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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 295 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 22 ms]
(6) IRSwT
(7) TempFilterProof [SOUND, 75 ms]
(8) IntTRS
(9) RankingReductionPairProof [EQUIVALENT, 0 ms]
(10) IntTRS
(11) RankingReductionPairProof [EQUIVALENT, 1 ms]
(12) YES


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(0)
Obligation:
Rules:
f1_0_main_ConstantStackPush(arg1, arg2, arg3) -> f458_0_sort_GE(arg1P, arg2P, arg3P) :|: 1 = arg1P
f458_0_sort_GE(x, x1, x2) -> f543_0_sort_GE(x3, x4, x5) :|: 100 - x = x5 && 0 = x4 && x = x3 && x <= 99 && 0 <= x - 1
f543_0_sort_GE(x6, x9, x10) -> f458_0_sort_GE(x11, x14, x15) :|: x6 + 1 = x11 && x10 <= x9
f543_0_sort_GE(x16, x17, x18) -> f543_0_sort_GE(x19, x20, x21) :|: x17 <= 99 && x17 <= x18 - 1 && -1 <= x17 - 1 && x17 <= 98 && x22 <= x23 && 0 <= x16 - 1 && x16 = x19 && x17 + 1 = x20 && 100 - x16 = x21
f543_0_sort_GE(x24, x25, x26) -> f543_0_sort_GE(x27, x28, x29) :|: x25 <= 99 && x25 <= x26 - 1 && -1 <= x25 - 1 && x25 <= 98 && 0 <= x24 - 1 && x30 <= x31 - 1 && x24 = x27 && x25 + 1 = x28 && 100 - x24 = x29
__init(x32, x33, x34) -> f1_0_main_ConstantStackPush(x35, x36, x37) :|: 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:
f1_0_main_ConstantStackPush(arg1, arg2, arg3) -> f458_0_sort_GE(arg1P, arg2P, arg3P) :|: 1 = arg1P
f458_0_sort_GE(x, x1, x2) -> f543_0_sort_GE(x3, x4, x5) :|: 100 - x = x5 && 0 = x4 && x = x3 && x <= 99 && 0 <= x - 1
f543_0_sort_GE(x6, x9, x10) -> f458_0_sort_GE(x11, x14, x15) :|: x6 + 1 = x11 && x10 <= x9
f543_0_sort_GE(x16, x17, x18) -> f543_0_sort_GE(x19, x20, x21) :|: x17 <= 99 && x17 <= x18 - 1 && -1 <= x17 - 1 && x17 <= 98 && x22 <= x23 && 0 <= x16 - 1 && x16 = x19 && x17 + 1 = x20 && 100 - x16 = x21
f543_0_sort_GE(x24, x25, x26) -> f543_0_sort_GE(x27, x28, x29) :|: x25 <= 99 && x25 <= x26 - 1 && -1 <= x25 - 1 && x25 <= 98 && 0 <= x24 - 1 && x30 <= x31 - 1 && x24 = x27 && x25 + 1 = x28 && 100 - x24 = x29
__init(x32, x33, x34) -> f1_0_main_ConstantStackPush(x35, x36, x37) :|: 0 <= 0
Start term: __init(arg1, arg2, arg3)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_ConstantStackPush(arg1, arg2, arg3) -> f458_0_sort_GE(arg1P, arg2P, arg3P) :|: 1 = arg1P
(2) f458_0_sort_GE(x, x1, x2) -> f543_0_sort_GE(x3, x4, x5) :|: 100 - x = x5 && 0 = x4 && x = x3 && x <= 99 && 0 <= x - 1
(3) f543_0_sort_GE(x6, x9, x10) -> f458_0_sort_GE(x11, x14, x15) :|: x6 + 1 = x11 && x10 <= x9
(4) f543_0_sort_GE(x16, x17, x18) -> f543_0_sort_GE(x19, x20, x21) :|: x17 <= 99 && x17 <= x18 - 1 && -1 <= x17 - 1 && x17 <= 98 && x22 <= x23 && 0 <= x16 - 1 && x16 = x19 && x17 + 1 = x20 && 100 - x16 = x21
(5) f543_0_sort_GE(x24, x25, x26) -> f543_0_sort_GE(x27, x28, x29) :|: x25 <= 99 && x25 <= x26 - 1 && -1 <= x25 - 1 && x25 <= 98 && 0 <= x24 - 1 && x30 <= x31 - 1 && x24 = x27 && x25 + 1 = x28 && 100 - x24 = x29
(6) __init(x32, x33, x34) -> f1_0_main_ConstantStackPush(x35, x36, x37) :|: 0 <= 0

Arcs:
(1) -> (2)
(2) -> (4), (5)
(3) -> (2)
(4) -> (3), (4), (5)
(5) -> (3), (4), (5)
(6) -> (1)

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) f458_0_sort_GE(x, x1, x2) -> f543_0_sort_GE(x3, x4, x5) :|: 100 - x = x5 && 0 = x4 && x = x3 && x <= 99 && 0 <= x - 1
(2) f543_0_sort_GE(x6, x9, x10) -> f458_0_sort_GE(x11, x14, x15) :|: x6 + 1 = x11 && x10 <= x9
(3) f543_0_sort_GE(x16, x17, x18) -> f543_0_sort_GE(x19, x20, x21) :|: x17 <= 99 && x17 <= x18 - 1 && -1 <= x17 - 1 && x17 <= 98 && x22 <= x23 && 0 <= x16 - 1 && x16 = x19 && x17 + 1 = x20 && 100 - x16 = x21
(4) f543_0_sort_GE(x24, x25, x26) -> f543_0_sort_GE(x27, x28, x29) :|: x25 <= 99 && x25 <= x26 - 1 && -1 <= x25 - 1 && x25 <= 98 && 0 <= x24 - 1 && x30 <= x31 - 1 && x24 = x27 && x25 + 1 = x28 && 100 - x24 = x29

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

This digraph is fully evaluated!

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f543_0_sort_GE(x6:0, x9:0, x10:0) -> f543_0_sort_GE(x6:0 + 1, 0, 100 - (x6:0 + 1)) :|: x6:0 > -1 && x6:0 < 99 && x9:0 >= x10:0
f543_0_sort_GE(x16:0, x17:0, x18:0) -> f543_0_sort_GE(x16:0, x17:0 + 1, 100 - x16:0) :|: x23:0 >= x22:0 && x16:0 > 0 && x17:0 < 99 && x17:0 > -1 && x18:0 - 1 >= x17:0 && x17:0 < 100
f543_0_sort_GE(x24:0, x25:0, x26:0) -> f543_0_sort_GE(x24:0, x25:0 + 1, 100 - x24:0) :|: x24:0 > 0 && x31:0 - 1 >= x30:0 && x25:0 < 99 && x25:0 > -1 && x26:0 - 1 >= x25:0 && x25:0 < 100

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(7) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f543_0_sort_GE(INTEGER, VARIABLE, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(8)
Obligation:
Rules:
f543_0_sort_GE(x6:0, x9:0, x10:0) -> f543_0_sort_GE(c, c1, c2) :|: c2 = 100 - (x6:0 + 1) && (c1 = 0 && c = x6:0 + 1) && (x6:0 > -1 && x6:0 < 99 && x9:0 >= x10:0)
f543_0_sort_GE(x16:0, x17:0, x18:0) -> f543_0_sort_GE(x16:0, c3, c4) :|: c4 = 100 - x16:0 && c3 = x17:0 + 1 && (x23:0 >= x22:0 && x16:0 > 0 && x17:0 < 99 && x17:0 > -1 && x18:0 - 1 >= x17:0 && x17:0 < 100)
f543_0_sort_GE(x24:0, x25:0, x26:0) -> f543_0_sort_GE(x24:0, c5, c6) :|: c6 = 100 - x24:0 && c5 = x25:0 + 1 && (x24:0 > 0 && x31:0 - 1 >= x30:0 && x25:0 < 99 && x25:0 > -1 && x26:0 - 1 >= x25:0 && x25:0 < 100)

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(9) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f543_0_sort_GE ] = -1*f543_0_sort_GE_1

The following rules are decreasing:
f543_0_sort_GE(x6:0, x9:0, x10:0) -> f543_0_sort_GE(c, c1, c2) :|: c2 = 100 - (x6:0 + 1) && (c1 = 0 && c = x6:0 + 1) && (x6:0 > -1 && x6:0 < 99 && x9:0 >= x10:0)

The following rules are bounded:
f543_0_sort_GE(x6:0, x9:0, x10:0) -> f543_0_sort_GE(c, c1, c2) :|: c2 = 100 - (x6:0 + 1) && (c1 = 0 && c = x6:0 + 1) && (x6:0 > -1 && x6:0 < 99 && x9:0 >= x10:0)


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(10)
Obligation:
Rules:
f543_0_sort_GE(x16:0, x17:0, x18:0) -> f543_0_sort_GE(x16:0, c3, c4) :|: c4 = 100 - x16:0 && c3 = x17:0 + 1 && (x23:0 >= x22:0 && x16:0 > 0 && x17:0 < 99 && x17:0 > -1 && x18:0 - 1 >= x17:0 && x17:0 < 100)
f543_0_sort_GE(x24:0, x25:0, x26:0) -> f543_0_sort_GE(x24:0, c5, c6) :|: c6 = 100 - x24:0 && c5 = x25:0 + 1 && (x24:0 > 0 && x31:0 - 1 >= x30:0 && x25:0 < 99 && x25:0 > -1 && x26:0 - 1 >= x25:0 && x25:0 < 100)

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(11) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f543_0_sort_GE ] = -1*f543_0_sort_GE_2

The following rules are decreasing:
f543_0_sort_GE(x16:0, x17:0, x18:0) -> f543_0_sort_GE(x16:0, c3, c4) :|: c4 = 100 - x16:0 && c3 = x17:0 + 1 && (x23:0 >= x22:0 && x16:0 > 0 && x17:0 < 99 && x17:0 > -1 && x18:0 - 1 >= x17:0 && x17:0 < 100)
f543_0_sort_GE(x24:0, x25:0, x26:0) -> f543_0_sort_GE(x24:0, c5, c6) :|: c6 = 100 - x24:0 && c5 = x25:0 + 1 && (x24:0 > 0 && x31:0 - 1 >= x30:0 && x25:0 < 99 && x25:0 > -1 && x26:0 - 1 >= x25:0 && x25:0 < 100)

The following rules are bounded:
f543_0_sort_GE(x16:0, x17:0, x18:0) -> f543_0_sort_GE(x16:0, c3, c4) :|: c4 = 100 - x16:0 && c3 = x17:0 + 1 && (x23:0 >= x22:0 && x16:0 > 0 && x17:0 < 99 && x17:0 > -1 && x18:0 - 1 >= x17:0 && x17:0 < 100)
f543_0_sort_GE(x24:0, x25:0, x26:0) -> f543_0_sort_GE(x24:0, c5, c6) :|: c6 = 100 - x24:0 && c5 = x25:0 + 1 && (x24:0 > 0 && x31:0 - 1 >= x30:0 && x25:0 < 99 && x25:0 > -1 && x26:0 - 1 >= x25:0 && x25:0 < 100)


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(12)
YES