NO
proof of prog.inttrs
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given IRSwT could be disproven:

(0) IRSwT
(1) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(2) IRSwT
(3) IRSwTTerminationDigraphProof [EQUIVALENT, 82 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 17 ms]
(6) IRSwT
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) FilterProof [EQUIVALENT, 0 ms]
(10) IntTRS
(11) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(12) IntTRS
(13) IntTRSPeriodicNontermProof [COMPLETE, 0 ms]
(14) NO


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(0)
Obligation:
Rules:
f34_0_loop_Inc(arg1, arg2, arg3) -> f34_0_loop_Inc(arg1P, arg2P, arg3P) :|: arg3 = arg3P && arg2 + 1 = arg2P && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg1P <= arg1
f1_0_main_Load(x, x1, x2) -> f34_0_loop_Inc(x3, x4, x5) :|: x1 = x5 && x1 + 1 = x4 && 0 <= x3 - 1 && 0 <= x - 1 && -1 <= x1 - 1 && x3 <= x
__init(x6, x7, x8) -> f1_0_main_Load(x9, x10, x11) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3)

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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:
f34_0_loop_Inc(arg1, arg2, arg3) -> f34_0_loop_Inc(arg1P, arg2P, arg3P) :|: arg3 = arg3P && arg2 + 1 = arg2P && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg1P <= arg1
f1_0_main_Load(x, x1, x2) -> f34_0_loop_Inc(x3, x4, x5) :|: x1 = x5 && x1 + 1 = x4 && 0 <= x3 - 1 && 0 <= x - 1 && -1 <= x1 - 1 && x3 <= x
__init(x6, x7, x8) -> f1_0_main_Load(x9, x10, x11) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f34_0_loop_Inc(arg1, arg2, arg3) -> f34_0_loop_Inc(arg1P, arg2P, arg3P) :|: arg3 = arg3P && arg2 + 1 = arg2P && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg1P <= arg1
(2) f1_0_main_Load(x, x1, x2) -> f34_0_loop_Inc(x3, x4, x5) :|: x1 = x5 && x1 + 1 = x4 && 0 <= x3 - 1 && 0 <= x - 1 && -1 <= x1 - 1 && x3 <= x
(3) __init(x6, x7, x8) -> f1_0_main_Load(x9, x10, x11) :|: 0 <= 0

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) f34_0_loop_Inc(arg1, arg2, arg3) -> f34_0_loop_Inc(arg1P, arg2P, arg3P) :|: arg3 = arg3P && arg2 + 1 = arg2P && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg1P <= arg1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f34_0_loop_Inc(arg1:0, arg2:0, arg3:0) -> f34_0_loop_Inc(arg1P:0, arg2:0 + 1, arg3:0) :|: arg1:0 > 0 && arg1P:0 > 0 && arg1P:0 <= arg1:0

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(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:

   f34_0_loop_Inc(x1, x2, x3) -> f34_0_loop_Inc(x1)

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(8)
Obligation:
Rules:
f34_0_loop_Inc(arg1:0) -> f34_0_loop_Inc(arg1P:0) :|: arg1:0 > 0 && arg1P:0 > 0 && arg1P:0 <= arg1:0

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(9) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f34_0_loop_Inc(INTEGER)
Replaced non-predefined constructor symbols by 0.
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(10)
Obligation:
Rules:
f34_0_loop_Inc(arg1:0) -> f34_0_loop_Inc(arg1P:0) :|: arg1:0 > 0 && arg1P:0 > 0 && arg1P:0 <= arg1:0

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(11) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(12)
Obligation:
Rules:
f34_0_loop_Inc(arg1:0:0) -> f34_0_loop_Inc(arg1P:0:0) :|: arg1:0:0 > 0 && arg1P:0:0 > 0 && arg1P:0:0 <= arg1:0:0

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(13) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, arg1:0:0) -> f(1, arg1P:0:0) :|: pc = 1 && (arg1:0:0 > 0 && arg1P:0:0 > 0 && arg1P:0:0 <= arg1:0:0)
Witness term starting non-terminating reduction: f(1, 16)
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(14)
NO