LTS Termination Proof

by T2Cert

Input

Integer Transition System

Initial Location: 11

Transitions: (pre-variables and post-variables)

0	0	1:	tmp_0 ≤ 0 ∧ − tmp_0 ≤ 0 ∧ − x6_post + x6_post ≤ 0 ∧ x6_post − x6_post ≤ 0 ∧ − x6_0 + x6_0 ≤ 0 ∧ x6_0 − x6_0 ≤ 0 ∧ − x4_post + x4_post ≤ 0 ∧ x4_post − x4_post ≤ 0 ∧ − x4_0 + x4_0 ≤ 0 ∧ x4_0 − x4_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − ret_foo7_post + ret_foo7_post ≤ 0 ∧ ret_foo7_post − ret_foo7_post ≤ 0 ∧ − ret_foo7_0 + ret_foo7_0 ≤ 0 ∧ ret_foo7_0 − ret_foo7_0 ≤ 0 ∧ − ret_foo5_post + ret_foo5_post ≤ 0 ∧ ret_foo5_post − ret_foo5_post ≤ 0 ∧ − ret_foo5_0 + ret_foo5_0 ≤ 0 ∧ ret_foo5_0 − ret_foo5_0 ≤ 0 ∧ − il_post + il_post ≤ 0 ∧ il_post − il_post ≤ 0 ∧ − il_0 + il_0 ≤ 0 ∧ il_0 − il_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0
0	1	2:	1 − tmp_0 ≤ 0 ∧ − x6_post + x6_post ≤ 0 ∧ x6_post − x6_post ≤ 0 ∧ − x6_0 + x6_0 ≤ 0 ∧ x6_0 − x6_0 ≤ 0 ∧ − x4_post + x4_post ≤ 0 ∧ x4_post − x4_post ≤ 0 ∧ − x4_0 + x4_0 ≤ 0 ∧ x4_0 − x4_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − ret_foo7_post + ret_foo7_post ≤ 0 ∧ ret_foo7_post − ret_foo7_post ≤ 0 ∧ − ret_foo7_0 + ret_foo7_0 ≤ 0 ∧ ret_foo7_0 − ret_foo7_0 ≤ 0 ∧ − ret_foo5_post + ret_foo5_post ≤ 0 ∧ ret_foo5_post − ret_foo5_post ≤ 0 ∧ − ret_foo5_0 + ret_foo5_0 ≤ 0 ∧ ret_foo5_0 − ret_foo5_0 ≤ 0 ∧ − il_post + il_post ≤ 0 ∧ il_post − il_post ≤ 0 ∧ − il_0 + il_0 ≤ 0 ∧ il_0 − il_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0
0	2	2:	1 + tmp_0 ≤ 0 ∧ − x6_post + x6_post ≤ 0 ∧ x6_post − x6_post ≤ 0 ∧ − x6_0 + x6_0 ≤ 0 ∧ x6_0 − x6_0 ≤ 0 ∧ − x4_post + x4_post ≤ 0 ∧ x4_post − x4_post ≤ 0 ∧ − x4_0 + x4_0 ≤ 0 ∧ x4_0 − x4_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − ret_foo7_post + ret_foo7_post ≤ 0 ∧ ret_foo7_post − ret_foo7_post ≤ 0 ∧ − ret_foo7_0 + ret_foo7_0 ≤ 0 ∧ ret_foo7_0 − ret_foo7_0 ≤ 0 ∧ − ret_foo5_post + ret_foo5_post ≤ 0 ∧ ret_foo5_post − ret_foo5_post ≤ 0 ∧ − ret_foo5_0 + ret_foo5_0 ≤ 0 ∧ ret_foo5_0 − ret_foo5_0 ≤ 0 ∧ − il_post + il_post ≤ 0 ∧ il_post − il_post ≤ 0 ∧ − il_0 + il_0 ≤ 0 ∧ il_0 − il_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0
3	3	0:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − il_0 + x4_post ≤ 0 ∧ il_0 − x4_post ≤ 0 ∧ − ret_foo5_post + tmp_post ≤ 0 ∧ ret_foo5_post − tmp_post ≤ 0 ∧ ret_foo5_0 − ret_foo5_post ≤ 0 ∧ − ret_foo5_0 + ret_foo5_post ≤ 0 ∧ tmp_0 − tmp_post ≤ 0 ∧ − tmp_0 + tmp_post ≤ 0 ∧ x4_0 − x4_post ≤ 0 ∧ − x4_0 + x4_post ≤ 0 ∧ − x6_post + x6_post ≤ 0 ∧ x6_post − x6_post ≤ 0 ∧ − x6_0 + x6_0 ≤ 0 ∧ x6_0 − x6_0 ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − ret_foo7_post + ret_foo7_post ≤ 0 ∧ ret_foo7_post − ret_foo7_post ≤ 0 ∧ − ret_foo7_0 + ret_foo7_0 ≤ 0 ∧ ret_foo7_0 − ret_foo7_0 ≤ 0 ∧ − il_post + il_post ≤ 0 ∧ il_post − il_post ≤ 0 ∧ − il_0 + il_0 ≤ 0 ∧ il_0 − il_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0
4	4	5:	− x6_post + x6_post ≤ 0 ∧ x6_post − x6_post ≤ 0 ∧ − x6_0 + x6_0 ≤ 0 ∧ x6_0 − x6_0 ≤ 0 ∧ − x4_post + x4_post ≤ 0 ∧ x4_post − x4_post ≤ 0 ∧ − x4_0 + x4_0 ≤ 0 ∧ x4_0 − x4_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − ret_foo7_post + ret_foo7_post ≤ 0 ∧ ret_foo7_post − ret_foo7_post ≤ 0 ∧ − ret_foo7_0 + ret_foo7_0 ≤ 0 ∧ ret_foo7_0 − ret_foo7_0 ≤ 0 ∧ − ret_foo5_post + ret_foo5_post ≤ 0 ∧ ret_foo5_post − ret_foo5_post ≤ 0 ∧ − ret_foo5_0 + ret_foo5_0 ≤ 0 ∧ ret_foo5_0 − ret_foo5_0 ≤ 0 ∧ − il_post + il_post ≤ 0 ∧ il_post − il_post ≤ 0 ∧ − il_0 + il_0 ≤ 0 ∧ il_0 − il_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0
6	5	7:	0 ≤ 0 ∧ 0 ≤ 0 ∧ −1 − il_0 + il_post ≤ 0 ∧ 1 + il_0 − il_post ≤ 0 ∧ il_0 − il_post ≤ 0 ∧ − il_0 + il_post ≤ 0 ∧ − x6_post + x6_post ≤ 0 ∧ x6_post − x6_post ≤ 0 ∧ − x6_0 + x6_0 ≤ 0 ∧ x6_0 − x6_0 ≤ 0 ∧ − x4_post + x4_post ≤ 0 ∧ x4_post − x4_post ≤ 0 ∧ − x4_0 + x4_0 ≤ 0 ∧ x4_0 − x4_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − ret_foo7_post + ret_foo7_post ≤ 0 ∧ ret_foo7_post − ret_foo7_post ≤ 0 ∧ − ret_foo7_0 + ret_foo7_0 ≤ 0 ∧ ret_foo7_0 − ret_foo7_0 ≤ 0 ∧ − ret_foo5_post + ret_foo5_post ≤ 0 ∧ ret_foo5_post − ret_foo5_post ≤ 0 ∧ − ret_foo5_0 + ret_foo5_0 ≤ 0 ∧ ret_foo5_0 − ret_foo5_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0
8	6	4:	tmp___0_0 ≤ 0 ∧ − tmp___0_0 ≤ 0 ∧ − x6_post + x6_post ≤ 0 ∧ x6_post − x6_post ≤ 0 ∧ − x6_0 + x6_0 ≤ 0 ∧ x6_0 − x6_0 ≤ 0 ∧ − x4_post + x4_post ≤ 0 ∧ x4_post − x4_post ≤ 0 ∧ − x4_0 + x4_0 ≤ 0 ∧ x4_0 − x4_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − ret_foo7_post + ret_foo7_post ≤ 0 ∧ ret_foo7_post − ret_foo7_post ≤ 0 ∧ − ret_foo7_0 + ret_foo7_0 ≤ 0 ∧ ret_foo7_0 − ret_foo7_0 ≤ 0 ∧ − ret_foo5_post + ret_foo5_post ≤ 0 ∧ ret_foo5_post − ret_foo5_post ≤ 0 ∧ − ret_foo5_0 + ret_foo5_0 ≤ 0 ∧ ret_foo5_0 − ret_foo5_0 ≤ 0 ∧ − il_post + il_post ≤ 0 ∧ il_post − il_post ≤ 0 ∧ − il_0 + il_0 ≤ 0 ∧ il_0 − il_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0
8	7	6:	1 − tmp___0_0 ≤ 0 ∧ − x6_post + x6_post ≤ 0 ∧ x6_post − x6_post ≤ 0 ∧ − x6_0 + x6_0 ≤ 0 ∧ x6_0 − x6_0 ≤ 0 ∧ − x4_post + x4_post ≤ 0 ∧ x4_post − x4_post ≤ 0 ∧ − x4_0 + x4_0 ≤ 0 ∧ x4_0 − x4_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − ret_foo7_post + ret_foo7_post ≤ 0 ∧ ret_foo7_post − ret_foo7_post ≤ 0 ∧ − ret_foo7_0 + ret_foo7_0 ≤ 0 ∧ ret_foo7_0 − ret_foo7_0 ≤ 0 ∧ − ret_foo5_post + ret_foo5_post ≤ 0 ∧ ret_foo5_post − ret_foo5_post ≤ 0 ∧ − ret_foo5_0 + ret_foo5_0 ≤ 0 ∧ ret_foo5_0 − ret_foo5_0 ≤ 0 ∧ − il_post + il_post ≤ 0 ∧ il_post − il_post ≤ 0 ∧ − il_0 + il_0 ≤ 0 ∧ il_0 − il_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0
8	8	6:	1 + tmp___0_0 ≤ 0 ∧ − x6_post + x6_post ≤ 0 ∧ x6_post − x6_post ≤ 0 ∧ − x6_0 + x6_0 ≤ 0 ∧ x6_0 − x6_0 ≤ 0 ∧ − x4_post + x4_post ≤ 0 ∧ x4_post − x4_post ≤ 0 ∧ − x4_0 + x4_0 ≤ 0 ∧ x4_0 − x4_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − ret_foo7_post + ret_foo7_post ≤ 0 ∧ ret_foo7_post − ret_foo7_post ≤ 0 ∧ − ret_foo7_0 + ret_foo7_0 ≤ 0 ∧ ret_foo7_0 − ret_foo7_0 ≤ 0 ∧ − ret_foo5_post + ret_foo5_post ≤ 0 ∧ ret_foo5_post − ret_foo5_post ≤ 0 ∧ − ret_foo5_0 + ret_foo5_0 ≤ 0 ∧ ret_foo5_0 − ret_foo5_0 ≤ 0 ∧ − il_post + il_post ≤ 0 ∧ il_post − il_post ≤ 0 ∧ − il_0 + il_0 ≤ 0 ∧ il_0 − il_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0
7	9	9:	− x6_post + x6_post ≤ 0 ∧ x6_post − x6_post ≤ 0 ∧ − x6_0 + x6_0 ≤ 0 ∧ x6_0 − x6_0 ≤ 0 ∧ − x4_post + x4_post ≤ 0 ∧ x4_post − x4_post ≤ 0 ∧ − x4_0 + x4_0 ≤ 0 ∧ x4_0 − x4_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − ret_foo7_post + ret_foo7_post ≤ 0 ∧ ret_foo7_post − ret_foo7_post ≤ 0 ∧ − ret_foo7_0 + ret_foo7_0 ≤ 0 ∧ ret_foo7_0 − ret_foo7_0 ≤ 0 ∧ − ret_foo5_post + ret_foo5_post ≤ 0 ∧ ret_foo5_post − ret_foo5_post ≤ 0 ∧ − ret_foo5_0 + ret_foo5_0 ≤ 0 ∧ ret_foo5_0 − ret_foo5_0 ≤ 0 ∧ − il_post + il_post ≤ 0 ∧ il_post − il_post ≤ 0 ∧ − il_0 + il_0 ≤ 0 ∧ il_0 − il_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0
9	10	4:	___const_10_0 − il_0 ≤ 0 ∧ − x6_post + x6_post ≤ 0 ∧ x6_post − x6_post ≤ 0 ∧ − x6_0 + x6_0 ≤ 0 ∧ x6_0 − x6_0 ≤ 0 ∧ − x4_post + x4_post ≤ 0 ∧ x4_post − x4_post ≤ 0 ∧ − x4_0 + x4_0 ≤ 0 ∧ x4_0 − x4_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − ret_foo7_post + ret_foo7_post ≤ 0 ∧ ret_foo7_post − ret_foo7_post ≤ 0 ∧ − ret_foo7_0 + ret_foo7_0 ≤ 0 ∧ ret_foo7_0 − ret_foo7_0 ≤ 0 ∧ − ret_foo5_post + ret_foo5_post ≤ 0 ∧ ret_foo5_post − ret_foo5_post ≤ 0 ∧ − ret_foo5_0 + ret_foo5_0 ≤ 0 ∧ ret_foo5_0 − ret_foo5_0 ≤ 0 ∧ − il_post + il_post ≤ 0 ∧ il_post − il_post ≤ 0 ∧ − il_0 + il_0 ≤ 0 ∧ il_0 − il_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0
9	11	8:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − ___const_10_0 + il_0 ≤ 0 ∧ − il_0 + x6_post ≤ 0 ∧ il_0 − x6_post ≤ 0 ∧ − ret_foo7_post + tmp___0_post ≤ 0 ∧ ret_foo7_post − tmp___0_post ≤ 0 ∧ ret_foo7_0 − ret_foo7_post ≤ 0 ∧ − ret_foo7_0 + ret_foo7_post ≤ 0 ∧ tmp___0_0 − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_post ≤ 0 ∧ x6_0 − x6_post ≤ 0 ∧ − x6_0 + x6_post ≤ 0 ∧ − x4_post + x4_post ≤ 0 ∧ x4_post − x4_post ≤ 0 ∧ − x4_0 + x4_0 ≤ 0 ∧ x4_0 − x4_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − ret_foo5_post + ret_foo5_post ≤ 0 ∧ ret_foo5_post − ret_foo5_post ≤ 0 ∧ − ret_foo5_0 + ret_foo5_0 ≤ 0 ∧ ret_foo5_0 − ret_foo5_0 ≤ 0 ∧ − il_post + il_post ≤ 0 ∧ il_post − il_post ≤ 0 ∧ − il_0 + il_0 ≤ 0 ∧ il_0 − il_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0
1	12	7:	0 ≤ 0 ∧ 0 ≤ 0 ∧ il_post ≤ 0 ∧ − il_post ≤ 0 ∧ il_0 − il_post ≤ 0 ∧ − il_0 + il_post ≤ 0 ∧ − x6_post + x6_post ≤ 0 ∧ x6_post − x6_post ≤ 0 ∧ − x6_0 + x6_0 ≤ 0 ∧ x6_0 − x6_0 ≤ 0 ∧ − x4_post + x4_post ≤ 0 ∧ x4_post − x4_post ≤ 0 ∧ − x4_0 + x4_0 ≤ 0 ∧ x4_0 − x4_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − ret_foo7_post + ret_foo7_post ≤ 0 ∧ ret_foo7_post − ret_foo7_post ≤ 0 ∧ − ret_foo7_0 + ret_foo7_0 ≤ 0 ∧ ret_foo7_0 − ret_foo7_0 ≤ 0 ∧ − ret_foo5_post + ret_foo5_post ≤ 0 ∧ ret_foo5_post − ret_foo5_post ≤ 0 ∧ − ret_foo5_0 + ret_foo5_0 ≤ 0 ∧ ret_foo5_0 − ret_foo5_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0
2	13	1:	___const_10_0 − il_0 ≤ 0 ∧ − x6_post + x6_post ≤ 0 ∧ x6_post − x6_post ≤ 0 ∧ − x6_0 + x6_0 ≤ 0 ∧ x6_0 − x6_0 ≤ 0 ∧ − x4_post + x4_post ≤ 0 ∧ x4_post − x4_post ≤ 0 ∧ − x4_0 + x4_0 ≤ 0 ∧ x4_0 − x4_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − ret_foo7_post + ret_foo7_post ≤ 0 ∧ ret_foo7_post − ret_foo7_post ≤ 0 ∧ − ret_foo7_0 + ret_foo7_0 ≤ 0 ∧ ret_foo7_0 − ret_foo7_0 ≤ 0 ∧ − ret_foo5_post + ret_foo5_post ≤ 0 ∧ ret_foo5_post − ret_foo5_post ≤ 0 ∧ − ret_foo5_0 + ret_foo5_0 ≤ 0 ∧ ret_foo5_0 − ret_foo5_0 ≤ 0 ∧ − il_post + il_post ≤ 0 ∧ il_post − il_post ≤ 0 ∧ − il_0 + il_0 ≤ 0 ∧ il_0 − il_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0
2	14	3:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − ___const_10_0 + il_0 ≤ 0 ∧ −1 − il_0 + il_post ≤ 0 ∧ 1 + il_0 − il_post ≤ 0 ∧ il_0 − il_post ≤ 0 ∧ − il_0 + il_post ≤ 0 ∧ − x6_post + x6_post ≤ 0 ∧ x6_post − x6_post ≤ 0 ∧ − x6_0 + x6_0 ≤ 0 ∧ x6_0 − x6_0 ≤ 0 ∧ − x4_post + x4_post ≤ 0 ∧ x4_post − x4_post ≤ 0 ∧ − x4_0 + x4_0 ≤ 0 ∧ x4_0 − x4_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − ret_foo7_post + ret_foo7_post ≤ 0 ∧ ret_foo7_post − ret_foo7_post ≤ 0 ∧ − ret_foo7_0 + ret_foo7_0 ≤ 0 ∧ ret_foo7_0 − ret_foo7_0 ≤ 0 ∧ − ret_foo5_post + ret_foo5_post ≤ 0 ∧ ret_foo5_post − ret_foo5_post ≤ 0 ∧ − ret_foo5_0 + ret_foo5_0 ≤ 0 ∧ ret_foo5_0 − ret_foo5_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0
10	15	3:	0 ≤ 0 ∧ 0 ≤ 0 ∧ il_post ≤ 0 ∧ − il_post ≤ 0 ∧ il_0 − il_post ≤ 0 ∧ − il_0 + il_post ≤ 0 ∧ − x6_post + x6_post ≤ 0 ∧ x6_post − x6_post ≤ 0 ∧ − x6_0 + x6_0 ≤ 0 ∧ x6_0 − x6_0 ≤ 0 ∧ − x4_post + x4_post ≤ 0 ∧ x4_post − x4_post ≤ 0 ∧ − x4_0 + x4_0 ≤ 0 ∧ x4_0 − x4_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − ret_foo7_post + ret_foo7_post ≤ 0 ∧ ret_foo7_post − ret_foo7_post ≤ 0 ∧ − ret_foo7_0 + ret_foo7_0 ≤ 0 ∧ ret_foo7_0 − ret_foo7_0 ≤ 0 ∧ − ret_foo5_post + ret_foo5_post ≤ 0 ∧ ret_foo5_post − ret_foo5_post ≤ 0 ∧ − ret_foo5_0 + ret_foo5_0 ≤ 0 ∧ ret_foo5_0 − ret_foo5_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0
11	16	10:	− x6_post + x6_post ≤ 0 ∧ x6_post − x6_post ≤ 0 ∧ − x6_0 + x6_0 ≤ 0 ∧ x6_0 − x6_0 ≤ 0 ∧ − x4_post + x4_post ≤ 0 ∧ x4_post − x4_post ≤ 0 ∧ − x4_0 + x4_0 ≤ 0 ∧ x4_0 − x4_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − ret_foo7_post + ret_foo7_post ≤ 0 ∧ ret_foo7_post − ret_foo7_post ≤ 0 ∧ − ret_foo7_0 + ret_foo7_0 ≤ 0 ∧ ret_foo7_0 − ret_foo7_0 ≤ 0 ∧ − ret_foo5_post + ret_foo5_post ≤ 0 ∧ ret_foo5_post − ret_foo5_post ≤ 0 ∧ − ret_foo5_0 + ret_foo5_0 ≤ 0 ∧ ret_foo5_0 − ret_foo5_0 ≤ 0 ∧ − il_post + il_post ≤ 0 ∧ il_post − il_post ≤ 0 ∧ − il_0 + il_0 ≤ 0 ∧ il_0 − il_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:

3	17	3:	− x6_post + x6_post ≤ 0 ∧ x6_post − x6_post ≤ 0 ∧ − x6_0 + x6_0 ≤ 0 ∧ x6_0 − x6_0 ≤ 0 ∧ − x4_post + x4_post ≤ 0 ∧ x4_post − x4_post ≤ 0 ∧ − x4_0 + x4_0 ≤ 0 ∧ x4_0 − x4_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − ret_foo7_post + ret_foo7_post ≤ 0 ∧ ret_foo7_post − ret_foo7_post ≤ 0 ∧ − ret_foo7_0 + ret_foo7_0 ≤ 0 ∧ ret_foo7_0 − ret_foo7_0 ≤ 0 ∧ − ret_foo5_post + ret_foo5_post ≤ 0 ∧ ret_foo5_post − ret_foo5_post ≤ 0 ∧ − ret_foo5_0 + ret_foo5_0 ≤ 0 ∧ ret_foo5_0 − ret_foo5_0 ≤ 0 ∧ − il_post + il_post ≤ 0 ∧ il_post − il_post ≤ 0 ∧ − il_0 + il_0 ≤ 0 ∧ il_0 − il_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0
7	24	7:	− x6_post + x6_post ≤ 0 ∧ x6_post − x6_post ≤ 0 ∧ − x6_0 + x6_0 ≤ 0 ∧ x6_0 − x6_0 ≤ 0 ∧ − x4_post + x4_post ≤ 0 ∧ x4_post − x4_post ≤ 0 ∧ − x4_0 + x4_0 ≤ 0 ∧ x4_0 − x4_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − ret_foo7_post + ret_foo7_post ≤ 0 ∧ ret_foo7_post − ret_foo7_post ≤ 0 ∧ − ret_foo7_0 + ret_foo7_0 ≤ 0 ∧ ret_foo7_0 − ret_foo7_0 ≤ 0 ∧ − ret_foo5_post + ret_foo5_post ≤ 0 ∧ ret_foo5_post − ret_foo5_post ≤ 0 ∧ − ret_foo5_0 + ret_foo5_0 ≤ 0 ∧ ret_foo5_0 − ret_foo5_0 ≤ 0 ∧ − il_post + il_post ≤ 0 ∧ il_post − il_post ≤ 0 ∧ − il_0 + il_0 ≤ 0 ∧ il_0 − il_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0

and for every transition t, a duplicate t is considered.

2 Transition Removal

We remove transitions 0, 4, 6, 10, 12, 13, 15, 16 using the following ranking functions, which are bounded by −21.

11:	0
10:	0
0:	0
2:	0
3:	0
1:	0
6:	0
7:	0
8:	0
9:	0
4:	0
5:	0
11:	−8
10:	−9
0:	−10
2:	−10
3:	−10
3_var_snapshot:	−10
3*:	−10
1:	−11
6:	−12
7:	−12
8:	−12
9:	−12
7_var_snapshot:	−12
7*:	−12
4:	−13
5:	−14

3 Location Addition

The following skip-transition is inserted and corresponding redirections w.r.t. the old location are performed.

3* 20 3: − x6_post + x6_post ≤ 0 ∧ x6_post − x6_post ≤ 0 ∧ − x6_0 + x6_0 ≤ 0 ∧ x6_0 − x6_0 ≤ 0 ∧ − x4_post + x4_post ≤ 0 ∧ x4_post − x4_post ≤ 0 ∧ − x4_0 + x4_0 ≤ 0 ∧ x4_0 − x4_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − ret_foo7_post + ret_foo7_post ≤ 0 ∧ ret_foo7_post − ret_foo7_post ≤ 0 ∧ − ret_foo7_0 + ret_foo7_0 ≤ 0 ∧ ret_foo7_0 − ret_foo7_0 ≤ 0 ∧ − ret_foo5_post + ret_foo5_post ≤ 0 ∧ ret_foo5_post − ret_foo5_post ≤ 0 ∧ − ret_foo5_0 + ret_foo5_0 ≤ 0 ∧ ret_foo5_0 − ret_foo5_0 ≤ 0 ∧ − il_post + il_post ≤ 0 ∧ il_post − il_post ≤ 0 ∧ − il_0 + il_0 ≤ 0 ∧ il_0 − il_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0

4 Location Addition

The following skip-transition is inserted and corresponding redirections w.r.t. the old location are performed.

3 18 3_var_snapshot: − x6_post + x6_post ≤ 0 ∧ x6_post − x6_post ≤ 0 ∧ − x6_0 + x6_0 ≤ 0 ∧ x6_0 − x6_0 ≤ 0 ∧ − x4_post + x4_post ≤ 0 ∧ x4_post − x4_post ≤ 0 ∧ − x4_0 + x4_0 ≤ 0 ∧ x4_0 − x4_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − ret_foo7_post + ret_foo7_post ≤ 0 ∧ ret_foo7_post − ret_foo7_post ≤ 0 ∧ − ret_foo7_0 + ret_foo7_0 ≤ 0 ∧ ret_foo7_0 − ret_foo7_0 ≤ 0 ∧ − ret_foo5_post + ret_foo5_post ≤ 0 ∧ ret_foo5_post − ret_foo5_post ≤ 0 ∧ − ret_foo5_0 + ret_foo5_0 ≤ 0 ∧ ret_foo5_0 − ret_foo5_0 ≤ 0 ∧ − il_post + il_post ≤ 0 ∧ il_post − il_post ≤ 0 ∧ − il_0 + il_0 ≤ 0 ∧ il_0 − il_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0

5 Location Addition

The following skip-transition is inserted and corresponding redirections w.r.t. the old location are performed.

7* 27 7: − x6_post + x6_post ≤ 0 ∧ x6_post − x6_post ≤ 0 ∧ − x6_0 + x6_0 ≤ 0 ∧ x6_0 − x6_0 ≤ 0 ∧ − x4_post + x4_post ≤ 0 ∧ x4_post − x4_post ≤ 0 ∧ − x4_0 + x4_0 ≤ 0 ∧ x4_0 − x4_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − ret_foo7_post + ret_foo7_post ≤ 0 ∧ ret_foo7_post − ret_foo7_post ≤ 0 ∧ − ret_foo7_0 + ret_foo7_0 ≤ 0 ∧ ret_foo7_0 − ret_foo7_0 ≤ 0 ∧ − ret_foo5_post + ret_foo5_post ≤ 0 ∧ ret_foo5_post − ret_foo5_post ≤ 0 ∧ − ret_foo5_0 + ret_foo5_0 ≤ 0 ∧ ret_foo5_0 − ret_foo5_0 ≤ 0 ∧ − il_post + il_post ≤ 0 ∧ il_post − il_post ≤ 0 ∧ − il_0 + il_0 ≤ 0 ∧ il_0 − il_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0

6 Location Addition

The following skip-transition is inserted and corresponding redirections w.r.t. the old location are performed.

7 25 7_var_snapshot: − x6_post + x6_post ≤ 0 ∧ x6_post − x6_post ≤ 0 ∧ − x6_0 + x6_0 ≤ 0 ∧ x6_0 − x6_0 ≤ 0 ∧ − x4_post + x4_post ≤ 0 ∧ x4_post − x4_post ≤ 0 ∧ − x4_0 + x4_0 ≤ 0 ∧ x4_0 − x4_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − ret_foo7_post + ret_foo7_post ≤ 0 ∧ ret_foo7_post − ret_foo7_post ≤ 0 ∧ − ret_foo7_0 + ret_foo7_0 ≤ 0 ∧ ret_foo7_0 − ret_foo7_0 ≤ 0 ∧ − ret_foo5_post + ret_foo5_post ≤ 0 ∧ ret_foo5_post − ret_foo5_post ≤ 0 ∧ − ret_foo5_0 + ret_foo5_0 ≤ 0 ∧ ret_foo5_0 − ret_foo5_0 ≤ 0 ∧ − il_post + il_post ≤ 0 ∧ il_post − il_post ≤ 0 ∧ − il_0 + il_0 ≤ 0 ∧ il_0 − il_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0

7 SCC Decomposition

We consider subproblems for each of the 2 SCC(s) of the program graph.

7.1 SCC Subproblem 1/2

Here we consider the SCC { 6, 7, 8, 9, 7_var_snapshot, 7* }.

7.1.1 Transition Removal

We remove transition 11 using the following ranking functions, which are bounded by 6.

6:	−4 + 7⋅___const_10_0 − 7⋅il_0
7:	2 + 7⋅___const_10_0 − 7⋅il_0
8:	−1 + 7⋅___const_10_0 − 7⋅il_0
9:	7⋅___const_10_0 − 7⋅il_0
7_var_snapshot:	1 + 7⋅___const_10_0 − 7⋅il_0
7*:	2 + 7⋅___const_10_0 − 7⋅il_0

7.1.2 Transition Removal

We remove transitions 25, 27, 5, 7, 8, 9 using the following ranking functions, which are bounded by −5.

6:	−1
7:	−3
8:	0
9:	−5
7_var_snapshot:	−4
7*:	−2

7.1.3 Splitting Cut-Point Transitions

We consider 1 subproblems corresponding to sets of cut-point transitions as follows.

7.1.3.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 24.

7.1.3.1.1 Splitting Cut-Point Transitions

There remain no cut-point transition to consider. Hence the cooperation termination is trivial.

7.2 SCC Subproblem 2/2

Here we consider the SCC { 0, 2, 3, 3_var_snapshot, 3* }.

7.2.1 Transition Removal

We remove transition 14 using the following ranking functions, which are bounded by 4.

0:	1 + 5⋅___const_10_0 − 5⋅il_0
2:	5⋅___const_10_0 − 5⋅il_0
3:	3 + 5⋅___const_10_0 − 5⋅il_0
3_var_snapshot:	2 + 5⋅___const_10_0 − 5⋅il_0
3*:	4 + 5⋅___const_10_0 − 5⋅il_0

7.2.2 Transition Removal

We remove transitions 18, 20, 2, 3 using the following ranking functions, which are bounded by −4.

0:	−3
2:	−4
3:	−1
3_var_snapshot:	−2
3*:	0

7.2.3 Transition Removal

We remove transition 1 using the following ranking functions, which are bounded by 0.

0:	tmp_0
2:	0
3:	0
3_var_snapshot:	0
3*:	0

7.2.4 Splitting Cut-Point Transitions

We consider 1 subproblems corresponding to sets of cut-point transitions as follows.

7.2.4.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 17.

7.2.4.1.1 Splitting Cut-Point Transitions

There remain no cut-point transition to consider. Hence the cooperation termination is trivial.

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