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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 70 ms]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IRSwT
(7) FilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) IntTRSPeriodicNontermProof [COMPLETE, 7 ms]
(10) NO


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(0)
Obligation:
Rules:
f1_0_main_ConstantStackPush(arg1, arg2) -> f43_0_loop_InvokeMethod(arg1P, arg2P) :|: -1 <= arg2 - 1 && 0 <= arg1 - 1
f43_0_loop_InvokeMethod(x, x1) -> f43_0_loop_InvokeMethod(x2, x3) :|: 0 <= 0
__init(x4, x5) -> f1_0_main_ConstantStackPush(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_ConstantStackPush(arg1, arg2) -> f43_0_loop_InvokeMethod(arg1P, arg2P) :|: -1 <= arg2 - 1 && 0 <= arg1 - 1
f43_0_loop_InvokeMethod(x, x1) -> f43_0_loop_InvokeMethod(x2, x3) :|: 0 <= 0
__init(x4, x5) -> f1_0_main_ConstantStackPush(x6, x7) :|: 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) -> f43_0_loop_InvokeMethod(arg1P, arg2P) :|: -1 <= arg2 - 1 && 0 <= arg1 - 1
(2) f43_0_loop_InvokeMethod(x, x1) -> f43_0_loop_InvokeMethod(x2, x3) :|: 0 <= 0
(3) __init(x4, x5) -> f1_0_main_ConstantStackPush(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) f43_0_loop_InvokeMethod(x, x1) -> f43_0_loop_InvokeMethod(x2, x3) :|: 0 <= 0

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f43_0_loop_InvokeMethod(x:0, x1:0) -> f43_0_loop_InvokeMethod(x2:0, x3:0) :|: TRUE

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(7) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f43_0_loop_InvokeMethod(VARIABLE, VARIABLE)
Replaced non-predefined constructor symbols by 0.
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(8)
Obligation:
Rules:
f43_0_loop_InvokeMethod(x:0, x1:0) -> f43_0_loop_InvokeMethod(x2:0, x3:0) :|: TRUE

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(9) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x:0, x1:0) -> f(1, x2:0, x3:0) :|: pc = 1 && TRUE
Witness term starting non-terminating reduction: f(1, 0, 0)
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(10)
NO