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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 81 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IRSwT
(7) FilterProof [EQUIVALENT, 3 ms]
(8) IntTRS
(9) IntTRSNonPeriodicNontermProof [COMPLETE, 0 ms]
(10) NO


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(0)
Obligation:
Rules:
f1_0_main_Load(arg1, arg2) -> f116_0_flip_EQ(arg1P, arg2P) :|: 0 <= arg1 - 1 && -1 <= arg2P - 1 && 1 <= arg2 - 1 && -1 <= arg1P - 1
f116_0_flip_EQ(x, x1) -> f116_0_flip_EQ(x2, x3) :|: x = x3 && x1 = x2 && 0 <= x - 1 && 0 <= x1 - 1
__init(x4, x5) -> f1_0_main_Load(x6, x7) :|: 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_Load(arg1, arg2) -> f116_0_flip_EQ(arg1P, arg2P) :|: 0 <= arg1 - 1 && -1 <= arg2P - 1 && 1 <= arg2 - 1 && -1 <= arg1P - 1
f116_0_flip_EQ(x, x1) -> f116_0_flip_EQ(x2, x3) :|: x = x3 && x1 = x2 && 0 <= x - 1 && 0 <= x1 - 1
__init(x4, x5) -> f1_0_main_Load(x6, x7) :|: 0 <= 0
Start term: __init(arg1, arg2)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1_0_main_Load(arg1, arg2) -> f116_0_flip_EQ(arg1P, arg2P) :|: 0 <= arg1 - 1 && -1 <= arg2P - 1 && 1 <= arg2 - 1 && -1 <= arg1P - 1
(2) f116_0_flip_EQ(x, x1) -> f116_0_flip_EQ(x2, x3) :|: x = x3 && x1 = x2 && 0 <= x - 1 && 0 <= x1 - 1
(3) __init(x4, x5) -> f1_0_main_Load(x6, x7) :|: 0 <= 0

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

This digraph is fully evaluated!
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(4)
Obligation:

Termination digraph:
Nodes:
(1) f116_0_flip_EQ(x, x1) -> f116_0_flip_EQ(x2, x3) :|: x = x3 && x1 = x2 && 0 <= x - 1 && 0 <= x1 - 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:
f116_0_flip_EQ(x3:0, x1:0) -> f116_0_flip_EQ(x1:0, x3:0) :|: x1:0 > 0 && x3:0 > 0

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(7) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f116_0_flip_EQ(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(8)
Obligation:
Rules:
f116_0_flip_EQ(x3:0, x1:0) -> f116_0_flip_EQ(x1:0, x3:0) :|: x1:0 > 0 && x3:0 > 0

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(9) IntTRSNonPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x3:0, x1:0) -> f(1, x1:0, x3:0) :|: pc = 1 && (x1:0 > 0 && x3:0 > 0)
Proved unsatisfiability of the following formula, indicating that the system is never left after entering:
(((run2_0 = ((1 * 1)) and run2_1 = ((run1_2 * 1)) and run2_2 = ((run1_1 * 1))) and (((run1_0 * 1)) = ((1 * 1)) and (((run1_2 * 1)) > 0 and ((run1_1 * 1)) > 0))) and !(((run2_0 * 1)) = ((1 * 1)) and (((run2_2 * 1)) > 0 and ((run2_1 * 1)) > 0)))
Proved satisfiability of the following formula, indicating that the system is entered at least once:
((run2_0 = ((1 * 1)) and run2_1 = ((run1_2 * 1)) and run2_2 = ((run1_1 * 1))) and (((run1_0 * 1)) = ((1 * 1)) and (((run1_2 * 1)) > 0 and ((run1_1 * 1)) > 0)))

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(10)
NO