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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 1016 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IRSwT
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) TempFilterProof [SOUND, 89 ms]
(10) IntTRS
(11) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(12) IntTRS
(13) RankingReductionPairProof [EQUIVALENT, 0 ms]
(14) YES


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

(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3, arg4) -> f162_0_power_GT(arg1P, arg2P, arg3P, arg4P) :|: 0 = arg2P && 0 = arg1P && 0 = arg2 && 0 <= arg1 - 1
f1_0_main_Load(x, x1, x2, x3) -> f97_0_random_GT(x4, x5, x6, x7) :|: 0 = x5 && 0 <= x4 - 1 && 0 <= x - 1 && 0 <= x1 - 1 && x4 <= x
f1_0_main_Load(x8, x9, x11, x12) -> f97_0_random_GT(x13, x15, x16, x17) :|: 0 <= x13 - 1 && 0 <= x8 - 1 && x13 <= x8 && 0 <= x9 - 1 && -1 <= x15 - 1
f97_0_random_GT(x18, x20, x21, x22) -> f162_0_power_GT(x23, x24, x25, x26) :|: 0 = x24 && x20 = x23 && 0 <= x18 - 1
f97_0_random_GT(x27, x28, x29, x30) -> f155_0_main_InvokeMethod(x31, x32, x33, x34) :|: x31 <= x27 && 1 <= x35 - 1 && 0 <= x27 - 1 && 0 <= x31 - 1 && x28 = x32 && 0 = x33
f97_0_random_GT(x36, x38, x39, x40) -> f155_0_main_InvokeMethod(x42, x43, x44, x45) :|: 1 <= x46 - 1 && -1 <= x44 - 1 && x42 <= x36 && 0 <= x36 - 1 && 0 <= x42 - 1 && x38 = x43
f155_0_main_InvokeMethod(x48, x49, x50, x51) -> f162_0_power_GT(x52, x53, x54, x55) :|: 0 <= x48 - 1 && 1 <= x56 - 1 && x49 = x52 && x50 = x53
f162_0_power_GT(x57, x58, x59, x60) -> f162_0_power_GT'(x61, x62, x63, x64) :|: x58 = x62 && x57 = x61 && 1 <= x58 - 1 && x57 <= 1
f162_0_power_GT'(x65, x66, x67, x68) -> f213_0_power_NE(x69, x70, x71, x72) :|: 1 <= x66 - 1 && x65 <= 1 && x66 - 2 * x73 <= 1 && 0 <= x66 - 2 * x73 && x65 = x69 && x66 = x70 && x66 - 2 * x73 = x71
f162_0_power_GT(x74, x75, x76, x77) -> f162_0_power_GT'(x78, x79, x80, x81) :|: x75 = x79 && x74 = x78 && 1 <= x75 - 1 && 2 <= x74 - 1
f162_0_power_GT'(x82, x83, x84, x85) -> f213_0_power_NE(x86, x87, x88, x89) :|: 1 <= x83 - 1 && 2 <= x82 - 1 && x83 - 2 * x90 <= 1 && 0 <= x83 - 2 * x90 && x82 = x86 && x83 = x87 && x83 - 2 * x90 = x88
f213_0_power_NE(x91, x92, x93, x94) -> f213_0_power_NE'(x95, x96, x97, x98) :|: 1 <= x92 - 1 && 0 <= x99 - 1 && x99 <= x92 - 1 && 0 = x93 && x91 = x95 && x92 = x96 && 0 = x97 && x94 = x98
f213_0_power_NE'(x100, x101, x102, x103) -> f162_0_power_GT(x104, x105, x106, x107) :|: x100 = x104 && 0 = x102 && 0 <= x101 - 2 * x105 && x101 - 2 * x105 <= 1 && 0 <= x105 - 1 && x105 <= x101 - 1 && 1 <= x101 - 1
f213_0_power_NE(x108, x109, x110, x111) -> f162_0_power_GT(x112, x113, x114, x115) :|: x109 - 1 = x113 && x108 = x112 && 1 = x110 && x109 - 1 <= x109 - 1 && 1 <= x109 - 1
__init(x116, x117, x118, x119) -> f1_0_main_Load(x120, x121, x122, x123) :|: 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_Load(arg1, arg2, arg3, arg4) -> f162_0_power_GT(arg1P, arg2P, arg3P, arg4P) :|: 0 = arg2P && 0 = arg1P && 0 = arg2 && 0 <= arg1 - 1
f1_0_main_Load(x, x1, x2, x3) -> f97_0_random_GT(x4, x5, x6, x7) :|: 0 = x5 && 0 <= x4 - 1 && 0 <= x - 1 && 0 <= x1 - 1 && x4 <= x
f1_0_main_Load(x8, x9, x11, x12) -> f97_0_random_GT(x13, x15, x16, x17) :|: 0 <= x13 - 1 && 0 <= x8 - 1 && x13 <= x8 && 0 <= x9 - 1 && -1 <= x15 - 1
f97_0_random_GT(x18, x20, x21, x22) -> f162_0_power_GT(x23, x24, x25, x26) :|: 0 = x24 && x20 = x23 && 0 <= x18 - 1
f97_0_random_GT(x27, x28, x29, x30) -> f155_0_main_InvokeMethod(x31, x32, x33, x34) :|: x31 <= x27 && 1 <= x35 - 1 && 0 <= x27 - 1 && 0 <= x31 - 1 && x28 = x32 && 0 = x33
f97_0_random_GT(x36, x38, x39, x40) -> f155_0_main_InvokeMethod(x42, x43, x44, x45) :|: 1 <= x46 - 1 && -1 <= x44 - 1 && x42 <= x36 && 0 <= x36 - 1 && 0 <= x42 - 1 && x38 = x43
f155_0_main_InvokeMethod(x48, x49, x50, x51) -> f162_0_power_GT(x52, x53, x54, x55) :|: 0 <= x48 - 1 && 1 <= x56 - 1 && x49 = x52 && x50 = x53
f162_0_power_GT(x57, x58, x59, x60) -> f162_0_power_GT'(x61, x62, x63, x64) :|: x58 = x62 && x57 = x61 && 1 <= x58 - 1 && x57 <= 1
f162_0_power_GT'(x65, x66, x67, x68) -> f213_0_power_NE(x69, x70, x71, x72) :|: 1 <= x66 - 1 && x65 <= 1 && x66 - 2 * x73 <= 1 && 0 <= x66 - 2 * x73 && x65 = x69 && x66 = x70 && x66 - 2 * x73 = x71
f162_0_power_GT(x74, x75, x76, x77) -> f162_0_power_GT'(x78, x79, x80, x81) :|: x75 = x79 && x74 = x78 && 1 <= x75 - 1 && 2 <= x74 - 1
f162_0_power_GT'(x82, x83, x84, x85) -> f213_0_power_NE(x86, x87, x88, x89) :|: 1 <= x83 - 1 && 2 <= x82 - 1 && x83 - 2 * x90 <= 1 && 0 <= x83 - 2 * x90 && x82 = x86 && x83 = x87 && x83 - 2 * x90 = x88
f213_0_power_NE(x91, x92, x93, x94) -> f213_0_power_NE'(x95, x96, x97, x98) :|: 1 <= x92 - 1 && 0 <= x99 - 1 && x99 <= x92 - 1 && 0 = x93 && x91 = x95 && x92 = x96 && 0 = x97 && x94 = x98
f213_0_power_NE'(x100, x101, x102, x103) -> f162_0_power_GT(x104, x105, x106, x107) :|: x100 = x104 && 0 = x102 && 0 <= x101 - 2 * x105 && x101 - 2 * x105 <= 1 && 0 <= x105 - 1 && x105 <= x101 - 1 && 1 <= x101 - 1
f213_0_power_NE(x108, x109, x110, x111) -> f162_0_power_GT(x112, x113, x114, x115) :|: x109 - 1 = x113 && x108 = x112 && 1 = x110 && x109 - 1 <= x109 - 1 && 1 <= x109 - 1
__init(x116, x117, x118, x119) -> f1_0_main_Load(x120, x121, x122, x123) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_Load(arg1, arg2, arg3, arg4) -> f162_0_power_GT(arg1P, arg2P, arg3P, arg4P) :|: 0 = arg2P && 0 = arg1P && 0 = arg2 && 0 <= arg1 - 1
(2) f1_0_main_Load(x, x1, x2, x3) -> f97_0_random_GT(x4, x5, x6, x7) :|: 0 = x5 && 0 <= x4 - 1 && 0 <= x - 1 && 0 <= x1 - 1 && x4 <= x
(3) f1_0_main_Load(x8, x9, x11, x12) -> f97_0_random_GT(x13, x15, x16, x17) :|: 0 <= x13 - 1 && 0 <= x8 - 1 && x13 <= x8 && 0 <= x9 - 1 && -1 <= x15 - 1
(4) f97_0_random_GT(x18, x20, x21, x22) -> f162_0_power_GT(x23, x24, x25, x26) :|: 0 = x24 && x20 = x23 && 0 <= x18 - 1
(5) f97_0_random_GT(x27, x28, x29, x30) -> f155_0_main_InvokeMethod(x31, x32, x33, x34) :|: x31 <= x27 && 1 <= x35 - 1 && 0 <= x27 - 1 && 0 <= x31 - 1 && x28 = x32 && 0 = x33
(6) f97_0_random_GT(x36, x38, x39, x40) -> f155_0_main_InvokeMethod(x42, x43, x44, x45) :|: 1 <= x46 - 1 && -1 <= x44 - 1 && x42 <= x36 && 0 <= x36 - 1 && 0 <= x42 - 1 && x38 = x43
(7) f155_0_main_InvokeMethod(x48, x49, x50, x51) -> f162_0_power_GT(x52, x53, x54, x55) :|: 0 <= x48 - 1 && 1 <= x56 - 1 && x49 = x52 && x50 = x53
(8) f162_0_power_GT(x57, x58, x59, x60) -> f162_0_power_GT'(x61, x62, x63, x64) :|: x58 = x62 && x57 = x61 && 1 <= x58 - 1 && x57 <= 1
(9) f162_0_power_GT'(x65, x66, x67, x68) -> f213_0_power_NE(x69, x70, x71, x72) :|: 1 <= x66 - 1 && x65 <= 1 && x66 - 2 * x73 <= 1 && 0 <= x66 - 2 * x73 && x65 = x69 && x66 = x70 && x66 - 2 * x73 = x71
(10) f162_0_power_GT(x74, x75, x76, x77) -> f162_0_power_GT'(x78, x79, x80, x81) :|: x75 = x79 && x74 = x78 && 1 <= x75 - 1 && 2 <= x74 - 1
(11) f162_0_power_GT'(x82, x83, x84, x85) -> f213_0_power_NE(x86, x87, x88, x89) :|: 1 <= x83 - 1 && 2 <= x82 - 1 && x83 - 2 * x90 <= 1 && 0 <= x83 - 2 * x90 && x82 = x86 && x83 = x87 && x83 - 2 * x90 = x88
(12) f213_0_power_NE(x91, x92, x93, x94) -> f213_0_power_NE'(x95, x96, x97, x98) :|: 1 <= x92 - 1 && 0 <= x99 - 1 && x99 <= x92 - 1 && 0 = x93 && x91 = x95 && x92 = x96 && 0 = x97 && x94 = x98
(13) f213_0_power_NE'(x100, x101, x102, x103) -> f162_0_power_GT(x104, x105, x106, x107) :|: x100 = x104 && 0 = x102 && 0 <= x101 - 2 * x105 && x101 - 2 * x105 <= 1 && 0 <= x105 - 1 && x105 <= x101 - 1 && 1 <= x101 - 1
(14) f213_0_power_NE(x108, x109, x110, x111) -> f162_0_power_GT(x112, x113, x114, x115) :|: x109 - 1 = x113 && x108 = x112 && 1 = x110 && x109 - 1 <= x109 - 1 && 1 <= x109 - 1
(15) __init(x116, x117, x118, x119) -> f1_0_main_Load(x120, x121, x122, x123) :|: 0 <= 0

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

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

(4)
Obligation:

Termination digraph:
Nodes:
(1) f162_0_power_GT(x57, x58, x59, x60) -> f162_0_power_GT'(x61, x62, x63, x64) :|: x58 = x62 && x57 = x61 && 1 <= x58 - 1 && x57 <= 1
(2) f213_0_power_NE'(x100, x101, x102, x103) -> f162_0_power_GT(x104, x105, x106, x107) :|: x100 = x104 && 0 = x102 && 0 <= x101 - 2 * x105 && x101 - 2 * x105 <= 1 && 0 <= x105 - 1 && x105 <= x101 - 1 && 1 <= x101 - 1
(3) f213_0_power_NE(x91, x92, x93, x94) -> f213_0_power_NE'(x95, x96, x97, x98) :|: 1 <= x92 - 1 && 0 <= x99 - 1 && x99 <= x92 - 1 && 0 = x93 && x91 = x95 && x92 = x96 && 0 = x97 && x94 = x98
(4) f162_0_power_GT'(x82, x83, x84, x85) -> f213_0_power_NE(x86, x87, x88, x89) :|: 1 <= x83 - 1 && 2 <= x82 - 1 && x83 - 2 * x90 <= 1 && 0 <= x83 - 2 * x90 && x82 = x86 && x83 = x87 && x83 - 2 * x90 = x88
(5) f162_0_power_GT(x74, x75, x76, x77) -> f162_0_power_GT'(x78, x79, x80, x81) :|: x75 = x79 && x74 = x78 && 1 <= x75 - 1 && 2 <= x74 - 1
(6) f213_0_power_NE(x108, x109, x110, x111) -> f162_0_power_GT(x112, x113, x114, x115) :|: x109 - 1 = x113 && x108 = x112 && 1 = x110 && x109 - 1 <= x109 - 1 && 1 <= x109 - 1
(7) f162_0_power_GT'(x65, x66, x67, x68) -> f213_0_power_NE(x69, x70, x71, x72) :|: 1 <= x66 - 1 && x65 <= 1 && x66 - 2 * x73 <= 1 && 0 <= x66 - 2 * x73 && x65 = x69 && x66 = x70 && x66 - 2 * x73 = x71

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

This digraph is fully evaluated!

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

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

(6)
Obligation:
Rules:
f162_0_power_GT'(x82:0, x83:0, x84:0, x85:0) -> f213_0_power_NE(x82:0, x83:0, x83:0 - 2 * x90:0, x89:0) :|: x83:0 - 2 * x90:0 <= 1 && x83:0 - 2 * x90:0 >= 0 && x82:0 > 2 && x83:0 > 1
f213_0_power_NE(x104:0, x92:0, cons_0, x94:0) -> f162_0_power_GT(x104:0, x105:0, x106:0, x107:0) :|: x92:0 - 1 >= x105:0 && x105:0 > 0 && x92:0 - 2 * x105:0 <= 1 && x92:0 - 2 * x105:0 >= 0 && x99:0 <= x92:0 - 1 && x99:0 > 0 && x92:0 > 1 && cons_0 = 0
f213_0_power_NE(x108:0, x109:0, cons_1, x111:0) -> f162_0_power_GT(x108:0, x109:0 - 1, x114:0, x115:0) :|: x109:0 > 1 && cons_1 = 1
f162_0_power_GT'(x65:0, x66:0, x67:0, x68:0) -> f213_0_power_NE(x65:0, x66:0, x66:0 - 2 * x73:0, x72:0) :|: x66:0 - 2 * x73:0 <= 1 && x66:0 - 2 * x73:0 >= 0 && x65:0 < 2 && x66:0 > 1
f162_0_power_GT(x57:0, x58:0, x59:0, x60:0) -> f162_0_power_GT'(x57:0, x58:0, x63:0, x64:0) :|: x57:0 < 2 && x58:0 > 1
f162_0_power_GT(x74:0, x75:0, x76:0, x77:0) -> f162_0_power_GT'(x74:0, x75:0, x80:0, x81:0) :|: x74:0 > 2 && x75:0 > 1

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

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

   f162_0_power_GT'(x1, x2, x3, x4) -> f162_0_power_GT'(x1, x2)
   f213_0_power_NE(x1, x2, x3, x4) -> f213_0_power_NE(x1, x2, x3)
   f162_0_power_GT(x1, x2, x3, x4) -> f162_0_power_GT(x1, x2)

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

(8)
Obligation:
Rules:
f162_0_power_GT'(x82:0, x83:0) -> f213_0_power_NE(x82:0, x83:0, x83:0 - 2 * x90:0) :|: x83:0 - 2 * x90:0 <= 1 && x83:0 - 2 * x90:0 >= 0 && x82:0 > 2 && x83:0 > 1
f213_0_power_NE(x104:0, x92:0, cons_0) -> f162_0_power_GT(x104:0, x105:0) :|: x92:0 - 1 >= x105:0 && x105:0 > 0 && x92:0 - 2 * x105:0 <= 1 && x92:0 - 2 * x105:0 >= 0 && x99:0 <= x92:0 - 1 && x99:0 > 0 && x92:0 > 1 && cons_0 = 0
f213_0_power_NE(x108:0, x109:0, cons_1) -> f162_0_power_GT(x108:0, x109:0 - 1) :|: x109:0 > 1 && cons_1 = 1
f162_0_power_GT'(x65:0, x66:0) -> f213_0_power_NE(x65:0, x66:0, x66:0 - 2 * x73:0) :|: x66:0 - 2 * x73:0 <= 1 && x66:0 - 2 * x73:0 >= 0 && x65:0 < 2 && x66:0 > 1
f162_0_power_GT(x57:0, x58:0) -> f162_0_power_GT'(x57:0, x58:0) :|: x57:0 < 2 && x58:0 > 1
f162_0_power_GT(x74:0, x75:0) -> f162_0_power_GT'(x74:0, x75:0) :|: x74:0 > 2 && x75:0 > 1

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

(9) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f162_0_power_GT'(INTEGER, INTEGER)
f213_0_power_NE(VARIABLE, INTEGER, INTEGER)
f162_0_power_GT(VARIABLE, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(10)
Obligation:
Rules:
f162_0_power_GT'(x82:0, x83:0) -> f213_0_power_NE(x82:0, x83:0, c) :|: c = x83:0 - 2 * x90:0 && (x83:0 - 2 * x90:0 <= 1 && x83:0 - 2 * x90:0 >= 0 && x82:0 > 2 && x83:0 > 1)
f213_0_power_NE(x104:0, x92:0, c1) -> f162_0_power_GT(x104:0, x105:0) :|: c1 = 0 && (x92:0 - 1 >= x105:0 && x105:0 > 0 && x92:0 - 2 * x105:0 <= 1 && x92:0 - 2 * x105:0 >= 0 && x99:0 <= x92:0 - 1 && x99:0 > 0 && x92:0 > 1 && cons_0 = 0)
f213_0_power_NE(x108:0, x109:0, c2) -> f162_0_power_GT(x108:0, c3) :|: c3 = x109:0 - 1 && c2 = 1 && (x109:0 > 1 && cons_1 = 1)
f162_0_power_GT'(x65:0, x66:0) -> f213_0_power_NE(x65:0, x66:0, c4) :|: c4 = x66:0 - 2 * x73:0 && (x66:0 - 2 * x73:0 <= 1 && x66:0 - 2 * x73:0 >= 0 && x65:0 < 2 && x66:0 > 1)
f162_0_power_GT(x57:0, x58:0) -> f162_0_power_GT'(x57:0, x58:0) :|: x57:0 < 2 && x58:0 > 1
f162_0_power_GT(x74:0, x75:0) -> f162_0_power_GT'(x74:0, x75:0) :|: x74:0 > 2 && x75:0 > 1

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

(11) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f162_0_power_GT'(x, x1)] = x1
[f213_0_power_NE(x2, x3, x4)] = x3
[f162_0_power_GT(x5, x6)] = x6

The following rules are decreasing:
f213_0_power_NE(x104:0, x92:0, c1) -> f162_0_power_GT(x104:0, x105:0) :|: c1 = 0 && (x92:0 - 1 >= x105:0 && x105:0 > 0 && x92:0 - 2 * x105:0 <= 1 && x92:0 - 2 * x105:0 >= 0 && x99:0 <= x92:0 - 1 && x99:0 > 0 && x92:0 > 1 && cons_0 = 0)
f213_0_power_NE(x108:0, x109:0, c2) -> f162_0_power_GT(x108:0, c3) :|: c3 = x109:0 - 1 && c2 = 1 && (x109:0 > 1 && cons_1 = 1)
The following rules are bounded:
f162_0_power_GT'(x82:0, x83:0) -> f213_0_power_NE(x82:0, x83:0, c) :|: c = x83:0 - 2 * x90:0 && (x83:0 - 2 * x90:0 <= 1 && x83:0 - 2 * x90:0 >= 0 && x82:0 > 2 && x83:0 > 1)
f213_0_power_NE(x104:0, x92:0, c1) -> f162_0_power_GT(x104:0, x105:0) :|: c1 = 0 && (x92:0 - 1 >= x105:0 && x105:0 > 0 && x92:0 - 2 * x105:0 <= 1 && x92:0 - 2 * x105:0 >= 0 && x99:0 <= x92:0 - 1 && x99:0 > 0 && x92:0 > 1 && cons_0 = 0)
f213_0_power_NE(x108:0, x109:0, c2) -> f162_0_power_GT(x108:0, c3) :|: c3 = x109:0 - 1 && c2 = 1 && (x109:0 > 1 && cons_1 = 1)
f162_0_power_GT'(x65:0, x66:0) -> f213_0_power_NE(x65:0, x66:0, c4) :|: c4 = x66:0 - 2 * x73:0 && (x66:0 - 2 * x73:0 <= 1 && x66:0 - 2 * x73:0 >= 0 && x65:0 < 2 && x66:0 > 1)
f162_0_power_GT(x57:0, x58:0) -> f162_0_power_GT'(x57:0, x58:0) :|: x57:0 < 2 && x58:0 > 1
f162_0_power_GT(x74:0, x75:0) -> f162_0_power_GT'(x74:0, x75:0) :|: x74:0 > 2 && x75:0 > 1

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

(12)
Obligation:
Rules:
f162_0_power_GT'(x82:0, x83:0) -> f213_0_power_NE(x82:0, x83:0, c) :|: c = x83:0 - 2 * x90:0 && (x83:0 - 2 * x90:0 <= 1 && x83:0 - 2 * x90:0 >= 0 && x82:0 > 2 && x83:0 > 1)
f162_0_power_GT'(x65:0, x66:0) -> f213_0_power_NE(x65:0, x66:0, c4) :|: c4 = x66:0 - 2 * x73:0 && (x66:0 - 2 * x73:0 <= 1 && x66:0 - 2 * x73:0 >= 0 && x65:0 < 2 && x66:0 > 1)
f162_0_power_GT(x57:0, x58:0) -> f162_0_power_GT'(x57:0, x58:0) :|: x57:0 < 2 && x58:0 > 1
f162_0_power_GT(x74:0, x75:0) -> f162_0_power_GT'(x74:0, x75:0) :|: x74:0 > 2 && x75:0 > 1

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(13) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f162_0_power_GT' ] = 0
[ f213_0_power_NE ] = -1
[ f162_0_power_GT ] = 1/2*f162_0_power_GT_2

The following rules are decreasing:
f162_0_power_GT'(x82:0, x83:0) -> f213_0_power_NE(x82:0, x83:0, c) :|: c = x83:0 - 2 * x90:0 && (x83:0 - 2 * x90:0 <= 1 && x83:0 - 2 * x90:0 >= 0 && x82:0 > 2 && x83:0 > 1)
f162_0_power_GT'(x65:0, x66:0) -> f213_0_power_NE(x65:0, x66:0, c4) :|: c4 = x66:0 - 2 * x73:0 && (x66:0 - 2 * x73:0 <= 1 && x66:0 - 2 * x73:0 >= 0 && x65:0 < 2 && x66:0 > 1)
f162_0_power_GT(x57:0, x58:0) -> f162_0_power_GT'(x57:0, x58:0) :|: x57:0 < 2 && x58:0 > 1
f162_0_power_GT(x74:0, x75:0) -> f162_0_power_GT'(x74:0, x75:0) :|: x74:0 > 2 && x75:0 > 1

The following rules are bounded:
f162_0_power_GT'(x82:0, x83:0) -> f213_0_power_NE(x82:0, x83:0, c) :|: c = x83:0 - 2 * x90:0 && (x83:0 - 2 * x90:0 <= 1 && x83:0 - 2 * x90:0 >= 0 && x82:0 > 2 && x83:0 > 1)
f162_0_power_GT'(x65:0, x66:0) -> f213_0_power_NE(x65:0, x66:0, c4) :|: c4 = x66:0 - 2 * x73:0 && (x66:0 - 2 * x73:0 <= 1 && x66:0 - 2 * x73:0 >= 0 && x65:0 < 2 && x66:0 > 1)
f162_0_power_GT(x57:0, x58:0) -> f162_0_power_GT'(x57:0, x58:0) :|: x57:0 < 2 && x58:0 > 1
f162_0_power_GT(x74:0, x75:0) -> f162_0_power_GT'(x74:0, x75:0) :|: x74:0 > 2 && x75:0 > 1


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(14)
YES