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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 77 ms]
(4) TRUE


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(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2) -> f74_0_main_LE(arg1P, arg2P) :|: 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg2 - 1
f74_0_main_LE(x, x1) -> f74_0_main_LE'(x2, x3) :|: x - 2 * x4 = 0 && 0 <= x - 1 && x = x2
f74_0_main_LE'(x6, x8) -> f74_0_main_LE(x9, x10) :|: 0 <= x6 - 1 && x6 - 2 * x11 = 0 && x6 - 2 * x11 <= 1 && 0 <= x6 - 2 * x11 && x6 - 1 = x9
__init(x12, x13) -> f1_0_main_Load(x14, x15) :|: 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) -> f74_0_main_LE(arg1P, arg2P) :|: 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg2 - 1
f74_0_main_LE(x, x1) -> f74_0_main_LE'(x2, x3) :|: x - 2 * x4 = 0 && 0 <= x - 1 && x = x2
f74_0_main_LE'(x6, x8) -> f74_0_main_LE(x9, x10) :|: 0 <= x6 - 1 && x6 - 2 * x11 = 0 && x6 - 2 * x11 <= 1 && 0 <= x6 - 2 * x11 && x6 - 1 = x9
__init(x12, x13) -> f1_0_main_Load(x14, x15) :|: 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) -> f74_0_main_LE(arg1P, arg2P) :|: 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg2 - 1
(2) f74_0_main_LE(x, x1) -> f74_0_main_LE'(x2, x3) :|: x - 2 * x4 = 0 && 0 <= x - 1 && x = x2
(3) f74_0_main_LE'(x6, x8) -> f74_0_main_LE(x9, x10) :|: 0 <= x6 - 1 && x6 - 2 * x11 = 0 && x6 - 2 * x11 <= 1 && 0 <= x6 - 2 * x11 && x6 - 1 = x9
(4) __init(x12, x13) -> f1_0_main_Load(x14, x15) :|: 0 <= 0

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

This digraph is fully evaluated!
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(4)
TRUE