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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 86 ms]
(4) TRUE


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(0)
Obligation:
Rules:
l0(___patmp1HAT0, ___patmp2HAT0, k_208HAT0, k_243HAT0, len_263HAT0) -> l1(___patmp1HATpost, ___patmp2HATpost, k_208HATpost, k_243HATpost, len_263HATpost) :|: k_208HAT0 = k_208HATpost && 0 <= -1 + k_243HATpost && k_243HATpost = ___patmp2HATpost && len_263HATpost = ___patmp1HATpost && ___patmp2HATpost = k_208HAT0 && ___patmp1HATpost = 1 && 0 <= k_208HAT0
l2(x, x1, x2, x3, x4) -> l3(x5, x6, x7, x8, x9) :|: x4 = x9 && x3 = x8 && x2 = x7 && x1 = x6 && x = x5
l4(x10, x11, x12, x13, x14) -> l0(x15, x16, x17, x18, x19) :|: x14 = x19 && x13 = x18 && x12 = x17 && x11 = x16 && x10 = x15
Start term: l4(___patmp1HAT0, ___patmp2HAT0, k_208HAT0, k_243HAT0, len_263HAT0)

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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(___patmp1HAT0, ___patmp2HAT0, k_208HAT0, k_243HAT0, len_263HAT0) -> l1(___patmp1HATpost, ___patmp2HATpost, k_208HATpost, k_243HATpost, len_263HATpost) :|: k_208HAT0 = k_208HATpost && 0 <= -1 + k_243HATpost && k_243HATpost = ___patmp2HATpost && len_263HATpost = ___patmp1HATpost && ___patmp2HATpost = k_208HAT0 && ___patmp1HATpost = 1 && 0 <= k_208HAT0
l2(x, x1, x2, x3, x4) -> l3(x5, x6, x7, x8, x9) :|: x4 = x9 && x3 = x8 && x2 = x7 && x1 = x6 && x = x5
l4(x10, x11, x12, x13, x14) -> l0(x15, x16, x17, x18, x19) :|: x14 = x19 && x13 = x18 && x12 = x17 && x11 = x16 && x10 = x15
Start term: l4(___patmp1HAT0, ___patmp2HAT0, k_208HAT0, k_243HAT0, len_263HAT0)

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(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(___patmp1HAT0, ___patmp2HAT0, k_208HAT0, k_243HAT0, len_263HAT0) -> l1(___patmp1HATpost, ___patmp2HATpost, k_208HATpost, k_243HATpost, len_263HATpost) :|: k_208HAT0 = k_208HATpost && 0 <= -1 + k_243HATpost && k_243HATpost = ___patmp2HATpost && len_263HATpost = ___patmp1HATpost && ___patmp2HATpost = k_208HAT0 && ___patmp1HATpost = 1 && 0 <= k_208HAT0
(2) l2(x, x1, x2, x3, x4) -> l3(x5, x6, x7, x8, x9) :|: x4 = x9 && x3 = x8 && x2 = x7 && x1 = x6 && x = x5
(3) l4(x10, x11, x12, x13, x14) -> l0(x15, x16, x17, x18, x19) :|: x14 = x19 && x13 = x18 && x12 = x17 && x11 = x16 && x10 = x15

Arcs:
(3) -> (1)

This digraph is fully evaluated!
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(4)
TRUE