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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 743 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 5 ms]
        (7) IRSwT
        (8) TempFilterProof [SOUND, 61 ms]
        (9) IntTRS
        (10) RankingReductionPairProof [EQUIVALENT, 30 ms]
        (11) IntTRS
        (12) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 8 ms]
        (16) IRSwT
        (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (18) IRSwT
        (19) FilterProof [EQUIVALENT, 0 ms]
        (20) IntTRS
        (21) IntTRSCompressionProof [EQUIVALENT, 2 ms]
        (22) IntTRS
        (23) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (24) IntTRS
        (25) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (26) IntTRS
        (27) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (28) IntTRS
        (29) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (30) YES


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

(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3, arg4, arg5) -> f2311_0_getVariables_InvokeMethod(arg1P, arg2P, arg3P, arg4P, arg5P) :|: -1 <= x7 - 1 && 0 <= arg2 - 1 && arg1P <= arg1 && 0 <= arg1 - 1 && 0 <= arg1P - 1 && 3 <= arg2P - 1
f1220_0_create_Return(x, x1, x2, x3, x4) -> f2311_0_getVariables_InvokeMethod(x5, x6, x8, x9, x10) :|: x4 = x10 && x3 = x9 && x2 = x8 && x3 + 5 <= x1 && x4 + 5 <= x1 && 3 <= x6 - 1 && 0 <= x5 - 1 && 3 <= x1 - 1 && 0 <= x - 1 && x6 <= x1 && x5 + 3 <= x1 && x5 <= x
f1_0_main_Load(x11, x12, x13, x14, x15) -> f804_0_create_GT(x16, x17, x18, x19, x20) :|: 1 = x18 && x12 = x17 && 0 <= x11 - 1 && 0 <= x12 - 1 && -1 <= x16 - 1
f804_0_create_GT(x21, x22, x23, x24, x25) -> f2072_0_create_GE(x26, x27, x28, x29, x30) :|: x23 + 1 = x30 && x22 = x29 && 0 = x27 && x21 = x26 && -1 <= x28 - 1 && x23 <= x22 - 1 && 0 <= x23 - 1 && 1 <= x21 - 1 && -1 <= x22 - 1
f2072_0_create_GE(x31, x32, x33, x35, x36) -> f804_0_create_GT(x37, x38, x39, x40, x41) :|: x36 = x39 && x35 = x38 && x31 - 1 = x37 && x31 - 1 <= x31 - 1 && 1 <= x36 - 1 && 0 <= x33 - 1 && 1 <= x31 - 1 && x32 <= x33 - 1
f2072_0_create_GE(x42, x43, x44, x45, x46) -> f2072_0_create_GE(x47, x48, x49, x50, x51) :|: x45 = x50 && x44 = x49 && x43 + 1 = x48 && x42 = x47 && x42 - 1 <= x42 - 1 && 1 <= x46 - 1 && 0 <= x44 - 1 && 1 <= x42 - 1 && x43 <= x44 - 1
f2311_0_getVariables_InvokeMethod(x52, x53, x54, x55, x56) -> f2992_0_collectVariables_NULL(x57, x58, x59, x60, x61) :|: 0 <= x62 - 1 && 1 <= x54 - 1 && x57 - 1 <= x52 && x57 + 2 <= x53 && x58 + 3 <= x53 && 0 <= x52 - 1 && 3 <= x53 - 1 && 1 <= x57 - 1 && 0 <= x58 - 1 && x56 + 5 <= x53 && x55 + 5 <= x53 && x54 = x59
f2992_0_collectVariables_NULL(x63, x64, x65, x66, x67) -> f2992_0_collectVariables_NULL(x68, x69, x70, x71, x72) :|: x65 = x70 && -1 <= x69 - 1 && 0 <= x68 - 1 && 2 <= x64 - 1 && 0 <= x63 - 1 && x69 + 3 <= x64 && 1 <= x65 - 1 && x68 <= x63
f2992_0_collectVariables_NULL(x73, x74, x75, x76, x77) -> f2992_0_collectVariables_NULL(x78, x79, x80, x81, x82) :|: x75 = x80 && -1 <= x79 - 1 && 0 <= x78 - 1 && 2 <= x74 - 1 && 0 <= x73 - 1 && 1 <= x75 - 1 && x79 + 2 <= x74
f2992_0_collectVariables_NULL(x83, x84, x85, x86, x87) -> f2992_0_collectVariables_NULL(x88, x89, x90, x91, x92) :|: x85 = x90 && -1 <= x89 - 1 && 2 <= x88 - 1 && 2 <= x84 - 1 && 0 <= x83 - 1 && x89 + 2 <= x84
__init(x93, x94, x95, x96, x97) -> f1_0_main_Load(x98, x99, x100, x101, x102) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4, arg5)

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

(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, arg5) -> f2311_0_getVariables_InvokeMethod(arg1P, arg2P, arg3P, arg4P, arg5P) :|: -1 <= x7 - 1 && 0 <= arg2 - 1 && arg1P <= arg1 && 0 <= arg1 - 1 && 0 <= arg1P - 1 && 3 <= arg2P - 1
f1220_0_create_Return(x, x1, x2, x3, x4) -> f2311_0_getVariables_InvokeMethod(x5, x6, x8, x9, x10) :|: x4 = x10 && x3 = x9 && x2 = x8 && x3 + 5 <= x1 && x4 + 5 <= x1 && 3 <= x6 - 1 && 0 <= x5 - 1 && 3 <= x1 - 1 && 0 <= x - 1 && x6 <= x1 && x5 + 3 <= x1 && x5 <= x
f1_0_main_Load(x11, x12, x13, x14, x15) -> f804_0_create_GT(x16, x17, x18, x19, x20) :|: 1 = x18 && x12 = x17 && 0 <= x11 - 1 && 0 <= x12 - 1 && -1 <= x16 - 1
f804_0_create_GT(x21, x22, x23, x24, x25) -> f2072_0_create_GE(x26, x27, x28, x29, x30) :|: x23 + 1 = x30 && x22 = x29 && 0 = x27 && x21 = x26 && -1 <= x28 - 1 && x23 <= x22 - 1 && 0 <= x23 - 1 && 1 <= x21 - 1 && -1 <= x22 - 1
f2072_0_create_GE(x31, x32, x33, x35, x36) -> f804_0_create_GT(x37, x38, x39, x40, x41) :|: x36 = x39 && x35 = x38 && x31 - 1 = x37 && x31 - 1 <= x31 - 1 && 1 <= x36 - 1 && 0 <= x33 - 1 && 1 <= x31 - 1 && x32 <= x33 - 1
f2072_0_create_GE(x42, x43, x44, x45, x46) -> f2072_0_create_GE(x47, x48, x49, x50, x51) :|: x45 = x50 && x44 = x49 && x43 + 1 = x48 && x42 = x47 && x42 - 1 <= x42 - 1 && 1 <= x46 - 1 && 0 <= x44 - 1 && 1 <= x42 - 1 && x43 <= x44 - 1
f2311_0_getVariables_InvokeMethod(x52, x53, x54, x55, x56) -> f2992_0_collectVariables_NULL(x57, x58, x59, x60, x61) :|: 0 <= x62 - 1 && 1 <= x54 - 1 && x57 - 1 <= x52 && x57 + 2 <= x53 && x58 + 3 <= x53 && 0 <= x52 - 1 && 3 <= x53 - 1 && 1 <= x57 - 1 && 0 <= x58 - 1 && x56 + 5 <= x53 && x55 + 5 <= x53 && x54 = x59
f2992_0_collectVariables_NULL(x63, x64, x65, x66, x67) -> f2992_0_collectVariables_NULL(x68, x69, x70, x71, x72) :|: x65 = x70 && -1 <= x69 - 1 && 0 <= x68 - 1 && 2 <= x64 - 1 && 0 <= x63 - 1 && x69 + 3 <= x64 && 1 <= x65 - 1 && x68 <= x63
f2992_0_collectVariables_NULL(x73, x74, x75, x76, x77) -> f2992_0_collectVariables_NULL(x78, x79, x80, x81, x82) :|: x75 = x80 && -1 <= x79 - 1 && 0 <= x78 - 1 && 2 <= x74 - 1 && 0 <= x73 - 1 && 1 <= x75 - 1 && x79 + 2 <= x74
f2992_0_collectVariables_NULL(x83, x84, x85, x86, x87) -> f2992_0_collectVariables_NULL(x88, x89, x90, x91, x92) :|: x85 = x90 && -1 <= x89 - 1 && 2 <= x88 - 1 && 2 <= x84 - 1 && 0 <= x83 - 1 && x89 + 2 <= x84
__init(x93, x94, x95, x96, x97) -> f1_0_main_Load(x98, x99, x100, x101, x102) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4, arg5)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_Load(arg1, arg2, arg3, arg4, arg5) -> f2311_0_getVariables_InvokeMethod(arg1P, arg2P, arg3P, arg4P, arg5P) :|: -1 <= x7 - 1 && 0 <= arg2 - 1 && arg1P <= arg1 && 0 <= arg1 - 1 && 0 <= arg1P - 1 && 3 <= arg2P - 1
(2) f1220_0_create_Return(x, x1, x2, x3, x4) -> f2311_0_getVariables_InvokeMethod(x5, x6, x8, x9, x10) :|: x4 = x10 && x3 = x9 && x2 = x8 && x3 + 5 <= x1 && x4 + 5 <= x1 && 3 <= x6 - 1 && 0 <= x5 - 1 && 3 <= x1 - 1 && 0 <= x - 1 && x6 <= x1 && x5 + 3 <= x1 && x5 <= x
(3) f1_0_main_Load(x11, x12, x13, x14, x15) -> f804_0_create_GT(x16, x17, x18, x19, x20) :|: 1 = x18 && x12 = x17 && 0 <= x11 - 1 && 0 <= x12 - 1 && -1 <= x16 - 1
(4) f804_0_create_GT(x21, x22, x23, x24, x25) -> f2072_0_create_GE(x26, x27, x28, x29, x30) :|: x23 + 1 = x30 && x22 = x29 && 0 = x27 && x21 = x26 && -1 <= x28 - 1 && x23 <= x22 - 1 && 0 <= x23 - 1 && 1 <= x21 - 1 && -1 <= x22 - 1
(5) f2072_0_create_GE(x31, x32, x33, x35, x36) -> f804_0_create_GT(x37, x38, x39, x40, x41) :|: x36 = x39 && x35 = x38 && x31 - 1 = x37 && x31 - 1 <= x31 - 1 && 1 <= x36 - 1 && 0 <= x33 - 1 && 1 <= x31 - 1 && x32 <= x33 - 1
(6) f2072_0_create_GE(x42, x43, x44, x45, x46) -> f2072_0_create_GE(x47, x48, x49, x50, x51) :|: x45 = x50 && x44 = x49 && x43 + 1 = x48 && x42 = x47 && x42 - 1 <= x42 - 1 && 1 <= x46 - 1 && 0 <= x44 - 1 && 1 <= x42 - 1 && x43 <= x44 - 1
(7) f2311_0_getVariables_InvokeMethod(x52, x53, x54, x55, x56) -> f2992_0_collectVariables_NULL(x57, x58, x59, x60, x61) :|: 0 <= x62 - 1 && 1 <= x54 - 1 && x57 - 1 <= x52 && x57 + 2 <= x53 && x58 + 3 <= x53 && 0 <= x52 - 1 && 3 <= x53 - 1 && 1 <= x57 - 1 && 0 <= x58 - 1 && x56 + 5 <= x53 && x55 + 5 <= x53 && x54 = x59
(8) f2992_0_collectVariables_NULL(x63, x64, x65, x66, x67) -> f2992_0_collectVariables_NULL(x68, x69, x70, x71, x72) :|: x65 = x70 && -1 <= x69 - 1 && 0 <= x68 - 1 && 2 <= x64 - 1 && 0 <= x63 - 1 && x69 + 3 <= x64 && 1 <= x65 - 1 && x68 <= x63
(9) f2992_0_collectVariables_NULL(x73, x74, x75, x76, x77) -> f2992_0_collectVariables_NULL(x78, x79, x80, x81, x82) :|: x75 = x80 && -1 <= x79 - 1 && 0 <= x78 - 1 && 2 <= x74 - 1 && 0 <= x73 - 1 && 1 <= x75 - 1 && x79 + 2 <= x74
(10) f2992_0_collectVariables_NULL(x83, x84, x85, x86, x87) -> f2992_0_collectVariables_NULL(x88, x89, x90, x91, x92) :|: x85 = x90 && -1 <= x89 - 1 && 2 <= x88 - 1 && 2 <= x84 - 1 && 0 <= x83 - 1 && x89 + 2 <= x84
(11) __init(x93, x94, x95, x96, x97) -> f1_0_main_Load(x98, x99, x100, x101, x102) :|: 0 <= 0

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

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) f804_0_create_GT(x21, x22, x23, x24, x25) -> f2072_0_create_GE(x26, x27, x28, x29, x30) :|: x23 + 1 = x30 && x22 = x29 && 0 = x27 && x21 = x26 && -1 <= x28 - 1 && x23 <= x22 - 1 && 0 <= x23 - 1 && 1 <= x21 - 1 && -1 <= x22 - 1
(2) f2072_0_create_GE(x31, x32, x33, x35, x36) -> f804_0_create_GT(x37, x38, x39, x40, x41) :|: x36 = x39 && x35 = x38 && x31 - 1 = x37 && x31 - 1 <= x31 - 1 && 1 <= x36 - 1 && 0 <= x33 - 1 && 1 <= x31 - 1 && x32 <= x33 - 1
(3) f2072_0_create_GE(x42, x43, x44, x45, x46) -> f2072_0_create_GE(x47, x48, x49, x50, x51) :|: x45 = x50 && x44 = x49 && x43 + 1 = x48 && x42 = x47 && x42 - 1 <= x42 - 1 && 1 <= x46 - 1 && 0 <= x44 - 1 && 1 <= x42 - 1 && x43 <= x44 - 1

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

This digraph is fully evaluated!

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

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

(7)
Obligation:
Rules:
f2072_0_create_GE(x31:0, x32:0, x33:0, x29:0, x36:0) -> f2072_0_create_GE(x31:0 - 1, 0, x28:0, x29:0, x36:0 + 1) :|: x29:0 > -1 && x33:0 - 1 >= x32:0 && x33:0 > 0 && x36:0 <= x29:0 - 1 && x28:0 > -1 && x36:0 > 1 && x31:0 > 2
f2072_0_create_GE(x42:0, x43:0, x44:0, x45:0, x46:0) -> f2072_0_create_GE(x42:0, x43:0 + 1, x44:0, x45:0, x51:0) :|: x42:0 > 1 && x44:0 - 1 >= x43:0 && x46:0 > 1 && x44:0 > 0

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

(8) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f2072_0_create_GE(INTEGER, VARIABLE, INTEGER, VARIABLE, VARIABLE)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(9)
Obligation:
Rules:
f2072_0_create_GE(x31:0, x32:0, x33:0, x29:0, x36:0) -> f2072_0_create_GE(c, c1, x28:0, x29:0, c2) :|: c2 = x36:0 + 1 && (c1 = 0 && c = x31:0 - 1) && (x29:0 > -1 && x33:0 - 1 >= x32:0 && x33:0 > 0 && x36:0 <= x29:0 - 1 && x28:0 > -1 && x36:0 > 1 && x31:0 > 2)
f2072_0_create_GE(x42:0, x43:0, x44:0, x45:0, x46:0) -> f2072_0_create_GE(x42:0, c3, x44:0, x45:0, x51:0) :|: c3 = x43:0 + 1 && (x42:0 > 1 && x44:0 - 1 >= x43:0 && x46:0 > 1 && x44:0 > 0)

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

(10) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f2072_0_create_GE ] = f2072_0_create_GE_1

The following rules are decreasing:
f2072_0_create_GE(x31:0, x32:0, x33:0, x29:0, x36:0) -> f2072_0_create_GE(c, c1, x28:0, x29:0, c2) :|: c2 = x36:0 + 1 && (c1 = 0 && c = x31:0 - 1) && (x29:0 > -1 && x33:0 - 1 >= x32:0 && x33:0 > 0 && x36:0 <= x29:0 - 1 && x28:0 > -1 && x36:0 > 1 && x31:0 > 2)

The following rules are bounded:
f2072_0_create_GE(x31:0, x32:0, x33:0, x29:0, x36:0) -> f2072_0_create_GE(c, c1, x28:0, x29:0, c2) :|: c2 = x36:0 + 1 && (c1 = 0 && c = x31:0 - 1) && (x29:0 > -1 && x33:0 - 1 >= x32:0 && x33:0 > 0 && x36:0 <= x29:0 - 1 && x28:0 > -1 && x36:0 > 1 && x31:0 > 2)
f2072_0_create_GE(x42:0, x43:0, x44:0, x45:0, x46:0) -> f2072_0_create_GE(x42:0, c3, x44:0, x45:0, x51:0) :|: c3 = x43:0 + 1 && (x42:0 > 1 && x44:0 - 1 >= x43:0 && x46:0 > 1 && x44:0 > 0)


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

(11)
Obligation:
Rules:
f2072_0_create_GE(x42:0, x43:0, x44:0, x45:0, x46:0) -> f2072_0_create_GE(x42:0, c3, x44:0, x45:0, x51:0) :|: c3 = x43:0 + 1 && (x42:0 > 1 && x44:0 - 1 >= x43:0 && x46:0 > 1 && x44:0 > 0)

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

(12) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f2072_0_create_GE ] = f2072_0_create_GE_3 + -1*f2072_0_create_GE_2

The following rules are decreasing:
f2072_0_create_GE(x42:0, x43:0, x44:0, x45:0, x46:0) -> f2072_0_create_GE(x42:0, c3, x44:0, x45:0, x51:0) :|: c3 = x43:0 + 1 && (x42:0 > 1 && x44:0 - 1 >= x43:0 && x46:0 > 1 && x44:0 > 0)

The following rules are bounded:
f2072_0_create_GE(x42:0, x43:0, x44:0, x45:0, x46:0) -> f2072_0_create_GE(x42:0, c3, x44:0, x45:0, x51:0) :|: c3 = x43:0 + 1 && (x42:0 > 1 && x44:0 - 1 >= x43:0 && x46:0 > 1 && x44:0 > 0)


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

(13)
YES

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

(14)
Obligation:

Termination digraph:
Nodes:
(1) f2992_0_collectVariables_NULL(x63, x64, x65, x66, x67) -> f2992_0_collectVariables_NULL(x68, x69, x70, x71, x72) :|: x65 = x70 && -1 <= x69 - 1 && 0 <= x68 - 1 && 2 <= x64 - 1 && 0 <= x63 - 1 && x69 + 3 <= x64 && 1 <= x65 - 1 && x68 <= x63
(2) f2992_0_collectVariables_NULL(x73, x74, x75, x76, x77) -> f2992_0_collectVariables_NULL(x78, x79, x80, x81, x82) :|: x75 = x80 && -1 <= x79 - 1 && 0 <= x78 - 1 && 2 <= x74 - 1 && 0 <= x73 - 1 && 1 <= x75 - 1 && x79 + 2 <= x74
(3) f2992_0_collectVariables_NULL(x83, x84, x85, x86, x87) -> f2992_0_collectVariables_NULL(x88, x89, x90, x91, x92) :|: x85 = x90 && -1 <= x89 - 1 && 2 <= x88 - 1 && 2 <= x84 - 1 && 0 <= x83 - 1 && x89 + 2 <= x84

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

This digraph is fully evaluated!

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

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

(16)
Obligation:
Rules:
f2992_0_collectVariables_NULL(x73:0, x74:0, x75:0, x76:0, x77:0) -> f2992_0_collectVariables_NULL(x78:0, x79:0, x75:0, x81:0, x82:0) :|: x75:0 > 1 && x79:0 + 2 <= x74:0 && x73:0 > 0 && x74:0 > 2 && x79:0 > -1 && x78:0 > 0
f2992_0_collectVariables_NULL(x83:0, x84:0, x85:0, x86:0, x87:0) -> f2992_0_collectVariables_NULL(x88:0, x89:0, x85:0, x91:0, x92:0) :|: x83:0 > 0 && x89:0 + 2 <= x84:0 && x84:0 > 2 && x89:0 > -1 && x88:0 > 2
f2992_0_collectVariables_NULL(x63:0, x64:0, x65:0, x66:0, x67:0) -> f2992_0_collectVariables_NULL(x68:0, x69:0, x65:0, x71:0, x72:0) :|: x65:0 > 1 && x68:0 <= x63:0 && x69:0 + 3 <= x64:0 && x63:0 > 0 && x64:0 > 2 && x69:0 > -1 && x68:0 > 0

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

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

   f2992_0_collectVariables_NULL(x1, x2, x3, x4, x5) -> f2992_0_collectVariables_NULL(x1, x2, x3)

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

(18)
Obligation:
Rules:
f2992_0_collectVariables_NULL(x73:0, x74:0, x75:0) -> f2992_0_collectVariables_NULL(x78:0, x79:0, x75:0) :|: x75:0 > 1 && x79:0 + 2 <= x74:0 && x73:0 > 0 && x74:0 > 2 && x79:0 > -1 && x78:0 > 0
f2992_0_collectVariables_NULL(x83:0, x84:0, x85:0) -> f2992_0_collectVariables_NULL(x88:0, x89:0, x85:0) :|: x83:0 > 0 && x89:0 + 2 <= x84:0 && x84:0 > 2 && x89:0 > -1 && x88:0 > 2
f2992_0_collectVariables_NULL(x63:0, x64:0, x65:0) -> f2992_0_collectVariables_NULL(x68:0, x69:0, x65:0) :|: x65:0 > 1 && x68:0 <= x63:0 && x69:0 + 3 <= x64:0 && x63:0 > 0 && x64:0 > 2 && x69:0 > -1 && x68:0 > 0

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

(19) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f2992_0_collectVariables_NULL(INTEGER, INTEGER, VARIABLE)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(20)
Obligation:
Rules:
f2992_0_collectVariables_NULL(x73:0, x74:0, x75:0) -> f2992_0_collectVariables_NULL(x78:0, x79:0, x75:0) :|: x75:0 > 1 && x79:0 + 2 <= x74:0 && x73:0 > 0 && x74:0 > 2 && x79:0 > -1 && x78:0 > 0
f2992_0_collectVariables_NULL(x83:0, x84:0, x85:0) -> f2992_0_collectVariables_NULL(x88:0, x89:0, x85:0) :|: x83:0 > 0 && x89:0 + 2 <= x84:0 && x84:0 > 2 && x89:0 > -1 && x88:0 > 2
f2992_0_collectVariables_NULL(x63:0, x64:0, x65:0) -> f2992_0_collectVariables_NULL(x68:0, x69:0, x65:0) :|: x65:0 > 1 && x68:0 <= x63:0 && x69:0 + 3 <= x64:0 && x63:0 > 0 && x64:0 > 2 && x69:0 > -1 && x68:0 > 0

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(21) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(22)
Obligation:
Rules:
f2992_0_collectVariables_NULL(x73:0:0, x74:0:0, x75:0:0) -> f2992_0_collectVariables_NULL(x78:0:0, x79:0:0, x75:0:0) :|: x79:0:0 > -1 && x78:0:0 > 0 && x74:0:0 > 2 && x73:0:0 > 0 && x79:0:0 + 2 <= x74:0:0 && x75:0:0 > 1
f2992_0_collectVariables_NULL(x83:0:0, x84:0:0, x85:0:0) -> f2992_0_collectVariables_NULL(x88:0:0, x89:0:0, x85:0:0) :|: x89:0:0 > -1 && x88:0:0 > 2 && x84:0:0 > 2 && x89:0:0 + 2 <= x84:0:0 && x83:0:0 > 0
f2992_0_collectVariables_NULL(x63:0:0, x64:0:0, x65:0:0) -> f2992_0_collectVariables_NULL(x68:0:0, x69:0:0, x65:0:0) :|: x69:0:0 > -1 && x68:0:0 > 0 && x64:0:0 > 2 && x63:0:0 > 0 && x69:0:0 + 3 <= x64:0:0 && x68:0:0 <= x63:0:0 && x65:0:0 > 1

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(23) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f2992_0_collectVariables_NULL(x, x1, x2)] = -4 + x1 + x2

The following rules are decreasing:
f2992_0_collectVariables_NULL(x73:0:0, x74:0:0, x75:0:0) -> f2992_0_collectVariables_NULL(x78:0:0, x79:0:0, x75:0:0) :|: x79:0:0 > -1 && x78:0:0 > 0 && x74:0:0 > 2 && x73:0:0 > 0 && x79:0:0 + 2 <= x74:0:0 && x75:0:0 > 1
f2992_0_collectVariables_NULL(x83:0:0, x84:0:0, x85:0:0) -> f2992_0_collectVariables_NULL(x88:0:0, x89:0:0, x85:0:0) :|: x89:0:0 > -1 && x88:0:0 > 2 && x84:0:0 > 2 && x89:0:0 + 2 <= x84:0:0 && x83:0:0 > 0
f2992_0_collectVariables_NULL(x63:0:0, x64:0:0, x65:0:0) -> f2992_0_collectVariables_NULL(x68:0:0, x69:0:0, x65:0:0) :|: x69:0:0 > -1 && x68:0:0 > 0 && x64:0:0 > 2 && x63:0:0 > 0 && x69:0:0 + 3 <= x64:0:0 && x68:0:0 <= x63:0:0 && x65:0:0 > 1
The following rules are bounded:
f2992_0_collectVariables_NULL(x73:0:0, x74:0:0, x75:0:0) -> f2992_0_collectVariables_NULL(x78:0:0, x79:0:0, x75:0:0) :|: x79:0:0 > -1 && x78:0:0 > 0 && x74:0:0 > 2 && x73:0:0 > 0 && x79:0:0 + 2 <= x74:0:0 && x75:0:0 > 1
f2992_0_collectVariables_NULL(x63:0:0, x64:0:0, x65:0:0) -> f2992_0_collectVariables_NULL(x68:0:0, x69:0:0, x65:0:0) :|: x69:0:0 > -1 && x68:0:0 > 0 && x64:0:0 > 2 && x63:0:0 > 0 && x69:0:0 + 3 <= x64:0:0 && x68:0:0 <= x63:0:0 && x65:0:0 > 1

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(24)
Obligation:
Rules:
f2992_0_collectVariables_NULL(x83:0:0, x84:0:0, x85:0:0) -> f2992_0_collectVariables_NULL(x88:0:0, x89:0:0, x85:0:0) :|: x89:0:0 > -1 && x88:0:0 > 2 && x84:0:0 > 2 && x89:0:0 + 2 <= x84:0:0 && x83:0:0 > 0

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(25) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(26)
Obligation:
Rules:
f2992_0_collectVariables_NULL(x83:0:0:0, x84:0:0:0, x85:0:0:0) -> f2992_0_collectVariables_NULL(x88:0:0:0, x89:0:0:0, x85:0:0:0) :|: x89:0:0:0 + 2 <= x84:0:0:0 && x83:0:0:0 > 0 && x84:0:0:0 > 2 && x88:0:0:0 > 2 && x89:0:0:0 > -1

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

   f2992_0_collectVariables_NULL(x1, x2, x3) -> f2992_0_collectVariables_NULL(x1, x2)

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(28)
Obligation:
Rules:
f2992_0_collectVariables_NULL(x83:0:0:0, x84:0:0:0) -> f2992_0_collectVariables_NULL(x88:0:0:0, x89:0:0:0) :|: x89:0:0:0 + 2 <= x84:0:0:0 && x83:0:0:0 > 0 && x84:0:0:0 > 2 && x88:0:0:0 > 2 && x89:0:0:0 > -1

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(29) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f2992_0_collectVariables_NULL ] = 1/2*f2992_0_collectVariables_NULL_2

The following rules are decreasing:
f2992_0_collectVariables_NULL(x83:0:0:0, x84:0:0:0) -> f2992_0_collectVariables_NULL(x88:0:0:0, x89:0:0:0) :|: x89:0:0:0 + 2 <= x84:0:0:0 && x83:0:0:0 > 0 && x84:0:0:0 > 2 && x88:0:0:0 > 2 && x89:0:0:0 > -1

The following rules are bounded:
f2992_0_collectVariables_NULL(x83:0:0:0, x84:0:0:0) -> f2992_0_collectVariables_NULL(x88:0:0:0, x89:0:0:0) :|: x89:0:0:0 + 2 <= x84:0:0:0 && x83:0:0:0 > 0 && x84:0:0:0 > 2 && x88:0:0:0 > 2 && x89:0:0:0 > -1


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(30)
YES