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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 782 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 27 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 36 ms]
        (11) IntTRS
        (12) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 3 ms]
        (16) IRSwT
        (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (18) IRSwT
        (19) TempFilterProof [SOUND, 10 ms]
        (20) IntTRS
        (21) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (22) YES
    (23) IRSwT
        (24) IntTRSCompressionProof [EQUIVALENT, 7 ms]
        (25) IRSwT
        (26) TempFilterProof [SOUND, 32 ms]
        (27) IntTRS
        (28) RankingReductionPairProof [EQUIVALENT, 14 ms]
        (29) IntTRS
        (30) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (31) YES


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

(0)
Obligation:
Rules:
f303_0_createIntList_Return(arg1, arg2, arg3, arg4) -> f517_0_random_ArrayAccess(arg1P, arg2P, arg3P, arg4P) :|: -1 <= arg1P - 1 && -1 <= arg1 - 1 && arg1P <= arg1
f1_0_main_Load(x, x1, x2, x3) -> f517_0_random_ArrayAccess(x4, x5, x6, x8) :|: -1 <= x4 - 1 && 0 <= x - 1
f517_0_random_ArrayAccess(x9, x10, x11, x12) -> f704_0_nth_LE(x13, x14, x15, x16) :|: 0 <= x17 - 1 && -1 <= x15 - 1 && x13 <= x9 && x14 <= x9 && -1 <= x9 - 1 && -1 <= x13 - 1 && -1 <= x14 - 1 && x17 + 1 = x16
f704_0_nth_LE(x18, x19, x20, x21) -> f754_0_main_LE(x22, x23, x24, x25) :|: x21 = x24 && x23 + 2 <= x19 && -1 <= x22 - 1 && 0 <= x19 - 1 && -1 <= x18 - 1 && x20 <= 1 && x22 <= x18
f704_0_nth_LE(x26, x27, x28, x29) -> f704_0_nth_LE(x30, x31, x32, x33) :|: x29 = x33 && x28 - 1 = x32 && -1 <= x31 - 1 && -1 <= x30 - 1 && 0 <= x27 - 1 && -1 <= x26 - 1 && x31 + 1 <= x27 && 1 <= x28 - 1 && x30 <= x26
f754_0_main_LE(x34, x35, x36, x37) -> f964_0_nth_LE(x38, x39, x40, x41) :|: x36 + 1 = x41 && -1 <= x39 - 1 && -1 <= x38 - 1 && 0 <= x34 - 1 && x39 + 1 <= x34 && x38 + 1 <= x34 && 0 <= x35 - 1 && 0 <= x36 - 1 && -1 <= x40 - 1
f964_0_nth_LE(x42, x43, x44, x45) -> f754_0_main_LE(x46, x47, x48, x49) :|: x45 = x48 && x47 + 2 <= x43 && -1 <= x46 - 1 && 0 <= x43 - 1 && -1 <= x42 - 1 && x44 <= 1 && x46 <= x42
f964_0_nth_LE(x50, x51, x52, x53) -> f964_0_nth_LE(x54, x55, x56, x57) :|: x53 = x57 && x52 - 1 = x56 && -1 <= x55 - 1 && -1 <= x54 - 1 && 0 <= x51 - 1 && -1 <= x50 - 1 && x55 + 1 <= x51 && 1 <= x52 - 1 && x54 <= x50
f964_0_nth_LE(x58, x59, x60, x61) -> f754_0_main_LE(x62, x63, x64, x65) :|: x61 = x64 && 0 = x63 && -1 <= x62 - 1 && -1 <= x59 - 1 && -1 <= x58 - 1 && x60 <= 1 && x62 <= x58
f964_0_nth_LE(x66, x67, x68, x69) -> f754_0_main_LE(x70, x71, x72, x73) :|: x69 = x72 && 0 = x71 && -1 <= x70 - 1 && -1 <= x67 - 1 && -1 <= x66 - 1 && 1 <= x68 - 1 && x70 <= x66
f1_0_main_Load(x74, x75, x76, x77) -> f673_0_createIntList_LE(x78, x79, x80, x81) :|: 1 = x79 && 0 <= x74 - 1 && -1 <= x78 - 1 && -1 <= x75 - 1
f673_0_createIntList_LE(x82, x83, x84, x85) -> f673_0_createIntList_LE(x86, x87, x88, x89) :|: x83 + 1 = x87 && x82 - 1 = x86 && 0 <= x83 - 1 && 0 <= x82 - 1
__init(x90, x91, x92, x93) -> f1_0_main_Load(x94, x95, x96, x97) :|: 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:
f303_0_createIntList_Return(arg1, arg2, arg3, arg4) -> f517_0_random_ArrayAccess(arg1P, arg2P, arg3P, arg4P) :|: -1 <= arg1P - 1 && -1 <= arg1 - 1 && arg1P <= arg1
f1_0_main_Load(x, x1, x2, x3) -> f517_0_random_ArrayAccess(x4, x5, x6, x8) :|: -1 <= x4 - 1 && 0 <= x - 1
f517_0_random_ArrayAccess(x9, x10, x11, x12) -> f704_0_nth_LE(x13, x14, x15, x16) :|: 0 <= x17 - 1 && -1 <= x15 - 1 && x13 <= x9 && x14 <= x9 && -1 <= x9 - 1 && -1 <= x13 - 1 && -1 <= x14 - 1 && x17 + 1 = x16
f704_0_nth_LE(x18, x19, x20, x21) -> f754_0_main_LE(x22, x23, x24, x25) :|: x21 = x24 && x23 + 2 <= x19 && -1 <= x22 - 1 && 0 <= x19 - 1 && -1 <= x18 - 1 && x20 <= 1 && x22 <= x18
f704_0_nth_LE(x26, x27, x28, x29) -> f704_0_nth_LE(x30, x31, x32, x33) :|: x29 = x33 && x28 - 1 = x32 && -1 <= x31 - 1 && -1 <= x30 - 1 && 0 <= x27 - 1 && -1 <= x26 - 1 && x31 + 1 <= x27 && 1 <= x28 - 1 && x30 <= x26
f754_0_main_LE(x34, x35, x36, x37) -> f964_0_nth_LE(x38, x39, x40, x41) :|: x36 + 1 = x41 && -1 <= x39 - 1 && -1 <= x38 - 1 && 0 <= x34 - 1 && x39 + 1 <= x34 && x38 + 1 <= x34 && 0 <= x35 - 1 && 0 <= x36 - 1 && -1 <= x40 - 1
f964_0_nth_LE(x42, x43, x44, x45) -> f754_0_main_LE(x46, x47, x48, x49) :|: x45 = x48 && x47 + 2 <= x43 && -1 <= x46 - 1 && 0 <= x43 - 1 && -1 <= x42 - 1 && x44 <= 1 && x46 <= x42
f964_0_nth_LE(x50, x51, x52, x53) -> f964_0_nth_LE(x54, x55, x56, x57) :|: x53 = x57 && x52 - 1 = x56 && -1 <= x55 - 1 && -1 <= x54 - 1 && 0 <= x51 - 1 && -1 <= x50 - 1 && x55 + 1 <= x51 && 1 <= x52 - 1 && x54 <= x50
f964_0_nth_LE(x58, x59, x60, x61) -> f754_0_main_LE(x62, x63, x64, x65) :|: x61 = x64 && 0 = x63 && -1 <= x62 - 1 && -1 <= x59 - 1 && -1 <= x58 - 1 && x60 <= 1 && x62 <= x58
f964_0_nth_LE(x66, x67, x68, x69) -> f754_0_main_LE(x70, x71, x72, x73) :|: x69 = x72 && 0 = x71 && -1 <= x70 - 1 && -1 <= x67 - 1 && -1 <= x66 - 1 && 1 <= x68 - 1 && x70 <= x66
f1_0_main_Load(x74, x75, x76, x77) -> f673_0_createIntList_LE(x78, x79, x80, x81) :|: 1 = x79 && 0 <= x74 - 1 && -1 <= x78 - 1 && -1 <= x75 - 1
f673_0_createIntList_LE(x82, x83, x84, x85) -> f673_0_createIntList_LE(x86, x87, x88, x89) :|: x83 + 1 = x87 && x82 - 1 = x86 && 0 <= x83 - 1 && 0 <= x82 - 1
__init(x90, x91, x92, x93) -> f1_0_main_Load(x94, x95, x96, x97) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f303_0_createIntList_Return(arg1, arg2, arg3, arg4) -> f517_0_random_ArrayAccess(arg1P, arg2P, arg3P, arg4P) :|: -1 <= arg1P - 1 && -1 <= arg1 - 1 && arg1P <= arg1
(2) f1_0_main_Load(x, x1, x2, x3) -> f517_0_random_ArrayAccess(x4, x5, x6, x8) :|: -1 <= x4 - 1 && 0 <= x - 1
(3) f517_0_random_ArrayAccess(x9, x10, x11, x12) -> f704_0_nth_LE(x13, x14, x15, x16) :|: 0 <= x17 - 1 && -1 <= x15 - 1 && x13 <= x9 && x14 <= x9 && -1 <= x9 - 1 && -1 <= x13 - 1 && -1 <= x14 - 1 && x17 + 1 = x16
(4) f704_0_nth_LE(x18, x19, x20, x21) -> f754_0_main_LE(x22, x23, x24, x25) :|: x21 = x24 && x23 + 2 <= x19 && -1 <= x22 - 1 && 0 <= x19 - 1 && -1 <= x18 - 1 && x20 <= 1 && x22 <= x18
(5) f704_0_nth_LE(x26, x27, x28, x29) -> f704_0_nth_LE(x30, x31, x32, x33) :|: x29 = x33 && x28 - 1 = x32 && -1 <= x31 - 1 && -1 <= x30 - 1 && 0 <= x27 - 1 && -1 <= x26 - 1 && x31 + 1 <= x27 && 1 <= x28 - 1 && x30 <= x26
(6) f754_0_main_LE(x34, x35, x36, x37) -> f964_0_nth_LE(x38, x39, x40, x41) :|: x36 + 1 = x41 && -1 <= x39 - 1 && -1 <= x38 - 1 && 0 <= x34 - 1 && x39 + 1 <= x34 && x38 + 1 <= x34 && 0 <= x35 - 1 && 0 <= x36 - 1 && -1 <= x40 - 1
(7) f964_0_nth_LE(x42, x43, x44, x45) -> f754_0_main_LE(x46, x47, x48, x49) :|: x45 = x48 && x47 + 2 <= x43 && -1 <= x46 - 1 && 0 <= x43 - 1 && -1 <= x42 - 1 && x44 <= 1 && x46 <= x42
(8) f964_0_nth_LE(x50, x51, x52, x53) -> f964_0_nth_LE(x54, x55, x56, x57) :|: x53 = x57 && x52 - 1 = x56 && -1 <= x55 - 1 && -1 <= x54 - 1 && 0 <= x51 - 1 && -1 <= x50 - 1 && x55 + 1 <= x51 && 1 <= x52 - 1 && x54 <= x50
(9) f964_0_nth_LE(x58, x59, x60, x61) -> f754_0_main_LE(x62, x63, x64, x65) :|: x61 = x64 && 0 = x63 && -1 <= x62 - 1 && -1 <= x59 - 1 && -1 <= x58 - 1 && x60 <= 1 && x62 <= x58
(10) f964_0_nth_LE(x66, x67, x68, x69) -> f754_0_main_LE(x70, x71, x72, x73) :|: x69 = x72 && 0 = x71 && -1 <= x70 - 1 && -1 <= x67 - 1 && -1 <= x66 - 1 && 1 <= x68 - 1 && x70 <= x66
(11) f1_0_main_Load(x74, x75, x76, x77) -> f673_0_createIntList_LE(x78, x79, x80, x81) :|: 1 = x79 && 0 <= x74 - 1 && -1 <= x78 - 1 && -1 <= x75 - 1
(12) f673_0_createIntList_LE(x82, x83, x84, x85) -> f673_0_createIntList_LE(x86, x87, x88, x89) :|: x83 + 1 = x87 && x82 - 1 = x86 && 0 <= x83 - 1 && 0 <= x82 - 1
(13) __init(x90, x91, x92, x93) -> f1_0_main_Load(x94, x95, x96, x97) :|: 0 <= 0

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

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) f673_0_createIntList_LE(x82, x83, x84, x85) -> f673_0_createIntList_LE(x86, x87, x88, x89) :|: x83 + 1 = x87 && x82 - 1 = x86 && 0 <= x83 - 1 && 0 <= x82 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(7)
Obligation:
Rules:
f673_0_createIntList_LE(x82:0, x83:0, x84:0, x85:0) -> f673_0_createIntList_LE(x82:0 - 1, x83:0 + 1, x88:0, x89:0) :|: x82:0 > 0 && x83:0 > 0

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

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

   f673_0_createIntList_LE(x1, x2, x3, x4) -> f673_0_createIntList_LE(x1, x2)

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

(9)
Obligation:
Rules:
f673_0_createIntList_LE(x82:0, x83:0) -> f673_0_createIntList_LE(x82:0 - 1, x83:0 + 1) :|: x82:0 > 0 && x83:0 > 0

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

(10) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f673_0_createIntList_LE(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(11)
Obligation:
Rules:
f673_0_createIntList_LE(x82:0, x83:0) -> f673_0_createIntList_LE(c, c1) :|: c1 = x83:0 + 1 && c = x82:0 - 1 && (x82:0 > 0 && x83:0 > 0)

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

(12) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f673_0_createIntList_LE ] = f673_0_createIntList_LE_1

The following rules are decreasing:
f673_0_createIntList_LE(x82:0, x83:0) -> f673_0_createIntList_LE(c, c1) :|: c1 = x83:0 + 1 && c = x82:0 - 1 && (x82:0 > 0 && x83:0 > 0)

The following rules are bounded:
f673_0_createIntList_LE(x82:0, x83:0) -> f673_0_createIntList_LE(c, c1) :|: c1 = x83:0 + 1 && c = x82:0 - 1 && (x82:0 > 0 && x83:0 > 0)


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

(13)
YES

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

(14)
Obligation:

Termination digraph:
Nodes:
(1) f704_0_nth_LE(x26, x27, x28, x29) -> f704_0_nth_LE(x30, x31, x32, x33) :|: x29 = x33 && x28 - 1 = x32 && -1 <= x31 - 1 && -1 <= x30 - 1 && 0 <= x27 - 1 && -1 <= x26 - 1 && x31 + 1 <= x27 && 1 <= x28 - 1 && x30 <= x26

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(16)
Obligation:
Rules:
f704_0_nth_LE(x26:0, x27:0, x28:0, x29:0) -> f704_0_nth_LE(x30:0, x31:0, x28:0 - 1, x29:0) :|: x28:0 > 1 && x30:0 <= x26:0 && x31:0 + 1 <= x27:0 && x26:0 > -1 && x27:0 > 0 && x31:0 > -1 && x30:0 > -1

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

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

   f704_0_nth_LE(x1, x2, x3, x4) -> f704_0_nth_LE(x1, x2, x3)

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

(18)
Obligation:
Rules:
f704_0_nth_LE(x26:0, x27:0, x28:0) -> f704_0_nth_LE(x30:0, x31:0, x28:0 - 1) :|: x28:0 > 1 && x30:0 <= x26:0 && x31:0 + 1 <= x27:0 && x26:0 > -1 && x27:0 > 0 && x31:0 > -1 && x30:0 > -1

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

(19) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f704_0_nth_LE(INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(20)
Obligation:
Rules:
f704_0_nth_LE(x26:0, x27:0, x28:0) -> f704_0_nth_LE(x30:0, x31:0, c) :|: c = x28:0 - 1 && (x28:0 > 1 && x30:0 <= x26:0 && x31:0 + 1 <= x27:0 && x26:0 > -1 && x27:0 > 0 && x31:0 > -1 && x30:0 > -1)

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

(21) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f704_0_nth_LE(x, x1, x2)] = x2

The following rules are decreasing:
f704_0_nth_LE(x26:0, x27:0, x28:0) -> f704_0_nth_LE(x30:0, x31:0, c) :|: c = x28:0 - 1 && (x28:0 > 1 && x30:0 <= x26:0 && x31:0 + 1 <= x27:0 && x26:0 > -1 && x27:0 > 0 && x31:0 > -1 && x30:0 > -1)
The following rules are bounded:
f704_0_nth_LE(x26:0, x27:0, x28:0) -> f704_0_nth_LE(x30:0, x31:0, c) :|: c = x28:0 - 1 && (x28:0 > 1 && x30:0 <= x26:0 && x31:0 + 1 <= x27:0 && x26:0 > -1 && x27:0 > 0 && x31:0 > -1 && x30:0 > -1)

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

(22)
YES

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

(23)
Obligation:

Termination digraph:
Nodes:
(1) f754_0_main_LE(x34, x35, x36, x37) -> f964_0_nth_LE(x38, x39, x40, x41) :|: x36 + 1 = x41 && -1 <= x39 - 1 && -1 <= x38 - 1 && 0 <= x34 - 1 && x39 + 1 <= x34 && x38 + 1 <= x34 && 0 <= x35 - 1 && 0 <= x36 - 1 && -1 <= x40 - 1
(2) f964_0_nth_LE(x42, x43, x44, x45) -> f754_0_main_LE(x46, x47, x48, x49) :|: x45 = x48 && x47 + 2 <= x43 && -1 <= x46 - 1 && 0 <= x43 - 1 && -1 <= x42 - 1 && x44 <= 1 && x46 <= x42
(3) f964_0_nth_LE(x50, x51, x52, x53) -> f964_0_nth_LE(x54, x55, x56, x57) :|: x53 = x57 && x52 - 1 = x56 && -1 <= x55 - 1 && -1 <= x54 - 1 && 0 <= x51 - 1 && -1 <= x50 - 1 && x55 + 1 <= x51 && 1 <= x52 - 1 && x54 <= x50

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

This digraph is fully evaluated!

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

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

(25)
Obligation:
Rules:
f964_0_nth_LE(x50:0, x51:0, x52:0, x53:0) -> f964_0_nth_LE(x54:0, x55:0, x52:0 - 1, x53:0) :|: x52:0 > 1 && x54:0 <= x50:0 && x55:0 + 1 <= x51:0 && x50:0 > -1 && x51:0 > 0 && x55:0 > -1 && x54:0 > -1
f964_0_nth_LE(x42:0, x43:0, x44:0, x45:0) -> f964_0_nth_LE(x38:0, x39:0, x40:0, x45:0 + 1) :|: x40:0 > -1 && x46:0 <= x42:0 && x44:0 < 2 && x45:0 > 0 && x42:0 > -1 && x47:0 > 0 && x43:0 > 0 && x46:0 >= x38:0 + 1 && x46:0 >= x39:0 + 1 && x47:0 + 2 <= x43:0 && x38:0 > -1 && x46:0 > 0 && x39:0 > -1

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

(26) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f964_0_nth_LE(INTEGER, INTEGER, INTEGER, VARIABLE)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(27)
Obligation:
Rules:
f964_0_nth_LE(x50:0, x51:0, x52:0, x53:0) -> f964_0_nth_LE(x54:0, x55:0, c, x53:0) :|: c = x52:0 - 1 && (x52:0 > 1 && x54:0 <= x50:0 && x55:0 + 1 <= x51:0 && x50:0 > -1 && x51:0 > 0 && x55:0 > -1 && x54:0 > -1)
f964_0_nth_LE(x42:0, x43:0, x44:0, x45:0) -> f964_0_nth_LE(x38:0, x39:0, x40:0, c1) :|: c1 = x45:0 + 1 && (x40:0 > -1 && x46:0 <= x42:0 && x44:0 < 2 && x45:0 > 0 && x42:0 > -1 && x47:0 > 0 && x43:0 > 0 && x46:0 >= x38:0 + 1 && x46:0 >= x39:0 + 1 && x47:0 + 2 <= x43:0 && x38:0 > -1 && x46:0 > 0 && x39:0 > -1)

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

(28) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f964_0_nth_LE ] = f964_0_nth_LE_1

The following rules are decreasing:
f964_0_nth_LE(x42:0, x43:0, x44:0, x45:0) -> f964_0_nth_LE(x38:0, x39:0, x40:0, c1) :|: c1 = x45:0 + 1 && (x40:0 > -1 && x46:0 <= x42:0 && x44:0 < 2 && x45:0 > 0 && x42:0 > -1 && x47:0 > 0 && x43:0 > 0 && x46:0 >= x38:0 + 1 && x46:0 >= x39:0 + 1 && x47:0 + 2 <= x43:0 && x38:0 > -1 && x46:0 > 0 && x39:0 > -1)

The following rules are bounded:
f964_0_nth_LE(x50:0, x51:0, x52:0, x53:0) -> f964_0_nth_LE(x54:0, x55:0, c, x53:0) :|: c = x52:0 - 1 && (x52:0 > 1 && x54:0 <= x50:0 && x55:0 + 1 <= x51:0 && x50:0 > -1 && x51:0 > 0 && x55:0 > -1 && x54:0 > -1)
f964_0_nth_LE(x42:0, x43:0, x44:0, x45:0) -> f964_0_nth_LE(x38:0, x39:0, x40:0, c1) :|: c1 = x45:0 + 1 && (x40:0 > -1 && x46:0 <= x42:0 && x44:0 < 2 && x45:0 > 0 && x42:0 > -1 && x47:0 > 0 && x43:0 > 0 && x46:0 >= x38:0 + 1 && x46:0 >= x39:0 + 1 && x47:0 + 2 <= x43:0 && x38:0 > -1 && x46:0 > 0 && x39:0 > -1)


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

(29)
Obligation:
Rules:
f964_0_nth_LE(x50:0, x51:0, x52:0, x53:0) -> f964_0_nth_LE(x54:0, x55:0, c, x53:0) :|: c = x52:0 - 1 && (x52:0 > 1 && x54:0 <= x50:0 && x55:0 + 1 <= x51:0 && x50:0 > -1 && x51:0 > 0 && x55:0 > -1 && x54:0 > -1)

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(30) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f964_0_nth_LE(x, x1, x2, x3)] = x2

The following rules are decreasing:
f964_0_nth_LE(x50:0, x51:0, x52:0, x53:0) -> f964_0_nth_LE(x54:0, x55:0, c, x53:0) :|: c = x52:0 - 1 && (x52:0 > 1 && x54:0 <= x50:0 && x55:0 + 1 <= x51:0 && x50:0 > -1 && x51:0 > 0 && x55:0 > -1 && x54:0 > -1)
The following rules are bounded:
f964_0_nth_LE(x50:0, x51:0, x52:0, x53:0) -> f964_0_nth_LE(x54:0, x55:0, c, x53:0) :|: c = x52:0 - 1 && (x52:0 > 1 && x54:0 <= x50:0 && x55:0 + 1 <= x51:0 && x50:0 > -1 && x51:0 > 0 && x55:0 > -1 && x54:0 > -1)

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(31)
YES