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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 805 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 45 ms]
        (7) IRSwT
        (8) TempFilterProof [SOUND, 33 ms]
        (9) IntTRS
        (10) PolynomialOrderProcessor [EQUIVALENT, 10 ms]
        (11) IntTRS
        (12) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 11 ms]
        (16) IRSwT
        (17) TempFilterProof [SOUND, 69 ms]
        (18) IntTRS
        (19) RankingReductionPairProof [EQUIVALENT, 29 ms]
        (20) IntTRS
        (21) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (22) YES


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

(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3, arg4) -> f1_0_main_Load'(arg1P, arg2P, arg3P, arg4P) :|: 0 <= 2 * x39 - 1 && 0 <= arg2 - 1 && 2 * x39 + 1 - 2 * x40 = 1 && -1 <= x39 - 1 && 0 <= arg1 - 1 && 2 <= x41 - 1 && arg1 = arg1P && arg2 = arg2P
f1_0_main_Load'(x, x1, x2, x3) -> f723_0_init_GE(x4, x5, x6, x7) :|: 0 <= 2 * x8 - 1 && 0 <= x1 - 1 && 2 * x8 + 1 - 2 * x9 = 1 && -1 <= x8 - 1 && 0 <= x - 1 && 2 <= x4 - 1 && 2 * x8 + 1 - 2 * x9 <= 1 && 0 <= 2 * x8 + 1 - 2 * x9 && 0 = x5 && 2 * x8 + 1 = x6
f723_0_init_GE(x10, x11, x12, x13) -> f873_0_init_GE(x14, x15, x16, x17) :|: x12 = x17 && 0 = x16 && x11 = x15 && x12 + 4 <= x10 && 2 <= x14 - 1 && 2 <= x10 - 1 && x11 <= 2 && x14 <= x10
f873_0_init_GE(x19, x20, x21, x22) -> f723_0_init_GE(x23, x24, x25, x26) :|: x22 = x25 && x20 + 1 = x24 && x22 + 4 <= x19 && 2 <= x23 - 1 && 2 <= x19 - 1 && 2 <= x21 - 1 && x23 <= x19
f873_0_init_GE(x27, x28, x29, x30) -> f873_0_init_GE(x31, x32, x33, x34) :|: x28 <= x30 - 1 && x29 <= 2 && x29 <= x35 - 1 && -1 <= x35 - 1 && x31 <= x27 && 2 <= x27 - 1 && 2 <= x31 - 1 && x30 + 4 <= x27 && x28 = x32 && x29 + 1 = x33 && x30 = x34
f723_0_init_GE(x36, x37, x38, x42) -> f723_0_init_GE'(x43, x44, x47, x48) :|: 1 <= x38 - 1 && 2 <= x37 - 1 && x49 <= x38 - 1 && x53 <= x38 - 1 && x54 <= x36 && 2 <= x36 - 1 && 2 <= x54 - 1 && x38 + 4 <= x36 && x36 = x43 && x37 = x44 && x38 = x47
f723_0_init_GE'(x55, x56, x59, x60) -> f1037_0_imprimer_GE(x61, x62, x63, x64) :|: 1 <= x59 - 1 && 2 <= x56 - 1 && x65 <= x59 - 1 && x66 <= x59 - 1 && x61 <= x55 && 2 <= x55 - 1 && 2 <= x61 - 1 && x59 + 4 <= x55 && 0 <= x59 - 2 * x65 && x59 - 2 * x65 <= 1 && x59 - 2 * x66 <= 1 && 0 <= x59 - 2 * x66 && 0 = x62 && x59 = x63
f1037_0_imprimer_GE(x67, x68, x69, x70) -> f1074_0_imprimer_GE(x71, x72, x73, x74) :|: x69 = x74 && 0 = x73 && x68 = x72 && x69 + 4 <= x67 && 2 <= x71 - 1 && 2 <= x67 - 1 && x68 <= x69 - 1 && x71 <= x67
f1074_0_imprimer_GE(x75, x76, x77, x78) -> f1037_0_imprimer_GE(x79, x80, x81, x82) :|: x78 = x81 && x76 + 1 = x80 && x78 + 4 <= x75 && 2 <= x79 - 1 && 2 <= x75 - 1 && x78 <= x77 && x79 <= x75
f1074_0_imprimer_GE(x83, x84, x85, x86) -> f1074_0_imprimer_GE(x87, x88, x89, x90) :|: x86 = x90 && x85 + 1 = x89 && x84 = x88 && x86 + 4 <= x83 && 2 <= x87 - 1 && 2 <= x83 - 1 && x85 <= x86 - 1 && x87 <= x83
__init(x91, x92, x93, x94) -> f1_0_main_Load(x95, x96, x97, x98) :|: 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) :|: 0 <= 2 * x39 - 1 && 0 <= arg2 - 1 && 2 * x39 + 1 - 2 * x40 = 1 && -1 <= x39 - 1 && 0 <= arg1 - 1 && 2 <= x41 - 1 && arg1 = arg1P && arg2 = arg2P
f1_0_main_Load'(x, x1, x2, x3) -> f723_0_init_GE(x4, x5, x6, x7) :|: 0 <= 2 * x8 - 1 && 0 <= x1 - 1 && 2 * x8 + 1 - 2 * x9 = 1 && -1 <= x8 - 1 && 0 <= x - 1 && 2 <= x4 - 1 && 2 * x8 + 1 - 2 * x9 <= 1 && 0 <= 2 * x8 + 1 - 2 * x9 && 0 = x5 && 2 * x8 + 1 = x6
f723_0_init_GE(x10, x11, x12, x13) -> f873_0_init_GE(x14, x15, x16, x17) :|: x12 = x17 && 0 = x16 && x11 = x15 && x12 + 4 <= x10 && 2 <= x14 - 1 && 2 <= x10 - 1 && x11 <= 2 && x14 <= x10
f873_0_init_GE(x19, x20, x21, x22) -> f723_0_init_GE(x23, x24, x25, x26) :|: x22 = x25 && x20 + 1 = x24 && x22 + 4 <= x19 && 2 <= x23 - 1 && 2 <= x19 - 1 && 2 <= x21 - 1 && x23 <= x19
f873_0_init_GE(x27, x28, x29, x30) -> f873_0_init_GE(x31, x32, x33, x34) :|: x28 <= x30 - 1 && x29 <= 2 && x29 <= x35 - 1 && -1 <= x35 - 1 && x31 <= x27 && 2 <= x27 - 1 && 2 <= x31 - 1 && x30 + 4 <= x27 && x28 = x32 && x29 + 1 = x33 && x30 = x34
f723_0_init_GE(x36, x37, x38, x42) -> f723_0_init_GE'(x43, x44, x47, x48) :|: 1 <= x38 - 1 && 2 <= x37 - 1 && x49 <= x38 - 1 && x53 <= x38 - 1 && x54 <= x36 && 2 <= x36 - 1 && 2 <= x54 - 1 && x38 + 4 <= x36 && x36 = x43 && x37 = x44 && x38 = x47
f723_0_init_GE'(x55, x56, x59, x60) -> f1037_0_imprimer_GE(x61, x62, x63, x64) :|: 1 <= x59 - 1 && 2 <= x56 - 1 && x65 <= x59 - 1 && x66 <= x59 - 1 && x61 <= x55 && 2 <= x55 - 1 && 2 <= x61 - 1 && x59 + 4 <= x55 && 0 <= x59 - 2 * x65 && x59 - 2 * x65 <= 1 && x59 - 2 * x66 <= 1 && 0 <= x59 - 2 * x66 && 0 = x62 && x59 = x63
f1037_0_imprimer_GE(x67, x68, x69, x70) -> f1074_0_imprimer_GE(x71, x72, x73, x74) :|: x69 = x74 && 0 = x73 && x68 = x72 && x69 + 4 <= x67 && 2 <= x71 - 1 && 2 <= x67 - 1 && x68 <= x69 - 1 && x71 <= x67
f1074_0_imprimer_GE(x75, x76, x77, x78) -> f1037_0_imprimer_GE(x79, x80, x81, x82) :|: x78 = x81 && x76 + 1 = x80 && x78 + 4 <= x75 && 2 <= x79 - 1 && 2 <= x75 - 1 && x78 <= x77 && x79 <= x75
f1074_0_imprimer_GE(x83, x84, x85, x86) -> f1074_0_imprimer_GE(x87, x88, x89, x90) :|: x86 = x90 && x85 + 1 = x89 && x84 = x88 && x86 + 4 <= x83 && 2 <= x87 - 1 && 2 <= x83 - 1 && x85 <= x86 - 1 && x87 <= x83
__init(x91, x92, x93, x94) -> f1_0_main_Load(x95, x96, x97, x98) :|: 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) :|: 0 <= 2 * x39 - 1 && 0 <= arg2 - 1 && 2 * x39 + 1 - 2 * x40 = 1 && -1 <= x39 - 1 && 0 <= arg1 - 1 && 2 <= x41 - 1 && arg1 = arg1P && arg2 = arg2P
(2) f1_0_main_Load'(x, x1, x2, x3) -> f723_0_init_GE(x4, x5, x6, x7) :|: 0 <= 2 * x8 - 1 && 0 <= x1 - 1 && 2 * x8 + 1 - 2 * x9 = 1 && -1 <= x8 - 1 && 0 <= x - 1 && 2 <= x4 - 1 && 2 * x8 + 1 - 2 * x9 <= 1 && 0 <= 2 * x8 + 1 - 2 * x9 && 0 = x5 && 2 * x8 + 1 = x6
(3) f723_0_init_GE(x10, x11, x12, x13) -> f873_0_init_GE(x14, x15, x16, x17) :|: x12 = x17 && 0 = x16 && x11 = x15 && x12 + 4 <= x10 && 2 <= x14 - 1 && 2 <= x10 - 1 && x11 <= 2 && x14 <= x10
(4) f873_0_init_GE(x19, x20, x21, x22) -> f723_0_init_GE(x23, x24, x25, x26) :|: x22 = x25 && x20 + 1 = x24 && x22 + 4 <= x19 && 2 <= x23 - 1 && 2 <= x19 - 1 && 2 <= x21 - 1 && x23 <= x19
(5) f873_0_init_GE(x27, x28, x29, x30) -> f873_0_init_GE(x31, x32, x33, x34) :|: x28 <= x30 - 1 && x29 <= 2 && x29 <= x35 - 1 && -1 <= x35 - 1 && x31 <= x27 && 2 <= x27 - 1 && 2 <= x31 - 1 && x30 + 4 <= x27 && x28 = x32 && x29 + 1 = x33 && x30 = x34
(6) f723_0_init_GE(x36, x37, x38, x42) -> f723_0_init_GE'(x43, x44, x47, x48) :|: 1 <= x38 - 1 && 2 <= x37 - 1 && x49 <= x38 - 1 && x53 <= x38 - 1 && x54 <= x36 && 2 <= x36 - 1 && 2 <= x54 - 1 && x38 + 4 <= x36 && x36 = x43 && x37 = x44 && x38 = x47
(7) f723_0_init_GE'(x55, x56, x59, x60) -> f1037_0_imprimer_GE(x61, x62, x63, x64) :|: 1 <= x59 - 1 && 2 <= x56 - 1 && x65 <= x59 - 1 && x66 <= x59 - 1 && x61 <= x55 && 2 <= x55 - 1 && 2 <= x61 - 1 && x59 + 4 <= x55 && 0 <= x59 - 2 * x65 && x59 - 2 * x65 <= 1 && x59 - 2 * x66 <= 1 && 0 <= x59 - 2 * x66 && 0 = x62 && x59 = x63
(8) f1037_0_imprimer_GE(x67, x68, x69, x70) -> f1074_0_imprimer_GE(x71, x72, x73, x74) :|: x69 = x74 && 0 = x73 && x68 = x72 && x69 + 4 <= x67 && 2 <= x71 - 1 && 2 <= x67 - 1 && x68 <= x69 - 1 && x71 <= x67
(9) f1074_0_imprimer_GE(x75, x76, x77, x78) -> f1037_0_imprimer_GE(x79, x80, x81, x82) :|: x78 = x81 && x76 + 1 = x80 && x78 + 4 <= x75 && 2 <= x79 - 1 && 2 <= x75 - 1 && x78 <= x77 && x79 <= x75
(10) f1074_0_imprimer_GE(x83, x84, x85, x86) -> f1074_0_imprimer_GE(x87, x88, x89, x90) :|: x86 = x90 && x85 + 1 = x89 && x84 = x88 && x86 + 4 <= x83 && 2 <= x87 - 1 && 2 <= x83 - 1 && x85 <= x86 - 1 && x87 <= x83
(11) __init(x91, x92, x93, x94) -> f1_0_main_Load(x95, x96, x97, x98) :|: 0 <= 0

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

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) f723_0_init_GE(x10, x11, x12, x13) -> f873_0_init_GE(x14, x15, x16, x17) :|: x12 = x17 && 0 = x16 && x11 = x15 && x12 + 4 <= x10 && 2 <= x14 - 1 && 2 <= x10 - 1 && x11 <= 2 && x14 <= x10
(2) f873_0_init_GE(x19, x20, x21, x22) -> f723_0_init_GE(x23, x24, x25, x26) :|: x22 = x25 && x20 + 1 = x24 && x22 + 4 <= x19 && 2 <= x23 - 1 && 2 <= x19 - 1 && 2 <= x21 - 1 && x23 <= x19
(3) f873_0_init_GE(x27, x28, x29, x30) -> f873_0_init_GE(x31, x32, x33, x34) :|: x28 <= x30 - 1 && x29 <= 2 && x29 <= x35 - 1 && -1 <= x35 - 1 && x31 <= x27 && 2 <= x27 - 1 && 2 <= x31 - 1 && x30 + 4 <= x27 && x28 = x32 && x29 + 1 = x33 && x30 = x34

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

This digraph is fully evaluated!

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

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

(7)
Obligation:
Rules:
f873_0_init_GE(x27:0, x28:0, x29:0, x30:0) -> f873_0_init_GE(x31:0, x28:0, x29:0 + 1, x30:0) :|: x31:0 > 2 && x30:0 + 4 <= x27:0 && x27:0 > 2 && x31:0 <= x27:0 && x35:0 > -1 && x35:0 - 1 >= x29:0 && x29:0 < 3 && x30:0 - 1 >= x28:0
f873_0_init_GE(x19:0, x20:0, x21:0, x17:0) -> f873_0_init_GE(x14:0, x20:0 + 1, 0, x17:0) :|: x23:0 >= x14:0 && x23:0 <= x19:0 && x21:0 > 2 && x20:0 < 2 && x19:0 > 2 && x23:0 > 2 && x14:0 > 2 && x23:0 >= x17:0 + 4 && x19:0 >= x17:0 + 4

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

(8) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f873_0_init_GE(INTEGER, INTEGER, VARIABLE, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(9)
Obligation:
Rules:
f873_0_init_GE(x27:0, x28:0, x29:0, x30:0) -> f873_0_init_GE(x31:0, x28:0, c, x30:0) :|: c = x29:0 + 1 && (x31:0 > 2 && x30:0 + 4 <= x27:0 && x27:0 > 2 && x31:0 <= x27:0 && x35:0 > -1 && x35:0 - 1 >= x29:0 && x29:0 < 3 && x30:0 - 1 >= x28:0)
f873_0_init_GE(x19:0, x20:0, x21:0, x17:0) -> f873_0_init_GE(x14:0, c1, c2, x17:0) :|: c2 = 0 && c1 = x20:0 + 1 && (x23:0 >= x14:0 && x23:0 <= x19:0 && x21:0 > 2 && x20:0 < 2 && x19:0 > 2 && x23:0 > 2 && x14:0 > 2 && x23:0 >= x17:0 + 4 && x19:0 >= x17:0 + 4)

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

(10) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f873_0_init_GE(x, x1, x2, x3)] = 1 - x1

The following rules are decreasing:
f873_0_init_GE(x19:0, x20:0, x21:0, x17:0) -> f873_0_init_GE(x14:0, c1, c2, x17:0) :|: c2 = 0 && c1 = x20:0 + 1 && (x23:0 >= x14:0 && x23:0 <= x19:0 && x21:0 > 2 && x20:0 < 2 && x19:0 > 2 && x23:0 > 2 && x14:0 > 2 && x23:0 >= x17:0 + 4 && x19:0 >= x17:0 + 4)
The following rules are bounded:
f873_0_init_GE(x19:0, x20:0, x21:0, x17:0) -> f873_0_init_GE(x14:0, c1, c2, x17:0) :|: c2 = 0 && c1 = x20:0 + 1 && (x23:0 >= x14:0 && x23:0 <= x19:0 && x21:0 > 2 && x20:0 < 2 && x19:0 > 2 && x23:0 > 2 && x14:0 > 2 && x23:0 >= x17:0 + 4 && x19:0 >= x17:0 + 4)

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

(11)
Obligation:
Rules:
f873_0_init_GE(x27:0, x28:0, x29:0, x30:0) -> f873_0_init_GE(x31:0, x28:0, c, x30:0) :|: c = x29:0 + 1 && (x31:0 > 2 && x30:0 + 4 <= x27:0 && x27:0 > 2 && x31:0 <= x27:0 && x35:0 > -1 && x35:0 - 1 >= x29:0 && x29:0 < 3 && x30:0 - 1 >= x28:0)

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

(12) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f873_0_init_GE(x, x1, x2, x3)] = 2 - x2

The following rules are decreasing:
f873_0_init_GE(x27:0, x28:0, x29:0, x30:0) -> f873_0_init_GE(x31:0, x28:0, c, x30:0) :|: c = x29:0 + 1 && (x31:0 > 2 && x30:0 + 4 <= x27:0 && x27:0 > 2 && x31:0 <= x27:0 && x35:0 > -1 && x35:0 - 1 >= x29:0 && x29:0 < 3 && x30:0 - 1 >= x28:0)
The following rules are bounded:
f873_0_init_GE(x27:0, x28:0, x29:0, x30:0) -> f873_0_init_GE(x31:0, x28:0, c, x30:0) :|: c = x29:0 + 1 && (x31:0 > 2 && x30:0 + 4 <= x27:0 && x27:0 > 2 && x31:0 <= x27:0 && x35:0 > -1 && x35:0 - 1 >= x29:0 && x29:0 < 3 && x30:0 - 1 >= x28:0)

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

(13)
YES

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

(14)
Obligation:

Termination digraph:
Nodes:
(1) f1037_0_imprimer_GE(x67, x68, x69, x70) -> f1074_0_imprimer_GE(x71, x72, x73, x74) :|: x69 = x74 && 0 = x73 && x68 = x72 && x69 + 4 <= x67 && 2 <= x71 - 1 && 2 <= x67 - 1 && x68 <= x69 - 1 && x71 <= x67
(2) f1074_0_imprimer_GE(x75, x76, x77, x78) -> f1037_0_imprimer_GE(x79, x80, x81, x82) :|: x78 = x81 && x76 + 1 = x80 && x78 + 4 <= x75 && 2 <= x79 - 1 && 2 <= x75 - 1 && x78 <= x77 && x79 <= x75
(3) f1074_0_imprimer_GE(x83, x84, x85, x86) -> f1074_0_imprimer_GE(x87, x88, x89, x90) :|: x86 = x90 && x85 + 1 = x89 && x84 = x88 && x86 + 4 <= x83 && 2 <= x87 - 1 && 2 <= x83 - 1 && x85 <= x86 - 1 && x87 <= x83

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

This digraph is fully evaluated!

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

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

(16)
Obligation:
Rules:
f1074_0_imprimer_GE(x83:0, x84:0, x85:0, x86:0) -> f1074_0_imprimer_GE(x87:0, x84:0, x85:0 + 1, x86:0) :|: x86:0 - 1 >= x85:0 && x87:0 <= x83:0 && x83:0 > 2 && x86:0 + 4 <= x83:0 && x87:0 > 2
f1074_0_imprimer_GE(x75:0, x76:0, x77:0, x74:0) -> f1074_0_imprimer_GE(x71:0, x76:0 + 1, 0, x74:0) :|: x79:0 >= x71:0 && x79:0 <= x75:0 && x77:0 >= x74:0 && x76:0 + 1 <= x74:0 - 1 && x75:0 > 2 && x79:0 > 2 && x71:0 > 2 && x79:0 >= x74:0 + 4 && x75:0 >= x74:0 + 4

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

(17) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f1074_0_imprimer_GE(INTEGER, VARIABLE, VARIABLE, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(18)
Obligation:
Rules:
f1074_0_imprimer_GE(x83:0, x84:0, x85:0, x86:0) -> f1074_0_imprimer_GE(x87:0, x84:0, c, x86:0) :|: c = x85:0 + 1 && (x86:0 - 1 >= x85:0 && x87:0 <= x83:0 && x83:0 > 2 && x86:0 + 4 <= x83:0 && x87:0 > 2)
f1074_0_imprimer_GE(x75:0, x76:0, x77:0, x74:0) -> f1074_0_imprimer_GE(x71:0, c1, c2, x74:0) :|: c2 = 0 && c1 = x76:0 + 1 && (x79:0 >= x71:0 && x79:0 <= x75:0 && x77:0 >= x74:0 && x76:0 + 1 <= x74:0 - 1 && x75:0 > 2 && x79:0 > 2 && x71:0 > 2 && x79:0 >= x74:0 + 4 && x75:0 >= x74:0 + 4)

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

(19) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f1074_0_imprimer_GE ] = 2*f1074_0_imprimer_GE_4 + -2*f1074_0_imprimer_GE_2

The following rules are decreasing:
f1074_0_imprimer_GE(x75:0, x76:0, x77:0, x74:0) -> f1074_0_imprimer_GE(x71:0, c1, c2, x74:0) :|: c2 = 0 && c1 = x76:0 + 1 && (x79:0 >= x71:0 && x79:0 <= x75:0 && x77:0 >= x74:0 && x76:0 + 1 <= x74:0 - 1 && x75:0 > 2 && x79:0 > 2 && x71:0 > 2 && x79:0 >= x74:0 + 4 && x75:0 >= x74:0 + 4)

The following rules are bounded:
f1074_0_imprimer_GE(x75:0, x76:0, x77:0, x74:0) -> f1074_0_imprimer_GE(x71:0, c1, c2, x74:0) :|: c2 = 0 && c1 = x76:0 + 1 && (x79:0 >= x71:0 && x79:0 <= x75:0 && x77:0 >= x74:0 && x76:0 + 1 <= x74:0 - 1 && x75:0 > 2 && x79:0 > 2 && x71:0 > 2 && x79:0 >= x74:0 + 4 && x75:0 >= x74:0 + 4)


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

(20)
Obligation:
Rules:
f1074_0_imprimer_GE(x83:0, x84:0, x85:0, x86:0) -> f1074_0_imprimer_GE(x87:0, x84:0, c, x86:0) :|: c = x85:0 + 1 && (x86:0 - 1 >= x85:0 && x87:0 <= x83:0 && x83:0 > 2 && x86:0 + 4 <= x83:0 && x87:0 > 2)

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

(21) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f1074_0_imprimer_GE ] = f1074_0_imprimer_GE_4 + -1*f1074_0_imprimer_GE_3

The following rules are decreasing:
f1074_0_imprimer_GE(x83:0, x84:0, x85:0, x86:0) -> f1074_0_imprimer_GE(x87:0, x84:0, c, x86:0) :|: c = x85:0 + 1 && (x86:0 - 1 >= x85:0 && x87:0 <= x83:0 && x83:0 > 2 && x86:0 + 4 <= x83:0 && x87:0 > 2)

The following rules are bounded:
f1074_0_imprimer_GE(x83:0, x84:0, x85:0, x86:0) -> f1074_0_imprimer_GE(x87:0, x84:0, c, x86:0) :|: c = x85:0 + 1 && (x86:0 - 1 >= x85:0 && x87:0 <= x83:0 && x83:0 > 2 && x86:0 + 4 <= x83:0 && x87:0 > 2)


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(22)
YES