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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 77 ms]
(4) TRUE


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(0)
Obligation:
Rules:
l0(Result_4HAT0, x_5HAT0) -> l1(Result_4HATpost, x_5HATpost) :|: Result_4HAT0 = Result_4HATpost && x_5HATpost = 1 + x_5HAT0 && -1 * x_5HAT0 <= 0
l0(x, x1) -> l1(x2, x3) :|: x1 = x3 && x = x2 && 0 <= -1 - x1
l2(x4, x5) -> l0(x6, x7) :|: x5 = x7 && x4 = x6
l1(x8, x9) -> l3(x10, x11) :|: x9 = x11 && x10 = x10
l4(x12, x13) -> l2(x14, x15) :|: x13 = x15 && x12 = x14
Start term: l4(Result_4HAT0, x_5HAT0)

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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(Result_4HAT0, x_5HAT0) -> l1(Result_4HATpost, x_5HATpost) :|: Result_4HAT0 = Result_4HATpost && x_5HATpost = 1 + x_5HAT0 && -1 * x_5HAT0 <= 0
l0(x, x1) -> l1(x2, x3) :|: x1 = x3 && x = x2 && 0 <= -1 - x1
l2(x4, x5) -> l0(x6, x7) :|: x5 = x7 && x4 = x6
l1(x8, x9) -> l3(x10, x11) :|: x9 = x11 && x10 = x10
l4(x12, x13) -> l2(x14, x15) :|: x13 = x15 && x12 = x14
Start term: l4(Result_4HAT0, x_5HAT0)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(Result_4HAT0, x_5HAT0) -> l1(Result_4HATpost, x_5HATpost) :|: Result_4HAT0 = Result_4HATpost && x_5HATpost = 1 + x_5HAT0 && -1 * x_5HAT0 <= 0
(2) l0(x, x1) -> l1(x2, x3) :|: x1 = x3 && x = x2 && 0 <= -1 - x1
(3) l2(x4, x5) -> l0(x6, x7) :|: x5 = x7 && x4 = x6
(4) l1(x8, x9) -> l3(x10, x11) :|: x9 = x11 && x10 = x10
(5) l4(x12, x13) -> l2(x14, x15) :|: x13 = x15 && x12 = x14

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

This digraph is fully evaluated!
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(4)
TRUE