > 0 && x85:0 <= x81:0 && x85:0 > 0 && x81:0 > 0 && cons_1 = 1
f712_0_main_ArrayAccess(x72:0, x73:0, x74:0) -> f753_0_main_InvokeMethod(x76:0, x73:0, x74:0, x74:0) :|: x72:0 > 0 && x76:0 > 0 && x76:0 <= x72:0 && x74:0 - 1 >= x73:0 && x80:0 > -1 && x74:0 > 0
f712_0_main_ArrayAccess(x54:0, x55:0, x56:0) -> f753_0_main_InvokeMethod(x58:0, x55:0, x60:0, x56:0) :|: x54:0 > 0 && x58:0 > 0 && x58:0 <= x54:0 && x56:0 - 1 >= x55:0 && x62:0 > -1 && x56:0 > 0
f626_0_main_GE(x, x1, x2) -> f712_0_main_ArrayAccess(x4, x1, x2) :|: x6 > 0 && x7 >= x4 && x > 0 && x7 > 0 && x >= x7 && x4 > 0 && x8 > -1 && x2 > 0 && x2 - 1 >= x1
f626_0_main_GE(x9, x10, x11) -> f712_0_main_ArrayAccess(x13, x10, x11) :|: x13 <= x15 && x15 > 0 && x9 > 0 && x13 > 0 && x15 <= x9 && x16 > -1 && x11 > 0 && x11 - 1 >= x10
f712_0_main_ArrayAccess(x63:0, x64:0, x65:0) -> f753_0_main_InvokeMethod(x67:0, x64:0, 1, x65:0) :|: x65:0 > 0 && x65:0 - 1 >= x64:0 && x67:0 <= x63:0 && x67:0 > 0 && x63:0 > 0
f753_0_main_InvokeMethod(x89:0, x90:0, x91:0, x92:0) -> f626_0_main_GE(x93:0, x90:0 + 1, x92:0) :|: x92:0 > 0 && x91:0 > 0 && x93:0 <= x89:0 && x93:0 > 0 && x89:0 > 0

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

(10) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f626_0_main_GE(INTEGER, INTEGER, INTEGER)
f712_0_main_ArrayAccess(INTEGER, INTEGER, INTEGER)
f753_0_main_InvokeMethod(INTEGER, VARIABLE, VARIABLE, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(11)
Obligation:
Rules:
f626_0_main_GE(x18:0, x19:0, x20:0) -> f712_0_main_ArrayAccess(x41:0, x19:0, x20:0) :|: x20:0 - 1 >= x19:0 && x20:0 > 0 && x23:0 <= x18:0 && x41:0 <= x23:0 && x18:0 > 0 && x41:0 > 0 && x23:0 > 0
f753_0_main_InvokeMethod(x81:0, x82:0, c, x84:0) -> f626_0_main_GE(x85:0, c1, x84:0) :|: c1 = x82:0 + 1 && c = 1 && (x84:0 > 0 && x85:0 <= x81:0 && x85:0 > 0 && x81:0 > 0 && cons_1 = 1)
f712_0_main_ArrayAccess(x72:0, x73:0, x74:0) -> f753_0_main_InvokeMethod(x76:0, x73:0, x74:0, x74:0) :|: x72:0 > 0 && x76:0 > 0 && x76:0 <= x72:0 && x74:0 - 1 >= x73:0 && x80:0 > -1 && x74:0 > 0
f712_0_main_ArrayAccess(x54:0, x55:0, x56:0) -> f753_0_main_InvokeMethod(x58:0, x55:0, x60:0, x56:0) :|: x54:0 > 0 && x58:0 > 0 && x58:0 <= x54:0 && x56:0 - 1 >= x55:0 && x62:0 > -1 && x56:0 > 0
f626_0_main_GE(x, x1, x2) -> f712_0_main_ArrayAccess(x4, x1, x2) :|: x6 > 0 && x7 >= x4 && x > 0 && x7 > 0 && x >= x7 && x4 > 0 && x8 > -1 && x2 > 0 && x2 - 1 >= x1
f626_0_main_GE(x9, x10, x11) -> f712_0_main_ArrayAccess(x13, x10, x11) :|: x13 <= x15 && x15 > 0 && x9 > 0 && x13 > 0 && x15 <= x9 && x16 > -1 && x11 > 0 && x11 - 1 >= x10
f712_0_main_ArrayAccess(x63:0, x64:0, x65:0) -> f753_0_main_InvokeMethod(x67:0, x64:0, c2, x65:0) :|: c2 = 1 && (x65:0 > 0 && x65:0 - 1 >= x64:0 && x67:0 <= x63:0 && x67:0 > 0 && x63:0 > 0)
f753_0_main_InvokeMethod(x89:0, x90:0, x91:0, x92:0) -> f626_0_main_GE(x93:0, c3, x92:0) :|: c3 = x90:0 + 1 && (x92:0 > 0 && x91:0 > 0 && x93:0 <= x89:0 && x93:0 > 0 && x89:0 > 0)

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

(12) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f626_0_main_GE ] = 3*f626_0_main_GE_3 + -3*f626_0_main_GE_2
[ f712_0_main_ArrayAccess ] = -3*f712_0_main_ArrayAccess_2 + 3*f712_0_main_ArrayAccess_3 + -1
[ f753_0_main_InvokeMethod ] = 3*f753_0_main_InvokeMethod_4 + -3*f753_0_main_InvokeMethod_2 + -2

The following rules are decreasing:
f626_0_main_GE(x18:0, x19:0, x20:0) -> f712_0_main_ArrayAccess(x41:0, x19:0, x20:0) :|: x20:0 - 1 >= x19:0 && x20:0 > 0 && x23:0 <= x18:0 && x41:0 <= x23:0 && x18:0 > 0 && x41:0 > 0 && x23:0 > 0
f753_0_main_InvokeMethod(x81:0, x82:0, c, x84:0) -> f626_0_main_GE(x85:0, c1, x84:0) :|: c1 = x82:0 + 1 && c = 1 && (x84:0 > 0 && x85:0 <= x81:0 && x85:0 > 0 && x81:0 > 0 && cons_1 = 1)
f712_0_main_ArrayAccess(x72:0, x73:0, x74:0) -> f753_0_main_InvokeMethod(x76:0, x73:0, x74:0, x74:0) :|: x72:0 > 0 && x76:0 > 0 && x76:0 <= x72:0 && x74:0 - 1 >= x73:0 && x80:0 > -1 && x74:0 > 0
f712_0_main_ArrayAccess(x54:0, x55:0, x56:0) -> f753_0_main_InvokeMethod(x58:0, x55:0, x60:0, x56:0) :|: x54:0 > 0 && x58:0 > 0 && x58:0 <= x54:0 && x56:0 - 1 >= x55:0 && x62:0 > -1 && x56:0 > 0
f626_0_main_GE(x, x1, x2) -> f712_0_main_ArrayAccess(x4, x1, x2) :|: x6 > 0 && x7 >= x4 && x > 0 && x7 > 0 && x >= x7 && x4 > 0 && x8 > -1 && x2 > 0 && x2 - 1 >= x1
f626_0_main_GE(x9, x10, x11) -> f712_0_main_ArrayAccess(x13, x10, x11) :|: x13 <= x15 && x15 > 0 && x9 > 0 && x13 > 0 && x15 <= x9 && x16 > -1 && x11 > 0 && x11 - 1 >= x10
f712_0_main_ArrayAccess(x63:0, x64:0, x65:0) -> f753_0_main_InvokeMethod(x67:0, x64:0, c2, x65:0) :|: c2 = 1 && (x65:0 > 0 && x65:0 - 1 >= x64:0 && x67:0 <= x63:0 && x67:0 > 0 && x63:0 > 0)
f753_0_main_InvokeMethod(x89:0, x90:0, x91:0, x92:0) -> f626_0_main_GE(x93:0, c3, x92:0) :|: c3 = x90:0 + 1 && (x92:0 > 0 && x91:0 > 0 && x93:0 <= x89:0 && x93:0 > 0 && x89:0 > 0)

The following rules are bounded:
f626_0_main_GE(x18:0, x19:0, x20:0) -> f712_0_main_ArrayAccess(x41:0, x19:0, x20:0) :|: x20:0 - 1 >= x19:0 && x20:0 > 0 && x23:0 <= x18:0 && x41:0 <= x23:0 && x18:0 > 0 && x41:0 > 0 && x23:0 > 0
f712_0_main_ArrayAccess(x72:0, x73:0, x74:0) -> f753_0_main_InvokeMethod(x76:0, x73:0, x74:0, x74:0) :|: x72:0 > 0 && x76:0 > 0 && x76:0 <= x72:0 && x74:0 - 1 >= x73:0 && x80:0 > -1 && x74:0 > 0
f712_0_main_ArrayAccess(x54:0, x55:0, x56:0) -> f753_0_main_InvokeMethod(x58:0, x55:0, x60:0, x56:0) :|: x54:0 > 0 && x58:0 > 0 && x58:0 <= x54:0 && x56:0 - 1 >= x55:0 && x62:0 > -1 && x56:0 > 0
f626_0_main_GE(x, x1, x2) -> f712_0_main_ArrayAccess(x4, x1, x2) :|: x6 > 0 && x7 >= x4 && x > 0 && x7 > 0 && x >= x7 && x4 > 0 && x8 > -1 && x2 > 0 && x2 - 1 >= x1
f626_0_main_GE(x9, x10, x11) -> f712_0_main_ArrayAccess(x13, x10, x11) :|: x13 <= x15 && x15 > 0 && x9 > 0 && x13 > 0 && x15 <= x9 && x16 > -1 && x11 > 0 && x11 - 1 >= x10
f712_0_main_ArrayAccess(x63:0, x64:0, x65:0) -> f753_0_main_InvokeMethod(x67:0, x64:0, c2, x65:0) :|: c2 = 1 && (x65:0 > 0 && x65:0 - 1 >= x64:0 && x67:0 <= x63:0 && x67:0 > 0 && x63:0 > 0)


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

(13)
Obligation:
Rules:
f753_0_main_InvokeMethod(x81:0, x82:0, c, x84:0) -> f626_0_main_GE(x85:0, c1, x84:0) :|: c1 = x82:0 + 1 && c = 1 && (x84:0 > 0 && x85:0 <= x81:0 && x85:0 > 0 && x81:0 > 0 && cons_1 = 1)
f753_0_main_InvokeMethod(x89:0, x90:0, x91:0, x92:0) -> f626_0_main_GE(x93:0, c3, x92:0) :|: c3 = x90:0 + 1 && (x92:0 > 0 && x91:0 > 0 && x93:0 <= x89:0 && x93:0 > 0 && x89:0 > 0)

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

(14) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f753_0_main_InvokeMethod ] = 0
[ f626_0_main_GE ] = -1*f626_0_main_GE_1

The following rules are decreasing:
f753_0_main_InvokeMethod(x81:0, x82:0, c, x84:0) -> f626_0_main_GE(x85:0, c1, x84:0) :|: c1 = x82:0 + 1 && c = 1 && (x84:0 > 0 && x85:0 <= x81:0 && x85:0 > 0 && x81:0 > 0 && cons_1 = 1)
f753_0_main_InvokeMethod(x89:0, x90:0, x91:0, x92:0) -> f626_0_main_GE(x93:0, c3, x92:0) :|: c3 = x90:0 + 1 && (x92:0 > 0 && x91:0 > 0 && x93:0 <= x89:0 && x93:0 > 0 && x89:0 > 0)

The following rules are bounded:
f753_0_main_InvokeMethod(x81:0, x82:0, c, x84:0) -> f626_0_main_GE(x85:0, c1, x84:0) :|: c1 = x82:0 + 1 && c = 1 && (x84:0 > 0 && x85:0 <= x81:0 && x85:0 > 0 && x81:0 > 0 && cons_1 = 1)
f753_0_main_InvokeMethod(x89:0, x90:0, x91:0, x92:0) -> f626_0_main_GE(x93:0, c3, x92:0) :|: c3 = x90:0 + 1 && (x92:0 > 0 && x91:0 > 0 && x93:0 <= x89:0 && x93:0 > 0 && x89:0 > 0)


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

(15)
YES

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

(16)
Obligation:

Termination digraph:
Nodes:
(1) f116_0_even_NE(x130, x131, x132, x133) -> f168_0_odd_NE(x134, x135, x136, x137) :|: x130 - 1 = x134 && x130 - 1 <= x130 - 1 && 1 <= x130 - 1
(2) f168_0_odd_NE(x138, x139, x140, x141) -> f116_0_even_NE(x142, x143, x144, x145) :|: x138 - 1 = x142 && x138 - 1 <= x138 - 1 && 1 <= x138 - 1

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

This digraph is fully evaluated!

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

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

(18)
Obligation:
Rules:
f116_0_even_NE(x130:0, x131:0, x132:0, x133:0) -> f116_0_even_NE(x130:0 - 2, x143:0, x144:0, x145:0) :|: x130:0 > 2

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

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

   f116_0_even_NE(x1, x2, x3, x4) -> f116_0_even_NE(x1)

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

(20)
Obligation:
Rules:
f116_0_even_NE(x130:0) -> f116_0_even_NE(x130:0 - 2) :|: x130:0 > 2

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

(21) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f116_0_even_NE(INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(22)
Obligation:
Rules:
f116_0_even_NE(x130:0) -> f116_0_even_NE(c) :|: c = x130:0 - 2 && x130:0 > 2

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

(23) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f116_0_even_NE(x)] = x

The following rules are decreasing:
f116_0_even_NE(x130:0) -> f116_0_even_NE(c) :|: c = x130:0 - 2 && x130:0 > 2
The following rules are bounded:
f116_0_even_NE(x130:0) -> f116_0_even_NE(c) :|: c = x130:0 - 2 && x130:0 > 2

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

(24)
YES

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

(25)
Obligation:

Termination digraph:
Nodes:
(1) f60_0_power_GT(x97, x98, x99, x100) -> f60_0_power_GT'(x101, x102, x103, x104) :|: 0 <= x97 - 1 && 1 <= x98 - 1 && 1 <= x97 * x97 && 0 <= x105 - 1 && x105 <= x98 - 1 && x97 = x101 && x98 = x102
(2) f60_0_power_GT'(x106, x107, x108, x109) -> f60_0_power_GT(x110, x111, x112, x113) :|: x106 * x106 = x110 && 0 <= x107 - 2 * x111 && x107 - 2 * x111 <= 1 && 0 <= x111 - 1 && x111 <= x107 - 1 && 1 <= x106 * x106 && 1 <= x107 - 1 && 0 <= x106 - 1

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

This digraph is fully evaluated!

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

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

(27)
Obligation:
Rules:
f60_0_power_GT(x101:0, x102:0, x99:0, x100:0) -> f60_0_power_GT(x101:0 * x101:0, x111:0, x112:0, x113:0) :|: x105:0 <= x102:0 - 1 && x105:0 > 0 && x111:0 <= x102:0 - 1 && x101:0 * x101:0 >= 1 && x111:0 > 0 && x101:0 > 0 && x102:0 > 1 && x102:0 - 2 * x111:0 >= 0 && x102:0 - 2 * x111:0 <= 1

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

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

   f60_0_power_GT(x1, x2, x3, x4) -> f60_0_power_GT(x1, x2)

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

(29)
Obligation:
Rules:
f60_0_power_GT(x101:0, x102:0) -> f60_0_power_GT(x101:0 * x101:0, x111:0) :|: x105:0 <= x102:0 - 1 && x105:0 > 0 && x111:0 <= x102:0 - 1 && x101:0 * x101:0 >= 1 && x111:0 > 0 && x101:0 > 0 && x102:0 > 1 && x102:0 - 2 * x111:0 >= 0 && x102:0 - 2 * x111:0 <= 1

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

(30) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f60_0_power_GT(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(31)
Obligation:
Rules:
f60_0_power_GT(x101:0, x102:0) -> f60_0_power_GT(c, x111:0) :|: c = x101:0 * x101:0 && (x105:0 <= x102:0 - 1 && x105:0 > 0 && x111:0 <= x102:0 - 1 && x101:0 * x101:0 >= 1 && x111:0 > 0 && x101:0 > 0 && x102:0 > 1 && x102:0 - 2 * x111:0 >= 0 && x102:0 - 2 * x111:0 <= 1)

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

(32) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f60_0_power_GT(x, x1)] = x1

The following rules are decreasing:
f60_0_power_GT(x101:0, x102:0) -> f60_0_power_GT(c, x111:0) :|: c = x101:0 * x101:0 && (x105:0 <= x102:0 - 1 && x105:0 > 0 && x111:0 <= x102:0 - 1 && x101:0 * x101:0 >= 1 && x111:0 > 0 && x101:0 > 0 && x102:0 > 1 && x102:0 - 2 * x111:0 >= 0 && x102:0 - 2 * x111:0 <= 1)
The following rules are bounded:
f60_0_power_GT(x101:0, x102:0) -> f60_0_power_GT(c, x111:0) :|: c = x101:0 * x101:0 && (x105:0 <= x102:0 - 1 && x105:0 > 0 && x111:0 <= x102:0 - 1 && x101:0 * x101:0 >= 1 && x111:0 > 0 && x101:0 > 0 && x102:0 > 1 && x102:0 - 2 * x111:0 >= 0 && x102:0 - 2 * x111:0 <= 1)

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

(33)
YES