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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 153 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IRSwT
(7) IRSwTChainingProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms]
(10) TRUE


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(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2) -> f1_0_main_Load'(arg1P, arg2P) :|: -1 <= arg2 - 1 && -1 <= x2 - 1 && 0 <= arg1 - 1 && arg1 = arg1P && arg2 = arg2P
f1_0_main_Load'(x, x1) -> f80_0_main_EQ(x3, x4) :|: -1 <= x1 - 1 && -1 <= x3 - 1 && 0 <= x - 1 && x3 - 3 * x5 <= 2 && 0 <= x3 - 3 * x5 && x3 - 3 * x5 = x4
f80_0_main_EQ(x6, x7) -> f80_0_main_EQ'(x9, x10) :|: x7 = x10 && x6 = x9 && 0 <= x7 - 1
f80_0_main_EQ'(x12, x13) -> f80_0_main_EQ(x14, x15) :|: 0 <= x13 - 1 && x12 + 1 - 3 * x16 <= 2 && 0 <= x12 + 1 - 3 * x16 && x12 + 1 = x14 && x12 + 1 - 3 * x16 = x15
__init(x17, x18) -> f1_0_main_Load(x19, x20) :|: 0 <= 0
Start term: __init(arg1, arg2)

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(1) IRSFormatTransformerProof (EQUIVALENT)
Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
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(2)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2) -> f1_0_main_Load'(arg1P, arg2P) :|: -1 <= arg2 - 1 && -1 <= x2 - 1 && 0 <= arg1 - 1 && arg1 = arg1P && arg2 = arg2P
f1_0_main_Load'(x, x1) -> f80_0_main_EQ(x3, x4) :|: -1 <= x1 - 1 && -1 <= x3 - 1 && 0 <= x - 1 && x3 - 3 * x5 <= 2 && 0 <= x3 - 3 * x5 && x3 - 3 * x5 = x4
f80_0_main_EQ(x6, x7) -> f80_0_main_EQ'(x9, x10) :|: x7 = x10 && x6 = x9 && 0 <= x7 - 1
f80_0_main_EQ'(x12, x13) -> f80_0_main_EQ(x14, x15) :|: 0 <= x13 - 1 && x12 + 1 - 3 * x16 <= 2 && 0 <= x12 + 1 - 3 * x16 && x12 + 1 = x14 && x12 + 1 - 3 * x16 = x15
__init(x17, x18) -> f1_0_main_Load(x19, x20) :|: 0 <= 0
Start term: __init(arg1, arg2)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_Load(arg1, arg2) -> f1_0_main_Load'(arg1P, arg2P) :|: -1 <= arg2 - 1 && -1 <= x2 - 1 && 0 <= arg1 - 1 && arg1 = arg1P && arg2 = arg2P
(2) f1_0_main_Load'(x, x1) -> f80_0_main_EQ(x3, x4) :|: -1 <= x1 - 1 && -1 <= x3 - 1 && 0 <= x - 1 && x3 - 3 * x5 <= 2 && 0 <= x3 - 3 * x5 && x3 - 3 * x5 = x4
(3) f80_0_main_EQ(x6, x7) -> f80_0_main_EQ'(x9, x10) :|: x7 = x10 && x6 = x9 && 0 <= x7 - 1
(4) f80_0_main_EQ'(x12, x13) -> f80_0_main_EQ(x14, x15) :|: 0 <= x13 - 1 && x12 + 1 - 3 * x16 <= 2 && 0 <= x12 + 1 - 3 * x16 && x12 + 1 = x14 && x12 + 1 - 3 * x16 = x15
(5) __init(x17, x18) -> f1_0_main_Load(x19, x20) :|: 0 <= 0

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) f80_0_main_EQ(x6, x7) -> f80_0_main_EQ'(x9, x10) :|: x7 = x10 && x6 = x9 && 0 <= x7 - 1
(2) f80_0_main_EQ'(x12, x13) -> f80_0_main_EQ(x14, x15) :|: 0 <= x13 - 1 && x12 + 1 - 3 * x16 <= 2 && 0 <= x12 + 1 - 3 * x16 && x12 + 1 = x14 && x12 + 1 - 3 * x16 = x15

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

This digraph is fully evaluated!

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f80_0_main_EQ(x6:0, x10:0) -> f80_0_main_EQ(x6:0 + 1, x6:0 + 1 - 3 * x16:0) :|: x6:0 + 1 - 3 * x16:0 >= 0 && x6:0 + 1 - 3 * x16:0 <= 2 && x10:0 > 0

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(7) IRSwTChainingProof (EQUIVALENT)
Chaining!
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(8)
Obligation:
Rules:
f80_0_main_EQ(x, x1) -> f80_0_main_EQ(x + 2, x + 2 + -3 * x5) :|: TRUE && x + -3 * x2 <= 1 && x1 >= 1 && x + -3 * x5 >= -2 && x + -3 * x5 <= 0 && x + -3 * x2 >= 0

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(9) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f80_0_main_EQ(x, x1) -> f80_0_main_EQ(x + 2, x + 2 + -3 * x5) :|: TRUE && x + -3 * x2 <= 1 && x1 >= 1 && x + -3 * x5 >= -2 && x + -3 * x5 <= 0 && x + -3 * x2 >= 0

No arcs!

This digraph is fully evaluated!
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(10)
TRUE