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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 1586 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (7) IRSwT
        (8) TempFilterProof [SOUND, 52 ms]
        (9) IntTRS
        (10) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (11) IntTRS
        (12) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (16) IRSwT
        (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (18) IRSwT
        (19) TempFilterProof [SOUND, 78 ms]
        (20) IntTRS
        (21) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (22) IntTRS
        (23) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (24) IntTRS
        (25) RankingReductionPairProof [EQUIVALENT, 3 ms]
        (26) YES


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

(0)
Obligation:
Rules:
f1_0_main_ConstantStackPush(arg1, arg2, arg3, arg4) -> f117_0_main_GT(arg1P, arg2P, arg3P, arg4P) :|: arg2 = arg3P && 0 = arg2P && 0 <= arg1P - 1 && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg1P <= arg1
f117_0_main_GT(x, x1, x2, x3) -> f197_0_main_GT(x4, x5, x6, x7) :|: x2 = x7 && 0 = x6 && x1 = x5 && 0 <= x4 - 1 && 0 <= x - 1 && x4 <= x && -1 <= x2 - 1 && x1 <= x2
f197_0_main_GT(x8, x9, x10, x11) -> f117_0_main_GT(x12, x13, x14, x15) :|: x11 = x14 && x9 + 1 = x13 && 0 <= x12 - 1 && 0 <= x8 - 1 && x12 <= x8 && -1 <= x11 - 1 && x11 <= x10 - 1
f197_0_main_GT(x16, x17, x18, x19) -> f216_0_parts_GT(x20, x21, x22, x23) :|: x17 = x21 && x18 = x20 && 0 <= x16 - 1 && x18 <= x19 && x17 <= x19
f197_0_main_GT(x24, x25, x26, x27) -> f197_0_main_GT(x28, x29, x30, x31) :|: x27 = x31 && x26 + 1 = x30 && 0 = x29 && 0 = x25 && 0 <= x28 - 1 && 0 <= x24 - 1 && x28 <= x24 && x26 <= x27 && -1 <= x27 - 1
f197_0_main_GT(x32, x33, x34, x35) -> f197_0_main_GT(x36, x37, x38, x39) :|: x35 = x39 && 1 = x38 && x33 = x37 && 0 = x34 && 0 <= x36 - 1 && 0 <= x32 - 1 && x36 <= x32 && -1 <= x35 - 1 && x33 <= x35
f310_0_parts_Return(x40, x41, x42, x43) -> f197_0_main_GT(x44, x45, x46, x48) :|: x43 = x48 && x42 + 1 = x46 && x41 = x45 && 0 <= x44 - 1 && 0 <= x40 - 1 && -1 <= x43 - 1 && x44 <= x40
f197_0_main_GT(x49, x51, x52, x53) -> f197_0_main_GT(x54, x55, x56, x57) :|: x53 = x57 && x52 + 1 = x56 && x51 = x55 && 0 <= x54 - 1 && 0 <= x49 - 1 && x54 <= x49 && -1 <= x53 - 1 && x52 <= x53 && x51 <= x53
f216_0_parts_GT(x58, x59, x60, x61) -> f216_0_parts_GT(x62, x63, x64, x65) :|: x59 = x63 && x59 = x62 && 1 <= x58 - 1 && x59 <= x58 - 1 && 0 <= x59 - 1
f216_0_parts_GT(x66, x67, x68, x69) -> f216_0_parts_GT(x70, x71, x72, x73) :|: x67 - x66 = x71 && x66 = x70 && 0 <= x66 - 1 && x66 <= x67 && 0 <= x67 - 1
f216_0_parts_GT(x74, x75, x76, x77) -> f409_0_parts_InvokeMethod(x78, x79, x80, x81) :|: x74 - 1 = x80 && x75 = x79 && x74 = x78 && x74 <= x75 && x75 - x74 = 0 && 0 <= x74 - 1 && 0 <= x75 - 1
f314_0_parts_Return(x82, x83, x84, x85) -> f409_0_parts_InvokeMethod(x86, x87, x88, x89) :|: x83 - 1 = x88 && x82 = x87 && x83 = x86 && 0 <= x83 - 1
f216_0_parts_GT(x90, x91, x92, x93) -> f409_0_parts_InvokeMethod(x94, x95, x96, x97) :|: x90 - 1 = x96 && x91 = x95 && x90 = x94 && 0 <= x90 - 1 && x90 <= x91 && 0 <= x91 - 1
f409_0_parts_InvokeMethod(x98, x99, x100, x101) -> f216_0_parts_GT(x102, x103, x104, x105) :|: 0 <= x99 - 1 && 0 <= x98 - 1 && 0 <= x106 - 1 && x100 <= x98 - 1 && x100 = x102 && x99 = x103
f216_0_parts_GT(x107, x108, x109, x110) -> f216_0_parts_GT(x111, x112, x113, x114) :|: 0 <= x108 - 1 && 1 <= x107 - 1 && x107 <= x108 && x107 - 1 <= x107 - 1 && 0 <= x115 - 1 && x107 - 1 = x111 && x108 = x112
__init(x116, x117, x118, x119) -> f1_0_main_ConstantStackPush(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_ConstantStackPush(arg1, arg2, arg3, arg4) -> f117_0_main_GT(arg1P, arg2P, arg3P, arg4P) :|: arg2 = arg3P && 0 = arg2P && 0 <= arg1P - 1 && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg1P <= arg1
f117_0_main_GT(x, x1, x2, x3) -> f197_0_main_GT(x4, x5, x6, x7) :|: x2 = x7 && 0 = x6 && x1 = x5 && 0 <= x4 - 1 && 0 <= x - 1 && x4 <= x && -1 <= x2 - 1 && x1 <= x2
f197_0_main_GT(x8, x9, x10, x11) -> f117_0_main_GT(x12, x13, x14, x15) :|: x11 = x14 && x9 + 1 = x13 && 0 <= x12 - 1 && 0 <= x8 - 1 && x12 <= x8 && -1 <= x11 - 1 && x11 <= x10 - 1
f197_0_main_GT(x16, x17, x18, x19) -> f216_0_parts_GT(x20, x21, x22, x23) :|: x17 = x21 && x18 = x20 && 0 <= x16 - 1 && x18 <= x19 && x17 <= x19
f197_0_main_GT(x24, x25, x26, x27) -> f197_0_main_GT(x28, x29, x30, x31) :|: x27 = x31 && x26 + 1 = x30 && 0 = x29 && 0 = x25 && 0 <= x28 - 1 && 0 <= x24 - 1 && x28 <= x24 && x26 <= x27 && -1 <= x27 - 1
f197_0_main_GT(x32, x33, x34, x35) -> f197_0_main_GT(x36, x37, x38, x39) :|: x35 = x39 && 1 = x38 && x33 = x37 && 0 = x34 && 0 <= x36 - 1 && 0 <= x32 - 1 && x36 <= x32 && -1 <= x35 - 1 && x33 <= x35
f310_0_parts_Return(x40, x41, x42, x43) -> f197_0_main_GT(x44, x45, x46, x48) :|: x43 = x48 && x42 + 1 = x46 && x41 = x45 && 0 <= x44 - 1 && 0 <= x40 - 1 && -1 <= x43 - 1 && x44 <= x40
f197_0_main_GT(x49, x51, x52, x53) -> f197_0_main_GT(x54, x55, x56, x57) :|: x53 = x57 && x52 + 1 = x56 && x51 = x55 && 0 <= x54 - 1 && 0 <= x49 - 1 && x54 <= x49 && -1 <= x53 - 1 && x52 <= x53 && x51 <= x53
f216_0_parts_GT(x58, x59, x60, x61) -> f216_0_parts_GT(x62, x63, x64, x65) :|: x59 = x63 && x59 = x62 && 1 <= x58 - 1 && x59 <= x58 - 1 && 0 <= x59 - 1
f216_0_parts_GT(x66, x67, x68, x69) -> f216_0_parts_GT(x70, x71, x72, x73) :|: x67 - x66 = x71 && x66 = x70 && 0 <= x66 - 1 && x66 <= x67 && 0 <= x67 - 1
f216_0_parts_GT(x74, x75, x76, x77) -> f409_0_parts_InvokeMethod(x78, x79, x80, x81) :|: x74 - 1 = x80 && x75 = x79 && x74 = x78 && x74 <= x75 && x75 - x74 = 0 && 0 <= x74 - 1 && 0 <= x75 - 1
f314_0_parts_Return(x82, x83, x84, x85) -> f409_0_parts_InvokeMethod(x86, x87, x88, x89) :|: x83 - 1 = x88 && x82 = x87 && x83 = x86 && 0 <= x83 - 1
f216_0_parts_GT(x90, x91, x92, x93) -> f409_0_parts_InvokeMethod(x94, x95, x96, x97) :|: x90 - 1 = x96 && x91 = x95 && x90 = x94 && 0 <= x90 - 1 && x90 <= x91 && 0 <= x91 - 1
f409_0_parts_InvokeMethod(x98, x99, x100, x101) -> f216_0_parts_GT(x102, x103, x104, x105) :|: 0 <= x99 - 1 && 0 <= x98 - 1 && 0 <= x106 - 1 && x100 <= x98 - 1 && x100 = x102 && x99 = x103
f216_0_parts_GT(x107, x108, x109, x110) -> f216_0_parts_GT(x111, x112, x113, x114) :|: 0 <= x108 - 1 && 1 <= x107 - 1 && x107 <= x108 && x107 - 1 <= x107 - 1 && 0 <= x115 - 1 && x107 - 1 = x111 && x108 = x112
__init(x116, x117, x118, x119) -> f1_0_main_ConstantStackPush(x120, x121, x122, x123) :|: 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) -> f117_0_main_GT(arg1P, arg2P, arg3P, arg4P) :|: arg2 = arg3P && 0 = arg2P && 0 <= arg1P - 1 && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg1P <= arg1
(2) f117_0_main_GT(x, x1, x2, x3) -> f197_0_main_GT(x4, x5, x6, x7) :|: x2 = x7 && 0 = x6 && x1 = x5 && 0 <= x4 - 1 && 0 <= x - 1 && x4 <= x && -1 <= x2 - 1 && x1 <= x2
(3) f197_0_main_GT(x8, x9, x10, x11) -> f117_0_main_GT(x12, x13, x14, x15) :|: x11 = x14 && x9 + 1 = x13 && 0 <= x12 - 1 && 0 <= x8 - 1 && x12 <= x8 && -1 <= x11 - 1 && x11 <= x10 - 1
(4) f197_0_main_GT(x16, x17, x18, x19) -> f216_0_parts_GT(x20, x21, x22, x23) :|: x17 = x21 && x18 = x20 && 0 <= x16 - 1 && x18 <= x19 && x17 <= x19
(5) f197_0_main_GT(x24, x25, x26, x27) -> f197_0_main_GT(x28, x29, x30, x31) :|: x27 = x31 && x26 + 1 = x30 && 0 = x29 && 0 = x25 && 0 <= x28 - 1 && 0 <= x24 - 1 && x28 <= x24 && x26 <= x27 && -1 <= x27 - 1
(6) f197_0_main_GT(x32, x33, x34, x35) -> f197_0_main_GT(x36, x37, x38, x39) :|: x35 = x39 && 1 = x38 && x33 = x37 && 0 = x34 && 0 <= x36 - 1 && 0 <= x32 - 1 && x36 <= x32 && -1 <= x35 - 1 && x33 <= x35
(7) f310_0_parts_Return(x40, x41, x42, x43) -> f197_0_main_GT(x44, x45, x46, x48) :|: x43 = x48 && x42 + 1 = x46 && x41 = x45 && 0 <= x44 - 1 && 0 <= x40 - 1 && -1 <= x43 - 1 && x44 <= x40
(8) f197_0_main_GT(x49, x51, x52, x53) -> f197_0_main_GT(x54, x55, x56, x57) :|: x53 = x57 && x52 + 1 = x56 && x51 = x55 && 0 <= x54 - 1 && 0 <= x49 - 1 && x54 <= x49 && -1 <= x53 - 1 && x52 <= x53 && x51 <= x53
(9) f216_0_parts_GT(x58, x59, x60, x61) -> f216_0_parts_GT(x62, x63, x64, x65) :|: x59 = x63 && x59 = x62 && 1 <= x58 - 1 && x59 <= x58 - 1 && 0 <= x59 - 1
(10) f216_0_parts_GT(x66, x67, x68, x69) -> f216_0_parts_GT(x70, x71, x72, x73) :|: x67 - x66 = x71 && x66 = x70 && 0 <= x66 - 1 && x66 <= x67 && 0 <= x67 - 1
(11) f216_0_parts_GT(x74, x75, x76, x77) -> f409_0_parts_InvokeMethod(x78, x79, x80, x81) :|: x74 - 1 = x80 && x75 = x79 && x74 = x78 && x74 <= x75 && x75 - x74 = 0 && 0 <= x74 - 1 && 0 <= x75 - 1
(12) f314_0_parts_Return(x82, x83, x84, x85) -> f409_0_parts_InvokeMethod(x86, x87, x88, x89) :|: x83 - 1 = x88 && x82 = x87 && x83 = x86 && 0 <= x83 - 1
(13) f216_0_parts_GT(x90, x91, x92, x93) -> f409_0_parts_InvokeMethod(x94, x95, x96, x97) :|: x90 - 1 = x96 && x91 = x95 && x90 = x94 && 0 <= x90 - 1 && x90 <= x91 && 0 <= x91 - 1
(14) f409_0_parts_InvokeMethod(x98, x99, x100, x101) -> f216_0_parts_GT(x102, x103, x104, x105) :|: 0 <= x99 - 1 && 0 <= x98 - 1 && 0 <= x106 - 1 && x100 <= x98 - 1 && x100 = x102 && x99 = x103
(15) f216_0_parts_GT(x107, x108, x109, x110) -> f216_0_parts_GT(x111, x112, x113, x114) :|: 0 <= x108 - 1 && 1 <= x107 - 1 && x107 <= x108 && x107 - 1 <= x107 - 1 && 0 <= x115 - 1 && x107 - 1 = x111 && x108 = x112
(16) __init(x116, x117, x118, x119) -> f1_0_main_ConstantStackPush(x120, x121, x122, x123) :|: 0 <= 0

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

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) f117_0_main_GT(x, x1, x2, x3) -> f197_0_main_GT(x4, x5, x6, x7) :|: x2 = x7 && 0 = x6 && x1 = x5 && 0 <= x4 - 1 && 0 <= x - 1 && x4 <= x && -1 <= x2 - 1 && x1 <= x2
(2) f197_0_main_GT(x8, x9, x10, x11) -> f117_0_main_GT(x12, x13, x14, x15) :|: x11 = x14 && x9 + 1 = x13 && 0 <= x12 - 1 && 0 <= x8 - 1 && x12 <= x8 && -1 <= x11 - 1 && x11 <= x10 - 1
(3) f197_0_main_GT(x24, x25, x26, x27) -> f197_0_main_GT(x28, x29, x30, x31) :|: x27 = x31 && x26 + 1 = x30 && 0 = x29 && 0 = x25 && 0 <= x28 - 1 && 0 <= x24 - 1 && x28 <= x24 && x26 <= x27 && -1 <= x27 - 1
(4) f197_0_main_GT(x32, x33, x34, x35) -> f197_0_main_GT(x36, x37, x38, x39) :|: x35 = x39 && 1 = x38 && x33 = x37 && 0 = x34 && 0 <= x36 - 1 && 0 <= x32 - 1 && x36 <= x32 && -1 <= x35 - 1 && x33 <= x35
(5) f197_0_main_GT(x49, x51, x52, x53) -> f197_0_main_GT(x54, x55, x56, x57) :|: x53 = x57 && x52 + 1 = x56 && x51 = x55 && 0 <= x54 - 1 && 0 <= x49 - 1 && x54 <= x49 && -1 <= x53 - 1 && x52 <= x53 && x51 <= x53

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

This digraph is fully evaluated!

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

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

(7)
Obligation:
Rules:
f197_0_main_GT(x24:0, cons_0, x26:0, x27:0) -> f197_0_main_GT(x28:0, 0, x26:0 + 1, x27:0) :|: x27:0 >= x26:0 && x27:0 > -1 && x28:0 <= x24:0 && x28:0 > 0 && x24:0 > 0 && cons_0 = 0
f197_0_main_GT(x8:0, x9:0, x10:0, x11:0) -> f197_0_main_GT(x4:0, x9:0 + 1, 0, x11:0) :|: x9:0 + 1 <= x11:0 && x11:0 <= x10:0 - 1 && x11:0 > -1 && x8:0 >= x12:0 && x4:0 <= x12:0 && x8:0 > 0 && x4:0 > 0 && x12:0 > 0
f197_0_main_GT(x, x1, x2, x3) -> f197_0_main_GT(x4, x1, 1, x3) :|: x3 > -1 && x3 >= x1 && x4 <= x && x4 > 0 && x > 0 && x2 = 0
f197_0_main_GT(x49:0, x51:0, x52:0, x53:0) -> f197_0_main_GT(x54:0, x51:0, x52:0 + 1, x53:0) :|: x53:0 >= x52:0 && x53:0 >= x51:0 && x53:0 > -1 && x54:0 <= x49:0 && x54:0 > 0 && x49:0 > 0

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

(8) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f197_0_main_GT(INTEGER, VARIABLE, VARIABLE, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(9)
Obligation:
Rules:
f197_0_main_GT(x24:0, c, x26:0, x27:0) -> f197_0_main_GT(x28:0, c1, c2, x27:0) :|: c2 = x26:0 + 1 && (c1 = 0 && c = 0) && (x27:0 >= x26:0 && x27:0 > -1 && x28:0 <= x24:0 && x28:0 > 0 && x24:0 > 0 && cons_0 = 0)
f197_0_main_GT(x8:0, x9:0, x10:0, x11:0) -> f197_0_main_GT(x4:0, c3, c4, x11:0) :|: c4 = 0 && c3 = x9:0 + 1 && (x9:0 + 1 <= x11:0 && x11:0 <= x10:0 - 1 && x11:0 > -1 && x8:0 >= x12:0 && x4:0 <= x12:0 && x8:0 > 0 && x4:0 > 0 && x12:0 > 0)
f197_0_main_GT(x, x1, c5, x3) -> f197_0_main_GT(x4, x1, c6, x3) :|: c6 = 1 && c5 = 0 && (x3 > -1 && x3 >= x1 && x4 <= x && x4 > 0 && x > 0 && x2 = 0)
f197_0_main_GT(x49:0, x51:0, x52:0, x53:0) -> f197_0_main_GT(x54:0, x51:0, c7, x53:0) :|: c7 = x52:0 + 1 && (x53:0 >= x52:0 && x53:0 >= x51:0 && x53:0 > -1 && x54:0 <= x49:0 && x54:0 > 0 && x49:0 > 0)

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

(10) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f197_0_main_GT(x, x1, x2, x3)] = -x1 + x3

The following rules are decreasing:
f197_0_main_GT(x8:0, x9:0, x10:0, x11:0) -> f197_0_main_GT(x4:0, c3, c4, x11:0) :|: c4 = 0 && c3 = x9:0 + 1 && (x9:0 + 1 <= x11:0 && x11:0 <= x10:0 - 1 && x11:0 > -1 && x8:0 >= x12:0 && x4:0 <= x12:0 && x8:0 > 0 && x4:0 > 0 && x12:0 > 0)
The following rules are bounded:
f197_0_main_GT(x24:0, c, x26:0, x27:0) -> f197_0_main_GT(x28:0, c1, c2, x27:0) :|: c2 = x26:0 + 1 && (c1 = 0 && c = 0) && (x27:0 >= x26:0 && x27:0 > -1 && x28:0 <= x24:0 && x28:0 > 0 && x24:0 > 0 && cons_0 = 0)
f197_0_main_GT(x8:0, x9:0, x10:0, x11:0) -> f197_0_main_GT(x4:0, c3, c4, x11:0) :|: c4 = 0 && c3 = x9:0 + 1 && (x9:0 + 1 <= x11:0 && x11:0 <= x10:0 - 1 && x11:0 > -1 && x8:0 >= x12:0 && x4:0 <= x12:0 && x8:0 > 0 && x4:0 > 0 && x12:0 > 0)
f197_0_main_GT(x, x1, c5, x3) -> f197_0_main_GT(x4, x1, c6, x3) :|: c6 = 1 && c5 = 0 && (x3 > -1 && x3 >= x1 && x4 <= x && x4 > 0 && x > 0 && x2 = 0)
f197_0_main_GT(x49:0, x51:0, x52:0, x53:0) -> f197_0_main_GT(x54:0, x51:0, c7, x53:0) :|: c7 = x52:0 + 1 && (x53:0 >= x52:0 && x53:0 >= x51:0 && x53:0 > -1 && x54:0 <= x49:0 && x54:0 > 0 && x49:0 > 0)

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

(11)
Obligation:
Rules:
f197_0_main_GT(x24:0, c, x26:0, x27:0) -> f197_0_main_GT(x28:0, c1, c2, x27:0) :|: c2 = x26:0 + 1 && (c1 = 0 && c = 0) && (x27:0 >= x26:0 && x27:0 > -1 && x28:0 <= x24:0 && x28:0 > 0 && x24:0 > 0 && cons_0 = 0)
f197_0_main_GT(x, x1, c5, x3) -> f197_0_main_GT(x4, x1, c6, x3) :|: c6 = 1 && c5 = 0 && (x3 > -1 && x3 >= x1 && x4 <= x && x4 > 0 && x > 0 && x2 = 0)
f197_0_main_GT(x49:0, x51:0, x52:0, x53:0) -> f197_0_main_GT(x54:0, x51:0, c7, x53:0) :|: c7 = x52:0 + 1 && (x53:0 >= x52:0 && x53:0 >= x51:0 && x53:0 > -1 && x54:0 <= x49:0 && x54:0 > 0 && x49:0 > 0)

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

(12) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f197_0_main_GT(x, x1, x2, x3)] = -x2 + x3

The following rules are decreasing:
f197_0_main_GT(x24:0, c, x26:0, x27:0) -> f197_0_main_GT(x28:0, c1, c2, x27:0) :|: c2 = x26:0 + 1 && (c1 = 0 && c = 0) && (x27:0 >= x26:0 && x27:0 > -1 && x28:0 <= x24:0 && x28:0 > 0 && x24:0 > 0 && cons_0 = 0)
f197_0_main_GT(x, x1, c5, x3) -> f197_0_main_GT(x4, x1, c6, x3) :|: c6 = 1 && c5 = 0 && (x3 > -1 && x3 >= x1 && x4 <= x && x4 > 0 && x > 0 && x2 = 0)
f197_0_main_GT(x49:0, x51:0, x52:0, x53:0) -> f197_0_main_GT(x54:0, x51:0, c7, x53:0) :|: c7 = x52:0 + 1 && (x53:0 >= x52:0 && x53:0 >= x51:0 && x53:0 > -1 && x54:0 <= x49:0 && x54:0 > 0 && x49:0 > 0)
The following rules are bounded:
f197_0_main_GT(x24:0, c, x26:0, x27:0) -> f197_0_main_GT(x28:0, c1, c2, x27:0) :|: c2 = x26:0 + 1 && (c1 = 0 && c = 0) && (x27:0 >= x26:0 && x27:0 > -1 && x28:0 <= x24:0 && x28:0 > 0 && x24:0 > 0 && cons_0 = 0)
f197_0_main_GT(x, x1, c5, x3) -> f197_0_main_GT(x4, x1, c6, x3) :|: c6 = 1 && c5 = 0 && (x3 > -1 && x3 >= x1 && x4 <= x && x4 > 0 && x > 0 && x2 = 0)
f197_0_main_GT(x49:0, x51:0, x52:0, x53:0) -> f197_0_main_GT(x54:0, x51:0, c7, x53:0) :|: c7 = x52:0 + 1 && (x53:0 >= x52:0 && x53:0 >= x51:0 && x53:0 > -1 && x54:0 <= x49:0 && x54:0 > 0 && x49:0 > 0)

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(13)
YES

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(14)
Obligation:

Termination digraph:
Nodes:
(1) f216_0_parts_GT(x58, x59, x60, x61) -> f216_0_parts_GT(x62, x63, x64, x65) :|: x59 = x63 && x59 = x62 && 1 <= x58 - 1 && x59 <= x58 - 1 && 0 <= x59 - 1
(2) f216_0_parts_GT(x66, x67, x68, x69) -> f216_0_parts_GT(x70, x71, x72, x73) :|: x67 - x66 = x71 && x66 = x70 && 0 <= x66 - 1 && x66 <= x67 && 0 <= x67 - 1
(3) f409_0_parts_InvokeMethod(x98, x99, x100, x101) -> f216_0_parts_GT(x102, x103, x104, x105) :|: 0 <= x99 - 1 && 0 <= x98 - 1 && 0 <= x106 - 1 && x100 <= x98 - 1 && x100 = x102 && x99 = x103
(4) f216_0_parts_GT(x90, x91, x92, x93) -> f409_0_parts_InvokeMethod(x94, x95, x96, x97) :|: x90 - 1 = x96 && x91 = x95 && x90 = x94 && 0 <= x90 - 1 && x90 <= x91 && 0 <= x91 - 1
(5) f216_0_parts_GT(x107, x108, x109, x110) -> f216_0_parts_GT(x111, x112, x113, x114) :|: 0 <= x108 - 1 && 1 <= x107 - 1 && x107 <= x108 && x107 - 1 <= x107 - 1 && 0 <= x115 - 1 && x107 - 1 = x111 && x108 = x112
(6) f216_0_parts_GT(x74, x75, x76, x77) -> f409_0_parts_InvokeMethod(x78, x79, x80, x81) :|: x74 - 1 = x80 && x75 = x79 && x74 = x78 && x74 <= x75 && x75 - x74 = 0 && 0 <= x74 - 1 && 0 <= x75 - 1

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

This digraph is fully evaluated!

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(15) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(16)
Obligation:
Rules:
f216_0_parts_GT(x74:0, x103:0, x76:0, x77:0) -> f216_0_parts_GT(x74:0 - 1, x103:0, x104:0, x105:0) :|: x103:0 - x74:0 = 0 && x74:0 <= x103:0 && x106:0 > 0 && x74:0 > 0 && x103:0 > 0
f216_0_parts_GT(x58:0, x59:0, x60:0, x61:0) -> f216_0_parts_GT(x59:0, x59:0, x64:0, x65:0) :|: x59:0 <= x58:0 - 1 && x58:0 > 1 && x59:0 > 0
f216_0_parts_GT(x107:0, x108:0, x109:0, x110:0) -> f216_0_parts_GT(x107:0 - 1, x108:0, x113:0, x114:0) :|: x108:0 >= x107:0 && x115:0 > 0 && x107:0 > 1 && x108:0 > 0
f216_0_parts_GT(x66:0, x67:0, x68:0, x69:0) -> f216_0_parts_GT(x66:0, x67:0 - x66:0, x72:0, x73:0) :|: x67:0 >= x66:0 && x66:0 > 0 && x67:0 > 0
f216_0_parts_GT(x, x1, x2, x3) -> f216_0_parts_GT(x - 1, x1, x4, x5) :|: x <= x1 && x6 > 0 && x > 0 && x1 > 0

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

   f216_0_parts_GT(x1, x2, x3, x4) -> f216_0_parts_GT(x1, x2)

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(18)
Obligation:
Rules:
f216_0_parts_GT(x74:0, x103:0) -> f216_0_parts_GT(x74:0 - 1, x103:0) :|: x103:0 - x74:0 = 0 && x74:0 <= x103:0 && x106:0 > 0 && x74:0 > 0 && x103:0 > 0
f216_0_parts_GT(x58:0, x59:0) -> f216_0_parts_GT(x59:0, x59:0) :|: x59:0 <= x58:0 - 1 && x58:0 > 1 && x59:0 > 0
f216_0_parts_GT(x107:0, x108:0) -> f216_0_parts_GT(x107:0 - 1, x108:0) :|: x108:0 >= x107:0 && x115:0 > 0 && x107:0 > 1 && x108:0 > 0
f216_0_parts_GT(x66:0, x67:0) -> f216_0_parts_GT(x66:0, x67:0 - x66:0) :|: x67:0 >= x66:0 && x66:0 > 0 && x67:0 > 0
f216_0_parts_GT(x, x1) -> f216_0_parts_GT(x - 1, x1) :|: x <= x1 && x6 > 0 && x > 0 && x1 > 0

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(19) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f216_0_parts_GT(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(20)
Obligation:
Rules:
f216_0_parts_GT(x74:0, x103:0) -> f216_0_parts_GT(c, x103:0) :|: c = x74:0 - 1 && (x103:0 - x74:0 = 0 && x74:0 <= x103:0 && x106:0 > 0 && x74:0 > 0 && x103:0 > 0)
f216_0_parts_GT(x58:0, x59:0) -> f216_0_parts_GT(x59:0, x59:0) :|: x59:0 <= x58:0 - 1 && x58:0 > 1 && x59:0 > 0
f216_0_parts_GT(x107:0, x108:0) -> f216_0_parts_GT(c1, x108:0) :|: c1 = x107:0 - 1 && (x108:0 >= x107:0 && x115:0 > 0 && x107:0 > 1 && x108:0 > 0)
f216_0_parts_GT(x66:0, x67:0) -> f216_0_parts_GT(x66:0, c2) :|: c2 = x67:0 - x66:0 && (x67:0 >= x66:0 && x66:0 > 0 && x67:0 > 0)
f216_0_parts_GT(x, x1) -> f216_0_parts_GT(c3, x1) :|: c3 = x - 1 && (x <= x1 && x6 > 0 && x > 0 && x1 > 0)

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(21) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f216_0_parts_GT(x, x1)] = x1

The following rules are decreasing:
f216_0_parts_GT(x66:0, x67:0) -> f216_0_parts_GT(x66:0, c2) :|: c2 = x67:0 - x66:0 && (x67:0 >= x66:0 && x66:0 > 0 && x67:0 > 0)
The following rules are bounded:
f216_0_parts_GT(x74:0, x103:0) -> f216_0_parts_GT(c, x103:0) :|: c = x74:0 - 1 && (x103:0 - x74:0 = 0 && x74:0 <= x103:0 && x106:0 > 0 && x74:0 > 0 && x103:0 > 0)
f216_0_parts_GT(x107:0, x108:0) -> f216_0_parts_GT(c1, x108:0) :|: c1 = x107:0 - 1 && (x108:0 >= x107:0 && x115:0 > 0 && x107:0 > 1 && x108:0 > 0)
f216_0_parts_GT(x66:0, x67:0) -> f216_0_parts_GT(x66:0, c2) :|: c2 = x67:0 - x66:0 && (x67:0 >= x66:0 && x66:0 > 0 && x67:0 > 0)
f216_0_parts_GT(x, x1) -> f216_0_parts_GT(c3, x1) :|: c3 = x - 1 && (x <= x1 && x6 > 0 && x > 0 && x1 > 0)

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(22)
Obligation:
Rules:
f216_0_parts_GT(x74:0, x103:0) -> f216_0_parts_GT(c, x103:0) :|: c = x74:0 - 1 && (x103:0 - x74:0 = 0 && x74:0 <= x103:0 && x106:0 > 0 && x74:0 > 0 && x103:0 > 0)
f216_0_parts_GT(x58:0, x59:0) -> f216_0_parts_GT(x59:0, x59:0) :|: x59:0 <= x58:0 - 1 && x58:0 > 1 && x59:0 > 0
f216_0_parts_GT(x107:0, x108:0) -> f216_0_parts_GT(c1, x108:0) :|: c1 = x107:0 - 1 && (x108:0 >= x107:0 && x115:0 > 0 && x107:0 > 1 && x108:0 > 0)
f216_0_parts_GT(x, x1) -> f216_0_parts_GT(c3, x1) :|: c3 = x - 1 && (x <= x1 && x6 > 0 && x > 0 && x1 > 0)

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(23) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f216_0_parts_GT(x, x1)] = x

The following rules are decreasing:
f216_0_parts_GT(x74:0, x103:0) -> f216_0_parts_GT(c, x103:0) :|: c = x74:0 - 1 && (x103:0 - x74:0 = 0 && x74:0 <= x103:0 && x106:0 > 0 && x74:0 > 0 && x103:0 > 0)
f216_0_parts_GT(x58:0, x59:0) -> f216_0_parts_GT(x59:0, x59:0) :|: x59:0 <= x58:0 - 1 && x58:0 > 1 && x59:0 > 0
f216_0_parts_GT(x107:0, x108:0) -> f216_0_parts_GT(c1, x108:0) :|: c1 = x107:0 - 1 && (x108:0 >= x107:0 && x115:0 > 0 && x107:0 > 1 && x108:0 > 0)
f216_0_parts_GT(x, x1) -> f216_0_parts_GT(c3, x1) :|: c3 = x - 1 && (x <= x1 && x6 > 0 && x > 0 && x1 > 0)
The following rules are bounded:
f216_0_parts_GT(x74:0, x103:0) -> f216_0_parts_GT(c, x103:0) :|: c = x74:0 - 1 && (x103:0 - x74:0 = 0 && x74:0 <= x103:0 && x106:0 > 0 && x74:0 > 0 && x103:0 > 0)
f216_0_parts_GT(x58:0, x59:0) -> f216_0_parts_GT(x59:0, x59:0) :|: x59:0 <= x58:0 - 1 && x58:0 > 1 && x59:0 > 0
f216_0_parts_GT(x107:0, x108:0) -> f216_0_parts_GT(c1, x108:0) :|: c1 = x107:0 - 1 && (x108:0 >= x107:0 && x115:0 > 0 && x107:0 > 1 && x108:0 > 0)

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(24)
Obligation:
Rules:
f216_0_parts_GT(x, x1) -> f216_0_parts_GT(c3, x1) :|: c3 = x - 1 && (x <= x1 && x6 > 0 && x > 0 && x1 > 0)

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(25) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f216_0_parts_GT ] = f216_0_parts_GT_1

The following rules are decreasing:
f216_0_parts_GT(x, x1) -> f216_0_parts_GT(c3, x1) :|: c3 = x - 1 && (x <= x1 && x6 > 0 && x > 0 && x1 > 0)

The following rules are bounded:
f216_0_parts_GT(x, x1) -> f216_0_parts_GT(c3, x1) :|: c3 = x - 1 && (x <= x1 && x6 > 0 && x > 0 && x1 > 0)


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(26)
YES