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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 377 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 11 ms]
(6) IRSwT
(7) IRSwTChainingProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) IRSwTTerminationDigraphProof [EQUIVALENT, 71 ms]
(10) AND
    (11) IRSwT
        (12) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (13) IRSwT
        (14) TempFilterProof [SOUND, 12 ms]
        (15) IntTRS
        (16) RankingReductionPairProof [EQUIVALENT, 5 ms]
        (17) YES
    (18) IRSwT
        (19) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (20) IRSwT
        (21) TempFilterProof [SOUND, 71 ms]
        (22) IntTRS
        (23) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (24) IntTRS
        (25) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (26) IntTRS
        (27) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (28) IntTRS
        (29) RankingReductionPairProof [EQUIVALENT, 4 ms]
        (30) YES


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

(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3, arg4) -> f1_0_main_Load'(arg1P, arg2P, arg3P, arg4P) :|: arg2 = arg2P && arg1 = arg1P && -1 <= arg2 - 1 && 0 <= arg1 - 1
f1_0_main_Load'(x, x1, x2, x3) -> f384_0_iter_LT(x4, x5, x6, x7) :|: 0 <= x - 1 && -1 <= x1 - 1 && 0 <= x1 - 5 * x8 && x1 - 5 * x8 <= 4 && 0 <= x1 - 4 * x9 && x1 - 4 * x9 <= 3 && 0 <= x1 - 5 * x10 && x1 - 5 * x10 <= 4 && x1 - 4 * x11 <= 3 && 0 <= x1 - 4 * x11 && x1 = x4 && x1 - 5 * x8 = x5 && x1 - 4 * x9 = x6 && x1 + x1 - 5 * x10 + 3 * x1 - 12 * x11 = x7
f384_0_iter_LT(x12, x13, x14, x15) -> f384_0_iter_LT(x20, x21, x22, x23) :|: x12 - 1 + x13 + 3 * x14 = x23 && x14 = x22 && x13 = x21 && x12 - 1 = x20 && x13 <= x12 - 1 && -1 <= x15 - 1
f384_0_iter_LT(x24, x25, x26, x27) -> f384_0_iter_LT(x28, x29, x30, x31) :|: x24 + 1 + x25 - 2 + 3 * x26 = x31 && x26 = x30 && x25 - 2 = x29 && x24 + 1 = x28 && x24 <= x25 && -1 <= x27 - 1 && x26 <= x25 - 1
f384_0_iter_LT(x32, x33, x34, x35) -> f384_0_iter_LT(x36, x37, x38, x39) :|: x32 + 1 + x33 + 1 + 3 * x34 - 3 = x39 && x34 - 1 = x38 && x33 + 1 = x37 && x32 + 1 = x36 && x32 <= x33 && x33 <= x34 && -1 <= x35 - 1
__init(x40, x41, x42, x43) -> f1_0_main_Load(x44, x45, x46, x47) :|: 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) -> f1_0_main_Load'(arg1P, arg2P, arg3P, arg4P) :|: arg2 = arg2P && arg1 = arg1P && -1 <= arg2 - 1 && 0 <= arg1 - 1
f1_0_main_Load'(x, x1, x2, x3) -> f384_0_iter_LT(x4, x5, x6, x7) :|: 0 <= x - 1 && -1 <= x1 - 1 && 0 <= x1 - 5 * x8 && x1 - 5 * x8 <= 4 && 0 <= x1 - 4 * x9 && x1 - 4 * x9 <= 3 && 0 <= x1 - 5 * x10 && x1 - 5 * x10 <= 4 && x1 - 4 * x11 <= 3 && 0 <= x1 - 4 * x11 && x1 = x4 && x1 - 5 * x8 = x5 && x1 - 4 * x9 = x6 && x1 + x1 - 5 * x10 + 3 * x1 - 12 * x11 = x7
f384_0_iter_LT(x12, x13, x14, x15) -> f384_0_iter_LT(x20, x21, x22, x23) :|: x12 - 1 + x13 + 3 * x14 = x23 && x14 = x22 && x13 = x21 && x12 - 1 = x20 && x13 <= x12 - 1 && -1 <= x15 - 1
f384_0_iter_LT(x24, x25, x26, x27) -> f384_0_iter_LT(x28, x29, x30, x31) :|: x24 + 1 + x25 - 2 + 3 * x26 = x31 && x26 = x30 && x25 - 2 = x29 && x24 + 1 = x28 && x24 <= x25 && -1 <= x27 - 1 && x26 <= x25 - 1
f384_0_iter_LT(x32, x33, x34, x35) -> f384_0_iter_LT(x36, x37, x38, x39) :|: x32 + 1 + x33 + 1 + 3 * x34 - 3 = x39 && x34 - 1 = x38 && x33 + 1 = x37 && x32 + 1 = x36 && x32 <= x33 && x33 <= x34 && -1 <= x35 - 1
__init(x40, x41, x42, x43) -> f1_0_main_Load(x44, x45, x46, x47) :|: 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) -> f1_0_main_Load'(arg1P, arg2P, arg3P, arg4P) :|: arg2 = arg2P && arg1 = arg1P && -1 <= arg2 - 1 && 0 <= arg1 - 1
(2) f1_0_main_Load'(x, x1, x2, x3) -> f384_0_iter_LT(x4, x5, x6, x7) :|: 0 <= x - 1 && -1 <= x1 - 1 && 0 <= x1 - 5 * x8 && x1 - 5 * x8 <= 4 && 0 <= x1 - 4 * x9 && x1 - 4 * x9 <= 3 && 0 <= x1 - 5 * x10 && x1 - 5 * x10 <= 4 && x1 - 4 * x11 <= 3 && 0 <= x1 - 4 * x11 && x1 = x4 && x1 - 5 * x8 = x5 && x1 - 4 * x9 = x6 && x1 + x1 - 5 * x10 + 3 * x1 - 12 * x11 = x7
(3) f384_0_iter_LT(x12, x13, x14, x15) -> f384_0_iter_LT(x20, x21, x22, x23) :|: x12 - 1 + x13 + 3 * x14 = x23 && x14 = x22 && x13 = x21 && x12 - 1 = x20 && x13 <= x12 - 1 && -1 <= x15 - 1
(4) f384_0_iter_LT(x24, x25, x26, x27) -> f384_0_iter_LT(x28, x29, x30, x31) :|: x24 + 1 + x25 - 2 + 3 * x26 = x31 && x26 = x30 && x25 - 2 = x29 && x24 + 1 = x28 && x24 <= x25 && -1 <= x27 - 1 && x26 <= x25 - 1
(5) f384_0_iter_LT(x32, x33, x34, x35) -> f384_0_iter_LT(x36, x37, x38, x39) :|: x32 + 1 + x33 + 1 + 3 * x34 - 3 = x39 && x34 - 1 = x38 && x33 + 1 = x37 && x32 + 1 = x36 && x32 <= x33 && x33 <= x34 && -1 <= x35 - 1
(6) __init(x40, x41, x42, x43) -> f1_0_main_Load(x44, x45, x46, x47) :|: 0 <= 0

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

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

(4)
Obligation:

Termination digraph:
Nodes:
(1) f384_0_iter_LT(x12, x13, x14, x15) -> f384_0_iter_LT(x20, x21, x22, x23) :|: x12 - 1 + x13 + 3 * x14 = x23 && x14 = x22 && x13 = x21 && x12 - 1 = x20 && x13 <= x12 - 1 && -1 <= x15 - 1
(2) f384_0_iter_LT(x24, x25, x26, x27) -> f384_0_iter_LT(x28, x29, x30, x31) :|: x24 + 1 + x25 - 2 + 3 * x26 = x31 && x26 = x30 && x25 - 2 = x29 && x24 + 1 = x28 && x24 <= x25 && -1 <= x27 - 1 && x26 <= x25 - 1
(3) f384_0_iter_LT(x32, x33, x34, x35) -> f384_0_iter_LT(x36, x37, x38, x39) :|: x32 + 1 + x33 + 1 + 3 * x34 - 3 = x39 && x34 - 1 = x38 && x33 + 1 = x37 && x32 + 1 = x36 && x32 <= x33 && x33 <= x34 && -1 <= x35 - 1

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

This digraph is fully evaluated!

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

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

(6)
Obligation:
Rules:
f384_0_iter_LT(x24:0, x25:0, x26:0, x27:0) -> f384_0_iter_LT(x24:0 + 1, x25:0 - 2, x26:0, x24:0 + 1 + x25:0 - 2 + 3 * x26:0) :|: x27:0 > -1 && x25:0 >= x24:0 && x26:0 <= x25:0 - 1
f384_0_iter_LT(x12:0, x13:0, x14:0, x15:0) -> f384_0_iter_LT(x12:0 - 1, x13:0, x14:0, x12:0 - 1 + x13:0 + 3 * x14:0) :|: x15:0 > -1 && x13:0 <= x12:0 - 1
f384_0_iter_LT(x32:0, x33:0, x34:0, x35:0) -> f384_0_iter_LT(x32:0 + 1, x33:0 + 1, x34:0 - 1, x32:0 + 1 + x33:0 + 1 + 3 * x34:0 - 3) :|: x34:0 >= x33:0 && x33:0 >= x32:0 && x35:0 > -1

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

(7) IRSwTChainingProof (EQUIVALENT)
Chaining!
----------------------------------------

(8)
Obligation:
Rules:
f384_0_iter_LT(x, x1, x2, x3) -> f384_0_iter_LT(x + 2, x1 + -4, x2, x + x1 + -2 + 3 * x2) :|: TRUE && x3 >= 0 && x + x1 + 3 * x2 >= 1 && x1 + -1 * x >= 3 && x2 + -1 * x1 <= -3
f384_0_iter_LT(x12:0, x13:0, x14:0, x15:0) -> f384_0_iter_LT(x12:0 - 1, x13:0, x14:0, x12:0 - 1 + x13:0 + 3 * x14:0) :|: x15:0 > -1 && x13:0 <= x12:0 - 1
f384_0_iter_LT(x8, x9, x10, x11) -> f384_0_iter_LT(x8, x9 + -2, x10, x8 + x9 + -2 + 3 * x10) :|: TRUE && x11 >= 0 && x9 + -1 * x8 >= 0 && x10 + -1 * x9 <= -1 && x8 + x9 + 3 * x10 >= 1 && x9 + -1 * x8 <= 2
f384_0_iter_LT(x32:0, x33:0, x34:0, x35:0) -> f384_0_iter_LT(x32:0 + 1, x33:0 + 1, x34:0 - 1, x32:0 + 1 + x33:0 + 1 + 3 * x34:0 - 3) :|: x34:0 >= x33:0 && x33:0 >= x32:0 && x35:0 > -1
f384_0_iter_LT(x16, x17, x18, x19) -> f384_0_iter_LT(x16 + 2, x17 + -1, x18 + -1, x16 + x17 + -2 + 3 * x18) :|: TRUE && x19 >= 0 && x18 + -1 * x17 <= -1 && x18 + -1 * x17 >= -2 && x17 + -1 * x16 >= 3 && x16 + x17 + 3 * x18 >= 1

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

(9) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f384_0_iter_LT(x, x1, x2, x3) -> f384_0_iter_LT(x + 2, x1 + -4, x2, x + x1 + -2 + 3 * x2) :|: TRUE && x3 >= 0 && x + x1 + 3 * x2 >= 1 && x1 + -1 * x >= 3 && x2 + -1 * x1 <= -3
(2) f384_0_iter_LT(x12:0, x13:0, x14:0, x15:0) -> f384_0_iter_LT(x12:0 - 1, x13:0, x14:0, x12:0 - 1 + x13:0 + 3 * x14:0) :|: x15:0 > -1 && x13:0 <= x12:0 - 1
(3) f384_0_iter_LT(x8, x9, x10, x11) -> f384_0_iter_LT(x8, x9 + -2, x10, x8 + x9 + -2 + 3 * x10) :|: TRUE && x11 >= 0 && x9 + -1 * x8 >= 0 && x10 + -1 * x9 <= -1 && x8 + x9 + 3 * x10 >= 1 && x9 + -1 * x8 <= 2
(4) f384_0_iter_LT(x32:0, x33:0, x34:0, x35:0) -> f384_0_iter_LT(x32:0 + 1, x33:0 + 1, x34:0 - 1, x32:0 + 1 + x33:0 + 1 + 3 * x34:0 - 3) :|: x34:0 >= x33:0 && x33:0 >= x32:0 && x35:0 > -1
(5) f384_0_iter_LT(x16, x17, x18, x19) -> f384_0_iter_LT(x16 + 2, x17 + -1, x18 + -1, x16 + x17 + -2 + 3 * x18) :|: TRUE && x19 >= 0 && x18 + -1 * x17 <= -1 && x18 + -1 * x17 >= -2 && x17 + -1 * x16 >= 3 && x16 + x17 + 3 * x18 >= 1

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

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

(10)
Complex Obligation (AND)

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

(11)
Obligation:

Termination digraph:
Nodes:
(1) f384_0_iter_LT(x, x1, x2, x3) -> f384_0_iter_LT(x + 2, x1 + -4, x2, x + x1 + -2 + 3 * x2) :|: TRUE && x3 >= 0 && x + x1 + 3 * x2 >= 1 && x1 + -1 * x >= 3 && x2 + -1 * x1 <= -3

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(13)
Obligation:
Rules:
f384_0_iter_LT(x:0, x1:0, x2:0, x3:0) -> f384_0_iter_LT(x:0 + 2, x1:0 - 4, x2:0, x:0 + x1:0 - 2 + 3 * x2:0) :|: x1:0 + -1 * x:0 >= 3 && x2:0 + -1 * x1:0 <= -3 && x3:0 > -1 && x:0 + x1:0 + 3 * x2:0 >= 1

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

(14) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f384_0_iter_LT(INTEGER, INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(15)
Obligation:
Rules:
f384_0_iter_LT(x:0, x1:0, x2:0, x3:0) -> f384_0_iter_LT(c, c1, x2:0, c2) :|: c2 = x:0 + x1:0 - 2 + 3 * x2:0 && (c1 = x1:0 - 4 && c = x:0 + 2) && (x1:0 + -1 * x:0 >= 3 && x2:0 + -1 * x1:0 <= -3 && x3:0 > -1 && x:0 + x1:0 + 3 * x2:0 >= 1)

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

(16) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f384_0_iter_LT ] = 1/6*f384_0_iter_LT_2 + -1/6*f384_0_iter_LT_1

The following rules are decreasing:
f384_0_iter_LT(x:0, x1:0, x2:0, x3:0) -> f384_0_iter_LT(c, c1, x2:0, c2) :|: c2 = x:0 + x1:0 - 2 + 3 * x2:0 && (c1 = x1:0 - 4 && c = x:0 + 2) && (x1:0 + -1 * x:0 >= 3 && x2:0 + -1 * x1:0 <= -3 && x3:0 > -1 && x:0 + x1:0 + 3 * x2:0 >= 1)

The following rules are bounded:
f384_0_iter_LT(x:0, x1:0, x2:0, x3:0) -> f384_0_iter_LT(c, c1, x2:0, c2) :|: c2 = x:0 + x1:0 - 2 + 3 * x2:0 && (c1 = x1:0 - 4 && c = x:0 + 2) && (x1:0 + -1 * x:0 >= 3 && x2:0 + -1 * x1:0 <= -3 && x3:0 > -1 && x:0 + x1:0 + 3 * x2:0 >= 1)


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

(17)
YES

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

(18)
Obligation:

Termination digraph:
Nodes:
(1) f384_0_iter_LT(x12:0, x13:0, x14:0, x15:0) -> f384_0_iter_LT(x12:0 - 1, x13:0, x14:0, x12:0 - 1 + x13:0 + 3 * x14:0) :|: x15:0 > -1 && x13:0 <= x12:0 - 1
(2) f384_0_iter_LT(x8, x9, x10, x11) -> f384_0_iter_LT(x8, x9 + -2, x10, x8 + x9 + -2 + 3 * x10) :|: TRUE && x11 >= 0 && x9 + -1 * x8 >= 0 && x10 + -1 * x9 <= -1 && x8 + x9 + 3 * x10 >= 1 && x9 + -1 * x8 <= 2
(3) f384_0_iter_LT(x16, x17, x18, x19) -> f384_0_iter_LT(x16 + 2, x17 + -1, x18 + -1, x16 + x17 + -2 + 3 * x18) :|: TRUE && x19 >= 0 && x18 + -1 * x17 <= -1 && x18 + -1 * x17 >= -2 && x17 + -1 * x16 >= 3 && x16 + x17 + 3 * x18 >= 1
(4) f384_0_iter_LT(x32:0, x33:0, x34:0, x35:0) -> f384_0_iter_LT(x32:0 + 1, x33:0 + 1, x34:0 - 1, x32:0 + 1 + x33:0 + 1 + 3 * x34:0 - 3) :|: x34:0 >= x33:0 && x33:0 >= x32:0 && x35:0 > -1

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

This digraph is fully evaluated!

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

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

(20)
Obligation:
Rules:
f384_0_iter_LT(x8:0, x9:0, x10:0, x11:0) -> f384_0_iter_LT(x8:0, x9:0 - 2, x10:0, x8:0 + x9:0 - 2 + 3 * x10:0) :|: x8:0 + x9:0 + 3 * x10:0 >= 1 && x9:0 + -1 * x8:0 <= 2 && x10:0 + -1 * x9:0 <= -1 && x11:0 > -1 && x9:0 + -1 * x8:0 >= 0
f384_0_iter_LT(x32:0:0, x33:0:0, x34:0:0, x35:0:0) -> f384_0_iter_LT(x32:0:0 + 1, x33:0:0 + 1, x34:0:0 - 1, x32:0:0 + 1 + x33:0:0 + 1 + 3 * x34:0:0 - 3) :|: x34:0:0 >= x33:0:0 && x33:0:0 >= x32:0:0 && x35:0:0 > -1
f384_0_iter_LT(x12:0:0, x13:0:0, x14:0:0, x15:0:0) -> f384_0_iter_LT(x12:0:0 - 1, x13:0:0, x14:0:0, x12:0:0 - 1 + x13:0:0 + 3 * x14:0:0) :|: x15:0:0 > -1 && x13:0:0 <= x12:0:0 - 1
f384_0_iter_LT(x16:0, x17:0, x18:0, x19:0) -> f384_0_iter_LT(x16:0 + 2, x17:0 - 1, x18:0 - 1, x16:0 + x17:0 - 2 + 3 * x18:0) :|: x17:0 + -1 * x16:0 >= 3 && x16:0 + x17:0 + 3 * x18:0 >= 1 && x18:0 + -1 * x17:0 >= -2 && x19:0 > -1 && x18:0 + -1 * x17:0 <= -1

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

(21) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f384_0_iter_LT(INTEGER, INTEGER, VARIABLE, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(22)
Obligation:
Rules:
f384_0_iter_LT(x8:0, x9:0, x10:0, x11:0) -> f384_0_iter_LT(x8:0, c, x10:0, c1) :|: c1 = x8:0 + x9:0 - 2 + 3 * x10:0 && c = x9:0 - 2 && (x8:0 + x9:0 + 3 * x10:0 >= 1 && x9:0 + -1 * x8:0 <= 2 && x10:0 + -1 * x9:0 <= -1 && x11:0 > -1 && x9:0 + -1 * x8:0 >= 0)
f384_0_iter_LT(x32:0:0, x33:0:0, x34:0:0, x35:0:0) -> f384_0_iter_LT(c2, c3, c4, c5) :|: c5 = x32:0:0 + 1 + x33:0:0 + 1 + 3 * x34:0:0 - 3 && (c4 = x34:0:0 - 1 && (c3 = x33:0:0 + 1 && c2 = x32:0:0 + 1)) && (x34:0:0 >= x33:0:0 && x33:0:0 >= x32:0:0 && x35:0:0 > -1)
f384_0_iter_LT(x12:0:0, x13:0:0, x14:0:0, x15:0:0) -> f384_0_iter_LT(c6, x13:0:0, x14:0:0, c7) :|: c7 = x12:0:0 - 1 + x13:0:0 + 3 * x14:0:0 && c6 = x12:0:0 - 1 && (x15:0:0 > -1 && x13:0:0 <= x12:0:0 - 1)
f384_0_iter_LT(x16:0, x17:0, x18:0, x19:0) -> f384_0_iter_LT(c8, c9, c10, c11) :|: c11 = x16:0 + x17:0 - 2 + 3 * x18:0 && (c10 = x18:0 - 1 && (c9 = x17:0 - 1 && c8 = x16:0 + 2)) && (x17:0 + -1 * x16:0 >= 3 && x16:0 + x17:0 + 3 * x18:0 >= 1 && x18:0 + -1 * x17:0 >= -2 && x19:0 > -1 && x18:0 + -1 * x17:0 <= -1)

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

(23) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f384_0_iter_LT ] = f384_0_iter_LT_1 + f384_0_iter_LT_2 + 3*f384_0_iter_LT_3

The following rules are decreasing:
f384_0_iter_LT(x8:0, x9:0, x10:0, x11:0) -> f384_0_iter_LT(x8:0, c, x10:0, c1) :|: c1 = x8:0 + x9:0 - 2 + 3 * x10:0 && c = x9:0 - 2 && (x8:0 + x9:0 + 3 * x10:0 >= 1 && x9:0 + -1 * x8:0 <= 2 && x10:0 + -1 * x9:0 <= -1 && x11:0 > -1 && x9:0 + -1 * x8:0 >= 0)
f384_0_iter_LT(x32:0:0, x33:0:0, x34:0:0, x35:0:0) -> f384_0_iter_LT(c2, c3, c4, c5) :|: c5 = x32:0:0 + 1 + x33:0:0 + 1 + 3 * x34:0:0 - 3 && (c4 = x34:0:0 - 1 && (c3 = x33:0:0 + 1 && c2 = x32:0:0 + 1)) && (x34:0:0 >= x33:0:0 && x33:0:0 >= x32:0:0 && x35:0:0 > -1)
f384_0_iter_LT(x12:0:0, x13:0:0, x14:0:0, x15:0:0) -> f384_0_iter_LT(c6, x13:0:0, x14:0:0, c7) :|: c7 = x12:0:0 - 1 + x13:0:0 + 3 * x14:0:0 && c6 = x12:0:0 - 1 && (x15:0:0 > -1 && x13:0:0 <= x12:0:0 - 1)
f384_0_iter_LT(x16:0, x17:0, x18:0, x19:0) -> f384_0_iter_LT(c8, c9, c10, c11) :|: c11 = x16:0 + x17:0 - 2 + 3 * x18:0 && (c10 = x18:0 - 1 && (c9 = x17:0 - 1 && c8 = x16:0 + 2)) && (x17:0 + -1 * x16:0 >= 3 && x16:0 + x17:0 + 3 * x18:0 >= 1 && x18:0 + -1 * x17:0 >= -2 && x19:0 > -1 && x18:0 + -1 * x17:0 <= -1)

The following rules are bounded:
f384_0_iter_LT(x8:0, x9:0, x10:0, x11:0) -> f384_0_iter_LT(x8:0, c, x10:0, c1) :|: c1 = x8:0 + x9:0 - 2 + 3 * x10:0 && c = x9:0 - 2 && (x8:0 + x9:0 + 3 * x10:0 >= 1 && x9:0 + -1 * x8:0 <= 2 && x10:0 + -1 * x9:0 <= -1 && x11:0 > -1 && x9:0 + -1 * x8:0 >= 0)


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(24)
Obligation:
Rules:
f384_0_iter_LT(x32:0:0, x33:0:0, x34:0:0, x35:0:0) -> f384_0_iter_LT(c2, c3, c4, c5) :|: c5 = x32:0:0 + 1 + x33:0:0 + 1 + 3 * x34:0:0 - 3 && (c4 = x34:0:0 - 1 && (c3 = x33:0:0 + 1 && c2 = x32:0:0 + 1)) && (x34:0:0 >= x33:0:0 && x33:0:0 >= x32:0:0 && x35:0:0 > -1)
f384_0_iter_LT(x12:0:0, x13:0:0, x14:0:0, x15:0:0) -> f384_0_iter_LT(c6, x13:0:0, x14:0:0, c7) :|: c7 = x12:0:0 - 1 + x13:0:0 + 3 * x14:0:0 && c6 = x12:0:0 - 1 && (x15:0:0 > -1 && x13:0:0 <= x12:0:0 - 1)
f384_0_iter_LT(x16:0, x17:0, x18:0, x19:0) -> f384_0_iter_LT(c8, c9, c10, c11) :|: c11 = x16:0 + x17:0 - 2 + 3 * x18:0 && (c10 = x18:0 - 1 && (c9 = x17:0 - 1 && c8 = x16:0 + 2)) && (x17:0 + -1 * x16:0 >= 3 && x16:0 + x17:0 + 3 * x18:0 >= 1 && x18:0 + -1 * x17:0 >= -2 && x19:0 > -1 && x18:0 + -1 * x17:0 <= -1)

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(25) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f384_0_iter_LT ] = 23*f384_0_iter_LT_3 + 10*f384_0_iter_LT_2 + 4*f384_0_iter_LT_1 + 1

The following rules are decreasing:
f384_0_iter_LT(x32:0:0, x33:0:0, x34:0:0, x35:0:0) -> f384_0_iter_LT(c2, c3, c4, c5) :|: c5 = x32:0:0 + 1 + x33:0:0 + 1 + 3 * x34:0:0 - 3 && (c4 = x34:0:0 - 1 && (c3 = x33:0:0 + 1 && c2 = x32:0:0 + 1)) && (x34:0:0 >= x33:0:0 && x33:0:0 >= x32:0:0 && x35:0:0 > -1)
f384_0_iter_LT(x12:0:0, x13:0:0, x14:0:0, x15:0:0) -> f384_0_iter_LT(c6, x13:0:0, x14:0:0, c7) :|: c7 = x12:0:0 - 1 + x13:0:0 + 3 * x14:0:0 && c6 = x12:0:0 - 1 && (x15:0:0 > -1 && x13:0:0 <= x12:0:0 - 1)
f384_0_iter_LT(x16:0, x17:0, x18:0, x19:0) -> f384_0_iter_LT(c8, c9, c10, c11) :|: c11 = x16:0 + x17:0 - 2 + 3 * x18:0 && (c10 = x18:0 - 1 && (c9 = x17:0 - 1 && c8 = x16:0 + 2)) && (x17:0 + -1 * x16:0 >= 3 && x16:0 + x17:0 + 3 * x18:0 >= 1 && x18:0 + -1 * x17:0 >= -2 && x19:0 > -1 && x18:0 + -1 * x17:0 <= -1)

The following rules are bounded:
f384_0_iter_LT(x16:0, x17:0, x18:0, x19:0) -> f384_0_iter_LT(c8, c9, c10, c11) :|: c11 = x16:0 + x17:0 - 2 + 3 * x18:0 && (c10 = x18:0 - 1 && (c9 = x17:0 - 1 && c8 = x16:0 + 2)) && (x17:0 + -1 * x16:0 >= 3 && x16:0 + x17:0 + 3 * x18:0 >= 1 && x18:0 + -1 * x17:0 >= -2 && x19:0 > -1 && x18:0 + -1 * x17:0 <= -1)


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(26)
Obligation:
Rules:
f384_0_iter_LT(x32:0:0, x33:0:0, x34:0:0, x35:0:0) -> f384_0_iter_LT(c2, c3, c4, c5) :|: c5 = x32:0:0 + 1 + x33:0:0 + 1 + 3 * x34:0:0 - 3 && (c4 = x34:0:0 - 1 && (c3 = x33:0:0 + 1 && c2 = x32:0:0 + 1)) && (x34:0:0 >= x33:0:0 && x33:0:0 >= x32:0:0 && x35:0:0 > -1)
f384_0_iter_LT(x12:0:0, x13:0:0, x14:0:0, x15:0:0) -> f384_0_iter_LT(c6, x13:0:0, x14:0:0, c7) :|: c7 = x12:0:0 - 1 + x13:0:0 + 3 * x14:0:0 && c6 = x12:0:0 - 1 && (x15:0:0 > -1 && x13:0:0 <= x12:0:0 - 1)

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(27) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f384_0_iter_LT ] = -1*f384_0_iter_LT_2 + f384_0_iter_LT_1

The following rules are decreasing:
f384_0_iter_LT(x12:0:0, x13:0:0, x14:0:0, x15:0:0) -> f384_0_iter_LT(c6, x13:0:0, x14:0:0, c7) :|: c7 = x12:0:0 - 1 + x13:0:0 + 3 * x14:0:0 && c6 = x12:0:0 - 1 && (x15:0:0 > -1 && x13:0:0 <= x12:0:0 - 1)

The following rules are bounded:
f384_0_iter_LT(x12:0:0, x13:0:0, x14:0:0, x15:0:0) -> f384_0_iter_LT(c6, x13:0:0, x14:0:0, c7) :|: c7 = x12:0:0 - 1 + x13:0:0 + 3 * x14:0:0 && c6 = x12:0:0 - 1 && (x15:0:0 > -1 && x13:0:0 <= x12:0:0 - 1)


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(28)
Obligation:
Rules:
f384_0_iter_LT(x32:0:0, x33:0:0, x34:0:0, x35:0:0) -> f384_0_iter_LT(c2, c3, c4, c5) :|: c5 = x32:0:0 + 1 + x33:0:0 + 1 + 3 * x34:0:0 - 3 && (c4 = x34:0:0 - 1 && (c3 = x33:0:0 + 1 && c2 = x32:0:0 + 1)) && (x34:0:0 >= x33:0:0 && x33:0:0 >= x32:0:0 && x35:0:0 > -1)

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(29) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f384_0_iter_LT ] = 1/2*f384_0_iter_LT_3 + -1/2*f384_0_iter_LT_1

The following rules are decreasing:
f384_0_iter_LT(x32:0:0, x33:0:0, x34:0:0, x35:0:0) -> f384_0_iter_LT(c2, c3, c4, c5) :|: c5 = x32:0:0 + 1 + x33:0:0 + 1 + 3 * x34:0:0 - 3 && (c4 = x34:0:0 - 1 && (c3 = x33:0:0 + 1 && c2 = x32:0:0 + 1)) && (x34:0:0 >= x33:0:0 && x33:0:0 >= x32:0:0 && x35:0:0 > -1)

The following rules are bounded:
f384_0_iter_LT(x32:0:0, x33:0:0, x34:0:0, x35:0:0) -> f384_0_iter_LT(c2, c3, c4, c5) :|: c5 = x32:0:0 + 1 + x33:0:0 + 1 + 3 * x34:0:0 - 3 && (c4 = x34:0:0 - 1 && (c3 = x33:0:0 + 1 && c2 = x32:0:0 + 1)) && (x34:0:0 >= x33:0:0 && x33:0:0 >= x32:0:0 && x35:0:0 > -1)


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(30)
YES