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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 310 ms]
(4) TRUE


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(0)
Obligation:
Rules:
l0(aHAT0, ret_returnOne3HAT0, tmpHAT0) -> l1(aHATpost, ret_returnOne3HATpost, tmpHATpost) :|: tmpHAT0 = tmpHATpost && ret_returnOne3HAT0 = ret_returnOne3HATpost && aHAT0 = aHATpost && 3 <= aHAT0
l0(x, x1, x2) -> l1(x3, x4, x5) :|: x2 = x5 && x1 = x4 && x = x3 && 1 + x <= 2
l0(x6, x7, x8) -> l2(x9, x10, x11) :|: x7 = x10 && x6 = x9 && x11 = 1 && 2 <= x6 && x6 <= 2
l2(x12, x13, x14) -> l3(x15, x16, x17) :|: x14 = x17 && x13 = x16 && x12 = x15
l4(x18, x19, x20) -> l0(x21, x22, x23) :|: x20 = x23 && x19 = x22 && x18 = x21 && 2 <= x18
l4(x24, x25, x26) -> l0(x27, x28, x29) :|: x26 = x29 && x25 = x28 && x24 = x27 && 1 + x24 <= 1
l4(x30, x31, x32) -> l2(x33, x34, x35) :|: x31 = x34 && x30 = x33 && x35 = 1 && 1 <= x30 && x30 <= 1
l1(x36, x37, x38) -> l2(x39, x40, x41) :|: x37 = x40 && x36 = x39 && x41 = 0
l5(x42, x43, x44) -> l4(x45, x46, x47) :|: x48 = -1 && x46 = 1 && x45 = x46 && x44 = x47
l6(x49, x50, x51) -> l5(x52, x53, x54) :|: x51 = x54 && x50 = x53 && x49 = x52
Start term: l6(aHAT0, ret_returnOne3HAT0, tmpHAT0)

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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:
l0(aHAT0, ret_returnOne3HAT0, tmpHAT0) -> l1(aHATpost, ret_returnOne3HATpost, tmpHATpost) :|: tmpHAT0 = tmpHATpost && ret_returnOne3HAT0 = ret_returnOne3HATpost && aHAT0 = aHATpost && 3 <= aHAT0
l0(x, x1, x2) -> l1(x3, x4, x5) :|: x2 = x5 && x1 = x4 && x = x3 && 1 + x <= 2
l0(x6, x7, x8) -> l2(x9, x10, x11) :|: x7 = x10 && x6 = x9 && x11 = 1 && 2 <= x6 && x6 <= 2
l2(x12, x13, x14) -> l3(x15, x16, x17) :|: x14 = x17 && x13 = x16 && x12 = x15
l4(x18, x19, x20) -> l0(x21, x22, x23) :|: x20 = x23 && x19 = x22 && x18 = x21 && 2 <= x18
l4(x24, x25, x26) -> l0(x27, x28, x29) :|: x26 = x29 && x25 = x28 && x24 = x27 && 1 + x24 <= 1
l4(x30, x31, x32) -> l2(x33, x34, x35) :|: x31 = x34 && x30 = x33 && x35 = 1 && 1 <= x30 && x30 <= 1
l1(x36, x37, x38) -> l2(x39, x40, x41) :|: x37 = x40 && x36 = x39 && x41 = 0
l5(x42, x43, x44) -> l4(x45, x46, x47) :|: x48 = -1 && x46 = 1 && x45 = x46 && x44 = x47
l6(x49, x50, x51) -> l5(x52, x53, x54) :|: x51 = x54 && x50 = x53 && x49 = x52
Start term: l6(aHAT0, ret_returnOne3HAT0, tmpHAT0)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(aHAT0, ret_returnOne3HAT0, tmpHAT0) -> l1(aHATpost, ret_returnOne3HATpost, tmpHATpost) :|: tmpHAT0 = tmpHATpost && ret_returnOne3HAT0 = ret_returnOne3HATpost && aHAT0 = aHATpost && 3 <= aHAT0
(2) l0(x, x1, x2) -> l1(x3, x4, x5) :|: x2 = x5 && x1 = x4 && x = x3 && 1 + x <= 2
(3) l0(x6, x7, x8) -> l2(x9, x10, x11) :|: x7 = x10 && x6 = x9 && x11 = 1 && 2 <= x6 && x6 <= 2
(4) l2(x12, x13, x14) -> l3(x15, x16, x17) :|: x14 = x17 && x13 = x16 && x12 = x15
(5) l4(x18, x19, x20) -> l0(x21, x22, x23) :|: x20 = x23 && x19 = x22 && x18 = x21 && 2 <= x18
(6) l4(x24, x25, x26) -> l0(x27, x28, x29) :|: x26 = x29 && x25 = x28 && x24 = x27 && 1 + x24 <= 1
(7) l4(x30, x31, x32) -> l2(x33, x34, x35) :|: x31 = x34 && x30 = x33 && x35 = 1 && 1 <= x30 && x30 <= 1
(8) l1(x36, x37, x38) -> l2(x39, x40, x41) :|: x37 = x40 && x36 = x39 && x41 = 0
(9) l5(x42, x43, x44) -> l4(x45, x46, x47) :|: x48 = -1 && x46 = 1 && x45 = x46 && x44 = x47
(10) l6(x49, x50, x51) -> l5(x52, x53, x54) :|: x51 = x54 && x50 = x53 && x49 = x52

Arcs:
(1) -> (8)
(2) -> (8)
(3) -> (4)
(5) -> (1), (3)
(6) -> (2)
(7) -> (4)
(8) -> (4)
(9) -> (7)
(10) -> (9)

This digraph is fully evaluated!
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(4)
TRUE