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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 611 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (7) IRSwT
        (8) TempFilterProof [SOUND, 18 ms]
        (9) IntTRS
        (10) RankingReductionPairProof [EQUIVALENT, 8 ms]
        (11) YES
    (12) IRSwT
        (13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (14) IRSwT
        (15) TempFilterProof [SOUND, 44 ms]
        (16) IntTRS
        (17) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (18) IntTRS
        (19) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (20) YES
    (21) IRSwT
        (22) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (23) IRSwT
        (24) IRSwTChainingProof [EQUIVALENT, 0 ms]
        (25) IRSwT
        (26) IRSwTTerminationDigraphProof [EQUIVALENT, 7 ms]
        (27) IRSwT
        (28) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (29) IRSwT
        (30) TempFilterProof [SOUND, 5 ms]
        (31) IntTRS
        (32) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (33) YES


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

(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3, arg4) -> f254_0_main_GE(arg1P, arg2P, arg3P, arg4P) :|: arg2 = arg4P && arg2 - 1 = arg3P && 0 = arg2P && 0 <= arg1P - 1 && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg1P <= arg1
f254_0_main_GE(x, x1, x2, x3) -> f254_0_main_GE(x4, x5, x6, x7) :|: x3 = x7 && x3 - 1 = x6 && x1 + 1 = x5 && 0 <= x4 - 1 && 0 <= x - 1 && x4 <= x && -1 <= x3 - 1 && x1 <= x3 - 1 && x1 <= x2 - 1
f254_0_main_GE(x8, x9, x10, x11) -> f494_0_main_GE(x12, x13, x14, x15) :|: x11 = x15 && x11 - 1 = x14 && 0 = x13 && 0 <= x12 - 1 && 0 <= x8 - 1 && x12 <= x8 && -1 <= x11 - 1 && x10 <= x9
f494_0_main_GE(x16, x17, x18, x19) -> f510_0_main_GE(x20, x21, x22, x23) :|: x19 = x23 && x17 + 1 = x22 && x17 = x20 && 0 <= x21 - 1 && 0 <= x16 - 1 && x21 <= x16 && x17 <= x18 - 1 && -1 <= x17 - 1
f510_0_main_GE(x24, x25, x26, x27) -> f494_0_main_GE(x28, x29, x30, x31) :|: x27 = x31 && x27 - 1 = x30 && x24 + 1 = x29 && 0 <= x28 - 1 && 0 <= x25 - 1 && x28 <= x25 && x27 <= x26 && -1 <= x27 - 1
f494_0_main_GE(x32, x33, x34, x35) -> f609_0_main_GE(x36, x37, x40, x41) :|: x35 = x41 && x35 - 1 = x40 && 0 = x37 && 0 <= x36 - 1 && 0 <= x32 - 1 && x36 <= x32 && -1 <= x35 - 1 && x34 <= x33
f609_0_main_GE(x42, x43, x44, x47) -> f609_0_main_GE(x48, x49, x50, x51) :|: x47 = x51 && x47 - 1 = x50 && x43 + 1 = x49 && 0 <= x48 - 1 && 0 <= x42 - 1 && x48 <= x42 && x43 <= x44 - 1 && -1 <= x47 - 1
f510_0_main_GE(x52, x53, x54, x55) -> f510_0_main_GE(x56, x57, x58, x59) :|: x54 <= x55 - 1 && x52 <= x55 - 1 && x60 <= x61 && x57 <= x53 && 0 <= x53 - 1 && 0 <= x57 - 1 && x52 = x56 && x54 + 1 = x58 && x55 = x59
f510_0_main_GE(x62, x63, x64, x65) -> f510_0_main_GE(x66, x67, x68, x69) :|: x64 <= x65 - 1 && x62 <= x65 - 1 && x70 <= x71 - 1 && x67 <= x63 && 0 <= x63 - 1 && 0 <= x67 - 1 && x62 = x66 && x64 + 1 = x68 && x65 = x69
__init(x72, x73, x74, x75) -> f1_0_main_Load(x76, x77, x78, x79) :|: 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) -> f254_0_main_GE(arg1P, arg2P, arg3P, arg4P) :|: arg2 = arg4P && arg2 - 1 = arg3P && 0 = arg2P && 0 <= arg1P - 1 && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg1P <= arg1
f254_0_main_GE(x, x1, x2, x3) -> f254_0_main_GE(x4, x5, x6, x7) :|: x3 = x7 && x3 - 1 = x6 && x1 + 1 = x5 && 0 <= x4 - 1 && 0 <= x - 1 && x4 <= x && -1 <= x3 - 1 && x1 <= x3 - 1 && x1 <= x2 - 1
f254_0_main_GE(x8, x9, x10, x11) -> f494_0_main_GE(x12, x13, x14, x15) :|: x11 = x15 && x11 - 1 = x14 && 0 = x13 && 0 <= x12 - 1 && 0 <= x8 - 1 && x12 <= x8 && -1 <= x11 - 1 && x10 <= x9
f494_0_main_GE(x16, x17, x18, x19) -> f510_0_main_GE(x20, x21, x22, x23) :|: x19 = x23 && x17 + 1 = x22 && x17 = x20 && 0 <= x21 - 1 && 0 <= x16 - 1 && x21 <= x16 && x17 <= x18 - 1 && -1 <= x17 - 1
f510_0_main_GE(x24, x25, x26, x27) -> f494_0_main_GE(x28, x29, x30, x31) :|: x27 = x31 && x27 - 1 = x30 && x24 + 1 = x29 && 0 <= x28 - 1 && 0 <= x25 - 1 && x28 <= x25 && x27 <= x26 && -1 <= x27 - 1
f494_0_main_GE(x32, x33, x34, x35) -> f609_0_main_GE(x36, x37, x40, x41) :|: x35 = x41 && x35 - 1 = x40 && 0 = x37 && 0 <= x36 - 1 && 0 <= x32 - 1 && x36 <= x32 && -1 <= x35 - 1 && x34 <= x33
f609_0_main_GE(x42, x43, x44, x47) -> f609_0_main_GE(x48, x49, x50, x51) :|: x47 = x51 && x47 - 1 = x50 && x43 + 1 = x49 && 0 <= x48 - 1 && 0 <= x42 - 1 && x48 <= x42 && x43 <= x44 - 1 && -1 <= x47 - 1
f510_0_main_GE(x52, x53, x54, x55) -> f510_0_main_GE(x56, x57, x58, x59) :|: x54 <= x55 - 1 && x52 <= x55 - 1 && x60 <= x61 && x57 <= x53 && 0 <= x53 - 1 && 0 <= x57 - 1 && x52 = x56 && x54 + 1 = x58 && x55 = x59
f510_0_main_GE(x62, x63, x64, x65) -> f510_0_main_GE(x66, x67, x68, x69) :|: x64 <= x65 - 1 && x62 <= x65 - 1 && x70 <= x71 - 1 && x67 <= x63 && 0 <= x63 - 1 && 0 <= x67 - 1 && x62 = x66 && x64 + 1 = x68 && x65 = x69
__init(x72, x73, x74, x75) -> f1_0_main_Load(x76, x77, x78, x79) :|: 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) -> f254_0_main_GE(arg1P, arg2P, arg3P, arg4P) :|: arg2 = arg4P && arg2 - 1 = arg3P && 0 = arg2P && 0 <= arg1P - 1 && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg1P <= arg1
(2) f254_0_main_GE(x, x1, x2, x3) -> f254_0_main_GE(x4, x5, x6, x7) :|: x3 = x7 && x3 - 1 = x6 && x1 + 1 = x5 && 0 <= x4 - 1 && 0 <= x - 1 && x4 <= x && -1 <= x3 - 1 && x1 <= x3 - 1 && x1 <= x2 - 1
(3) f254_0_main_GE(x8, x9, x10, x11) -> f494_0_main_GE(x12, x13, x14, x15) :|: x11 = x15 && x11 - 1 = x14 && 0 = x13 && 0 <= x12 - 1 && 0 <= x8 - 1 && x12 <= x8 && -1 <= x11 - 1 && x10 <= x9
(4) f494_0_main_GE(x16, x17, x18, x19) -> f510_0_main_GE(x20, x21, x22, x23) :|: x19 = x23 && x17 + 1 = x22 && x17 = x20 && 0 <= x21 - 1 && 0 <= x16 - 1 && x21 <= x16 && x17 <= x18 - 1 && -1 <= x17 - 1
(5) f510_0_main_GE(x24, x25, x26, x27) -> f494_0_main_GE(x28, x29, x30, x31) :|: x27 = x31 && x27 - 1 = x30 && x24 + 1 = x29 && 0 <= x28 - 1 && 0 <= x25 - 1 && x28 <= x25 && x27 <= x26 && -1 <= x27 - 1
(6) f494_0_main_GE(x32, x33, x34, x35) -> f609_0_main_GE(x36, x37, x40, x41) :|: x35 = x41 && x35 - 1 = x40 && 0 = x37 && 0 <= x36 - 1 && 0 <= x32 - 1 && x36 <= x32 && -1 <= x35 - 1 && x34 <= x33
(7) f609_0_main_GE(x42, x43, x44, x47) -> f609_0_main_GE(x48, x49, x50, x51) :|: x47 = x51 && x47 - 1 = x50 && x43 + 1 = x49 && 0 <= x48 - 1 && 0 <= x42 - 1 && x48 <= x42 && x43 <= x44 - 1 && -1 <= x47 - 1
(8) f510_0_main_GE(x52, x53, x54, x55) -> f510_0_main_GE(x56, x57, x58, x59) :|: x54 <= x55 - 1 && x52 <= x55 - 1 && x60 <= x61 && x57 <= x53 && 0 <= x53 - 1 && 0 <= x57 - 1 && x52 = x56 && x54 + 1 = x58 && x55 = x59
(9) f510_0_main_GE(x62, x63, x64, x65) -> f510_0_main_GE(x66, x67, x68, x69) :|: x64 <= x65 - 1 && x62 <= x65 - 1 && x70 <= x71 - 1 && x67 <= x63 && 0 <= x63 - 1 && 0 <= x67 - 1 && x62 = x66 && x64 + 1 = x68 && x65 = x69
(10) __init(x72, x73, x74, x75) -> f1_0_main_Load(x76, x77, x78, x79) :|: 0 <= 0

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

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) f254_0_main_GE(x, x1, x2, x3) -> f254_0_main_GE(x4, x5, x6, x7) :|: x3 = x7 && x3 - 1 = x6 && x1 + 1 = x5 && 0 <= x4 - 1 && 0 <= x - 1 && x4 <= x && -1 <= x3 - 1 && x1 <= x3 - 1 && x1 <= x2 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(7)
Obligation:
Rules:
f254_0_main_GE(x:0, x1:0, x2:0, x3:0) -> f254_0_main_GE(x4:0, x1:0 + 1, x3:0 - 1, x3:0) :|: x3:0 - 1 >= x1:0 && x2:0 - 1 >= x1:0 && x3:0 > -1 && x:0 >= x4:0 && x4:0 > 0 && x:0 > 0

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

(8) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f254_0_main_GE(INTEGER, INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(9)
Obligation:
Rules:
f254_0_main_GE(x:0, x1:0, x2:0, x3:0) -> f254_0_main_GE(x4:0, c, c1, x3:0) :|: c1 = x3:0 - 1 && c = x1:0 + 1 && (x3:0 - 1 >= x1:0 && x2:0 - 1 >= x1:0 && x3:0 > -1 && x:0 >= x4:0 && x4:0 > 0 && x:0 > 0)

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

(10) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f254_0_main_GE ] = f254_0_main_GE_4 + -1*f254_0_main_GE_2

The following rules are decreasing:
f254_0_main_GE(x:0, x1:0, x2:0, x3:0) -> f254_0_main_GE(x4:0, c, c1, x3:0) :|: c1 = x3:0 - 1 && c = x1:0 + 1 && (x3:0 - 1 >= x1:0 && x2:0 - 1 >= x1:0 && x3:0 > -1 && x:0 >= x4:0 && x4:0 > 0 && x:0 > 0)

The following rules are bounded:
f254_0_main_GE(x:0, x1:0, x2:0, x3:0) -> f254_0_main_GE(x4:0, c, c1, x3:0) :|: c1 = x3:0 - 1 && c = x1:0 + 1 && (x3:0 - 1 >= x1:0 && x2:0 - 1 >= x1:0 && x3:0 > -1 && x:0 >= x4:0 && x4:0 > 0 && x:0 > 0)


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

(11)
YES

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

(12)
Obligation:

Termination digraph:
Nodes:
(1) f494_0_main_GE(x16, x17, x18, x19) -> f510_0_main_GE(x20, x21, x22, x23) :|: x19 = x23 && x17 + 1 = x22 && x17 = x20 && 0 <= x21 - 1 && 0 <= x16 - 1 && x21 <= x16 && x17 <= x18 - 1 && -1 <= x17 - 1
(2) f510_0_main_GE(x24, x25, x26, x27) -> f494_0_main_GE(x28, x29, x30, x31) :|: x27 = x31 && x27 - 1 = x30 && x24 + 1 = x29 && 0 <= x28 - 1 && 0 <= x25 - 1 && x28 <= x25 && x27 <= x26 && -1 <= x27 - 1
(3) f510_0_main_GE(x52, x53, x54, x55) -> f510_0_main_GE(x56, x57, x58, x59) :|: x54 <= x55 - 1 && x52 <= x55 - 1 && x60 <= x61 && x57 <= x53 && 0 <= x53 - 1 && 0 <= x57 - 1 && x52 = x56 && x54 + 1 = x58 && x55 = x59
(4) f510_0_main_GE(x62, x63, x64, x65) -> f510_0_main_GE(x66, x67, x68, x69) :|: x64 <= x65 - 1 && x62 <= x65 - 1 && x70 <= x71 - 1 && x67 <= x63 && 0 <= x63 - 1 && 0 <= x67 - 1 && x62 = x66 && x64 + 1 = x68 && x65 = x69

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

This digraph is fully evaluated!

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

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

(14)
Obligation:
Rules:
f510_0_main_GE(x62:0, x63:0, x64:0, x65:0) -> f510_0_main_GE(x62:0, x67:0, x64:0 + 1, x65:0) :|: x63:0 > 0 && x67:0 > 0 && x67:0 <= x63:0 && x71:0 - 1 >= x70:0 && x65:0 - 1 >= x62:0 && x65:0 - 1 >= x64:0
f510_0_main_GE(x52:0, x53:0, x54:0, x55:0) -> f510_0_main_GE(x52:0, x57:0, x54:0 + 1, x55:0) :|: x53:0 > 0 && x57:0 > 0 && x57:0 <= x53:0 && x61:0 >= x60:0 && x55:0 - 1 >= x52:0 && x55:0 - 1 >= x54:0
f510_0_main_GE(x24:0, x25:0, x26:0, x23:0) -> f510_0_main_GE(x24:0 + 1, x21:0, x24:0 + 2, x23:0) :|: x24:0 > -2 && x23:0 > -1 && x26:0 >= x23:0 && x24:0 + 1 <= x23:0 - 2 && x28:0 <= x25:0 && x28:0 >= x21:0 && x25:0 > 0 && x21:0 > 0 && x28:0 > 0

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

(15) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f510_0_main_GE(INTEGER, INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(16)
Obligation:
Rules:
f510_0_main_GE(x62:0, x63:0, x64:0, x65:0) -> f510_0_main_GE(x62:0, x67:0, c, x65:0) :|: c = x64:0 + 1 && (x63:0 > 0 && x67:0 > 0 && x67:0 <= x63:0 && x71:0 - 1 >= x70:0 && x65:0 - 1 >= x62:0 && x65:0 - 1 >= x64:0)
f510_0_main_GE(x52:0, x53:0, x54:0, x55:0) -> f510_0_main_GE(x52:0, x57:0, c1, x55:0) :|: c1 = x54:0 + 1 && (x53:0 > 0 && x57:0 > 0 && x57:0 <= x53:0 && x61:0 >= x60:0 && x55:0 - 1 >= x52:0 && x55:0 - 1 >= x54:0)
f510_0_main_GE(x24:0, x25:0, x26:0, x23:0) -> f510_0_main_GE(c2, x21:0, c3, x23:0) :|: c3 = x24:0 + 2 && c2 = x24:0 + 1 && (x24:0 > -2 && x23:0 > -1 && x26:0 >= x23:0 && x24:0 + 1 <= x23:0 - 2 && x28:0 <= x25:0 && x28:0 >= x21:0 && x25:0 > 0 && x21:0 > 0 && x28:0 > 0)

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

(17) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f510_0_main_GE ] = f510_0_main_GE_4 + -1*f510_0_main_GE_1

The following rules are decreasing:
f510_0_main_GE(x24:0, x25:0, x26:0, x23:0) -> f510_0_main_GE(c2, x21:0, c3, x23:0) :|: c3 = x24:0 + 2 && c2 = x24:0 + 1 && (x24:0 > -2 && x23:0 > -1 && x26:0 >= x23:0 && x24:0 + 1 <= x23:0 - 2 && x28:0 <= x25:0 && x28:0 >= x21:0 && x25:0 > 0 && x21:0 > 0 && x28:0 > 0)

The following rules are bounded:
f510_0_main_GE(x62:0, x63:0, x64:0, x65:0) -> f510_0_main_GE(x62:0, x67:0, c, x65:0) :|: c = x64:0 + 1 && (x63:0 > 0 && x67:0 > 0 && x67:0 <= x63:0 && x71:0 - 1 >= x70:0 && x65:0 - 1 >= x62:0 && x65:0 - 1 >= x64:0)
f510_0_main_GE(x52:0, x53:0, x54:0, x55:0) -> f510_0_main_GE(x52:0, x57:0, c1, x55:0) :|: c1 = x54:0 + 1 && (x53:0 > 0 && x57:0 > 0 && x57:0 <= x53:0 && x61:0 >= x60:0 && x55:0 - 1 >= x52:0 && x55:0 - 1 >= x54:0)
f510_0_main_GE(x24:0, x25:0, x26:0, x23:0) -> f510_0_main_GE(c2, x21:0, c3, x23:0) :|: c3 = x24:0 + 2 && c2 = x24:0 + 1 && (x24:0 > -2 && x23:0 > -1 && x26:0 >= x23:0 && x24:0 + 1 <= x23:0 - 2 && x28:0 <= x25:0 && x28:0 >= x21:0 && x25:0 > 0 && x21:0 > 0 && x28:0 > 0)


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

(18)
Obligation:
Rules:
f510_0_main_GE(x62:0, x63:0, x64:0, x65:0) -> f510_0_main_GE(x62:0, x67:0, c, x65:0) :|: c = x64:0 + 1 && (x63:0 > 0 && x67:0 > 0 && x67:0 <= x63:0 && x71:0 - 1 >= x70:0 && x65:0 - 1 >= x62:0 && x65:0 - 1 >= x64:0)
f510_0_main_GE(x52:0, x53:0, x54:0, x55:0) -> f510_0_main_GE(x52:0, x57:0, c1, x55:0) :|: c1 = x54:0 + 1 && (x53:0 > 0 && x57:0 > 0 && x57:0 <= x53:0 && x61:0 >= x60:0 && x55:0 - 1 >= x52:0 && x55:0 - 1 >= x54:0)

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

(19) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f510_0_main_GE ] = f510_0_main_GE_4 + -1*f510_0_main_GE_3

The following rules are decreasing:
f510_0_main_GE(x62:0, x63:0, x64:0, x65:0) -> f510_0_main_GE(x62:0, x67:0, c, x65:0) :|: c = x64:0 + 1 && (x63:0 > 0 && x67:0 > 0 && x67:0 <= x63:0 && x71:0 - 1 >= x70:0 && x65:0 - 1 >= x62:0 && x65:0 - 1 >= x64:0)
f510_0_main_GE(x52:0, x53:0, x54:0, x55:0) -> f510_0_main_GE(x52:0, x57:0, c1, x55:0) :|: c1 = x54:0 + 1 && (x53:0 > 0 && x57:0 > 0 && x57:0 <= x53:0 && x61:0 >= x60:0 && x55:0 - 1 >= x52:0 && x55:0 - 1 >= x54:0)

The following rules are bounded:
f510_0_main_GE(x62:0, x63:0, x64:0, x65:0) -> f510_0_main_GE(x62:0, x67:0, c, x65:0) :|: c = x64:0 + 1 && (x63:0 > 0 && x67:0 > 0 && x67:0 <= x63:0 && x71:0 - 1 >= x70:0 && x65:0 - 1 >= x62:0 && x65:0 - 1 >= x64:0)
f510_0_main_GE(x52:0, x53:0, x54:0, x55:0) -> f510_0_main_GE(x52:0, x57:0, c1, x55:0) :|: c1 = x54:0 + 1 && (x53:0 > 0 && x57:0 > 0 && x57:0 <= x53:0 && x61:0 >= x60:0 && x55:0 - 1 >= x52:0 && x55:0 - 1 >= x54:0)


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

(20)
YES

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

(21)
Obligation:

Termination digraph:
Nodes:
(1) f609_0_main_GE(x42, x43, x44, x47) -> f609_0_main_GE(x48, x49, x50, x51) :|: x47 = x51 && x47 - 1 = x50 && x43 + 1 = x49 && 0 <= x48 - 1 && 0 <= x42 - 1 && x48 <= x42 && x43 <= x44 - 1 && -1 <= x47 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(23)
Obligation:
Rules:
f609_0_main_GE(x42:0, x43:0, x44:0, x47:0) -> f609_0_main_GE(x48:0, x43:0 + 1, x47:0 - 1, x47:0) :|: x44:0 - 1 >= x43:0 && x47:0 > -1 && x48:0 <= x42:0 && x48:0 > 0 && x42:0 > 0

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(24) IRSwTChainingProof (EQUIVALENT)
Chaining!
----------------------------------------

(25)
Obligation:
Rules:
f609_0_main_GE(x, x1, x2, x3) -> f609_0_main_GE(x9, x1 + 2, x3 + -1, x3) :|: TRUE && x2 + -1 * x1 >= 1 && x3 >= 0 && x4 + -1 * x <= 0 && x4 >= 1 && x >= 1 && x3 + -1 * x1 >= 3 && x9 + -1 * x4 <= 0 && x9 >= 1

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(26) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f609_0_main_GE(x, x1, x2, x3) -> f609_0_main_GE(x9, x1 + 2, x3 + -1, x3) :|: TRUE && x2 + -1 * x1 >= 1 && x3 >= 0 && x4 + -1 * x <= 0 && x4 >= 1 && x >= 1 && x3 + -1 * x1 >= 3 && x9 + -1 * x4 <= 0 && x9 >= 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!
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(27)
Obligation:

Termination digraph:
Nodes:
(1) f609_0_main_GE(x, x1, x2, x3) -> f609_0_main_GE(x9, x1 + 2, x3 + -1, x3) :|: TRUE && x2 + -1 * x1 >= 1 && x3 >= 0 && x4 + -1 * x <= 0 && x4 >= 1 && x >= 1 && x3 + -1 * x1 >= 3 && x9 + -1 * x4 <= 0 && x9 >= 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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(28) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(29)
Obligation:
Rules:
f609_0_main_GE(x:0, x1:0, x2:0, x3:0) -> f609_0_main_GE(x9:0, x1:0 + 2, x3:0 - 1, x3:0) :|: x9:0 + -1 * x4:0 <= 0 && x9:0 > 0 && x3:0 + -1 * x1:0 >= 3 && x:0 > 0 && x4:0 > 0 && x4:0 + -1 * x:0 <= 0 && x2:0 + -1 * x1:0 >= 1 && x3:0 > -1

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(30) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f609_0_main_GE(INTEGER, INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(31)
Obligation:
Rules:
f609_0_main_GE(x:0, x1:0, x2:0, x3:0) -> f609_0_main_GE(x9:0, c, c1, x3:0) :|: c1 = x3:0 - 1 && c = x1:0 + 2 && (x9:0 + -1 * x4:0 <= 0 && x9:0 > 0 && x3:0 + -1 * x1:0 >= 3 && x:0 > 0 && x4:0 > 0 && x4:0 + -1 * x:0 <= 0 && x2:0 + -1 * x1:0 >= 1 && x3:0 > -1)

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(32) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f609_0_main_GE(x, x1, x2, x3)] = -x1 + x3

The following rules are decreasing:
f609_0_main_GE(x:0, x1:0, x2:0, x3:0) -> f609_0_main_GE(x9:0, c, c1, x3:0) :|: c1 = x3:0 - 1 && c = x1:0 + 2 && (x9:0 + -1 * x4:0 <= 0 && x9:0 > 0 && x3:0 + -1 * x1:0 >= 3 && x:0 > 0 && x4:0 > 0 && x4:0 + -1 * x:0 <= 0 && x2:0 + -1 * x1:0 >= 1 && x3:0 > -1)
The following rules are bounded:
f609_0_main_GE(x:0, x1:0, x2:0, x3:0) -> f609_0_main_GE(x9:0, c, c1, x3:0) :|: c1 = x3:0 - 1 && c = x1:0 + 2 && (x9:0 + -1 * x4:0 <= 0 && x9:0 > 0 && x3:0 + -1 * x1:0 >= 3 && x:0 > 0 && x4:0 > 0 && x4:0 + -1 * x:0 <= 0 && x2:0 + -1 * x1:0 >= 1 && x3:0 > -1)

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(33)
YES