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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 167 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IRSwT
(7) IRSwTChainingProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) IRSwTTerminationDigraphProof [EQUIVALENT, 11 ms]
(10) IRSwT
(11) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(12) IRSwT
(13) TempFilterProof [SOUND, 1400 ms]
(14) IntTRS
(15) RankingReductionPairProof [EQUIVALENT, 1378 ms]
(16) YES


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(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2, arg3, arg4) -> f587_0_main_LT(arg1P, arg2P, arg3P, arg4P) :|: 2 = arg4P && arg1P - arg2P = arg3P && 0 <= arg1 - 1 && -1 <= arg2P - 1 && -1 <= arg2 - 1 && -1 <= arg1P - 1
f587_0_main_LT(x, x1, x2, x3) -> f587_0_main_LT(x4, x5, x6, x7) :|: -1 <= x3 - 1 && 0 <= x2 - 1 && -1 <= x10 - 1 && -1 <= x11 - 1 && -1 <= x1 - 1 && 0 <= x1 + x11 + 1 && x - x10 = x4 && x1 + x11 + 1 = x5 && x - x10 - (x1 + x11 + 1) = x6 && x3 + 2 = x7
__init(x12, x13, x14, x15) -> f1_0_main_Load(x16, x17, x18, x19) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4)

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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) -> f587_0_main_LT(arg1P, arg2P, arg3P, arg4P) :|: 2 = arg4P && arg1P - arg2P = arg3P && 0 <= arg1 - 1 && -1 <= arg2P - 1 && -1 <= arg2 - 1 && -1 <= arg1P - 1
f587_0_main_LT(x, x1, x2, x3) -> f587_0_main_LT(x4, x5, x6, x7) :|: -1 <= x3 - 1 && 0 <= x2 - 1 && -1 <= x10 - 1 && -1 <= x11 - 1 && -1 <= x1 - 1 && 0 <= x1 + x11 + 1 && x - x10 = x4 && x1 + x11 + 1 = x5 && x - x10 - (x1 + x11 + 1) = x6 && x3 + 2 = x7
__init(x12, x13, x14, x15) -> f1_0_main_Load(x16, x17, x18, x19) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3, arg4)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_Load(arg1, arg2, arg3, arg4) -> f587_0_main_LT(arg1P, arg2P, arg3P, arg4P) :|: 2 = arg4P && arg1P - arg2P = arg3P && 0 <= arg1 - 1 && -1 <= arg2P - 1 && -1 <= arg2 - 1 && -1 <= arg1P - 1
(2) f587_0_main_LT(x, x1, x2, x3) -> f587_0_main_LT(x4, x5, x6, x7) :|: -1 <= x3 - 1 && 0 <= x2 - 1 && -1 <= x10 - 1 && -1 <= x11 - 1 && -1 <= x1 - 1 && 0 <= x1 + x11 + 1 && x - x10 = x4 && x1 + x11 + 1 = x5 && x - x10 - (x1 + x11 + 1) = x6 && x3 + 2 = x7
(3) __init(x12, x13, x14, x15) -> f1_0_main_Load(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) f587_0_main_LT(x, x1, x2, x3) -> f587_0_main_LT(x4, x5, x6, x7) :|: -1 <= x3 - 1 && 0 <= x2 - 1 && -1 <= x10 - 1 && -1 <= x11 - 1 && -1 <= x1 - 1 && 0 <= x1 + x11 + 1 && x - x10 = x4 && x1 + x11 + 1 = x5 && x - x10 - (x1 + x11 + 1) = x6 && x3 + 2 = x7

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f587_0_main_LT(x:0, x1:0, x2:0, x3:0) -> f587_0_main_LT(x:0 - x10:0, x1:0 + x11:0 + 1, x:0 - x10:0 - (x1:0 + x11:0 + 1), x3:0 + 2) :|: x1:0 > -1 && x1:0 + x11:0 >= -1 && x11:0 > -1 && x10:0 > -1 && x2:0 > 0 && x3:0 > -1

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(7) IRSwTChainingProof (EQUIVALENT)
Chaining!
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(8)
Obligation:
Rules:
f587_0_main_LT(x, x1, x2, x3) -> f587_0_main_LT(x + -1 * x4 + -1 * x10, x1 + x5 + 2 + x11, x + -1 * x4 + -1 * x10 + -1 * x1 + -1 * x5 + -2 + -1 * x11, x3 + 4) :|: TRUE && x1 >= 0 && x1 + x5 >= -1 && x5 >= 0 && x4 >= 0 && x2 >= 1 && x3 >= 0 && x1 + x5 + x11 >= -2 && x11 >= 0 && x10 >= 0 && x + -1 * x4 + -1 * x1 + -1 * x5 >= 2

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(9) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f587_0_main_LT(x, x1, x2, x3) -> f587_0_main_LT(x + -1 * x4 + -1 * x10, x1 + x5 + 2 + x11, x + -1 * x4 + -1 * x10 + -1 * x1 + -1 * x5 + -2 + -1 * x11, x3 + 4) :|: TRUE && x1 >= 0 && x1 + x5 >= -1 && x5 >= 0 && x4 >= 0 && x2 >= 1 && x3 >= 0 && x1 + x5 + x11 >= -2 && x11 >= 0 && x10 >= 0 && x + -1 * x4 + -1 * x1 + -1 * x5 >= 2

Arcs:
(1) -> (1)

This digraph is fully evaluated!
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(10)
Obligation:

Termination digraph:
Nodes:
(1) f587_0_main_LT(x, x1, x2, x3) -> f587_0_main_LT(x + -1 * x4 + -1 * x10, x1 + x5 + 2 + x11, x + -1 * x4 + -1 * x10 + -1 * x1 + -1 * x5 + -2 + -1 * x11, x3 + 4) :|: TRUE && x1 >= 0 && x1 + x5 >= -1 && x5 >= 0 && x4 >= 0 && x2 >= 1 && x3 >= 0 && x1 + x5 + x11 >= -2 && x11 >= 0 && x10 >= 0 && x + -1 * x4 + -1 * x1 + -1 * x5 >= 2

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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(11) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(12)
Obligation:
Rules:
f587_0_main_LT(x:0, x1:0, x2:0, x3:0) -> f587_0_main_LT(x:0 + -1 * x4:0 + -1 * x10:0, x1:0 + x5:0 + 2 + x11:0, x:0 + -1 * x4:0 + -1 * x10:0 + -1 * x1:0 + -1 * x5:0 - 2 + -1 * x11:0, x3:0 + 4) :|: x10:0 > -1 && x:0 + -1 * x4:0 + -1 * x1:0 + -1 * x5:0 >= 2 && x11:0 > -1 && x1:0 + x5:0 + x11:0 >= -2 && x3:0 > -1 && x2:0 > 0 && x4:0 > -1 && x5:0 > -1 && x1:0 > -1 && x1:0 + x5:0 >= -1

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(13) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f587_0_main_LT(INTEGER, INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(14)
Obligation:
Rules:
f587_0_main_LT(x:0, x1:0, x2:0, x3:0) -> f587_0_main_LT(c, c1, c2, c3) :|: c3 = x3:0 + 4 && (c2 = x:0 + -1 * x4:0 + -1 * x10:0 + -1 * x1:0 + -1 * x5:0 - 2 + -1 * x11:0 && (c1 = x1:0 + x5:0 + 2 + x11:0 && c = x:0 + -1 * x4:0 + -1 * x10:0)) && (x10:0 > -1 && x:0 + -1 * x4:0 + -1 * x1:0 + -1 * x5:0 >= 2 && x11:0 > -1 && x1:0 + x5:0 + x11:0 >= -2 && x3:0 > -1 && x2:0 > 0 && x4:0 > -1 && x5:0 > -1 && x1:0 > -1 && x1:0 + x5:0 >= -1)

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(15) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f587_0_main_LT ] = -1/2*f587_0_main_LT_2 + 1/2*f587_0_main_LT_1

The following rules are decreasing:
f587_0_main_LT(x:0, x1:0, x2:0, x3:0) -> f587_0_main_LT(c, c1, c2, c3) :|: c3 = x3:0 + 4 && (c2 = x:0 + -1 * x4:0 + -1 * x10:0 + -1 * x1:0 + -1 * x5:0 - 2 + -1 * x11:0 && (c1 = x1:0 + x5:0 + 2 + x11:0 && c = x:0 + -1 * x4:0 + -1 * x10:0)) && (x10:0 > -1 && x:0 + -1 * x4:0 + -1 * x1:0 + -1 * x5:0 >= 2 && x11:0 > -1 && x1:0 + x5:0 + x11:0 >= -2 && x3:0 > -1 && x2:0 > 0 && x4:0 > -1 && x5:0 > -1 && x1:0 > -1 && x1:0 + x5:0 >= -1)

The following rules are bounded:
f587_0_main_LT(x:0, x1:0, x2:0, x3:0) -> f587_0_main_LT(c, c1, c2, c3) :|: c3 = x3:0 + 4 && (c2 = x:0 + -1 * x4:0 + -1 * x10:0 + -1 * x1:0 + -1 * x5:0 - 2 + -1 * x11:0 && (c1 = x1:0 + x5:0 + 2 + x11:0 && c = x:0 + -1 * x4:0 + -1 * x10:0)) && (x10:0 > -1 && x:0 + -1 * x4:0 + -1 * x1:0 + -1 * x5:0 >= 2 && x11:0 > -1 && x1:0 + x5:0 + x11:0 >= -2 && x3:0 > -1 && x2:0 > 0 && x4:0 > -1 && x5:0 > -1 && x1:0 > -1 && x1:0 + x5:0 >= -1)


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(16)
YES