MAYBE
proof of prog.inttrs
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given IRSwT could not be shown:

(0) IRSwT
(1) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(2) IRSwT
(3) IRSwTTerminationDigraphProof [EQUIVALENT, 1050 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 58 ms]
(6) IRSwT
(7) IRSwTChainingProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) IRSwTTerminationDigraphProof [EQUIVALENT, 228 ms]
(10) IRSwT
(11) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(12) IRSwT
(13) IRSwTChainingProof [EQUIVALENT, 0 ms]
(14) IRSwT
(15) IRSwTTerminationDigraphProof [EQUIVALENT, 256 ms]
(16) IRSwT
(17) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(18) IRSwT
(19) TempFilterProof [SOUND, 15.7 s]
(20) IRSwT
(21) IRSwTTerminationDigraphProof [EQUIVALENT, 148 ms]
(22) IRSwT
(23) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(24) IRSwT


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

(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3, arg4) -> f257_0_loop_GT(arg1P, arg2P, arg3P, arg4P) :|: 0 = arg3P && 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg2P - 1 && 2 <= arg2 - 1 && -1 <= arg4P - 1
f257_0_loop_GT(x, x1, x2, x3) -> f257_0_loop_GT'(x4, x5, x6, x7) :|: x8 <= x1 && 0 <= x3 - 1 && 1 = x2 && x = x4 && x1 = x5 && 1 = x6 && x3 = x7
f257_0_loop_GT'(x9, x10, x11, x12) -> f257_0_loop_GT(x13, x14, x15, x16) :|: x12 = x16 && 0 = x15 && 2 * x9 = x14 && 1 = x11 && 0 <= x10 - 2 * x13 && x10 - 2 * x13 <= 1 && x13 <= x10 && 0 <= x12 - 1
f257_0_loop_GT(x17, x18, x19, x21) -> f257_0_loop_GT'(x22, x23, x24, x25) :|: 0 <= x21 - 1 && x26 <= x17 && 0 = x19 && x17 = x22 && x18 = x23 && 0 = x24 && x21 = x25
f257_0_loop_GT'(x27, x28, x29, x30) -> f257_0_loop_GT(x32, x33, x34, x35) :|: 1 = x34 && x28 = x33 && 2 * x30 = x32 && 0 = x29 && 0 <= x27 - 2 * x35 && x27 - 2 * x35 <= 1 && 0 <= x30 - 1 && x35 <= x27
f257_0_loop_GT(x36, x37, x38, x39) -> f257_0_loop_GT'(x40, x42, x43, x44) :|: x45 <= x37 && 0 <= x36 - 1 && 1 = x38 && 0 = x39 && x36 = x40 && x37 = x42 && 1 = x43 && 0 = x44
f257_0_loop_GT'(x46, x47, x48, x49) -> f257_0_loop_GT(x50, x52, x53, x54) :|: 0 = x54 && 0 = x53 && 2 * x46 = x52 && 0 = x49 && 1 = x48 && 0 <= x47 - 2 * x50 && x47 - 2 * x50 <= 1 && x50 <= x47 && 0 <= x46 - 1
f257_0_loop_GT(x55, x56, x57, x58) -> f257_0_loop_GT'(x59, x60, x62, x63) :|: 0 <= x55 - 1 && x64 <= x55 - 1 && 0 = x57 && 0 = x58 && x55 = x59 && x56 = x60 && 0 = x62 && 0 = x63
f257_0_loop_GT'(x65, x66, x67, x68) -> f257_0_loop_GT(x69, x70, x71, x72) :|: 1 = x71 && x66 = x70 && 0 = x69 && 0 = x68 && 0 = x67 && 0 <= x65 - 2 * x72 && x65 - 2 * x72 <= 1 && 0 <= x65 - 1 && x72 <= x65 - 1
f257_0_loop_GT(x73, x74, x75, x76) -> f257_0_loop_GT'(x77, x78, x79, x80) :|: 0 <= x74 - 1 && x81 <= x74 - 1 && 0 = x73 && 1 = x75 && 0 = x76 && 0 = x77 && x74 = x78 && 1 = x79 && 0 = x80
f257_0_loop_GT'(x82, x83, x84, x85) -> f257_0_loop_GT(x86, x87, x88, x89) :|: 0 = x89 && 0 = x88 && 0 = x87 && 0 = x85 && 1 = x84 && 0 = x82 && 0 <= x83 - 2 * x86 && x83 - 2 * x86 <= 1 && 0 <= x83 - 1 && x86 <= x83 - 1
f257_0_loop_GT(x90, x91, x92, x93) -> f257_0_loop_GT(x94, x95, x96, x97) :|: 0 = x97 && 1 = x96 && x91 = x95 && 0 = x94 && 0 = x93 && 0 = x92 && 0 = x90 && 0 <= x91 - 1
__init(x98, x99, x100, x101) -> f1_0_main_Load(x102, x103, x104, x105) :|: 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) -> f257_0_loop_GT(arg1P, arg2P, arg3P, arg4P) :|: 0 = arg3P && 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg2P - 1 && 2 <= arg2 - 1 && -1 <= arg4P - 1
f257_0_loop_GT(x, x1, x2, x3) -> f257_0_loop_GT'(x4, x5, x6, x7) :|: x8 <= x1 && 0 <= x3 - 1 && 1 = x2 && x = x4 && x1 = x5 && 1 = x6 && x3 = x7
f257_0_loop_GT'(x9, x10, x11, x12) -> f257_0_loop_GT(x13, x14, x15, x16) :|: x12 = x16 && 0 = x15 && 2 * x9 = x14 && 1 = x11 && 0 <= x10 - 2 * x13 && x10 - 2 * x13 <= 1 && x13 <= x10 && 0 <= x12 - 1
f257_0_loop_GT(x17, x18, x19, x21) -> f257_0_loop_GT'(x22, x23, x24, x25) :|: 0 <= x21 - 1 && x26 <= x17 && 0 = x19 && x17 = x22 && x18 = x23 && 0 = x24 && x21 = x25
f257_0_loop_GT'(x27, x28, x29, x30) -> f257_0_loop_GT(x32, x33, x34, x35) :|: 1 = x34 && x28 = x33 && 2 * x30 = x32 && 0 = x29 && 0 <= x27 - 2 * x35 && x27 - 2 * x35 <= 1 && 0 <= x30 - 1 && x35 <= x27
f257_0_loop_GT(x36, x37, x38, x39) -> f257_0_loop_GT'(x40, x42, x43, x44) :|: x45 <= x37 && 0 <= x36 - 1 && 1 = x38 && 0 = x39 && x36 = x40 && x37 = x42 && 1 = x43 && 0 = x44
f257_0_loop_GT'(x46, x47, x48, x49) -> f257_0_loop_GT(x50, x52, x53, x54) :|: 0 = x54 && 0 = x53 && 2 * x46 = x52 && 0 = x49 && 1 = x48 && 0 <= x47 - 2 * x50 && x47 - 2 * x50 <= 1 && x50 <= x47 && 0 <= x46 - 1
f257_0_loop_GT(x55, x56, x57, x58) -> f257_0_loop_GT'(x59, x60, x62, x63) :|: 0 <= x55 - 1 && x64 <= x55 - 1 && 0 = x57 && 0 = x58 && x55 = x59 && x56 = x60 && 0 = x62 && 0 = x63
f257_0_loop_GT'(x65, x66, x67, x68) -> f257_0_loop_GT(x69, x70, x71, x72) :|: 1 = x71 && x66 = x70 && 0 = x69 && 0 = x68 && 0 = x67 && 0 <= x65 - 2 * x72 && x65 - 2 * x72 <= 1 && 0 <= x65 - 1 && x72 <= x65 - 1
f257_0_loop_GT(x73, x74, x75, x76) -> f257_0_loop_GT'(x77, x78, x79, x80) :|: 0 <= x74 - 1 && x81 <= x74 - 1 && 0 = x73 && 1 = x75 && 0 = x76 && 0 = x77 && x74 = x78 && 1 = x79 && 0 = x80
f257_0_loop_GT'(x82, x83, x84, x85) -> f257_0_loop_GT(x86, x87, x88, x89) :|: 0 = x89 && 0 = x88 && 0 = x87 && 0 = x85 && 1 = x84 && 0 = x82 && 0 <= x83 - 2 * x86 && x83 - 2 * x86 <= 1 && 0 <= x83 - 1 && x86 <= x83 - 1
f257_0_loop_GT(x90, x91, x92, x93) -> f257_0_loop_GT(x94, x95, x96, x97) :|: 0 = x97 && 1 = x96 && x91 = x95 && 0 = x94 && 0 = x93 && 0 = x92 && 0 = x90 && 0 <= x91 - 1
__init(x98, x99, x100, x101) -> f1_0_main_Load(x102, x103, x104, x105) :|: 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) -> f257_0_loop_GT(arg1P, arg2P, arg3P, arg4P) :|: 0 = arg3P && 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg2P - 1 && 2 <= arg2 - 1 && -1 <= arg4P - 1
(2) f257_0_loop_GT(x, x1, x2, x3) -> f257_0_loop_GT'(x4, x5, x6, x7) :|: x8 <= x1 && 0 <= x3 - 1 && 1 = x2 && x = x4 && x1 = x5 && 1 = x6 && x3 = x7
(3) f257_0_loop_GT'(x9, x10, x11, x12) -> f257_0_loop_GT(x13, x14, x15, x16) :|: x12 = x16 && 0 = x15 && 2 * x9 = x14 && 1 = x11 && 0 <= x10 - 2 * x13 && x10 - 2 * x13 <= 1 && x13 <= x10 && 0 <= x12 - 1
(4) f257_0_loop_GT(x17, x18, x19, x21) -> f257_0_loop_GT'(x22, x23, x24, x25) :|: 0 <= x21 - 1 && x26 <= x17 && 0 = x19 && x17 = x22 && x18 = x23 && 0 = x24 && x21 = x25
(5) f257_0_loop_GT'(x27, x28, x29, x30) -> f257_0_loop_GT(x32, x33, x34, x35) :|: 1 = x34 && x28 = x33 && 2 * x30 = x32 && 0 = x29 && 0 <= x27 - 2 * x35 && x27 - 2 * x35 <= 1 && 0 <= x30 - 1 && x35 <= x27
(6) f257_0_loop_GT(x36, x37, x38, x39) -> f257_0_loop_GT'(x40, x42, x43, x44) :|: x45 <= x37 && 0 <= x36 - 1 && 1 = x38 && 0 = x39 && x36 = x40 && x37 = x42 && 1 = x43 && 0 = x44
(7) f257_0_loop_GT'(x46, x47, x48, x49) -> f257_0_loop_GT(x50, x52, x53, x54) :|: 0 = x54 && 0 = x53 && 2 * x46 = x52 && 0 = x49 && 1 = x48 && 0 <= x47 - 2 * x50 && x47 - 2 * x50 <= 1 && x50 <= x47 && 0 <= x46 - 1
(8) f257_0_loop_GT(x55, x56, x57, x58) -> f257_0_loop_GT'(x59, x60, x62, x63) :|: 0 <= x55 - 1 && x64 <= x55 - 1 && 0 = x57 && 0 = x58 && x55 = x59 && x56 = x60 && 0 = x62 && 0 = x63
(9) f257_0_loop_GT'(x65, x66, x67, x68) -> f257_0_loop_GT(x69, x70, x71, x72) :|: 1 = x71 && x66 = x70 && 0 = x69 && 0 = x68 && 0 = x67 && 0 <= x65 - 2 * x72 && x65 - 2 * x72 <= 1 && 0 <= x65 - 1 && x72 <= x65 - 1
(10) f257_0_loop_GT(x73, x74, x75, x76) -> f257_0_loop_GT'(x77, x78, x79, x80) :|: 0 <= x74 - 1 && x81 <= x74 - 1 && 0 = x73 && 1 = x75 && 0 = x76 && 0 = x77 && x74 = x78 && 1 = x79 && 0 = x80
(11) f257_0_loop_GT'(x82, x83, x84, x85) -> f257_0_loop_GT(x86, x87, x88, x89) :|: 0 = x89 && 0 = x88 && 0 = x87 && 0 = x85 && 1 = x84 && 0 = x82 && 0 <= x83 - 2 * x86 && x83 - 2 * x86 <= 1 && 0 <= x83 - 1 && x86 <= x83 - 1
(12) f257_0_loop_GT(x90, x91, x92, x93) -> f257_0_loop_GT(x94, x95, x96, x97) :|: 0 = x97 && 1 = x96 && x91 = x95 && 0 = x94 && 0 = x93 && 0 = x92 && 0 = x90 && 0 <= x91 - 1
(13) __init(x98, x99, x100, x101) -> f1_0_main_Load(x102, x103, x104, x105) :|: 0 <= 0

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

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

(4)
Obligation:

Termination digraph:
Nodes:
(1) f257_0_loop_GT(x17, x18, x19, x21) -> f257_0_loop_GT'(x22, x23, x24, x25) :|: 0 <= x21 - 1 && x26 <= x17 && 0 = x19 && x17 = x22 && x18 = x23 && 0 = x24 && x21 = x25
(2) f257_0_loop_GT'(x9, x10, x11, x12) -> f257_0_loop_GT(x13, x14, x15, x16) :|: x12 = x16 && 0 = x15 && 2 * x9 = x14 && 1 = x11 && 0 <= x10 - 2 * x13 && x10 - 2 * x13 <= 1 && x13 <= x10 && 0 <= x12 - 1
(3) f257_0_loop_GT(x, x1, x2, x3) -> f257_0_loop_GT'(x4, x5, x6, x7) :|: x8 <= x1 && 0 <= x3 - 1 && 1 = x2 && x = x4 && x1 = x5 && 1 = x6 && x3 = x7
(4) f257_0_loop_GT'(x65, x66, x67, x68) -> f257_0_loop_GT(x69, x70, x71, x72) :|: 1 = x71 && x66 = x70 && 0 = x69 && 0 = x68 && 0 = x67 && 0 <= x65 - 2 * x72 && x65 - 2 * x72 <= 1 && 0 <= x65 - 1 && x72 <= x65 - 1
(5) f257_0_loop_GT(x55, x56, x57, x58) -> f257_0_loop_GT'(x59, x60, x62, x63) :|: 0 <= x55 - 1 && x64 <= x55 - 1 && 0 = x57 && 0 = x58 && x55 = x59 && x56 = x60 && 0 = x62 && 0 = x63
(6) f257_0_loop_GT'(x82, x83, x84, x85) -> f257_0_loop_GT(x86, x87, x88, x89) :|: 0 = x89 && 0 = x88 && 0 = x87 && 0 = x85 && 1 = x84 && 0 = x82 && 0 <= x83 - 2 * x86 && x83 - 2 * x86 <= 1 && 0 <= x83 - 1 && x86 <= x83 - 1
(7) f257_0_loop_GT(x73, x74, x75, x76) -> f257_0_loop_GT'(x77, x78, x79, x80) :|: 0 <= x74 - 1 && x81 <= x74 - 1 && 0 = x73 && 1 = x75 && 0 = x76 && 0 = x77 && x74 = x78 && 1 = x79 && 0 = x80
(8) f257_0_loop_GT(x90, x91, x92, x93) -> f257_0_loop_GT(x94, x95, x96, x97) :|: 0 = x97 && 1 = x96 && x91 = x95 && 0 = x94 && 0 = x93 && 0 = x92 && 0 = x90 && 0 <= x91 - 1
(9) f257_0_loop_GT'(x46, x47, x48, x49) -> f257_0_loop_GT(x50, x52, x53, x54) :|: 0 = x54 && 0 = x53 && 2 * x46 = x52 && 0 = x49 && 1 = x48 && 0 <= x47 - 2 * x50 && x47 - 2 * x50 <= 1 && x50 <= x47 && 0 <= x46 - 1
(10) f257_0_loop_GT(x36, x37, x38, x39) -> f257_0_loop_GT'(x40, x42, x43, x44) :|: x45 <= x37 && 0 <= x36 - 1 && 1 = x38 && 0 = x39 && x36 = x40 && x37 = x42 && 1 = x43 && 0 = x44
(11) f257_0_loop_GT'(x27, x28, x29, x30) -> f257_0_loop_GT(x32, x33, x34, x35) :|: 1 = x34 && x28 = x33 && 2 * x30 = x32 && 0 = x29 && 0 <= x27 - 2 * x35 && x27 - 2 * x35 <= 1 && 0 <= x30 - 1 && x35 <= x27

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

This digraph is fully evaluated!

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

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

(6)
Obligation:
Rules:
f257_0_loop_GT(x36:0, x37:0, cons_1, cons_0) -> f257_0_loop_GT'(x36:0, x37:0, 1, 0) :|: x45:0 <= x37:0 && x36:0 > 0 && cons_1 = 1 && cons_0 = 0
f257_0_loop_GT'(x, x1, x2, x3) -> f257_0_loop_GT(x4, 2 * x, 0, x3) :|: x4 <= x1 && x3 > 0 && x1 - 2 * x4 >= 0 && x1 - 2 * x4 <= 1 && x2 = 1
f257_0_loop_GT(x5, x6, x7, x8) -> f257_0_loop_GT(0, x6, 1, 0) :|: x6 > 0 && x5 = 0 && x7 = 0 && x8 = 0
f257_0_loop_GT(x9, x10, x11, x12) -> f257_0_loop_GT'(x9, x10, 0, x12) :|: x12 > 0 && x13 <= x9 && x11 = 0
f257_0_loop_GT(x14, x15, x16, x17) -> f257_0_loop_GT'(x14, x15, 0, 0) :|: x14 > 0 && x18 <= x14 - 1 && x16 = 0 && x17 = 0
f257_0_loop_GT'(x19, x20, x21, x22) -> f257_0_loop_GT(x23, 0, 0, 0) :|: x20 > 0 && x23 <= x20 - 1 && x20 - 2 * x23 >= 0 && x20 - 2 * x23 <= 1 && x19 = 0 && x21 = 1 && x22 = 0
f257_0_loop_GT'(x24, x25, x26, x27) -> f257_0_loop_GT(x28, 2 * x24, 0, 0) :|: x28 <= x25 && x24 > 0 && x25 - 2 * x28 >= 0 && x25 - 2 * x28 <= 1 && x26 = 1 && x27 = 0
f257_0_loop_GT(x29, x30, x31, x32) -> f257_0_loop_GT'(x29, x30, 1, x32) :|: x33 <= x30 && x32 > 0 && x31 = 1
f257_0_loop_GT(x34, x35, x36, x37) -> f257_0_loop_GT'(0, x35, 1, 0) :|: x35 > 0 && x38 <= x35 - 1 && x34 = 0 && x36 = 1 && x37 = 0
f257_0_loop_GT'(x39, x40, x41, x42) -> f257_0_loop_GT(0, x40, 1, x43) :|: x39 > 0 && x43 <= x39 - 1 && x39 - 2 * x43 >= 0 && x39 - 2 * x43 <= 1 && x41 = 0 && x42 = 0
f257_0_loop_GT'(x44, x45, x46, x47) -> f257_0_loop_GT(2 * x47, x45, 1, x48) :|: x47 > 0 && x48 <= x44 && x44 - 2 * x48 >= 0 && x44 - 2 * x48 <= 1 && x46 = 0

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

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

(8)
Obligation:
Rules:
f257_0_loop_GT'(x, x1, x2, x3) -> f257_0_loop_GT(x4, 2 * x, 0, x3) :|: x4 <= x1 && x3 > 0 && x1 - 2 * x4 >= 0 && x1 - 2 * x4 <= 1 && x2 = 1
f257_0_loop_GT(x5, x6, x7, x8) -> f257_0_loop_GT(0, x6, 1, 0) :|: x6 > 0 && x5 = 0 && x7 = 0 && x8 = 0
f257_0_loop_GT(x9, x10, x11, x12) -> f257_0_loop_GT'(x9, x10, 0, x12) :|: x12 > 0 && x13 <= x9 && x11 = 0
f257_0_loop_GT(x14, x15, x16, x17) -> f257_0_loop_GT'(x14, x15, 0, 0) :|: x14 > 0 && x18 <= x14 - 1 && x16 = 0 && x17 = 0
f257_0_loop_GT'(x19, x20, x21, x22) -> f257_0_loop_GT(x23, 0, 0, 0) :|: x20 > 0 && x23 <= x20 - 1 && x20 - 2 * x23 >= 0 && x20 - 2 * x23 <= 1 && x19 = 0 && x21 = 1 && x22 = 0
f257_0_loop_GT'(x24, x25, x26, x27) -> f257_0_loop_GT(x28, 2 * x24, 0, 0) :|: x28 <= x25 && x24 > 0 && x25 - 2 * x28 >= 0 && x25 - 2 * x28 <= 1 && x26 = 1 && x27 = 0
f257_0_loop_GT(x108, x109, x110, x111) -> f257_0_loop_GT(x117, 2 * x108, 0, 0) :|: TRUE && x112 + -1 * x109 <= 0 && x108 >= 1 && x110 = 1 && x117 + -1 * x109 <= 0 && x109 + -2 * x117 >= 0 && x109 + -2 * x117 <= 1 && x111 = 0
f257_0_loop_GT(x29, x30, x31, x32) -> f257_0_loop_GT'(x29, x30, 1, x32) :|: x33 <= x30 && x32 > 0 && x31 = 1
f257_0_loop_GT(x34, x35, x36, x37) -> f257_0_loop_GT'(0, x35, 1, 0) :|: x35 > 0 && x38 <= x35 - 1 && x34 = 0 && x36 = 1 && x37 = 0
f257_0_loop_GT'(x39, x40, x41, x42) -> f257_0_loop_GT(0, x40, 1, x43) :|: x39 > 0 && x43 <= x39 - 1 && x39 - 2 * x43 >= 0 && x39 - 2 * x43 <= 1 && x41 = 0 && x42 = 0
f257_0_loop_GT'(x44, x45, x46, x47) -> f257_0_loop_GT(2 * x47, x45, 1, x48) :|: x47 > 0 && x48 <= x44 && x44 - 2 * x48 >= 0 && x44 - 2 * x48 <= 1 && x46 = 0

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

(9) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f257_0_loop_GT'(x, x1, x2, x3) -> f257_0_loop_GT(x4, 2 * x, 0, x3) :|: x4 <= x1 && x3 > 0 && x1 - 2 * x4 >= 0 && x1 - 2 * x4 <= 1 && x2 = 1
(2) f257_0_loop_GT(x5, x6, x7, x8) -> f257_0_loop_GT(0, x6, 1, 0) :|: x6 > 0 && x5 = 0 && x7 = 0 && x8 = 0
(3) f257_0_loop_GT(x9, x10, x11, x12) -> f257_0_loop_GT'(x9, x10, 0, x12) :|: x12 > 0 && x13 <= x9 && x11 = 0
(4) f257_0_loop_GT(x14, x15, x16, x17) -> f257_0_loop_GT'(x14, x15, 0, 0) :|: x14 > 0 && x18 <= x14 - 1 && x16 = 0 && x17 = 0
(5) f257_0_loop_GT'(x19, x20, x21, x22) -> f257_0_loop_GT(x23, 0, 0, 0) :|: x20 > 0 && x23 <= x20 - 1 && x20 - 2 * x23 >= 0 && x20 - 2 * x23 <= 1 && x19 = 0 && x21 = 1 && x22 = 0
(6) f257_0_loop_GT'(x24, x25, x26, x27) -> f257_0_loop_GT(x28, 2 * x24, 0, 0) :|: x28 <= x25 && x24 > 0 && x25 - 2 * x28 >= 0 && x25 - 2 * x28 <= 1 && x26 = 1 && x27 = 0
(7) f257_0_loop_GT(x108, x109, x110, x111) -> f257_0_loop_GT(x117, 2 * x108, 0, 0) :|: TRUE && x112 + -1 * x109 <= 0 && x108 >= 1 && x110 = 1 && x117 + -1 * x109 <= 0 && x109 + -2 * x117 >= 0 && x109 + -2 * x117 <= 1 && x111 = 0
(8) f257_0_loop_GT(x29, x30, x31, x32) -> f257_0_loop_GT'(x29, x30, 1, x32) :|: x33 <= x30 && x32 > 0 && x31 = 1
(9) f257_0_loop_GT(x34, x35, x36, x37) -> f257_0_loop_GT'(0, x35, 1, 0) :|: x35 > 0 && x38 <= x35 - 1 && x34 = 0 && x36 = 1 && x37 = 0
(10) f257_0_loop_GT'(x39, x40, x41, x42) -> f257_0_loop_GT(0, x40, 1, x43) :|: x39 > 0 && x43 <= x39 - 1 && x39 - 2 * x43 >= 0 && x39 - 2 * x43 <= 1 && x41 = 0 && x42 = 0
(11) f257_0_loop_GT'(x44, x45, x46, x47) -> f257_0_loop_GT(2 * x47, x45, 1, x48) :|: x47 > 0 && x48 <= x44 && x44 - 2 * x48 >= 0 && x44 - 2 * x48 <= 1 && x46 = 0

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

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

(10)
Obligation:

Termination digraph:
Nodes:
(1) f257_0_loop_GT'(x, x1, x2, x3) -> f257_0_loop_GT(x4, 2 * x, 0, x3) :|: x4 <= x1 && x3 > 0 && x1 - 2 * x4 >= 0 && x1 - 2 * x4 <= 1 && x2 = 1
(2) f257_0_loop_GT(x29, x30, x31, x32) -> f257_0_loop_GT'(x29, x30, 1, x32) :|: x33 <= x30 && x32 > 0 && x31 = 1
(3) f257_0_loop_GT'(x39, x40, x41, x42) -> f257_0_loop_GT(0, x40, 1, x43) :|: x39 > 0 && x43 <= x39 - 1 && x39 - 2 * x43 >= 0 && x39 - 2 * x43 <= 1 && x41 = 0 && x42 = 0
(4) f257_0_loop_GT(x14, x15, x16, x17) -> f257_0_loop_GT'(x14, x15, 0, 0) :|: x14 > 0 && x18 <= x14 - 1 && x16 = 0 && x17 = 0
(5) f257_0_loop_GT'(x19, x20, x21, x22) -> f257_0_loop_GT(x23, 0, 0, 0) :|: x20 > 0 && x23 <= x20 - 1 && x20 - 2 * x23 >= 0 && x20 - 2 * x23 <= 1 && x19 = 0 && x21 = 1 && x22 = 0
(6) f257_0_loop_GT(x34, x35, x36, x37) -> f257_0_loop_GT'(0, x35, 1, 0) :|: x35 > 0 && x38 <= x35 - 1 && x34 = 0 && x36 = 1 && x37 = 0
(7) f257_0_loop_GT(x5, x6, x7, x8) -> f257_0_loop_GT(0, x6, 1, 0) :|: x6 > 0 && x5 = 0 && x7 = 0 && x8 = 0
(8) f257_0_loop_GT(x108, x109, x110, x111) -> f257_0_loop_GT(x117, 2 * x108, 0, 0) :|: TRUE && x112 + -1 * x109 <= 0 && x108 >= 1 && x110 = 1 && x117 + -1 * x109 <= 0 && x109 + -2 * x117 >= 0 && x109 + -2 * x117 <= 1 && x111 = 0
(9) f257_0_loop_GT'(x44, x45, x46, x47) -> f257_0_loop_GT(2 * x47, x45, 1, x48) :|: x47 > 0 && x48 <= x44 && x44 - 2 * x48 >= 0 && x44 - 2 * x48 <= 1 && x46 = 0
(10) f257_0_loop_GT(x9, x10, x11, x12) -> f257_0_loop_GT'(x9, x10, 0, x12) :|: x12 > 0 && x13 <= x9 && x11 = 0

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

This digraph is fully evaluated!

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

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

(12)
Obligation:
Rules:
f257_0_loop_GT'(x39:0, x40:0, cons_0, cons_01) -> f257_0_loop_GT(0, x40:0, 1, x43:0) :|: x39:0 - 2 * x43:0 >= 0 && x39:0 - 2 * x43:0 <= 1 && x43:0 <= x39:0 - 1 && x39:0 > 0 && cons_0 = 0 && cons_01 = 0
f257_0_loop_GT(x, x1, x2, x3) -> f257_0_loop_GT'(0, x1, 1, 0) :|: x1 > 0 && x4 <= x1 - 1 && x = 0 && x2 = 1 && x3 = 0
f257_0_loop_GT(x5, x6, x7, x8) -> f257_0_loop_GT(0, x6, 1, 0) :|: x6 > 0 && x5 = 0 && x7 = 0 && x8 = 0
f257_0_loop_GT'(x9, x10, x11, x12) -> f257_0_loop_GT(2 * x12, x10, 1, x13) :|: x9 - 2 * x13 >= 0 && x9 - 2 * x13 <= 1 && x13 <= x9 && x12 > 0 && x11 = 0
f257_0_loop_GT(x29:0, x30:0, cons_1, x32:0) -> f257_0_loop_GT'(x29:0, x30:0, 1, x32:0) :|: x33:0 <= x30:0 && x32:0 > 0 && cons_1 = 1
f257_0_loop_GT(x14, x15, x16, x17) -> f257_0_loop_GT'(x14, x15, 0, 0) :|: x14 > 0 && x18 <= x14 - 1 && x16 = 0 && x17 = 0
f257_0_loop_GT(x19, x20, x21, x22) -> f257_0_loop_GT'(x19, x20, 0, x22) :|: x22 > 0 && x19 >= x23 && x21 = 0
f257_0_loop_GT'(x24, x25, x26, x27) -> f257_0_loop_GT(x28, 2 * x24, 0, x27) :|: x25 - 2 * x28 >= 0 && x25 - 2 * x28 <= 1 && x27 > 0 && x28 <= x25 && x26 = 1
f257_0_loop_GT'(x29, x30, x31, x32) -> f257_0_loop_GT(x33, 0, 0, 0) :|: x30 - 2 * x33 >= 0 && x30 - 2 * x33 <= 1 && x33 <= x30 - 1 && x30 > 0 && x29 = 0 && x31 = 1 && x32 = 0
f257_0_loop_GT(x34, x35, x36, x37) -> f257_0_loop_GT(x38, 2 * x34, 0, 0) :|: x35 + -2 * x38 >= 0 && x35 + -2 * x38 <= 1 && x38 + -1 * x35 <= 0 && x39 + -1 * x35 <= 0 && x34 > 0 && x36 = 1 && x37 = 0

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

(13) IRSwTChainingProof (EQUIVALENT)
Chaining!
----------------------------------------

(14)
Obligation:
Rules:
f257_0_loop_GT(x, x1, x2, x3) -> f257_0_loop_GT'(0, x1, 1, 0) :|: x1 > 0 && x4 <= x1 - 1 && x = 0 && x2 = 1 && x3 = 0
f257_0_loop_GT'(x50, x51, x52, x53) -> f257_0_loop_GT'(0, x51, 1, 0) :|: TRUE && x50 + -2 * 0 >= 0 && x50 + -2 * 0 <= 1 && 0 + -1 * x50 <= -1 && x50 >= 1 && x51 >= 1 && x59 + -1 * x51 <= -1 && (x52 = 0 && x53 = 0 && x54 = 0)
f257_0_loop_GT(x5, x6, x7, x8) -> f257_0_loop_GT(0, x6, 1, 0) :|: x6 > 0 && x5 = 0 && x7 = 0 && x8 = 0
f257_0_loop_GT'(x9, x10, x11, x12) -> f257_0_loop_GT(2 * x12, x10, 1, x13) :|: x9 - 2 * x13 >= 0 && x9 - 2 * x13 <= 1 && x13 <= x9 && x12 > 0 && x11 = 0
f257_0_loop_GT(x29:0, x30:0, cons_1, x32:0) -> f257_0_loop_GT'(x29:0, x30:0, 1, x32:0) :|: x33:0 <= x30:0 && x32:0 > 0 && cons_1 = 1
f257_0_loop_GT'(x79, x80, x81, x82) -> f257_0_loop_GT'(0, x80, 1, x83) :|: TRUE && x79 + -2 * x83 >= 0 && x79 + -2 * x83 <= 1 && x83 + -1 * x79 <= -1 && x79 >= 1 && x88 + -1 * x80 <= 0 && x83 >= 1 && (x81 = 0 && x82 = 0)
f257_0_loop_GT(x14, x15, x16, x17) -> f257_0_loop_GT'(x14, x15, 0, 0) :|: x14 > 0 && x18 <= x14 - 1 && x16 = 0 && x17 = 0
f257_0_loop_GT(x19, x20, x21, x22) -> f257_0_loop_GT'(x19, x20, 0, x22) :|: x22 > 0 && x19 >= x23 && x21 = 0
f257_0_loop_GT'(x99, x100, x101, x102) -> f257_0_loop_GT'(0, x100, 0, x103) :|: TRUE && x99 + -2 * x103 >= 0 && x99 + -2 * x103 <= 1 && x103 + -1 * x99 <= -1 && x99 >= 1 && x103 >= 1 && -1 * x108 >= 0 && 0 = -1 && (x101 = 0 && x102 = 0)
f257_0_loop_GT'(x24, x25, x26, x27) -> f257_0_loop_GT(x28, 2 * x24, 0, x27) :|: x25 - 2 * x28 >= 0 && x25 - 2 * x28 <= 1 && x27 > 0 && x28 <= x25 && x26 = 1
f257_0_loop_GT'(x29, x30, x31, x32) -> f257_0_loop_GT(x33, 0, 0, 0) :|: x30 - 2 * x33 >= 0 && x30 - 2 * x33 <= 1 && x33 <= x30 - 1 && x30 > 0 && x29 = 0 && x31 = 1 && x32 = 0
f257_0_loop_GT(x34, x35, x36, x37) -> f257_0_loop_GT(x38, 2 * x34, 0, 0) :|: x35 + -2 * x38 >= 0 && x35 + -2 * x38 <= 1 && x38 + -1 * x35 <= 0 && x39 + -1 * x35 <= 0 && x34 > 0 && x36 = 1 && x37 = 0

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

(15) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f257_0_loop_GT(x, x1, x2, x3) -> f257_0_loop_GT'(0, x1, 1, 0) :|: x1 > 0 && x4 <= x1 - 1 && x = 0 && x2 = 1 && x3 = 0
(2) f257_0_loop_GT'(x50, x51, x52, x53) -> f257_0_loop_GT'(0, x51, 1, 0) :|: TRUE && x50 + -2 * 0 >= 0 && x50 + -2 * 0 <= 1 && 0 + -1 * x50 <= -1 && x50 >= 1 && x51 >= 1 && x59 + -1 * x51 <= -1 && (x52 = 0 && x53 = 0 && x54 = 0)
(3) f257_0_loop_GT(x5, x6, x7, x8) -> f257_0_loop_GT(0, x6, 1, 0) :|: x6 > 0 && x5 = 0 && x7 = 0 && x8 = 0
(4) f257_0_loop_GT'(x9, x10, x11, x12) -> f257_0_loop_GT(2 * x12, x10, 1, x13) :|: x9 - 2 * x13 >= 0 && x9 - 2 * x13 <= 1 && x13 <= x9 && x12 > 0 && x11 = 0
(5) f257_0_loop_GT(x29:0, x30:0, cons_1, x32:0) -> f257_0_loop_GT'(x29:0, x30:0, 1, x32:0) :|: x33:0 <= x30:0 && x32:0 > 0 && cons_1 = 1
(6) f257_0_loop_GT'(x79, x80, x81, x82) -> f257_0_loop_GT'(0, x80, 1, x83) :|: TRUE && x79 + -2 * x83 >= 0 && x79 + -2 * x83 <= 1 && x83 + -1 * x79 <= -1 && x79 >= 1 && x88 + -1 * x80 <= 0 && x83 >= 1 && (x81 = 0 && x82 = 0)
(7) f257_0_loop_GT(x14, x15, x16, x17) -> f257_0_loop_GT'(x14, x15, 0, 0) :|: x14 > 0 && x18 <= x14 - 1 && x16 = 0 && x17 = 0
(8) f257_0_loop_GT(x19, x20, x21, x22) -> f257_0_loop_GT'(x19, x20, 0, x22) :|: x22 > 0 && x19 >= x23 && x21 = 0
(9) f257_0_loop_GT'(x99, x100, x101, x102) -> f257_0_loop_GT'(0, x100, 0, x103) :|: TRUE && x99 + -2 * x103 >= 0 && x99 + -2 * x103 <= 1 && x103 + -1 * x99 <= -1 && x99 >= 1 && x103 >= 1 && -1 * x108 >= 0 && 0 = -1 && (x101 = 0 && x102 = 0)
(10) f257_0_loop_GT'(x24, x25, x26, x27) -> f257_0_loop_GT(x28, 2 * x24, 0, x27) :|: x25 - 2 * x28 >= 0 && x25 - 2 * x28 <= 1 && x27 > 0 && x28 <= x25 && x26 = 1
(11) f257_0_loop_GT'(x29, x30, x31, x32) -> f257_0_loop_GT(x33, 0, 0, 0) :|: x30 - 2 * x33 >= 0 && x30 - 2 * x33 <= 1 && x33 <= x30 - 1 && x30 > 0 && x29 = 0 && x31 = 1 && x32 = 0
(12) f257_0_loop_GT(x34, x35, x36, x37) -> f257_0_loop_GT(x38, 2 * x34, 0, 0) :|: x35 + -2 * x38 >= 0 && x35 + -2 * x38 <= 1 && x38 + -1 * x35 <= 0 && x39 + -1 * x35 <= 0 && x34 > 0 && x36 = 1 && x37 = 0

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

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

(16)
Obligation:

Termination digraph:
Nodes:
(1) f257_0_loop_GT(x, x1, x2, x3) -> f257_0_loop_GT'(0, x1, 1, 0) :|: x1 > 0 && x4 <= x1 - 1 && x = 0 && x2 = 1 && x3 = 0
(2) f257_0_loop_GT(x5, x6, x7, x8) -> f257_0_loop_GT(0, x6, 1, 0) :|: x6 > 0 && x5 = 0 && x7 = 0 && x8 = 0
(3) f257_0_loop_GT(x34, x35, x36, x37) -> f257_0_loop_GT(x38, 2 * x34, 0, 0) :|: x35 + -2 * x38 >= 0 && x35 + -2 * x38 <= 1 && x38 + -1 * x35 <= 0 && x39 + -1 * x35 <= 0 && x34 > 0 && x36 = 1 && x37 = 0
(4) f257_0_loop_GT'(x9, x10, x11, x12) -> f257_0_loop_GT(2 * x12, x10, 1, x13) :|: x9 - 2 * x13 >= 0 && x9 - 2 * x13 <= 1 && x13 <= x9 && x12 > 0 && x11 = 0
(5) f257_0_loop_GT(x19, x20, x21, x22) -> f257_0_loop_GT'(x19, x20, 0, x22) :|: x22 > 0 && x19 >= x23 && x21 = 0
(6) f257_0_loop_GT'(x24, x25, x26, x27) -> f257_0_loop_GT(x28, 2 * x24, 0, x27) :|: x25 - 2 * x28 >= 0 && x25 - 2 * x28 <= 1 && x27 > 0 && x28 <= x25 && x26 = 1
(7) f257_0_loop_GT'(x79, x80, x81, x82) -> f257_0_loop_GT'(0, x80, 1, x83) :|: TRUE && x79 + -2 * x83 >= 0 && x79 + -2 * x83 <= 1 && x83 + -1 * x79 <= -1 && x79 >= 1 && x88 + -1 * x80 <= 0 && x83 >= 1 && (x81 = 0 && x82 = 0)
(8) f257_0_loop_GT(x14, x15, x16, x17) -> f257_0_loop_GT'(x14, x15, 0, 0) :|: x14 > 0 && x18 <= x14 - 1 && x16 = 0 && x17 = 0
(9) f257_0_loop_GT'(x29, x30, x31, x32) -> f257_0_loop_GT(x33, 0, 0, 0) :|: x30 - 2 * x33 >= 0 && x30 - 2 * x33 <= 1 && x33 <= x30 - 1 && x30 > 0 && x29 = 0 && x31 = 1 && x32 = 0
(10) f257_0_loop_GT'(x50, x51, x52, x53) -> f257_0_loop_GT'(0, x51, 1, 0) :|: TRUE && x50 + -2 * 0 >= 0 && x50 + -2 * 0 <= 1 && 0 + -1 * x50 <= -1 && x50 >= 1 && x51 >= 1 && x59 + -1 * x51 <= -1 && (x52 = 0 && x53 = 0 && x54 = 0)
(11) f257_0_loop_GT(x29:0, x30:0, cons_1, x32:0) -> f257_0_loop_GT'(x29:0, x30:0, 1, x32:0) :|: x33:0 <= x30:0 && x32:0 > 0 && cons_1 = 1

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

This digraph is fully evaluated!

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

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

(18)
Obligation:
Rules:
f257_0_loop_GT(cons_0, x1:0, cons_1, cons_01) -> f257_0_loop_GT'(0, x1:0, 1, 0) :|: x1:0 > 0 && x4:0 <= x1:0 - 1 && cons_0 = 0 && cons_1 = 1 && cons_01 = 0
f257_0_loop_GT(x, x1, x2, x3) -> f257_0_loop_GT(0, x1, 1, 0) :|: x1 > 0 && x = 0 && x2 = 0 && x3 = 0
f257_0_loop_GT'(x4, x5, x6, x7) -> f257_0_loop_GT(x8, 2 * x4, 0, x7) :|: x7 > 0 && x8 <= x5 && x5 - 2 * x8 <= 1 && x5 - 2 * x8 >= 0 && x6 = 1
f257_0_loop_GT'(x9, x10, x11, x12) -> f257_0_loop_GT(x13, 0, 0, 0) :|: x13 <= x10 - 1 && x10 > 0 && x10 - 2 * x13 <= 1 && x10 - 2 * x13 >= 0 && x9 = 0 && x11 = 1 && x12 = 0
f257_0_loop_GT(x14, x15, x16, x17) -> f257_0_loop_GT'(x14, x15, 1, x17) :|: x18 <= x15 && x17 > 0 && x16 = 1
f257_0_loop_GT(x19, x20, x21, x22) -> f257_0_loop_GT'(x19, x20, 0, 0) :|: x19 > 0 && x23 <= x19 - 1 && x21 = 0 && x22 = 0
f257_0_loop_GT(x24, x25, x26, x27) -> f257_0_loop_GT'(x24, x25, 0, x27) :|: x27 > 0 && x28 <= x24 && x26 = 0
f257_0_loop_GT'(x29, x30, x31, x32) -> f257_0_loop_GT(2 * x32, x30, 1, x33) :|: x29 >= x33 && x32 > 0 && x29 - 2 * x33 <= 1 && x29 - 2 * x33 >= 0 && x31 = 0
f257_0_loop_GT'(x34, x35, x36, x37) -> f257_0_loop_GT'(0, x35, 1, x38) :|: x39 + -1 * x35 <= 0 && x38 > 0 && x34 > 0 && x38 + -1 * x34 <= -1 && x34 + -2 * x38 >= 0 && x34 + -2 * x38 <= 1 && x36 = 0 && x37 = 0
f257_0_loop_GT(x40, x41, x42, x43) -> f257_0_loop_GT(x44, 2 * x40, 0, 0) :|: x45 + -1 * x41 <= 0 && x40 > 0 && x44 + -1 * x41 <= 0 && x41 + -2 * x44 <= 1 && x41 + -2 * x44 >= 0 && x42 = 1 && x43 = 0
f257_0_loop_GT'(x46, x47, x48, x49) -> f257_0_loop_GT'(0, x47, 1, 0) :|: x47 > 0 && x50 + -1 * x47 <= -1 && -1 * x46 <= -1 && x46 > 0 && x46 < 2 && x48 = 0 && x49 = 0

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

(19) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f257_0_loop_GT(VARIABLE, VARIABLE, VARIABLE, VARIABLE)
f257_0_loop_GT'(VARIABLE, VARIABLE, VARIABLE, VARIABLE)
Replaced non-predefined constructor symbols by 0.The following proof was generated: 
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given IntTRS could not be shown:



- IntTRS
  - RankingReductionPairProof

Rules:
f257_0_loop_GT(c, x1:0, c1, c2) -> f257_0_loop_GT'(c3, x1:0, c4, c5) :|: c5 = 0 && (c4 = 1 && (c3 = 0 && (c2 = 0 && (c1 = 1 && c = 0)))) && (x1:0 > 0 && x4:0 <= x1:0 - 1 && cons_0 = 0 && cons_1 = 1 && cons_01 = 0)
f257_0_loop_GT(c6, x1, c7, c8) -> f257_0_loop_GT(c9, x1, c10, c11) :|: c11 = 0 && (c10 = 1 && (c9 = 0 && (c8 = 0 && (c7 = 0 && c6 = 0)))) && (x1 > 0 && x = 0 && x2 = 0 && x3 = 0)
f257_0_loop_GT'(x4, x5, c12, x7) -> f257_0_loop_GT(x8, c13, c14, x7) :|: c14 = 0 && (c13 = 2 * x4 && c12 = 1) && (x7 > 0 && x8 <= x5 && x5 - 2 * x8 <= 1 && x5 - 2 * x8 >= 0 && x6 = 1)
f257_0_loop_GT'(c15, x10, c16, c17) -> f257_0_loop_GT(x13, c18, c19, c20) :|: c20 = 0 && (c19 = 0 && (c18 = 0 && (c17 = 0 && (c16 = 1 && c15 = 0)))) && (x13 <= x10 - 1 && x10 > 0 && x10 - 2 * x13 <= 1 && x10 - 2 * x13 >= 0 && x9 = 0 && x11 = 1 && x12 = 0)
f257_0_loop_GT(x14, x15, c21, x17) -> f257_0_loop_GT'(x14, x15, c22, x17) :|: c22 = 1 && c21 = 1 && (x18 <= x15 && x17 > 0 && x16 = 1)
f257_0_loop_GT(x19, x20, c23, c24) -> f257_0_loop_GT'(x19, x20, c25, c26) :|: c26 = 0 && (c25 = 0 && (c24 = 0 && c23 = 0)) && (x19 > 0 && x23 <= x19 - 1 && x21 = 0 && x22 = 0)
f257_0_loop_GT(x24, x25, c27, x27) -> f257_0_loop_GT'(x24, x25, c28, x27) :|: c28 = 0 && c27 = 0 && (x27 > 0 && x28 <= x24 && x26 = 0)
f257_0_loop_GT'(x29, x30, c29, x32) -> f257_0_loop_GT(c30, x30, c31, x33) :|: c31 = 1 && (c30 = 2 * x32 && c29 = 0) && (x29 >= x33 && x32 > 0 && x29 - 2 * x33 <= 1 && x29 - 2 * x33 >= 0 && x31 = 0)
f257_0_loop_GT'(x34, x35, c32, c33) -> f257_0_loop_GT'(c34, x35, c35, x38) :|: c35 = 1 && (c34 = 0 && (c33 = 0 && c32 = 0)) && (x39 + -1 * x35 <= 0 && x38 > 0 && x34 > 0 && x38 + -1 * x34 <= -1 && x34 + -2 * x38 >= 0 && x34 + -2 * x38 <= 1 && x36 = 0 && x37 = 0)
f257_0_loop_GT(x40, x41, c36, c37) -> f257_0_loop_GT(x44, c38, c39, c40) :|: c40 = 0 && (c39 = 0 && (c38 = 2 * x40 && (c37 = 0 && c36 = 1))) && (x45 + -1 * x41 <= 0 && x40 > 0 && x44 + -1 * x41 <= 0 && x41 + -2 * x44 <= 1 && x41 + -2 * x44 >= 0 && x42 = 1 && x43 = 0)
f257_0_loop_GT'(x46, x47, c41, c42) -> f257_0_loop_GT'(c43, x47, c44, c45) :|: c45 = 0 && (c44 = 1 && (c43 = 0 && (c42 = 0 && c41 = 0))) && (x47 > 0 && x50 + -1 * x47 <= -1 && -1 * x46 <= -1 && x46 > 0 && x46 < 2 && x48 = 0 && x49 = 0)

Interpretation:
[ f257_0_loop_GT ] = 8*f257_0_loop_GT_4 + 4*f257_0_loop_GT_1 + 2*f257_0_loop_GT_2
[ f257_0_loop_GT' ] = 2*f257_0_loop_GT'_2 + 8*f257_0_loop_GT'_4 + 4*f257_0_loop_GT'_1

The following rules are decreasing:
f257_0_loop_GT'(x46, x47, c41, c42) -> f257_0_loop_GT'(c43, x47, c44, c45) :|: c45 = 0 && (c44 = 1 && (c43 = 0 && (c42 = 0 && c41 = 0))) && (x47 > 0 && x50 + -1 * x47 <= -1 && -1 * x46 <= -1 && x46 > 0 && x46 < 2 && x48 = 0 && x49 = 0)

The following rules are bounded:
f257_0_loop_GT'(c15, x10, c16, c17) -> f257_0_loop_GT(x13, c18, c19, c20) :|: c20 = 0 && (c19 = 0 && (c18 = 0 && (c17 = 0 && (c16 = 1 && c15 = 0)))) && (x13 <= x10 - 1 && x10 > 0 && x10 - 2 * x13 <= 1 && x10 - 2 * x13 >= 0 && x9 = 0 && x11 = 1 && x12 = 0)
f257_0_loop_GT(x40, x41, c36, c37) -> f257_0_loop_GT(x44, c38, c39, c40) :|: c40 = 0 && (c39 = 0 && (c38 = 2 * x40 && (c37 = 0 && c36 = 1))) && (x45 + -1 * x41 <= 0 && x40 > 0 && x44 + -1 * x41 <= 0 && x41 + -2 * x44 <= 1 && x41 + -2 * x44 >= 0 && x42 = 1 && x43 = 0)




- IntTRS
  - RankingReductionPairProof
    - AND
      - IntTRS
      - IntTRS
      - IntTRS

Rules:
f257_0_loop_GT(c, x1:0, c1, c2) -> f257_0_loop_GT'(c3, x1:0, c4, c5) :|: c5 = 0 && (c4 = 1 && (c3 = 0 && (c2 = 0 && (c1 = 1 && c = 0)))) && (x1:0 > 0 && x4:0 <= x1:0 - 1 && cons_0 = 0 && cons_1 = 1 && cons_01 = 0)
f257_0_loop_GT(c6, x1, c7, c8) -> f257_0_loop_GT(c9, x1, c10, c11) :|: c11 = 0 && (c10 = 1 && (c9 = 0 && (c8 = 0 && (c7 = 0 && c6 = 0)))) && (x1 > 0 && x = 0 && x2 = 0 && x3 = 0)
f257_0_loop_GT'(x4, x5, c12, x7) -> f257_0_loop_GT(x8, c13, c14, x7) :|: c14 = 0 && (c13 = 2 * x4 && c12 = 1) && (x7 > 0 && x8 <= x5 && x5 - 2 * x8 <= 1 && x5 - 2 * x8 >= 0 && x6 = 1)
f257_0_loop_GT'(c15, x10, c16, c17) -> f257_0_loop_GT(x13, c18, c19, c20) :|: c20 = 0 && (c19 = 0 && (c18 = 0 && (c17 = 0 && (c16 = 1 && c15 = 0)))) && (x13 <= x10 - 1 && x10 > 0 && x10 - 2 * x13 <= 1 && x10 - 2 * x13 >= 0 && x9 = 0 && x11 = 1 && x12 = 0)
f257_0_loop_GT(x14, x15, c21, x17) -> f257_0_loop_GT'(x14, x15, c22, x17) :|: c22 = 1 && c21 = 1 && (x18 <= x15 && x17 > 0 && x16 = 1)
f257_0_loop_GT(x19, x20, c23, c24) -> f257_0_loop_GT'(x19, x20, c25, c26) :|: c26 = 0 && (c25 = 0 && (c24 = 0 && c23 = 0)) && (x19 > 0 && x23 <= x19 - 1 && x21 = 0 && x22 = 0)
f257_0_loop_GT(x24, x25, c27, x27) -> f257_0_loop_GT'(x24, x25, c28, x27) :|: c28 = 0 && c27 = 0 && (x27 > 0 && x28 <= x24 && x26 = 0)
f257_0_loop_GT'(x29, x30, c29, x32) -> f257_0_loop_GT(c30, x30, c31, x33) :|: c31 = 1 && (c30 = 2 * x32 && c29 = 0) && (x29 >= x33 && x32 > 0 && x29 - 2 * x33 <= 1 && x29 - 2 * x33 >= 0 && x31 = 0)
f257_0_loop_GT'(x34, x35, c32, c33) -> f257_0_loop_GT'(c34, x35, c35, x38) :|: c35 = 1 && (c34 = 0 && (c33 = 0 && c32 = 0)) && (x39 + -1 * x35 <= 0 && x38 > 0 && x34 > 0 && x38 + -1 * x34 <= -1 && x34 + -2 * x38 >= 0 && x34 + -2 * x38 <= 1 && x36 = 0 && x37 = 0)
f257_0_loop_GT(x40, x41, c36, c37) -> f257_0_loop_GT(x44, c38, c39, c40) :|: c40 = 0 && (c39 = 0 && (c38 = 2 * x40 && (c37 = 0 && c36 = 1))) && (x45 + -1 * x41 <= 0 && x40 > 0 && x44 + -1 * x41 <= 0 && x41 + -2 * x44 <= 1 && x41 + -2 * x44 >= 0 && x42 = 1 && x43 = 0)



- IntTRS
  - RankingReductionPairProof
    - AND
      - IntTRS
      - IntTRS
      - IntTRS
        - RankingReductionPairProof

Rules:
f257_0_loop_GT(c, x1:0, c1, c2) -> f257_0_loop_GT'(c3, x1:0, c4, c5) :|: c5 = 0 && (c4 = 1 && (c3 = 0 && (c2 = 0 && (c1 = 1 && c = 0)))) && (x1:0 > 0 && x4:0 <= x1:0 - 1 && cons_0 = 0 && cons_1 = 1 && cons_01 = 0)
f257_0_loop_GT(c6, x1, c7, c8) -> f257_0_loop_GT(c9, x1, c10, c11) :|: c11 = 0 && (c10 = 1 && (c9 = 0 && (c8 = 0 && (c7 = 0 && c6 = 0)))) && (x1 > 0 && x = 0 && x2 = 0 && x3 = 0)
f257_0_loop_GT'(x4, x5, c12, x7) -> f257_0_loop_GT(x8, c13, c14, x7) :|: c14 = 0 && (c13 = 2 * x4 && c12 = 1) && (x7 > 0 && x8 <= x5 && x5 - 2 * x8 <= 1 && x5 - 2 * x8 >= 0 && x6 = 1)
f257_0_loop_GT(x14, x15, c21, x17) -> f257_0_loop_GT'(x14, x15, c22, x17) :|: c22 = 1 && c21 = 1 && (x18 <= x15 && x17 > 0 && x16 = 1)
f257_0_loop_GT(x19, x20, c23, c24) -> f257_0_loop_GT'(x19, x20, c25, c26) :|: c26 = 0 && (c25 = 0 && (c24 = 0 && c23 = 0)) && (x19 > 0 && x23 <= x19 - 1 && x21 = 0 && x22 = 0)
f257_0_loop_GT(x24, x25, c27, x27) -> f257_0_loop_GT'(x24, x25, c28, x27) :|: c28 = 0 && c27 = 0 && (x27 > 0 && x28 <= x24 && x26 = 0)
f257_0_loop_GT'(x29, x30, c29, x32) -> f257_0_loop_GT(c30, x30, c31, x33) :|: c31 = 1 && (c30 = 2 * x32 && c29 = 0) && (x29 >= x33 && x32 > 0 && x29 - 2 * x33 <= 1 && x29 - 2 * x33 >= 0 && x31 = 0)
f257_0_loop_GT'(x34, x35, c32, c33) -> f257_0_loop_GT'(c34, x35, c35, x38) :|: c35 = 1 && (c34 = 0 && (c33 = 0 && c32 = 0)) && (x39 + -1 * x35 <= 0 && x38 > 0 && x34 > 0 && x38 + -1 * x34 <= -1 && x34 + -2 * x38 >= 0 && x34 + -2 * x38 <= 1 && x36 = 0 && x37 = 0)
f257_0_loop_GT'(x46, x47, c41, c42) -> f257_0_loop_GT'(c43, x47, c44, c45) :|: c45 = 0 && (c44 = 1 && (c43 = 0 && (c42 = 0 && c41 = 0))) && (x47 > 0 && x50 + -1 * x47 <= -1 && -1 * x46 <= -1 && x46 > 0 && x46 < 2 && x48 = 0 && x49 = 0)

Interpretation:
[ f257_0_loop_GT ] = 8*f257_0_loop_GT_4 + 4*f257_0_loop_GT_1 + 2*f257_0_loop_GT_2
[ f257_0_loop_GT' ] = 2*f257_0_loop_GT'_2 + 8*f257_0_loop_GT'_4 + 4*f257_0_loop_GT'_1

The following rules are decreasing:
f257_0_loop_GT'(x46, x47, c41, c42) -> f257_0_loop_GT'(c43, x47, c44, c45) :|: c45 = 0 && (c44 = 1 && (c43 = 0 && (c42 = 0 && c41 = 0))) && (x47 > 0 && x50 + -1 * x47 <= -1 && -1 * x46 <= -1 && x46 > 0 && x46 < 2 && x48 = 0 && x49 = 0)

The following rules are bounded:
f257_0_loop_GT(c, x1:0, c1, c2) -> f257_0_loop_GT'(c3, x1:0, c4, c5) :|: c5 = 0 && (c4 = 1 && (c3 = 0 && (c2 = 0 && (c1 = 1 && c = 0)))) && (x1:0 > 0 && x4:0 <= x1:0 - 1 && cons_0 = 0 && cons_1 = 1 && cons_01 = 0)




- IntTRS
  - RankingReductionPairProof
    - AND
      - IntTRS
      - IntTRS
      - IntTRS
        - RankingReductionPairProof
          - AND
            - IntTRS
            - IntTRS
            - IntTRS

Rules:
f257_0_loop_GT(c, x1:0, c1, c2) -> f257_0_loop_GT'(c3, x1:0, c4, c5) :|: c5 = 0 && (c4 = 1 && (c3 = 0 && (c2 = 0 && (c1 = 1 && c = 0)))) && (x1:0 > 0 && x4:0 <= x1:0 - 1 && cons_0 = 0 && cons_1 = 1 && cons_01 = 0)
f257_0_loop_GT(c6, x1, c7, c8) -> f257_0_loop_GT(c9, x1, c10, c11) :|: c11 = 0 && (c10 = 1 && (c9 = 0 && (c8 = 0 && (c7 = 0 && c6 = 0)))) && (x1 > 0 && x = 0 && x2 = 0 && x3 = 0)
f257_0_loop_GT'(x4, x5, c12, x7) -> f257_0_loop_GT(x8, c13, c14, x7) :|: c14 = 0 && (c13 = 2 * x4 && c12 = 1) && (x7 > 0 && x8 <= x5 && x5 - 2 * x8 <= 1 && x5 - 2 * x8 >= 0 && x6 = 1)
f257_0_loop_GT(x14, x15, c21, x17) -> f257_0_loop_GT'(x14, x15, c22, x17) :|: c22 = 1 && c21 = 1 && (x18 <= x15 && x17 > 0 && x16 = 1)
f257_0_loop_GT(x19, x20, c23, c24) -> f257_0_loop_GT'(x19, x20, c25, c26) :|: c26 = 0 && (c25 = 0 && (c24 = 0 && c23 = 0)) && (x19 > 0 && x23 <= x19 - 1 && x21 = 0 && x22 = 0)
f257_0_loop_GT(x24, x25, c27, x27) -> f257_0_loop_GT'(x24, x25, c28, x27) :|: c28 = 0 && c27 = 0 && (x27 > 0 && x28 <= x24 && x26 = 0)
f257_0_loop_GT'(x29, x30, c29, x32) -> f257_0_loop_GT(c30, x30, c31, x33) :|: c31 = 1 && (c30 = 2 * x32 && c29 = 0) && (x29 >= x33 && x32 > 0 && x29 - 2 * x33 <= 1 && x29 - 2 * x33 >= 0 && x31 = 0)
f257_0_loop_GT'(x34, x35, c32, c33) -> f257_0_loop_GT'(c34, x35, c35, x38) :|: c35 = 1 && (c34 = 0 && (c33 = 0 && c32 = 0)) && (x39 + -1 * x35 <= 0 && x38 > 0 && x34 > 0 && x38 + -1 * x34 <= -1 && x34 + -2 * x38 >= 0 && x34 + -2 * x38 <= 1 && x36 = 0 && x37 = 0)



- IntTRS
  - RankingReductionPairProof
    - AND
      - IntTRS
      - IntTRS
      - IntTRS
        - RankingReductionPairProof
          - AND
            - IntTRS
            - IntTRS
            - IntTRS
              - RankingReductionPairProof

Rules:
f257_0_loop_GT(c6, x1, c7, c8) -> f257_0_loop_GT(c9, x1, c10, c11) :|: c11 = 0 && (c10 = 1 && (c9 = 0 && (c8 = 0 && (c7 = 0 && c6 = 0)))) && (x1 > 0 && x = 0 && x2 = 0 && x3 = 0)
f257_0_loop_GT'(x4, x5, c12, x7) -> f257_0_loop_GT(x8, c13, c14, x7) :|: c14 = 0 && (c13 = 2 * x4 && c12 = 1) && (x7 > 0 && x8 <= x5 && x5 - 2 * x8 <= 1 && x5 - 2 * x8 >= 0 && x6 = 1)
f257_0_loop_GT(x14, x15, c21, x17) -> f257_0_loop_GT'(x14, x15, c22, x17) :|: c22 = 1 && c21 = 1 && (x18 <= x15 && x17 > 0 && x16 = 1)
f257_0_loop_GT(x19, x20, c23, c24) -> f257_0_loop_GT'(x19, x20, c25, c26) :|: c26 = 0 && (c25 = 0 && (c24 = 0 && c23 = 0)) && (x19 > 0 && x23 <= x19 - 1 && x21 = 0 && x22 = 0)
f257_0_loop_GT(x24, x25, c27, x27) -> f257_0_loop_GT'(x24, x25, c28, x27) :|: c28 = 0 && c27 = 0 && (x27 > 0 && x28 <= x24 && x26 = 0)
f257_0_loop_GT'(x29, x30, c29, x32) -> f257_0_loop_GT(c30, x30, c31, x33) :|: c31 = 1 && (c30 = 2 * x32 && c29 = 0) && (x29 >= x33 && x32 > 0 && x29 - 2 * x33 <= 1 && x29 - 2 * x33 >= 0 && x31 = 0)
f257_0_loop_GT'(x34, x35, c32, c33) -> f257_0_loop_GT'(c34, x35, c35, x38) :|: c35 = 1 && (c34 = 0 && (c33 = 0 && c32 = 0)) && (x39 + -1 * x35 <= 0 && x38 > 0 && x34 > 0 && x38 + -1 * x34 <= -1 && x34 + -2 * x38 >= 0 && x34 + -2 * x38 <= 1 && x36 = 0 && x37 = 0)
f257_0_loop_GT'(x46, x47, c41, c42) -> f257_0_loop_GT'(c43, x47, c44, c45) :|: c45 = 0 && (c44 = 1 && (c43 = 0 && (c42 = 0 && c41 = 0))) && (x47 > 0 && x50 + -1 * x47 <= -1 && -1 * x46 <= -1 && x46 > 0 && x46 < 2 && x48 = 0 && x49 = 0)

Interpretation:
[ f257_0_loop_GT ] = 8*f257_0_loop_GT_4 + 4*f257_0_loop_GT_1 + 2*f257_0_loop_GT_2 + 1
[ f257_0_loop_GT' ] = 8*f257_0_loop_GT'_4 + 4*f257_0_loop_GT'_1 + 2*f257_0_loop_GT'_2 + 1

The following rules are decreasing:
f257_0_loop_GT'(x46, x47, c41, c42) -> f257_0_loop_GT'(c43, x47, c44, c45) :|: c45 = 0 && (c44 = 1 && (c43 = 0 && (c42 = 0 && c41 = 0))) && (x47 > 0 && x50 + -1 * x47 <= -1 && -1 * x46 <= -1 && x46 > 0 && x46 < 2 && x48 = 0 && x49 = 0)

The following rules are bounded:
f257_0_loop_GT'(x46, x47, c41, c42) -> f257_0_loop_GT'(c43, x47, c44, c45) :|: c45 = 0 && (c44 = 1 && (c43 = 0 && (c42 = 0 && c41 = 0))) && (x47 > 0 && x50 + -1 * x47 <= -1 && -1 * x46 <= -1 && x46 > 0 && x46 < 2 && x48 = 0 && x49 = 0)



- IntTRS
  - RankingReductionPairProof
    - AND
      - IntTRS
      - IntTRS
      - IntTRS
        - RankingReductionPairProof
          - AND
            - IntTRS
            - IntTRS
            - IntTRS
              - RankingReductionPairProof
                - IntTRS

Rules:
f257_0_loop_GT(c6, x1, c7, c8) -> f257_0_loop_GT(c9, x1, c10, c11) :|: c11 = 0 && (c10 = 1 && (c9 = 0 && (c8 = 0 && (c7 = 0 && c6 = 0)))) && (x1 > 0 && x = 0 && x2 = 0 && x3 = 0)
f257_0_loop_GT'(x4, x5, c12, x7) -> f257_0_loop_GT(x8, c13, c14, x7) :|: c14 = 0 && (c13 = 2 * x4 && c12 = 1) && (x7 > 0 && x8 <= x5 && x5 - 2 * x8 <= 1 && x5 - 2 * x8 >= 0 && x6 = 1)
f257_0_loop_GT(x14, x15, c21, x17) -> f257_0_loop_GT'(x14, x15, c22, x17) :|: c22 = 1 && c21 = 1 && (x18 <= x15 && x17 > 0 && x16 = 1)
f257_0_loop_GT(x19, x20, c23, c24) -> f257_0_loop_GT'(x19, x20, c25, c26) :|: c26 = 0 && (c25 = 0 && (c24 = 0 && c23 = 0)) && (x19 > 0 && x23 <= x19 - 1 && x21 = 0 && x22 = 0)
f257_0_loop_GT(x24, x25, c27, x27) -> f257_0_loop_GT'(x24, x25, c28, x27) :|: c28 = 0 && c27 = 0 && (x27 > 0 && x28 <= x24 && x26 = 0)
f257_0_loop_GT'(x29, x30, c29, x32) -> f257_0_loop_GT(c30, x30, c31, x33) :|: c31 = 1 && (c30 = 2 * x32 && c29 = 0) && (x29 >= x33 && x32 > 0 && x29 - 2 * x33 <= 1 && x29 - 2 * x33 >= 0 && x31 = 0)
f257_0_loop_GT'(x34, x35, c32, c33) -> f257_0_loop_GT'(c34, x35, c35, x38) :|: c35 = 1 && (c34 = 0 && (c33 = 0 && c32 = 0)) && (x39 + -1 * x35 <= 0 && x38 > 0 && x34 > 0 && x38 + -1 * x34 <= -1 && x34 + -2 * x38 >= 0 && x34 + -2 * x38 <= 1 && x36 = 0 && x37 = 0)



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

(20)
Obligation:
Rules:
f257_0_loop_GT(x, x1, x2, x3) -> f257_0_loop_GT(0, x1, 1, 0) :|: x1 > 0 && x = 0 && x2 = 0 && x3 = 0
f257_0_loop_GT'(x4, x5, x6, x7) -> f257_0_loop_GT(x8, 2 * x4, 0, x7) :|: x7 > 0 && x8 <= x5 && x5 - 2 * x8 <= 1 && x5 - 2 * x8 >= 0 && x6 = 1
f257_0_loop_GT(x14, x15, x16, x17) -> f257_0_loop_GT'(x14, x15, 1, x17) :|: x18 <= x15 && x17 > 0 && x16 = 1
f257_0_loop_GT(x19, x20, x21, x22) -> f257_0_loop_GT'(x19, x20, 0, 0) :|: x19 > 0 && x23 <= x19 - 1 && x21 = 0 && x22 = 0
f257_0_loop_GT(x24, x25, x26, x27) -> f257_0_loop_GT'(x24, x25, 0, x27) :|: x27 > 0 && x28 <= x24 && x26 = 0
f257_0_loop_GT'(x29, x30, x31, x32) -> f257_0_loop_GT(2 * x32, x30, 1, x33) :|: x29 >= x33 && x32 > 0 && x29 - 2 * x33 <= 1 && x29 - 2 * x33 >= 0 && x31 = 0
f257_0_loop_GT'(x34, x35, x36, x37) -> f257_0_loop_GT'(0, x35, 1, x38) :|: x39 + -1 * x35 <= 0 && x38 > 0 && x34 > 0 && x38 + -1 * x34 <= -1 && x34 + -2 * x38 >= 0 && x34 + -2 * x38 <= 1 && x36 = 0 && x37 = 0
f257_0_loop_GT(cons_0, x1:0, cons_1, cons_01) -> f257_0_loop_GT'(0, x1:0, 1, 0) :|: x1:0 > 0 && x4:0 <= x1:0 - 1 && cons_0 = 0 && cons_1 = 1 && cons_01 = 0
f257_0_loop_GT'(x9, x10, x11, x12) -> f257_0_loop_GT(x13, 0, 0, 0) :|: x13 <= x10 - 1 && x10 > 0 && x10 - 2 * x13 <= 1 && x10 - 2 * x13 >= 0 && x9 = 0 && x11 = 1 && x12 = 0
f257_0_loop_GT(x40, x41, x42, x43) -> f257_0_loop_GT(x44, 2 * x40, 0, 0) :|: x45 + -1 * x41 <= 0 && x40 > 0 && x44 + -1 * x41 <= 0 && x41 + -2 * x44 <= 1 && x41 + -2 * x44 >= 0 && x42 = 1 && x43 = 0

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

(21) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f257_0_loop_GT(x, x1, x2, x3) -> f257_0_loop_GT(0, x1, 1, 0) :|: x1 > 0 && x = 0 && x2 = 0 && x3 = 0
(2) f257_0_loop_GT'(x4, x5, x6, x7) -> f257_0_loop_GT(x8, 2 * x4, 0, x7) :|: x7 > 0 && x8 <= x5 && x5 - 2 * x8 <= 1 && x5 - 2 * x8 >= 0 && x6 = 1
(3) f257_0_loop_GT(x14, x15, x16, x17) -> f257_0_loop_GT'(x14, x15, 1, x17) :|: x18 <= x15 && x17 > 0 && x16 = 1
(4) f257_0_loop_GT(x19, x20, x21, x22) -> f257_0_loop_GT'(x19, x20, 0, 0) :|: x19 > 0 && x23 <= x19 - 1 && x21 = 0 && x22 = 0
(5) f257_0_loop_GT(x24, x25, x26, x27) -> f257_0_loop_GT'(x24, x25, 0, x27) :|: x27 > 0 && x28 <= x24 && x26 = 0
(6) f257_0_loop_GT'(x29, x30, x31, x32) -> f257_0_loop_GT(2 * x32, x30, 1, x33) :|: x29 >= x33 && x32 > 0 && x29 - 2 * x33 <= 1 && x29 - 2 * x33 >= 0 && x31 = 0
(7) f257_0_loop_GT'(x34, x35, x36, x37) -> f257_0_loop_GT'(0, x35, 1, x38) :|: x39 + -1 * x35 <= 0 && x38 > 0 && x34 > 0 && x38 + -1 * x34 <= -1 && x34 + -2 * x38 >= 0 && x34 + -2 * x38 <= 1 && x36 = 0 && x37 = 0
(8) f257_0_loop_GT(cons_0, x1:0, cons_1, cons_01) -> f257_0_loop_GT'(0, x1:0, 1, 0) :|: x1:0 > 0 && x4:0 <= x1:0 - 1 && cons_0 = 0 && cons_1 = 1 && cons_01 = 0
(9) f257_0_loop_GT'(x9, x10, x11, x12) -> f257_0_loop_GT(x13, 0, 0, 0) :|: x13 <= x10 - 1 && x10 > 0 && x10 - 2 * x13 <= 1 && x10 - 2 * x13 >= 0 && x9 = 0 && x11 = 1 && x12 = 0
(10) f257_0_loop_GT(x40, x41, x42, x43) -> f257_0_loop_GT(x44, 2 * x40, 0, 0) :|: x45 + -1 * x41 <= 0 && x40 > 0 && x44 + -1 * x41 <= 0 && x41 + -2 * x44 <= 1 && x41 + -2 * x44 >= 0 && x42 = 1 && x43 = 0

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

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

(22)
Obligation:

Termination digraph:
Nodes:
(1) f257_0_loop_GT(x, x1, x2, x3) -> f257_0_loop_GT(0, x1, 1, 0) :|: x1 > 0 && x = 0 && x2 = 0 && x3 = 0
(2) f257_0_loop_GT(x40, x41, x42, x43) -> f257_0_loop_GT(x44, 2 * x40, 0, 0) :|: x45 + -1 * x41 <= 0 && x40 > 0 && x44 + -1 * x41 <= 0 && x41 + -2 * x44 <= 1 && x41 + -2 * x44 >= 0 && x42 = 1 && x43 = 0
(3) f257_0_loop_GT'(x29, x30, x31, x32) -> f257_0_loop_GT(2 * x32, x30, 1, x33) :|: x29 >= x33 && x32 > 0 && x29 - 2 * x33 <= 1 && x29 - 2 * x33 >= 0 && x31 = 0
(4) f257_0_loop_GT(x24, x25, x26, x27) -> f257_0_loop_GT'(x24, x25, 0, x27) :|: x27 > 0 && x28 <= x24 && x26 = 0
(5) f257_0_loop_GT'(x4, x5, x6, x7) -> f257_0_loop_GT(x8, 2 * x4, 0, x7) :|: x7 > 0 && x8 <= x5 && x5 - 2 * x8 <= 1 && x5 - 2 * x8 >= 0 && x6 = 1
(6) f257_0_loop_GT'(x34, x35, x36, x37) -> f257_0_loop_GT'(0, x35, 1, x38) :|: x39 + -1 * x35 <= 0 && x38 > 0 && x34 > 0 && x38 + -1 * x34 <= -1 && x34 + -2 * x38 >= 0 && x34 + -2 * x38 <= 1 && x36 = 0 && x37 = 0
(7) f257_0_loop_GT(x19, x20, x21, x22) -> f257_0_loop_GT'(x19, x20, 0, 0) :|: x19 > 0 && x23 <= x19 - 1 && x21 = 0 && x22 = 0
(8) f257_0_loop_GT'(x9, x10, x11, x12) -> f257_0_loop_GT(x13, 0, 0, 0) :|: x13 <= x10 - 1 && x10 > 0 && x10 - 2 * x13 <= 1 && x10 - 2 * x13 >= 0 && x9 = 0 && x11 = 1 && x12 = 0
(9) f257_0_loop_GT(cons_0, x1:0, cons_1, cons_01) -> f257_0_loop_GT'(0, x1:0, 1, 0) :|: x1:0 > 0 && x4:0 <= x1:0 - 1 && cons_0 = 0 && cons_1 = 1 && cons_01 = 0
(10) f257_0_loop_GT(x14, x15, x16, x17) -> f257_0_loop_GT'(x14, x15, 1, x17) :|: x18 <= x15 && x17 > 0 && x16 = 1

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

This digraph is fully evaluated!

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

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

(24)
Obligation:
Rules:
f257_0_loop_GT'(x29:0, x30:0, cons_0, x32:0) -> f257_0_loop_GT(2 * x32:0, x30:0, 1, x33:0) :|: x29:0 - 2 * x33:0 <= 1 && x29:0 - 2 * x33:0 >= 0 && x32:0 > 0 && x33:0 <= x29:0 && cons_0 = 0
f257_0_loop_GT'(x, x1, x2, x3) -> f257_0_loop_GT'(0, x1, 1, x4) :|: x + -2 * x4 >= 0 && x + -2 * x4 <= 1 && x4 + -1 * x <= -1 && x > 0 && x4 > 0 && x5 + -1 * x1 <= 0 && x2 = 0 && x3 = 0
f257_0_loop_GT(x6, x7, x8, x9) -> f257_0_loop_GT'(0, x7, 1, 0) :|: x7 > 0 && x10 <= x7 - 1 && x6 = 0 && x8 = 1 && x9 = 0
f257_0_loop_GT'(x4:0, x5:0, cons_1, x7:0) -> f257_0_loop_GT(x8:0, 2 * x4:0, 0, x7:0) :|: x5:0 - 2 * x8:0 <= 1 && x5:0 - 2 * x8:0 >= 0 && x8:0 <= x5:0 && x7:0 > 0 && cons_1 = 1
f257_0_loop_GT(x11, x12, x13, x14) -> f257_0_loop_GT(0, x12, 1, 0) :|: x12 > 0 && x11 = 0 && x13 = 0 && x14 = 0
f257_0_loop_GT'(x15, x16, x17, x18) -> f257_0_loop_GT(x19, 0, 0, 0) :|: x16 - 2 * x19 <= 1 && x16 - 2 * x19 >= 0 && x16 > 0 && x19 <= x16 - 1 && x15 = 0 && x17 = 1 && x18 = 0
f257_0_loop_GT(x20, x21, x22, x23) -> f257_0_loop_GT'(x20, x21, 1, x23) :|: x24 <= x21 && x23 > 0 && x22 = 1
f257_0_loop_GT(x25, x26, x27, x28) -> f257_0_loop_GT'(x25, x26, 0, x28) :|: x28 > 0 && x29 <= x25 && x27 = 0
f257_0_loop_GT(x30, x31, x32, x33) -> f257_0_loop_GT'(x30, x31, 0, 0) :|: x30 > 0 && x34 <= x30 - 1 && x32 = 0 && x33 = 0
f257_0_loop_GT(x35, x36, x37, x38) -> f257_0_loop_GT(x39, 2 * x35, 0, 0) :|: x36 + -2 * x39 <= 1 && x36 + -2 * x39 >= 0 && x39 + -1 * x36 <= 0 && x35 > 0 && x40 + -1 * x36 <= 0 && x37 = 1 && x38 = 0