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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 127 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IRSwT
(7) TempFilterProof [SOUND, 36 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 12 ms]
(10) IntTRS
(11) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(12) YES


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(0)
Obligation:
Rules:
f1_0_main_ConstantStackPush(arg1, arg2) -> f139_0_main_GE(arg1P, arg2P) :|: 0 = arg1P
f139_0_main_GE(x, x1) -> f169_0_main_GE(x2, x3) :|: 3 = x3 && x = x2 && x <= 9
f169_0_main_GE(x4, x5) -> f139_0_main_GE(x6, x7) :|: x4 + 1 = x6 && 11 <= x5 - 1
f169_0_main_GE(x8, x9) -> f169_0_main_GE(x10, x11) :|: x9 + 1 = x11 && x8 = x10 && x9 <= 11
__init(x12, x13) -> f1_0_main_ConstantStackPush(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_ConstantStackPush(arg1, arg2) -> f139_0_main_GE(arg1P, arg2P) :|: 0 = arg1P
f139_0_main_GE(x, x1) -> f169_0_main_GE(x2, x3) :|: 3 = x3 && x = x2 && x <= 9
f169_0_main_GE(x4, x5) -> f139_0_main_GE(x6, x7) :|: x4 + 1 = x6 && 11 <= x5 - 1
f169_0_main_GE(x8, x9) -> f169_0_main_GE(x10, x11) :|: x9 + 1 = x11 && x8 = x10 && x9 <= 11
__init(x12, x13) -> f1_0_main_ConstantStackPush(x14, x15) :|: 0 <= 0
Start term: __init(arg1, arg2)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_ConstantStackPush(arg1, arg2) -> f139_0_main_GE(arg1P, arg2P) :|: 0 = arg1P
(2) f139_0_main_GE(x, x1) -> f169_0_main_GE(x2, x3) :|: 3 = x3 && x = x2 && x <= 9
(3) f169_0_main_GE(x4, x5) -> f139_0_main_GE(x6, x7) :|: x4 + 1 = x6 && 11 <= x5 - 1
(4) f169_0_main_GE(x8, x9) -> f169_0_main_GE(x10, x11) :|: x9 + 1 = x11 && x8 = x10 && x9 <= 11
(5) __init(x12, x13) -> f1_0_main_ConstantStackPush(x14, x15) :|: 0 <= 0

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) f139_0_main_GE(x, x1) -> f169_0_main_GE(x2, x3) :|: 3 = x3 && x = x2 && x <= 9
(2) f169_0_main_GE(x4, x5) -> f139_0_main_GE(x6, x7) :|: x4 + 1 = x6 && 11 <= x5 - 1
(3) f169_0_main_GE(x8, x9) -> f169_0_main_GE(x10, x11) :|: x9 + 1 = x11 && x8 = x10 && x9 <= 11

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

This digraph is fully evaluated!

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f169_0_main_GE(x10:0, x9:0) -> f169_0_main_GE(x10:0, x9:0 + 1) :|: x9:0 < 12
f169_0_main_GE(x4:0, x5:0) -> f169_0_main_GE(x4:0 + 1, 3) :|: x5:0 > 11 && x4:0 < 9

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(7) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f169_0_main_GE(VARIABLE, VARIABLE)
Replaced non-predefined constructor symbols by 0.
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(8)
Obligation:
Rules:
f169_0_main_GE(x10:0, x9:0) -> f169_0_main_GE(x10:0, c) :|: c = x9:0 + 1 && x9:0 < 12
f169_0_main_GE(x4:0, x5:0) -> f169_0_main_GE(c1, c2) :|: c2 = 3 && c1 = x4:0 + 1 && (x5:0 > 11 && x4:0 < 9)

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f169_0_main_GE(x, x1)] = 8 - x

The following rules are decreasing:
f169_0_main_GE(x4:0, x5:0) -> f169_0_main_GE(c1, c2) :|: c2 = 3 && c1 = x4:0 + 1 && (x5:0 > 11 && x4:0 < 9)
The following rules are bounded:
f169_0_main_GE(x4:0, x5:0) -> f169_0_main_GE(c1, c2) :|: c2 = 3 && c1 = x4:0 + 1 && (x5:0 > 11 && x4:0 < 9)

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(10)
Obligation:
Rules:
f169_0_main_GE(x10:0, x9:0) -> f169_0_main_GE(x10:0, c) :|: c = x9:0 + 1 && x9:0 < 12

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(11) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f169_0_main_GE(x, x1)] = 11 - x1

The following rules are decreasing:
f169_0_main_GE(x10:0, x9:0) -> f169_0_main_GE(x10:0, c) :|: c = x9:0 + 1 && x9:0 < 12
The following rules are bounded:
f169_0_main_GE(x10:0, x9:0) -> f169_0_main_GE(x10:0, c) :|: c = x9:0 + 1 && x9:0 < 12

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(12)
YES