LTS Termination Proof

by T2Cert

Input

Integer Transition System

Proof

1 Invariant Updates

The following invariants are asserted.

0: TRUE
1: i_19_post ≤ 0i_19_post ≤ 0i_19_0 ≤ 0i_19_0 ≤ 0
2: −1 + i_19_post ≤ 01 − i_19_post ≤ 0−1 + i_19_0 ≤ 01 − i_19_0 ≤ 01 − length_17_0 ≤ 0
3: TRUE
4: 2 − length_17_0 ≤ 0
5: 2 − length_17_0 ≤ 0
6: TRUE

The invariants are proved as follows.

IMPACT Invariant Proof

2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
4 9 4: tmp_23_post + tmp_23_post ≤ 0tmp_23_posttmp_23_post ≤ 0tmp_23_0 + tmp_23_0 ≤ 0tmp_23_0tmp_23_0 ≤ 0temp_26_post + temp_26_post ≤ 0temp_26_posttemp_26_post ≤ 0temp_26_0 + temp_26_0 ≤ 0temp_26_0temp_26_0 ≤ 0temp0_20_post + temp0_20_post ≤ 0temp0_20_posttemp0_20_post ≤ 0temp0_20_1 + temp0_20_1 ≤ 0temp0_20_1temp0_20_1 ≤ 0temp0_20_0 + temp0_20_0 ≤ 0temp0_20_0temp0_20_0 ≤ 0temp0_15_0 + temp0_15_0 ≤ 0temp0_15_0temp0_15_0 ≤ 0tail_14_post + tail_14_post ≤ 0tail_14_posttail_14_post ≤ 0tail_14_0 + tail_14_0 ≤ 0tail_14_0tail_14_0 ≤ 0result_dot_nondet_sdv_special_RETURN_VALUE_13_post + result_dot_nondet_sdv_special_RETURN_VALUE_13_post ≤ 0result_dot_nondet_sdv_special_RETURN_VALUE_13_postresult_dot_nondet_sdv_special_RETURN_VALUE_13_post ≤ 0result_dot_nondet_sdv_special_RETURN_VALUE_13_0 + result_dot_nondet_sdv_special_RETURN_VALUE_13_0 ≤ 0result_dot_nondet_sdv_special_RETURN_VALUE_13_0result_dot_nondet_sdv_special_RETURN_VALUE_13_0 ≤ 0result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22_post + result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22_post ≤ 0result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22_postresult_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22_post ≤ 0result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22_0 + result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22_0 ≤ 0result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22_0result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22_0 ≤ 0result_11_post + result_11_post ≤ 0result_11_postresult_11_post ≤ 0result_11_2 + result_11_2 ≤ 0result_11_2result_11_2 ≤ 0result_11_1 + result_11_1 ≤ 0result_11_1result_11_1 ≤ 0result_11_0 + result_11_0 ≤ 0result_11_0result_11_0 ≤ 0rcd_80_post + rcd_80_post ≤ 0rcd_80_postrcd_80_post ≤ 0rcd_80_0 + rcd_80_0 ≤ 0rcd_80_0rcd_80_0 ≤ 0rcd_50_post + rcd_50_post ≤ 0rcd_50_postrcd_50_post ≤ 0rcd_50_0 + rcd_50_0 ≤ 0rcd_50_0rcd_50_0 ≤ 0nondet_12_post + nondet_12_post ≤ 0nondet_12_postnondet_12_post ≤ 0nondet_12_1 + nondet_12_1 ≤ 0nondet_12_1nondet_12_1 ≤ 0nondet_12_0 + nondet_12_0 ≤ 0nondet_12_0nondet_12_0 ≤ 0length_17_post + length_17_post ≤ 0length_17_postlength_17_post ≤ 0length_17_0 + length_17_0 ≤ 0length_17_0length_17_0 ≤ 0i_86_post + i_86_post ≤ 0i_86_posti_86_post ≤ 0i_86_0 + i_86_0 ≤ 0i_86_0i_86_0 ≤ 0i_19_post + i_19_post ≤ 0i_19_posti_19_post ≤ 0i_19_0 + i_19_0 ≤ 0i_19_0i_19_0 ≤ 0head_SLAM_f_18_post + head_SLAM_f_18_post ≤ 0head_SLAM_f_18_posthead_SLAM_f_18_post ≤ 0head_SLAM_f_18_0 + head_SLAM_f_18_0 ≤ 0head_SLAM_f_18_0head_SLAM_f_18_0 ≤ 0head_21_post + head_21_post ≤ 0head_21_posthead_21_post ≤ 0head_21_0 + head_21_0 ≤ 0head_21_0head_21_0 ≤ 0head_16_post + head_16_post ≤ 0head_16_posthead_16_post ≤ 0head_16_0 + head_16_0 ≤ 0head_16_0head_16_0 ≤ 0
and for every transition t, a duplicate t is considered.

3 Transition Removal

We remove transitions 0, 1, 2, 3, 6, 7, 8 using the following ranking functions, which are bounded by −17.

6: 0
0: 0
1: 0
2: 0
4: 0
5: 0
3: 0
6: −7
0: −8
1: −9
2: −10
4: −11
5: −11
4_var_snapshot: −11
4*: −11
3: −15
Hints:
10 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
4 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
5 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
0 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
1 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
2 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
3 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
6 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
7 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
8 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]

4 Location Addition

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

4* 12 4: tmp_23_post + tmp_23_post ≤ 0tmp_23_posttmp_23_post ≤ 0tmp_23_0 + tmp_23_0 ≤ 0tmp_23_0tmp_23_0 ≤ 0temp_26_post + temp_26_post ≤ 0temp_26_posttemp_26_post ≤ 0temp_26_0 + temp_26_0 ≤ 0temp_26_0temp_26_0 ≤ 0temp0_20_post + temp0_20_post ≤ 0temp0_20_posttemp0_20_post ≤ 0temp0_20_1 + temp0_20_1 ≤ 0temp0_20_1temp0_20_1 ≤ 0temp0_20_0 + temp0_20_0 ≤ 0temp0_20_0temp0_20_0 ≤ 0temp0_15_0 + temp0_15_0 ≤ 0temp0_15_0temp0_15_0 ≤ 0tail_14_post + tail_14_post ≤ 0tail_14_posttail_14_post ≤ 0tail_14_0 + tail_14_0 ≤ 0tail_14_0tail_14_0 ≤ 0result_dot_nondet_sdv_special_RETURN_VALUE_13_post + result_dot_nondet_sdv_special_RETURN_VALUE_13_post ≤ 0result_dot_nondet_sdv_special_RETURN_VALUE_13_postresult_dot_nondet_sdv_special_RETURN_VALUE_13_post ≤ 0result_dot_nondet_sdv_special_RETURN_VALUE_13_0 + result_dot_nondet_sdv_special_RETURN_VALUE_13_0 ≤ 0result_dot_nondet_sdv_special_RETURN_VALUE_13_0result_dot_nondet_sdv_special_RETURN_VALUE_13_0 ≤ 0result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22_post + result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22_post ≤ 0result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22_postresult_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22_post ≤ 0result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22_0 + result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22_0 ≤ 0result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22_0result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22_0 ≤ 0result_11_post + result_11_post ≤ 0result_11_postresult_11_post ≤ 0result_11_2 + result_11_2 ≤ 0result_11_2result_11_2 ≤ 0result_11_1 + result_11_1 ≤ 0result_11_1result_11_1 ≤ 0result_11_0 + result_11_0 ≤ 0result_11_0result_11_0 ≤ 0rcd_80_post + rcd_80_post ≤ 0rcd_80_postrcd_80_post ≤ 0rcd_80_0 + rcd_80_0 ≤ 0rcd_80_0rcd_80_0 ≤ 0rcd_50_post + rcd_50_post ≤ 0rcd_50_postrcd_50_post ≤ 0rcd_50_0 + rcd_50_0 ≤ 0rcd_50_0rcd_50_0 ≤ 0nondet_12_post + nondet_12_post ≤ 0nondet_12_postnondet_12_post ≤ 0nondet_12_1 + nondet_12_1 ≤ 0nondet_12_1nondet_12_1 ≤ 0nondet_12_0 + nondet_12_0 ≤ 0nondet_12_0nondet_12_0 ≤ 0length_17_post + length_17_post ≤ 0length_17_postlength_17_post ≤ 0length_17_0 + length_17_0 ≤ 0length_17_0length_17_0 ≤ 0i_86_post + i_86_post ≤ 0i_86_posti_86_post ≤ 0i_86_0 + i_86_0 ≤ 0i_86_0i_86_0 ≤ 0i_19_post + i_19_post ≤ 0i_19_posti_19_post ≤ 0i_19_0 + i_19_0 ≤ 0i_19_0i_19_0 ≤ 0head_SLAM_f_18_post + head_SLAM_f_18_post ≤ 0head_SLAM_f_18_posthead_SLAM_f_18_post ≤ 0head_SLAM_f_18_0 + head_SLAM_f_18_0 ≤ 0head_SLAM_f_18_0head_SLAM_f_18_0 ≤ 0head_21_post + head_21_post ≤ 0head_21_posthead_21_post ≤ 0head_21_0 + head_21_0 ≤ 0head_21_0head_21_0 ≤ 0head_16_post + head_16_post ≤ 0head_16_posthead_16_post ≤ 0head_16_0 + head_16_0 ≤ 0head_16_0head_16_0 ≤ 0

5 Location Addition

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

4 10 4_var_snapshot: tmp_23_post + tmp_23_post ≤ 0tmp_23_posttmp_23_post ≤ 0tmp_23_0 + tmp_23_0 ≤ 0tmp_23_0tmp_23_0 ≤ 0temp_26_post + temp_26_post ≤ 0temp_26_posttemp_26_post ≤ 0temp_26_0 + temp_26_0 ≤ 0temp_26_0temp_26_0 ≤ 0temp0_20_post + temp0_20_post ≤ 0temp0_20_posttemp0_20_post ≤ 0temp0_20_1 + temp0_20_1 ≤ 0temp0_20_1temp0_20_1 ≤ 0temp0_20_0 + temp0_20_0 ≤ 0temp0_20_0temp0_20_0 ≤ 0temp0_15_0 + temp0_15_0 ≤ 0temp0_15_0temp0_15_0 ≤ 0tail_14_post + tail_14_post ≤ 0tail_14_posttail_14_post ≤ 0tail_14_0 + tail_14_0 ≤ 0tail_14_0tail_14_0 ≤ 0result_dot_nondet_sdv_special_RETURN_VALUE_13_post + result_dot_nondet_sdv_special_RETURN_VALUE_13_post ≤ 0result_dot_nondet_sdv_special_RETURN_VALUE_13_postresult_dot_nondet_sdv_special_RETURN_VALUE_13_post ≤ 0result_dot_nondet_sdv_special_RETURN_VALUE_13_0 + result_dot_nondet_sdv_special_RETURN_VALUE_13_0 ≤ 0result_dot_nondet_sdv_special_RETURN_VALUE_13_0result_dot_nondet_sdv_special_RETURN_VALUE_13_0 ≤ 0result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22_post + result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22_post ≤ 0result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22_postresult_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22_post ≤ 0result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22_0 + result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22_0 ≤ 0result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22_0result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22_0 ≤ 0result_11_post + result_11_post ≤ 0result_11_postresult_11_post ≤ 0result_11_2 + result_11_2 ≤ 0result_11_2result_11_2 ≤ 0result_11_1 + result_11_1 ≤ 0result_11_1result_11_1 ≤ 0result_11_0 + result_11_0 ≤ 0result_11_0result_11_0 ≤ 0rcd_80_post + rcd_80_post ≤ 0rcd_80_postrcd_80_post ≤ 0rcd_80_0 + rcd_80_0 ≤ 0rcd_80_0rcd_80_0 ≤ 0rcd_50_post + rcd_50_post ≤ 0rcd_50_postrcd_50_post ≤ 0rcd_50_0 + rcd_50_0 ≤ 0rcd_50_0rcd_50_0 ≤ 0nondet_12_post + nondet_12_post ≤ 0nondet_12_postnondet_12_post ≤ 0nondet_12_1 + nondet_12_1 ≤ 0nondet_12_1nondet_12_1 ≤ 0nondet_12_0 + nondet_12_0 ≤ 0nondet_12_0nondet_12_0 ≤ 0length_17_post + length_17_post ≤ 0length_17_postlength_17_post ≤ 0length_17_0 + length_17_0 ≤ 0length_17_0length_17_0 ≤ 0i_86_post + i_86_post ≤ 0i_86_posti_86_post ≤ 0i_86_0 + i_86_0 ≤ 0i_86_0i_86_0 ≤ 0i_19_post + i_19_post ≤ 0i_19_posti_19_post ≤ 0i_19_0 + i_19_0 ≤ 0i_19_0i_19_0 ≤ 0head_SLAM_f_18_post + head_SLAM_f_18_post ≤ 0head_SLAM_f_18_posthead_SLAM_f_18_post ≤ 0head_SLAM_f_18_0 + head_SLAM_f_18_0 ≤ 0head_SLAM_f_18_0head_SLAM_f_18_0 ≤ 0head_21_post + head_21_post ≤ 0head_21_posthead_21_post ≤ 0head_21_0 + head_21_0 ≤ 0head_21_0head_21_0 ≤ 0head_16_post + head_16_post ≤ 0head_16_posthead_16_post ≤ 0head_16_0 + head_16_0 ≤ 0head_16_0head_16_0 ≤ 0

6 SCC Decomposition

We consider subproblems for each of the 1 SCC(s) of the program graph.

6.1 SCC Subproblem 1/1

Here we consider the SCC { 4, 5, 4_var_snapshot, 4* }.

6.1.1 Transition Removal

We remove transition 4 using the following ranking functions, which are bounded by 0.

4: −2 − 4⋅i_19_0 + 4⋅length_17_0
5: −4⋅i_19_0 + 4⋅length_17_0
4_var_snapshot: −3 − 4⋅i_19_0 + 4⋅length_17_0
4*: −1 − 4⋅i_19_0 + 4⋅length_17_0
Hints:
10 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
12 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
4 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
5 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]

6.1.2 Transition Removal

We remove transitions 10, 12, 5 using the following ranking functions, which are bounded by −2.

4: −1
5: 1
4_var_snapshot: −2
4*: 0
Hints:
10 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
12 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
5 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]

6.1.3 Splitting Cut-Point Transitions

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

6.1.3.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 9.

6.1.3.1.1 Splitting Cut-Point Transitions

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

Tool configuration

T2Cert