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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 176 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IRSwT
(7) TempFilterProof [SOUND, 22 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(10) YES


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(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3, arg4, arg5) -> f262_0_take_GE(arg1P, arg2P, arg3P, arg4P, arg5P) :|: 0 = arg3P && 0 <= arg2P - 1 && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg2P <= arg1 && -1 <= arg4P - 1 && 1 <= arg2 - 1 && -1 <= arg5P - 1
f262_0_take_GE(x, x1, x2, x3, x4) -> f262_0_take_GE(x5, x6, x7, x8, x9) :|: x4 = x9 && x3 + 1 = x8 && x2 + 1 = x7 && x3 + 2 <= x && 0 <= x6 - 1 && 0 <= x5 - 1 && 0 <= x1 - 1 && 0 <= x - 1 && x6 <= x1 && x6 <= x && x5 - 1 <= x && x2 <= x4 - 1 && -1 <= x3 - 1
__init(x10, x11, x12, x13, x14) -> f1_0_main_Load(x15, x16, x17, x18, x19) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4, arg5)

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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, arg3, arg4, arg5) -> f262_0_take_GE(arg1P, arg2P, arg3P, arg4P, arg5P) :|: 0 = arg3P && 0 <= arg2P - 1 && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg2P <= arg1 && -1 <= arg4P - 1 && 1 <= arg2 - 1 && -1 <= arg5P - 1
f262_0_take_GE(x, x1, x2, x3, x4) -> f262_0_take_GE(x5, x6, x7, x8, x9) :|: x4 = x9 && x3 + 1 = x8 && x2 + 1 = x7 && x3 + 2 <= x && 0 <= x6 - 1 && 0 <= x5 - 1 && 0 <= x1 - 1 && 0 <= x - 1 && x6 <= x1 && x6 <= x && x5 - 1 <= x && x2 <= x4 - 1 && -1 <= x3 - 1
__init(x10, x11, x12, x13, x14) -> f1_0_main_Load(x15, x16, x17, x18, x19) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4, arg5)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_Load(arg1, arg2, arg3, arg4, arg5) -> f262_0_take_GE(arg1P, arg2P, arg3P, arg4P, arg5P) :|: 0 = arg3P && 0 <= arg2P - 1 && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg2P <= arg1 && -1 <= arg4P - 1 && 1 <= arg2 - 1 && -1 <= arg5P - 1
(2) f262_0_take_GE(x, x1, x2, x3, x4) -> f262_0_take_GE(x5, x6, x7, x8, x9) :|: x4 = x9 && x3 + 1 = x8 && x2 + 1 = x7 && x3 + 2 <= x && 0 <= x6 - 1 && 0 <= x5 - 1 && 0 <= x1 - 1 && 0 <= x - 1 && x6 <= x1 && x6 <= x && x5 - 1 <= x && x2 <= x4 - 1 && -1 <= x3 - 1
(3) __init(x10, x11, x12, x13, x14) -> f1_0_main_Load(x15, x16, x17, x18, x19) :|: 0 <= 0

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) f262_0_take_GE(x, x1, x2, x3, x4) -> f262_0_take_GE(x5, x6, x7, x8, x9) :|: x4 = x9 && x3 + 1 = x8 && x2 + 1 = x7 && x3 + 2 <= x && 0 <= x6 - 1 && 0 <= x5 - 1 && 0 <= x1 - 1 && 0 <= x - 1 && x6 <= x1 && x6 <= x && x5 - 1 <= x && x2 <= x4 - 1 && -1 <= x3 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f262_0_take_GE(x:0, x1:0, x2:0, x3:0, x4:0) -> f262_0_take_GE(x5:0, x6:0, x2:0 + 1, x3:0 + 1, x4:0) :|: x4:0 - 1 >= x2:0 && x3:0 > -1 && x:0 >= x5:0 - 1 && x:0 >= x6:0 && x6:0 <= x1:0 && x:0 > 0 && x1:0 > 0 && x5:0 > 0 && x:0 >= x3:0 + 2 && x6:0 > 0

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(7) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f262_0_take_GE(INTEGER, INTEGER, INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(8)
Obligation:
Rules:
f262_0_take_GE(x:0, x1:0, x2:0, x3:0, x4:0) -> f262_0_take_GE(x5:0, x6:0, c, c1, x4:0) :|: c1 = x3:0 + 1 && c = x2:0 + 1 && (x4:0 - 1 >= x2:0 && x3:0 > -1 && x:0 >= x5:0 - 1 && x:0 >= x6:0 && x6:0 <= x1:0 && x:0 > 0 && x1:0 > 0 && x5:0 > 0 && x:0 >= x3:0 + 2 && x6:0 > 0)

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f262_0_take_GE(x, x1, x2, x3, x4)] = -x2 + x4

The following rules are decreasing:
f262_0_take_GE(x:0, x1:0, x2:0, x3:0, x4:0) -> f262_0_take_GE(x5:0, x6:0, c, c1, x4:0) :|: c1 = x3:0 + 1 && c = x2:0 + 1 && (x4:0 - 1 >= x2:0 && x3:0 > -1 && x:0 >= x5:0 - 1 && x:0 >= x6:0 && x6:0 <= x1:0 && x:0 > 0 && x1:0 > 0 && x5:0 > 0 && x:0 >= x3:0 + 2 && x6:0 > 0)
The following rules are bounded:
f262_0_take_GE(x:0, x1:0, x2:0, x3:0, x4:0) -> f262_0_take_GE(x5:0, x6:0, c, c1, x4:0) :|: c1 = x3:0 + 1 && c = x2:0 + 1 && (x4:0 - 1 >= x2:0 && x3:0 > -1 && x:0 >= x5:0 - 1 && x:0 >= x6:0 && x6:0 <= x1:0 && x:0 > 0 && x1:0 > 0 && x5:0 > 0 && x:0 >= x3:0 + 2 && x6:0 > 0)

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(10)
YES