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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 145 ms]
(4) TRUE


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(0)
Obligation:
Rules:
f1_0_main_ConstantStackPush(arg1, arg2, arg3) -> f83_0_main_ArrayAccess(arg1P, arg2P, arg3P) :|: arg2 = arg3P && arg2 + 1 = arg2P && 0 <= arg1P - 1 && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg1P <= arg1
f83_0_main_ArrayAccess(x, x1, x2) -> f83_0_main_ArrayAccess(x3, x4, x5) :|: x2 = x5 && x2 + 1 = x4 && 0 <= x3 - 1 && 0 <= x - 1 && x3 <= x && -1 <= x2 - 1 && x1 <= x2 - 1
__init(x6, x7, x8) -> f1_0_main_ConstantStackPush(x9, x10, x11) :|: 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) -> f83_0_main_ArrayAccess(arg1P, arg2P, arg3P) :|: arg2 = arg3P && arg2 + 1 = arg2P && 0 <= arg1P - 1 && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg1P <= arg1
f83_0_main_ArrayAccess(x, x1, x2) -> f83_0_main_ArrayAccess(x3, x4, x5) :|: x2 = x5 && x2 + 1 = x4 && 0 <= x3 - 1 && 0 <= x - 1 && x3 <= x && -1 <= x2 - 1 && x1 <= x2 - 1
__init(x6, x7, x8) -> f1_0_main_ConstantStackPush(x9, x10, x11) :|: 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) -> f83_0_main_ArrayAccess(arg1P, arg2P, arg3P) :|: arg2 = arg3P && arg2 + 1 = arg2P && 0 <= arg1P - 1 && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg1P <= arg1
(2) f83_0_main_ArrayAccess(x, x1, x2) -> f83_0_main_ArrayAccess(x3, x4, x5) :|: x2 = x5 && x2 + 1 = x4 && 0 <= x3 - 1 && 0 <= x - 1 && x3 <= x && -1 <= x2 - 1 && x1 <= x2 - 1
(3) __init(x6, x7, x8) -> f1_0_main_ConstantStackPush(x9, x10, x11) :|: 0 <= 0

Arcs:
(3) -> (1)

This digraph is fully evaluated!
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(4)
TRUE