LTS Termination Proof

by T2Cert

Input

Integer Transition System
• Initial Location: 10
• Transitions: (pre-variables and post-variables)  0 0 1: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 10 − arg2 ≤ 0 ∧ 10 − arg2P ≤ 0 ∧ 5 − arg2 + arg6 ≤ 0 ∧ 3 − arg2 + arg7 ≤ 0 ∧ − arg3P ≤ 0 ∧ arg3P ≤ 0 ∧ − arg4P ≤ 0 ∧ arg4P ≤ 0 ∧ arg4 − arg5P ≤ 0 ∧ − arg4 + arg5P ≤ 0 ∧ arg6P − arg7P ≤ 0 ∧ − arg6P + arg7P ≤ 0 ∧ − arg8P ≤ 0 ∧ arg8P ≤ 0 ∧ − arg9P ≤ 0 ∧ arg9P ≤ 0 ∧ − arg10P ≤ 0 ∧ arg10P ≤ 0 ∧ − arg15P + arg3 ≤ 0 ∧ arg15P − arg3 ≤ 0 ∧ − arg16P + arg3 ≤ 0 ∧ arg16P − arg3 ≤ 0 ∧ − arg17P + arg4 ≤ 0 ∧ arg17P − arg4 ≤ 0 ∧ − arg19P + arg5 ≤ 0 ∧ arg19P − arg5 ≤ 0 ∧ − arg20P + arg6 ≤ 0 ∧ arg20P − arg6 ≤ 0 ∧ − arg23P + arg7 ≤ 0 ∧ arg23P − arg7 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − arg11P + arg11 ≤ 0 ∧ arg11P − arg11 ≤ 0 ∧ − arg12P + arg12 ≤ 0 ∧ arg12P − arg12 ≤ 0 ∧ − arg13P + arg13 ≤ 0 ∧ arg13P − arg13 ≤ 0 ∧ − arg14P + arg14 ≤ 0 ∧ arg14P − arg14 ≤ 0 ∧ − arg15P + arg15 ≤ 0 ∧ arg15P − arg15 ≤ 0 ∧ − arg16P + arg16 ≤ 0 ∧ arg16P − arg16 ≤ 0 ∧ − arg17P + arg17 ≤ 0 ∧ arg17P − arg17 ≤ 0 ∧ − arg18P + arg18 ≤ 0 ∧ arg18P − arg18 ≤ 0 ∧ − arg19P + arg19 ≤ 0 ∧ arg19P − arg19 ≤ 0 ∧ − arg20P + arg20 ≤ 0 ∧ arg20P − arg20 ≤ 0 ∧ − arg21P + arg21 ≤ 0 ∧ arg21P − arg21 ≤ 0 ∧ − arg22P + arg22 ≤ 0 ∧ arg22P − arg22 ≤ 0 ∧ − arg23P + arg23 ≤ 0 ∧ arg23P − arg23 ≤ 0 ∧ − arg24P + arg24 ≤ 0 ∧ arg24P − arg24 ≤ 0 ∧ − arg25P + arg25 ≤ 0 ∧ arg25P − arg25 ≤ 0 ∧ − x67 + x67 ≤ 0 ∧ x67 − x67 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x65 + x65 ≤ 0 ∧ x65 − x65 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x49 + x49 ≤ 0 ∧ x49 − x49 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 0 ∧ − x247 + x247 ≤ 0 ∧ x247 − x247 ≤ 0 ∧ − x212 + x212 ≤ 0 ∧ x212 − x212 ≤ 0 ∧ − x211 + x211 ≤ 0 ∧ x211 − x211 ≤ 0 ∧ − x170 + x170 ≤ 0 ∧ x170 − x170 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0 2 1 3: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − x25 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 7 − arg1P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − arg11P + arg11 ≤ 0 ∧ arg11P − arg11 ≤ 0 ∧ − arg12P + arg12 ≤ 0 ∧ arg12P − arg12 ≤ 0 ∧ − arg13P + arg13 ≤ 0 ∧ arg13P − arg13 ≤ 0 ∧ − arg14P + arg14 ≤ 0 ∧ arg14P − arg14 ≤ 0 ∧ − arg15P + arg15 ≤ 0 ∧ arg15P − arg15 ≤ 0 ∧ − arg16P + arg16 ≤ 0 ∧ arg16P − arg16 ≤ 0 ∧ − arg17P + arg17 ≤ 0 ∧ arg17P − arg17 ≤ 0 ∧ − arg18P + arg18 ≤ 0 ∧ arg18P − arg18 ≤ 0 ∧ − arg19P + arg19 ≤ 0 ∧ arg19P − arg19 ≤ 0 ∧ − arg20P + arg20 ≤ 0 ∧ arg20P − arg20 ≤ 0 ∧ − arg21P + arg21 ≤ 0 ∧ arg21P − arg21 ≤ 0 ∧ − arg22P + arg22 ≤ 0 ∧ arg22P − arg22 ≤ 0 ∧ − arg23P + arg23 ≤ 0 ∧ arg23P − arg23 ≤ 0 ∧ − arg24P + arg24 ≤ 0 ∧ arg24P − arg24 ≤ 0 ∧ − arg25P + arg25 ≤ 0 ∧ arg25P − arg25 ≤ 0 ∧ − x67 + x67 ≤ 0 ∧ x67 − x67 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x65 + x65 ≤ 0 ∧ x65 − x65 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x49 + x49 ≤ 0 ∧ x49 − x49 ≤ 0 ∧ − x247 + x247 ≤ 0 ∧ x247 − x247 ≤ 0 ∧ − x212 + x212 ≤ 0 ∧ x212 − x212 ≤ 0 ∧ − x211 + x211 ≤ 0 ∧ x211 − x211 ≤ 0 ∧ − x170 + x170 ≤ 0 ∧ x170 − x170 ≤ 0 3 3 5: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − arg2 ≤ 0 ∧ 1 − x49 ≤ 0 ∧ 1 − arg2 + x49 ≤ 0 ∧ 1 − arg3 + x50 ≤ 0 ∧ − arg3 ≤ 0 ∧ 1 − arg4 ≤ 0 ∧ 1 − x50 ≤ 0 ∧ 1 − x49 + x51 ≤ 0 ∧ 7 − arg1 ≤ 0 ∧ 10 − arg1P ≤ 0 ∧ 3 − arg2P ≤ 0 ∧ 1 − arg3P ≤ 0 ∧ 5 − arg1 + arg4 ≤ 0 ∧ 7 − arg1 + arg5 ≤ 0 ∧ 3 − arg1 + arg7 ≤ 0 ∧ 7 − arg1 + arg6 ≤ 0 ∧ − arg5P + arg7 ≤ 0 ∧ arg5P − arg7 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − arg11P + arg11 ≤ 0 ∧ arg11P − arg11 ≤ 0 ∧ − arg12P + arg12 ≤ 0 ∧ arg12P − arg12 ≤ 0 ∧ − arg13P + arg13 ≤ 0 ∧ arg13P − arg13 ≤ 0 ∧ − arg14P + arg14 ≤ 0 ∧ arg14P − arg14 ≤ 0 ∧ − arg15P + arg15 ≤ 0 ∧ arg15P − arg15 ≤ 0 ∧ − arg16P + arg16 ≤ 0 ∧ arg16P − arg16 ≤ 0 ∧ − arg17P + arg17 ≤ 0 ∧ arg17P − arg17 ≤ 0 ∧ − arg18P + arg18 ≤ 0 ∧ arg18P − arg18 ≤ 0 ∧ − arg19P + arg19 ≤ 0 ∧ arg19P − arg19 ≤ 0 ∧ − arg20P + arg20 ≤ 0 ∧ arg20P − arg20 ≤ 0 ∧ − arg21P + arg21 ≤ 0 ∧ arg21P − arg21 ≤ 0 ∧ − arg22P + arg22 ≤ 0 ∧ arg22P − arg22 ≤ 0 ∧ − arg23P + arg23 ≤ 0 ∧ arg23P − arg23 ≤ 0 ∧ − arg24P + arg24 ≤ 0 ∧ arg24P − arg24 ≤ 0 ∧ − arg25P + arg25 ≤ 0 ∧ arg25P − arg25 ≤ 0 ∧ − x67 + x67 ≤ 0 ∧ x67 − x67 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x65 + x65 ≤ 0 ∧ x65 − x65 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 0 ∧ − x247 + x247 ≤ 0 ∧ x247 − x247 ≤ 0 ∧ − x212 + x212 ≤ 0 ∧ x212 − x212 ≤ 0 ∧ − x211 + x211 ≤ 0 ∧ x211 − x211 ≤ 0 ∧ − x170 + x170 ≤ 0 ∧ x170 − x170 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 3 4 6: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − arg2 ≤ 0 ∧ 1 − x65 ≤ 0 ∧ 1 − arg2 + x65 ≤ 0 ∧ 1 − arg3 + x66 ≤ 0 ∧ − arg3 ≤ 0 ∧ 1 − x65 + x67 ≤ 0 ∧ 1 − arg4 ≤ 0 ∧ 7 − arg1 ≤ 0 ∧ 10 − arg1P ≤ 0 ∧ 3 − arg2P ≤ 0 ∧ 1 − arg3P ≤ 0 ∧ 5 − arg1 + arg4 ≤ 0 ∧ 7 − arg1 + arg5 ≤ 0 ∧ 3 − arg1 + arg7 ≤ 0 ∧ 7 − arg1 + arg6 ≤ 0 ∧ − arg5P + arg7 ≤ 0 ∧ arg5P − arg7 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − arg11P + arg11 ≤ 0 ∧ arg11P − arg11 ≤ 0 ∧ − arg12P + arg12 ≤ 0 ∧ arg12P − arg12 ≤ 0 ∧ − arg13P + arg13 ≤ 0 ∧ arg13P − arg13 ≤ 0 ∧ − arg14P + arg14 ≤ 0 ∧ arg14P − arg14 ≤ 0 ∧ − arg15P + arg15 ≤ 0 ∧ arg15P − arg15 ≤ 0 ∧ − arg16P + arg16 ≤ 0 ∧ arg16P − arg16 ≤ 0 ∧ − arg17P + arg17 ≤ 0 ∧ arg17P − arg17 ≤ 0 ∧ − arg18P + arg18 ≤ 0 ∧ arg18P − arg18 ≤ 0 ∧ − arg19P + arg19 ≤ 0 ∧ arg19P − arg19 ≤ 0 ∧ − arg20P + arg20 ≤ 0 ∧ arg20P − arg20 ≤ 0 ∧ − arg21P + arg21 ≤ 0 ∧ arg21P − arg21 ≤ 0 ∧ − arg22P + arg22 ≤ 0 ∧ arg22P − arg22 ≤ 0 ∧ − arg23P + arg23 ≤ 0 ∧ arg23P − arg23 ≤ 0 ∧ − arg24P + arg24 ≤ 0 ∧ arg24P − arg24 ≤ 0 ∧ − arg25P + arg25 ≤ 0 ∧ arg25P − arg25 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x49 + x49 ≤ 0 ∧ x49 − x49 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 0 ∧ − x247 + x247 ≤ 0 ∧ x247 − x247 ≤ 0 ∧ − x212 + x212 ≤ 0 ∧ x212 − x212 ≤ 0 ∧ − x211 + x211 ≤ 0 ∧ x211 − x211 ≤ 0 ∧ − x170 + x170 ≤ 0 ∧ x170 − x170 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 6 5 7: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 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 + arg1P − arg1 ≤ 0 ∧ 2 + arg1P − arg2 ≤ 0 ∧ 2 + arg1P − arg3 ≤ 0 ∧ 6 − arg1 ≤ 0 ∧ 3 − arg2 ≤ 0 ∧ 3 − arg3 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ 6 − arg2P ≤ 0 ∧ 1 − arg3P ≤ 0 ∧ 3 − arg4P ≤ 0 ∧ 5 − arg1 + arg4 ≤ 0 ∧ 3 − arg1 + arg5 ≤ 0 ∧ 3 − arg2 + arg6 ≤ 0 ∧ 2 − arg2 + arg7 ≤ 0 ∧ 2 − arg3 + arg7 ≤ 0 ∧ 3 − arg3 + arg6 ≤ 0 ∧ arg7 − arg8 ≤ 0 ∧ − arg7 + arg8 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − arg11P + arg11 ≤ 0 ∧ arg11P − arg11 ≤ 0 ∧ − arg12P + arg12 ≤ 0 ∧ arg12P − arg12 ≤ 0 ∧ − arg13P + arg13 ≤ 0 ∧ arg13P − arg13 ≤ 0 ∧ − arg14P + arg14 ≤ 0 ∧ arg14P − arg14 ≤ 0 ∧ − arg15P + arg15 ≤ 0 ∧ arg15P − arg15 ≤ 0 ∧ − arg16P + arg16 ≤ 0 ∧ arg16P − arg16 ≤ 0 ∧ − arg17P + arg17 ≤ 0 ∧ arg17P − arg17 ≤ 0 ∧ − arg18P + arg18 ≤ 0 ∧ arg18P − arg18 ≤ 0 ∧ − arg19P + arg19 ≤ 0 ∧ arg19P − arg19 ≤ 0 ∧ − arg20P + arg20 ≤ 0 ∧ arg20P − arg20 ≤ 0 ∧ − arg21P + arg21 ≤ 0 ∧ arg21P − arg21 ≤ 0 ∧ − arg22P + arg22 ≤ 0 ∧ arg22P − arg22 ≤ 0 ∧ − arg23P + arg23 ≤ 0 ∧ arg23P − arg23 ≤ 0 ∧ − arg24P + arg24 ≤ 0 ∧ arg24P − arg24 ≤ 0 ∧ − arg25P + arg25 ≤ 0 ∧ arg25P − arg25 ≤ 0 ∧ − x67 + x67 ≤ 0 ∧ x67 − x67 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x65 + x65 ≤ 0 ∧ x65 − x65 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x49 + x49 ≤ 0 ∧ x49 − x49 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 0 ∧ − x247 + x247 ≤ 0 ∧ x247 − x247 ≤ 0 ∧ − x212 + x212 ≤ 0 ∧ x212 − x212 ≤ 0 ∧ − x211 + x211 ≤ 0 ∧ x211 − x211 ≤ 0 ∧ − x170 + x170 ≤ 0 ∧ x170 − x170 ≤ 0 5 6 7: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 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 + arg1P − arg1 ≤ 0 ∧ 2 + arg1P − arg2 ≤ 0 ∧ 2 + arg1P − arg3 ≤ 0 ∧ 6 − arg1 ≤ 0 ∧ 3 − arg2 ≤ 0 ∧ 3 − arg3 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ 6 − arg2P ≤ 0 ∧ 1 − arg3P ≤ 0 ∧ 3 − arg4P ≤ 0 ∧ 5 − arg1 + arg4 ≤ 0 ∧ 3 − arg1 + arg5 ≤ 0 ∧ 3 − arg2 + arg6 ≤ 0 ∧ 2 − arg2 + arg7 ≤ 0 ∧ 2 − arg3 + arg7 ≤ 0 ∧ 3 − arg3 + arg6 ≤ 0 ∧ arg7 − arg8 ≤ 0 ∧ − arg7 + arg8 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − arg11P + arg11 ≤ 0 ∧ arg11P − arg11 ≤ 0 ∧ − arg12P + arg12 ≤ 0 ∧ arg12P − arg12 ≤ 0 ∧ − arg13P + arg13 ≤ 0 ∧ arg13P − arg13 ≤ 0 ∧ − arg14P + arg14 ≤ 0 ∧ arg14P − arg14 ≤ 0 ∧ − arg15P + arg15 ≤ 0 ∧ arg15P − arg15 ≤ 0 ∧ − arg16P + arg16 ≤ 0 ∧ arg16P − arg16 ≤ 0 ∧ − arg17P + arg17 ≤ 0 ∧ arg17P − arg17 ≤ 0 ∧ − arg18P + arg18 ≤ 0 ∧ arg18P − arg18 ≤ 0 ∧ − arg19P + arg19 ≤ 0 ∧ arg19P − arg19 ≤ 0 ∧ − arg20P + arg20 ≤ 0 ∧ arg20P − arg20 ≤ 0 ∧ − arg21P + arg21 ≤ 0 ∧ arg21P − arg21 ≤ 0 ∧ − arg22P + arg22 ≤ 0 ∧ arg22P − arg22 ≤ 0 ∧ − arg23P + arg23 ≤ 0 ∧ arg23P − arg23 ≤ 0 ∧ − arg24P + arg24 ≤ 0 ∧ arg24P − arg24 ≤ 0 ∧ − arg25P + arg25 ≤ 0 ∧ arg25P − arg25 ≤ 0 ∧ − x67 + x67 ≤ 0 ∧ x67 − x67 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x65 + x65 ≤ 0 ∧ x65 − x65 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x49 + x49 ≤ 0 ∧ x49 − x49 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 0 ∧ − x247 + x247 ≤ 0 ∧ x247 − x247 ≤ 0 ∧ − x212 + x212 ≤ 0 ∧ x212 − x212 ≤ 0 ∧ − x211 + x211 ≤ 0 ∧ x211 − x211 ≤ 0 ∧ − x170 + x170 ≤ 0 ∧ x170 − x170 ≤ 0 6 7 8: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 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 + arg1P − arg1 ≤ 0 ∧ 2 + arg1P − arg2 ≤ 0 ∧ arg1P − arg3 ≤ 0 ∧ 6 − arg1 ≤ 0 ∧ 3 − arg2 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ 6 − arg2P ≤ 0 ∧ 5 − arg3P ≤ 0 ∧ 1 − arg4P ≤ 0 ∧ 3 − arg5P ≤ 0 ∧ 5 − arg1 + arg4 ≤ 0 ∧ 3 − arg1 + arg5 ≤ 0 ∧ 3 − arg2 + arg6 ≤ 0 ∧ 2 − arg2 + arg7 ≤ 0 ∧ 2 − arg3 + arg8 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − arg11P + arg11 ≤ 0 ∧ arg11P − arg11 ≤ 0 ∧ − arg12P + arg12 ≤ 0 ∧ arg12P − arg12 ≤ 0 ∧ − arg13P + arg13 ≤ 0 ∧ arg13P − arg13 ≤ 0 ∧ − arg14P + arg14 ≤ 0 ∧ arg14P − arg14 ≤ 0 ∧ − arg15P + arg15 ≤ 0 ∧ arg15P − arg15 ≤ 0 ∧ − arg16P + arg16 ≤ 0 ∧ arg16P − arg16 ≤ 0 ∧ − arg17P + arg17 ≤ 0 ∧ arg17P − arg17 ≤ 0 ∧ − arg18P + arg18 ≤ 0 ∧ arg18P − arg18 ≤ 0 ∧ − arg19P + arg19 ≤ 0 ∧ arg19P − arg19 ≤ 0 ∧ − arg20P + arg20 ≤ 0 ∧ arg20P − arg20 ≤ 0 ∧ − arg21P + arg21 ≤ 0 ∧ arg21P − arg21 ≤ 0 ∧ − arg22P + arg22 ≤ 0 ∧ arg22P − arg22 ≤ 0 ∧ − arg23P + arg23 ≤ 0 ∧ arg23P − arg23 ≤ 0 ∧ − arg24P + arg24 ≤ 0 ∧ arg24P − arg24 ≤ 0 ∧ − arg25P + arg25 ≤ 0 ∧ arg25P − arg25 ≤ 0 ∧ − x67 + x67 ≤ 0 ∧ x67 − x67 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x65 + x65 ≤ 0 ∧ x65 − x65 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x49 + x49 ≤ 0 ∧ x49 − x49 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 0 ∧ − x247 + x247 ≤ 0 ∧ x247 − x247 ≤ 0 ∧ − x212 + x212 ≤ 0 ∧ x212 − x212 ≤ 0 ∧ − x211 + x211 ≤ 0 ∧ x211 − x211 ≤ 0 ∧ − x170 + x170 ≤ 0 ∧ x170 − x170 ≤ 0 5 8 8: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 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 + arg1P − arg1 ≤ 0 ∧ 2 + arg1P − arg2 ≤ 0 ∧ arg1P − arg3 ≤ 0 ∧ 6 − arg1 ≤ 0 ∧ 3 − arg2 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ 6 − arg2P ≤ 0 ∧ 5 − arg3P ≤ 0 ∧ 1 − arg4P ≤ 0 ∧ 3 − arg5P ≤ 0 ∧ 5 − arg1 + arg4 ≤ 0 ∧ 3 − arg1 + arg5 ≤ 0 ∧ 3 − arg2 + arg6 ≤ 0 ∧ 2 − arg2 + arg7 ≤ 0 ∧ 2 − arg3 + arg8 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − arg11P + arg11 ≤ 0 ∧ arg11P − arg11 ≤ 0 ∧ − arg12P + arg12 ≤ 0 ∧ arg12P − arg12 ≤ 0 ∧ − arg13P + arg13 ≤ 0 ∧ arg13P − arg13 ≤ 0 ∧ − arg14P + arg14 ≤ 0 ∧ arg14P − arg14 ≤ 0 ∧ − arg15P + arg15 ≤ 0 ∧ arg15P − arg15 ≤ 0 ∧ − arg16P + arg16 ≤ 0 ∧ arg16P − arg16 ≤ 0 ∧ − arg17P + arg17 ≤ 0 ∧ arg17P − arg17 ≤ 0 ∧ − arg18P + arg18 ≤ 0 ∧ arg18P − arg18 ≤ 0 ∧ − arg19P + arg19 ≤ 0 ∧ arg19P − arg19 ≤ 0 ∧ − arg20P + arg20 ≤ 0 ∧ arg20P − arg20 ≤ 0 ∧ − arg21P + arg21 ≤ 0 ∧ arg21P − arg21 ≤ 0 ∧ − arg22P + arg22 ≤ 0 ∧ arg22P − arg22 ≤ 0 ∧ − arg23P + arg23 ≤ 0 ∧ arg23P − arg23 ≤ 0 ∧ − arg24P + arg24 ≤ 0 ∧ arg24P − arg24 ≤ 0 ∧ − arg25P + arg25 ≤ 0 ∧ arg25P − arg25 ≤ 0 ∧ − x67 + x67 ≤ 0 ∧ x67 − x67 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x65 + x65 ≤ 0 ∧ x65 − x65 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x49 + x49 ≤ 0 ∧ x49 − x49 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 0 ∧ − x247 + x247 ≤ 0 ∧ x247 − x247 ≤ 0 ∧ − x212 + x212 ≤ 0 ∧ x212 − x212 ≤ 0 ∧ − x211 + x211 ≤ 0 ∧ x211 − x211 ≤ 0 ∧ − x170 + x170 ≤ 0 ∧ x170 − x170 ≤ 0 2 9 0: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − arg1P ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ −7 − arg1 + arg2P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 8 − arg2P ≤ 0 ∧ 1 − arg5P ≤ 0 ∧ −1 + arg5P ≤ 0 ∧ − arg6P ≤ 0 ∧ arg6P ≤ 0 ∧ − arg7P ≤ 0 ∧ arg7P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − arg11P + arg11 ≤ 0 ∧ arg11P − arg11 ≤ 0 ∧ − arg12P + arg12 ≤ 0 ∧ arg12P − arg12 ≤ 0 ∧ − arg13P + arg13 ≤ 0 ∧ arg13P − arg13 ≤ 0 ∧ − arg14P + arg14 ≤ 0 ∧ arg14P − arg14 ≤ 0 ∧ − arg15P + arg15 ≤ 0 ∧ arg15P − arg15 ≤ 0 ∧ − arg16P + arg16 ≤ 0 ∧ arg16P − arg16 ≤ 0 ∧ − arg17P + arg17 ≤ 0 ∧ arg17P − arg17 ≤ 0 ∧ − arg18P + arg18 ≤ 0 ∧ arg18P − arg18 ≤ 0 ∧ − arg19P + arg19 ≤ 0 ∧ arg19P − arg19 ≤ 0 ∧ − arg20P + arg20 ≤ 0 ∧ arg20P − arg20 ≤ 0 ∧ − arg21P + arg21 ≤ 0 ∧ arg21P − arg21 ≤ 0 ∧ − arg22P + arg22 ≤ 0 ∧ arg22P − arg22 ≤ 0 ∧ − arg23P + arg23 ≤ 0 ∧ arg23P − arg23 ≤ 0 ∧ − arg24P + arg24 ≤ 0 ∧ arg24P − arg24 ≤ 0 ∧ − arg25P + arg25 ≤ 0 ∧ arg25P − arg25 ≤ 0 ∧ − x67 + x67 ≤ 0 ∧ x67 − x67 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x65 + x65 ≤ 0 ∧ x65 − x65 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x49 + x49 ≤ 0 ∧ x49 − x49 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 0 ∧ − x247 + x247 ≤ 0 ∧ x247 − x247 ≤ 0 ∧ − x212 + x212 ≤ 0 ∧ x212 − x212 ≤ 0 ∧ − x211 + x211 ≤ 0 ∧ x211 − x211 ≤ 0 ∧ − x170 + x170 ≤ 0 ∧ x170 − x170 ≤ 0 1 10 9: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 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 − arg2 ≤ 0 ∧ 12 − arg1P ≤ 0 ∧ 5 + arg20 − arg2 ≤ 0 ∧ 9 + arg21 − arg2 ≤ 0 ∧ 3 + arg23 − arg2 ≤ 0 ∧ 9 + arg22 − arg2 ≤ 0 ∧ arg1 − arg2P ≤ 0 ∧ − arg1 + arg2P ≤ 0 ∧ arg13 − arg3P ≤ 0 ∧ − arg13 + arg3P ≤ 0 ∧ arg11 − arg4P ≤ 0 ∧ − arg11 + arg4P ≤ 0 ∧ − arg5P + arg7 ≤ 0 ∧ arg5P − arg7 ≤ 0 ∧ arg12 − arg6P ≤ 0 ∧ − arg12 + arg6P ≤ 0 ∧ arg6 − arg7P ≤ 0 ∧ − arg6 + arg7P ≤ 0 ∧ arg3 − arg9P ≤ 0 ∧ − arg3 + arg9P ≤ 0 ∧ − arg10P + arg14 ≤ 0 ∧ arg10P − arg14 ≤ 0 ∧ − arg11P + arg5 ≤ 0 ∧ arg11P − arg5 ≤ 0 ∧ − arg12P ≤ 0 ∧ arg12P ≤ 0 ∧ − arg13P + arg4 ≤ 0 ∧ arg13P − arg4 ≤ 0 ∧ − arg14P + arg8 ≤ 0 ∧ arg14P − arg8 ≤ 0 ∧ − arg15P + arg9 ≤ 0 ∧ arg15P − arg9 ≤ 0 ∧ arg10 − arg16P ≤ 0 ∧ − arg10 + arg16P ≤ 0 ∧ arg15 − arg17P ≤ 0 ∧ − arg15 + arg17P ≤ 0 ∧ arg16 − arg18P ≤ 0 ∧ − arg16 + arg18P ≤ 0 ∧ arg17 − arg19P ≤ 0 ∧ − arg17 + arg19P ≤ 0 ∧ arg19 − arg20P ≤ 0 ∧ − arg19 + arg20P ≤ 0 ∧ arg20 − arg21P ≤ 0 ∧ − arg20 + arg21P ≤ 0 ∧ arg23 − arg25P ≤ 0 ∧ − arg23 + arg25P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − arg11P + arg11 ≤ 0 ∧ arg11P − arg11 ≤ 0 ∧ − arg12P + arg12 ≤ 0 ∧ arg12P − arg12 ≤ 0 ∧ − arg13P + arg13 ≤ 0 ∧ arg13P − arg13 ≤ 0 ∧ − arg14P + arg14 ≤ 0 ∧ arg14P − arg14 ≤ 0 ∧ − arg15P + arg15 ≤ 0 ∧ arg15P − arg15 ≤ 0 ∧ − arg16P + arg16 ≤ 0 ∧ arg16P − arg16 ≤ 0 ∧ − arg17P + arg17 ≤ 0 ∧ arg17P − arg17 ≤ 0 ∧ − arg18P + arg18 ≤ 0 ∧ arg18P − arg18 ≤ 0 ∧ − arg19P + arg19 ≤ 0 ∧ arg19P − arg19 ≤ 0 ∧ − arg20P + arg20 ≤ 0 ∧ arg20P − arg20 ≤ 0 ∧ − arg21P + arg21 ≤ 0 ∧ arg21P − arg21 ≤ 0 ∧ − arg22P + arg22 ≤ 0 ∧ arg22P − arg22 ≤ 0 ∧ − arg23P + arg23 ≤ 0 ∧ arg23P − arg23 ≤ 0 ∧ − arg24P + arg24 ≤ 0 ∧ arg24P − arg24 ≤ 0 ∧ − arg25P + arg25 ≤ 0 ∧ arg25P − arg25 ≤ 0 ∧ − x67 + x67 ≤ 0 ∧ x67 − x67 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x65 + x65 ≤ 0 ∧ x65 − x65 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x49 + x49 ≤ 0 ∧ x49 − x49 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 0 ∧ − x247 + x247 ≤ 0 ∧ x247 − x247 ≤ 0 ∧ − x212 + x212 ≤ 0 ∧ x212 − x212 ≤ 0 ∧ − x211 + x211 ≤ 0 ∧ x211 − x211 ≤ 0 ∧ − x170 + x170 ≤ 0 ∧ x170 − x170 ≤ 0 9 11 9: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 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 − arg2 ≤ 0 ∧ − x170 ≤ 0 ∧ 1 − arg6 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ − arg20 ≤ 0 ∧ 1 + arg20 − x170 ≤ 0 ∧ 1 − arg10 ≤ 0 ∧ 1 − arg4 ≤ 0 ∧ 1 − arg13 ≤ 0 ∧ 1 − arg11 ≤ 0 ∧ 1 − arg12 ≤ 0 ∧ − x211 ≤ 0 ∧ 1 − arg9 ≤ 0 ∧ 1 − arg5 ≤ 0 ∧ 1 − arg18 ≤ 0 ∧ 1 − arg14 ≤ 0 ∧ 1 − arg19 ≤ 0 ∧ 1 − arg17 ≤ 0 ∧ 1 − arg15 ≤ 0 ∧ 1 − arg16 ≤ 0 ∧ − arg25 ≤ 0 ∧ − arg21 ≤ 0 ∧ 10 − arg1 ≤ 0 ∧ 10 − arg1P ≤ 0 ∧ 5 − arg1 + arg21 ≤ 0 ∧ 9 − arg1 + arg22 ≤ 0 ∧ 9 − arg1 + arg23 ≤ 0 ∧ 3 − arg1 + arg25 ≤ 0 ∧ 9 − arg1 + arg24 ≤ 0 ∧ −1 − arg2P + arg2 ≤ 0 ∧ 1 + arg2P − arg2 ≤ 0 ∧ 1 − arg20P + arg20 ≤ 0 ∧ −1 + arg20P − arg20 ≤ 0 ∧ 1 − arg21P + arg21 ≤ 0 ∧ −1 + arg21P − arg21 ≤ 0 ∧ 1 − arg25P + arg25 ≤ 0 ∧ −1 + arg25P − arg25 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg11P + arg11 ≤ 0 ∧ arg11P − arg11 ≤ 0 ∧ − arg13P + arg13 ≤ 0 ∧ arg13P − arg13 ≤ 0 ∧ − arg14P + arg14 ≤ 0 ∧ arg14P − arg14 ≤ 0 ∧ − arg15P + arg15 ≤ 0 ∧ arg15P − arg15 ≤ 0 ∧ − arg16P + arg16 ≤ 0 ∧ arg16P − arg16 ≤ 0 ∧ − arg17P + arg17 ≤ 0 ∧ arg17P − arg17 ≤ 0 ∧ − arg18P + arg18 ≤ 0 ∧ arg18P − arg18 ≤ 0 ∧ − arg19P + arg19 ≤ 0 ∧ arg19P − arg19 ≤ 0 ∧ − arg20P + arg20 ≤ 0 ∧ arg20P − arg20 ≤ 0 ∧ − arg21P + arg21 ≤ 0 ∧ arg21P − arg21 ≤ 0 ∧ − arg22P + arg22 ≤ 0 ∧ arg22P − arg22 ≤ 0 ∧ − arg23P + arg23 ≤ 0 ∧ arg23P − arg23 ≤ 0 ∧ − arg24P + arg24 ≤ 0 ∧ arg24P − arg24 ≤ 0 ∧ − arg25P + arg25 ≤ 0 ∧ arg25P − arg25 ≤ 0 ∧ − x67 + x67 ≤ 0 ∧ x67 − x67 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x65 + x65 ≤ 0 ∧ x65 − x65 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x49 + x49 ≤ 0 ∧ x49 − x49 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 0 ∧ − x247 + x247 ≤ 0 ∧ x247 − x247 ≤ 0 ∧ − x212 + x212 ≤ 0 ∧ x212 − x212 ≤ 0 ∧ − arg8P + arg8P ≤ 0 ∧ arg8P − arg8P ≤ 0 ∧ − arg8 + arg8 ≤ 0 ∧ arg8 − arg8 ≤ 0 ∧ − arg7P + arg7P ≤ 0 ∧ arg7P − arg7P ≤ 0 ∧ − arg7 + arg7 ≤ 0 ∧ arg7 − arg7 ≤ 0 ∧ − arg6P + arg6P ≤ 0 ∧ arg6P − arg6P ≤ 0 ∧ − arg6 + arg6 ≤ 0 ∧ arg6 − arg6 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0 ∧ − arg12P + arg12P ≤ 0 ∧ arg12P − arg12P ≤ 0 ∧ − arg12 + arg12 ≤ 0 ∧ arg12 − arg12 ≤ 0 ∧ − arg10P + arg10P ≤ 0 ∧ arg10P − arg10P ≤ 0 ∧ − arg10 + arg10 ≤ 0 ∧ arg10 − arg10 ≤ 0 9 12 9: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 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 − arg2 ≤ 0 ∧ − x212 ≤ 0 ∧ 1 − arg6 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ − arg20 ≤ 0 ∧ 1 + arg20 − x212 ≤ 0 ∧ 1 − arg10 ≤ 0 ∧ 1 − arg12 ≤ 0 ∧ − x247 ≤ 0 ∧ 1 − arg18 ≤ 0 ∧ 1 − arg19 ≤ 0 ∧ 1 − arg17 ≤ 0 ∧ 1 − arg8 ≤ 0 ∧ − arg25 ≤ 0 ∧ − arg21 ≤ 0 ∧ 12 − arg1 ≤ 0 ∧ 14 − arg1P ≤ 0 ∧ 5 − arg1 + arg21 ≤ 0 ∧ 9 − arg1 + arg22 ≤ 0 ∧ 9 − arg1 + arg23 ≤ 0 ∧ 3 − arg1 + arg25 ≤ 0 ∧ 9 − arg1 + arg24 ≤ 0 ∧ arg8 − arg9 ≤ 0 ∧ − arg8 + arg9 ≤ 0 ∧ arg10 − arg11 ≤ 0 ∧ − arg10 + arg11 ≤ 0 ∧ arg12 − arg13 ≤ 0 ∧ − arg12 + arg13 ≤ 0 ∧ − arg16 + arg7 ≤ 0 ∧ arg16 − arg7 ≤ 0 ∧ −1 − arg2P + arg2 ≤ 0 ∧ 1 + arg2P − arg2 ≤ 0 ∧ − arg3P ≤ 0 ∧ arg3P ≤ 0 ∧ 1 − arg4P ≤ 0 ∧ −1 + arg4P ≤ 0 ∧ 1 − arg5P ≤ 0 ∧ −1 + arg5P ≤ 0 ∧ − arg13P ≤ 0 ∧ arg13P ≤ 0 ∧ 2 − arg15P ≤ 0 ∧ −2 + arg15P ≤ 0 ∧ 1 − arg20P + arg20 ≤ 0 ∧ −1 + arg20P − arg20 ≤ 0 ∧ 1 − arg21P + arg21 ≤ 0 ∧ −1 + arg21P − arg21 ≤ 0 ∧ 1 − arg25P + arg25 ≤ 0 ∧ −1 + arg25P − arg25 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg11P + arg11 ≤ 0 ∧ arg11P − arg11 ≤ 0 ∧ − arg13P + arg13 ≤ 0 ∧ arg13P − arg13 ≤ 0 ∧ − arg14P + arg14 ≤ 0 ∧ arg14P − arg14 ≤ 0 ∧ − arg15P + arg15 ≤ 0 ∧ arg15P − arg15 ≤ 0 ∧ − arg16P + arg16 ≤ 0 ∧ arg16P − arg16 ≤ 0 ∧ − arg17P + arg17 ≤ 0 ∧ arg17P − arg17 ≤ 0 ∧ − arg18P + arg18 ≤ 0 ∧ arg18P − arg18 ≤ 0 ∧ − arg19P + arg19 ≤ 0 ∧ arg19P − arg19 ≤ 0 ∧ − arg20P + arg20 ≤ 0 ∧ arg20P − arg20 ≤ 0 ∧ − arg21P + arg21 ≤ 0 ∧ arg21P − arg21 ≤ 0 ∧ − arg22P + arg22 ≤ 0 ∧ arg22P − arg22 ≤ 0 ∧ − arg23P + arg23 ≤ 0 ∧ arg23P − arg23 ≤ 0 ∧ − arg24P + arg24 ≤ 0 ∧ arg24P − arg24 ≤ 0 ∧ − arg25P + arg25 ≤ 0 ∧ arg25P − arg25 ≤ 0 ∧ − x67 + x67 ≤ 0 ∧ x67 − x67 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x65 + x65 ≤ 0 ∧ x65 − x65 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x49 + x49 ≤ 0 ∧ x49 − x49 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 0 ∧ − x211 + x211 ≤ 0 ∧ x211 − x211 ≤ 0 ∧ − x170 + x170 ≤ 0 ∧ x170 − x170 ≤ 0 ∧ − arg8P + arg8P ≤ 0 ∧ arg8P − arg8P ≤ 0 ∧ − arg8 + arg8 ≤ 0 ∧ arg8 − arg8 ≤ 0 ∧ − arg12P + arg12P ≤ 0 ∧ arg12P − arg12P ≤ 0 ∧ − arg12 + arg12 ≤ 0 ∧ arg12 − arg12 ≤ 0 ∧ − arg10P + arg10P ≤ 0 ∧ arg10P − arg10P ≤ 0 ∧ − arg10 + arg10 ≤ 0 ∧ arg10 − arg10 ≤ 0 10 13 2: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − arg11P + arg11 ≤ 0 ∧ arg11P − arg11 ≤ 0 ∧ − arg12P + arg12 ≤ 0 ∧ arg12P − arg12 ≤ 0 ∧ − arg13P + arg13 ≤ 0 ∧ arg13P − arg13 ≤ 0 ∧ − arg14P + arg14 ≤ 0 ∧ arg14P − arg14 ≤ 0 ∧ − arg15P + arg15 ≤ 0 ∧ arg15P − arg15 ≤ 0 ∧ − arg16P + arg16 ≤ 0 ∧ arg16P − arg16 ≤ 0 ∧ − arg17P + arg17 ≤ 0 ∧ arg17P − arg17 ≤ 0 ∧ − arg18P + arg18 ≤ 0 ∧ arg18P − arg18 ≤ 0 ∧ − arg19P + arg19 ≤ 0 ∧ arg19P − arg19 ≤ 0 ∧ − arg20P + arg20 ≤ 0 ∧ arg20P − arg20 ≤ 0 ∧ − arg21P + arg21 ≤ 0 ∧ arg21P − arg21 ≤ 0 ∧ − arg22P + arg22 ≤ 0 ∧ arg22P − arg22 ≤ 0 ∧ − arg23P + arg23 ≤ 0 ∧ arg23P − arg23 ≤ 0 ∧ − arg24P + arg24 ≤ 0 ∧ arg24P − arg24 ≤ 0 ∧ − arg25P + arg25 ≤ 0 ∧ arg25P − arg25 ≤ 0 ∧ − x67 + x67 ≤ 0 ∧ x67 − x67 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x65 + x65 ≤ 0 ∧ x65 − x65 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x49 + x49 ≤ 0 ∧ x49 − x49 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 0 ∧ − x247 + x247 ≤ 0 ∧ x247 − x247 ≤ 0 ∧ − x212 + x212 ≤ 0 ∧ x212 − x212 ≤ 0 ∧ − x211 + x211 ≤ 0 ∧ x211 − x211 ≤ 0 ∧ − x170 + x170 ≤ 0 ∧ x170 − x170 ≤ 0

Proof

The following invariants are asserted.

 0: − arg1P ≤ 0 ∧ 8 − arg2P ≤ 0 ∧ −1 + arg5P ≤ 0 ∧ 1 − arg5P ≤ 0 ∧ arg6P ≤ 0 ∧ − arg6P ≤ 0 ∧ arg7P ≤ 0 ∧ − arg7P ≤ 0 ∧ − arg1 ≤ 0 ∧ 8 − arg2 ≤ 0 ∧ −1 + arg5 ≤ 0 ∧ 1 − arg5 ≤ 0 ∧ arg6 ≤ 0 ∧ − arg6 ≤ 0 ∧ arg7 ≤ 0 ∧ − arg7 ≤ 0 1: − arg1P ≤ 0 ∧ 10 − arg2P ≤ 0 ∧ arg3P ≤ 0 ∧ − arg3P ≤ 0 ∧ arg4P ≤ 0 ∧ − arg4P ≤ 0 ∧ arg8P ≤ 0 ∧ − arg8P ≤ 0 ∧ arg9P ≤ 0 ∧ − arg9P ≤ 0 ∧ arg10P ≤ 0 ∧ − arg10P ≤ 0 ∧ −1 + arg19P ≤ 0 ∧ arg20P ≤ 0 ∧ arg23P ≤ 0 ∧ − arg1 ≤ 0 ∧ 10 − arg2 ≤ 0 ∧ arg3 ≤ 0 ∧ − arg3 ≤ 0 ∧ arg4 ≤ 0 ∧ − arg4 ≤ 0 ∧ arg8 ≤ 0 ∧ − arg8 ≤ 0 ∧ arg9 ≤ 0 ∧ − arg9 ≤ 0 ∧ arg10 ≤ 0 ∧ − arg10 ≤ 0 ∧ −1 + arg19 ≤ 0 ∧ arg20 ≤ 0 ∧ arg23 ≤ 0 2: TRUE 3: 7 − arg1P ≤ 0 ∧ 7 − arg1 ≤ 0 ∧ − x25 ≤ 0 5: 10 − arg1P ≤ 0 ∧ 3 − arg2P ≤ 0 ∧ 1 − arg3P ≤ 0 ∧ 10 − arg1 ≤ 0 ∧ 3 − arg2 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ 1 − arg4 ≤ 0 ∧ − x25 ≤ 0 ∧ 1 − x49 ≤ 0 ∧ 1 − x50 ≤ 0 6: 10 − arg1P ≤ 0 ∧ 3 − arg2P ≤ 0 ∧ 1 − arg3P ≤ 0 ∧ 10 − arg1 ≤ 0 ∧ 3 − arg2 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ 1 − arg4 ≤ 0 ∧ − x25 ≤ 0 ∧ 1 − x65 ≤ 0 7: 1 − arg1P ≤ 0 ∧ 6 − arg2P ≤ 0 ∧ 1 − arg3P ≤ 0 ∧ 3 − arg4P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 6 − arg2 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ 3 − arg4 ≤ 0 ∧ − x25 ≤ 0 8: 1 − arg1P ≤ 0 ∧ 6 − arg2P ≤ 0 ∧ 5 − arg3P ≤ 0 ∧ 1 − arg4P ≤ 0 ∧ 3 − arg5P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 6 − arg2 ≤ 0 ∧ 5 − arg3 ≤ 0 ∧ 1 − arg4 ≤ 0 ∧ 3 − arg5 ≤ 0 ∧ − x25 ≤ 0 9: 1 − arg1P ≤ 0 ∧ arg12P ≤ 0 ∧ − arg12P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ arg12 ≤ 0 ∧ − arg12 ≤ 0 10: TRUE

The invariants are proved as follows.

IMPACT Invariant Proof

• nodes (location) invariant:  0 (0) − arg1P ≤ 0 ∧ 8 − arg2P ≤ 0 ∧ −1 + arg5P ≤ 0 ∧ 1 − arg5P ≤ 0 ∧ arg6P ≤ 0 ∧ − arg6P ≤ 0 ∧ arg7P ≤ 0 ∧ − arg7P ≤ 0 ∧ − arg1 ≤ 0 ∧ 8 − arg2 ≤ 0 ∧ −1 + arg5 ≤ 0 ∧ 1 − arg5 ≤ 0 ∧ arg6 ≤ 0 ∧ − arg6 ≤ 0 ∧ arg7 ≤ 0 ∧ − arg7 ≤ 0 1 (1) − arg1P ≤ 0 ∧ 10 − arg2P ≤ 0 ∧ arg3P ≤ 0 ∧ − arg3P ≤ 0 ∧ arg4P ≤ 0 ∧ − arg4P ≤ 0 ∧ arg8P ≤ 0 ∧ − arg8P ≤ 0 ∧ arg9P ≤ 0 ∧ − arg9P ≤ 0 ∧ arg10P ≤ 0 ∧ − arg10P ≤ 0 ∧ −1 + arg19P ≤ 0 ∧ arg20P ≤ 0 ∧ arg23P ≤ 0 ∧ − arg1 ≤ 0 ∧ 10 − arg2 ≤ 0 ∧ arg3 ≤ 0 ∧ − arg3 ≤ 0 ∧ arg4 ≤ 0 ∧ − arg4 ≤ 0 ∧ arg8 ≤ 0 ∧ − arg8 ≤ 0 ∧ arg9 ≤ 0 ∧ − arg9 ≤ 0 ∧ arg10 ≤ 0 ∧ − arg10 ≤ 0 ∧ −1 + arg19 ≤ 0 ∧ arg20 ≤ 0 ∧ arg23 ≤ 0 2 (2) TRUE 3 (3) 7 − arg1P ≤ 0 ∧ 7 − arg1 ≤ 0 ∧ − x25 ≤ 0 5 (5) 10 − arg1P ≤ 0 ∧ 3 − arg2P ≤ 0 ∧ 1 − arg3P ≤ 0 ∧ 10 − arg1 ≤ 0 ∧ 3 − arg2 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ 1 − arg4 ≤ 0 ∧ − x25 ≤ 0 ∧ 1 − x49 ≤ 0 ∧ 1 − x50 ≤ 0 6 (6) 10 − arg1P ≤ 0 ∧ 3 − arg2P ≤ 0 ∧ 1 − arg3P ≤ 0 ∧ 10 − arg1 ≤ 0 ∧ 3 − arg2 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ 1 − arg4 ≤ 0 ∧ − x25 ≤ 0 ∧ 1 − x65 ≤ 0 7 (7) 1 − arg1P ≤ 0 ∧ 6 − arg2P ≤ 0 ∧ 1 − arg3P ≤ 0 ∧ 3 − arg4P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 6 − arg2 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ 3 − arg4 ≤ 0 ∧ − x25 ≤ 0 8 (8) 1 − arg1P ≤ 0 ∧ 6 − arg2P ≤ 0 ∧ 5 − arg3P ≤ 0 ∧ 1 − arg4P ≤ 0 ∧ 3 − arg5P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 6 − arg2 ≤ 0 ∧ 5 − arg3 ≤ 0 ∧ 1 − arg4 ≤ 0 ∧ 3 − arg5 ≤ 0 ∧ − x25 ≤ 0 9 (9) 1 − arg1P ≤ 0 ∧ arg12P ≤ 0 ∧ − arg12P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ arg12 ≤ 0 ∧ − arg12 ≤ 0 10 (10) TRUE
• initial node: 10
• cover edges:
• transition edges:  0 0 1 1 10 9 2 1 3 2 9 0 3 3 5 3 4 6 5 6 7 5 8 8 6 5 7 6 7 8 9 11 9 9 12 9 10 13 2

2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
 9 14 9: − x67 + x67 ≤ 0 ∧ x67 − x67 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x65 + x65 ≤ 0 ∧ x65 − x65 ≤ 0 ∧ − x51 + x51 ≤ 0 ∧ x51 − x51 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x49 + x49 ≤ 0 ∧ x49 − x49 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 0 ∧ − x247 + x247 ≤ 0 ∧ x247 − x247 ≤ 0 ∧ − x212 + x212 ≤ 0 ∧ x212 − x212 ≤ 0 ∧ − x211 + x211 ≤ 0 ∧ x211 − x211 ≤ 0 ∧ − x170 + x170 ≤ 0 ∧ x170 − x170 ≤ 0 ∧ − arg9P + arg9P ≤ 0 ∧ arg9P − arg9P ≤ 0 ∧ − arg9 + arg9 ≤ 0 ∧ arg9 − arg9 ≤ 0 ∧ − arg8P + arg8P ≤ 0 ∧ arg8P − arg8P ≤ 0 ∧ − arg8 + arg8 ≤ 0 ∧ arg8 − arg8 ≤ 0 ∧ − arg7P + arg7P ≤ 0 ∧ arg7P − arg7P ≤ 0 ∧ − arg7 + arg7 ≤ 0 ∧ arg7 − arg7 ≤ 0 ∧ − arg6P + arg6P ≤ 0 ∧ arg6P − arg6P ≤ 0 ∧ − arg6 + arg6 ≤ 0 ∧ arg6 − arg6 ≤ 0 ∧ − arg5P + arg5P ≤ 0 ∧ arg5P − arg5P ≤ 0 ∧ − arg5 + arg5 ≤ 0 ∧ arg5 − arg5 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg25P + arg25P ≤ 0 ∧ arg25P − arg25P ≤ 0 ∧ − arg25 + arg25 ≤ 0 ∧ arg25 − arg25 ≤ 0 ∧ − arg24P + arg24P ≤ 0 ∧ arg24P − arg24P ≤ 0 ∧ − arg24 + arg24 ≤ 0 ∧ arg24 − arg24 ≤ 0 ∧ − arg23P + arg23P ≤ 0 ∧ arg23P − arg23P ≤ 0 ∧ − arg23 + arg23 ≤ 0 ∧ arg23 − arg23 ≤ 0 ∧ − arg22P + arg22P ≤ 0 ∧ arg22P − arg22P ≤ 0 ∧ − arg22 + arg22 ≤ 0 ∧ arg22 − arg22 ≤ 0 ∧ − arg21P + arg21P ≤ 0 ∧ arg21P − arg21P ≤ 0 ∧ − arg21 + arg21 ≤ 0 ∧ arg21 − arg21 ≤ 0 ∧ − arg20P + arg20P ≤ 0 ∧ arg20P − arg20P ≤ 0 ∧ − arg20 + arg20 ≤ 0 ∧ arg20 − arg20 ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg19P + arg19P ≤ 0 ∧ arg19P − arg19P ≤ 0 ∧ − arg19 + arg19 ≤ 0 ∧ arg19 − arg19 ≤ 0 ∧ − arg18P + arg18P ≤ 0 ∧ arg18P − arg18P ≤ 0 ∧ − arg18 + arg18 ≤ 0 ∧ arg18 − arg18 ≤ 0 ∧ − arg17P + arg17P ≤ 0 ∧ arg17P − arg17P ≤ 0 ∧ − arg17 + arg17 ≤ 0 ∧ arg17 − arg17 ≤ 0 ∧ − arg16P + arg16P ≤ 0 ∧ arg16P − arg16P ≤ 0 ∧ − arg16 + arg16 ≤ 0 ∧ arg16 − arg16 ≤ 0 ∧ − arg15P + arg15P ≤ 0 ∧ arg15P − arg15P ≤ 0 ∧ − arg15 + arg15 ≤ 0 ∧ arg15 − arg15 ≤ 0 ∧ − arg14P + arg14P ≤ 0 ∧ arg14P − arg14P ≤ 0 ∧ − arg14 + arg14 ≤ 0 ∧ arg14 − arg14 ≤ 0 ∧ − arg13P + arg13P ≤ 0 ∧ arg13P − arg13P ≤ 0 ∧ − arg13 + arg13 ≤ 0 ∧ arg13 − arg13 ≤ 0 ∧ − arg12P + arg12P ≤ 0 ∧ arg12P − arg12P ≤ 0 ∧ − arg12 + arg12 ≤ 0 ∧ arg12 − arg12 ≤ 0 ∧ − arg11P + arg11P ≤ 0 ∧ arg11P − arg11P ≤ 0 ∧ − arg11 + arg11 ≤ 0 ∧ arg11 − arg11 ≤ 0 ∧ − arg10P + arg10P ≤ 0 ∧ arg10P − arg10P ≤ 0 ∧ − arg10 + arg10 ≤ 0 ∧ arg10 − arg10 ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0
and for every transition t, a duplicate t is considered.

3 Transition Removal

We remove transitions 0, 1, 3, 4, 5, 6, 7, 8, 9, 10, 13 using the following ranking functions, which are bounded by −25.

 10: 0 2: 0 3: 0 5: 0 6: 0 7: 0 8: 0 0: 0 1: 0 9: 0 10: −11 2: −12 3: −13 5: −14 6: −15 7: −16 8: −17 0: −18 1: −19 9: −20 9_var_snapshot: −20 9*: −20

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

9* 17 9: x67 + x67 ≤ 0x67x67 ≤ 0x66 + x66 ≤ 0x66x66 ≤ 0x65 + x65 ≤ 0x65x65 ≤ 0x51 + x51 ≤ 0x51x51 ≤ 0x50 + x50 ≤ 0x50x50 ≤ 0x49 + x49 ≤ 0x49x49 ≤ 0x25 + x25 ≤ 0x25x25 ≤ 0x247 + x247 ≤ 0x247x247 ≤ 0x212 + x212 ≤ 0x212x212 ≤ 0x211 + x211 ≤ 0x211x211 ≤ 0x170 + x170 ≤ 0x170x170 ≤ 0arg9P + arg9P ≤ 0arg9Parg9P ≤ 0arg9 + arg9 ≤ 0arg9arg9 ≤ 0arg8P + arg8P ≤ 0arg8Parg8P ≤ 0arg8 + arg8 ≤ 0arg8arg8 ≤ 0arg7P + arg7P ≤ 0arg7Parg7P ≤ 0arg7 + arg7 ≤ 0arg7arg7 ≤ 0arg6P + arg6P ≤ 0arg6Parg6P ≤ 0arg6 + arg6 ≤ 0arg6arg6 ≤ 0arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg25P + arg25P ≤ 0arg25Parg25P ≤ 0arg25 + arg25 ≤ 0arg25arg25 ≤ 0arg24P + arg24P ≤ 0arg24Parg24P ≤ 0arg24 + arg24 ≤ 0arg24arg24 ≤ 0arg23P + arg23P ≤ 0arg23Parg23P ≤ 0arg23 + arg23 ≤ 0arg23arg23 ≤ 0arg22P + arg22P ≤ 0arg22Parg22P ≤ 0arg22 + arg22 ≤ 0arg22arg22 ≤ 0arg21P + arg21P ≤ 0arg21Parg21P ≤ 0arg21 + arg21 ≤ 0arg21arg21 ≤ 0arg20P + arg20P ≤ 0arg20Parg20P ≤ 0arg20 + arg20 ≤ 0arg20arg20 ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg19P + arg19P ≤ 0arg19Parg19P ≤ 0arg19 + arg19 ≤ 0arg19arg19 ≤ 0arg18P + arg18P ≤ 0arg18Parg18P ≤ 0arg18 + arg18 ≤ 0arg18arg18 ≤ 0arg17P + arg17P ≤ 0arg17Parg17P ≤ 0arg17 + arg17 ≤ 0arg17arg17 ≤ 0arg16P + arg16P ≤ 0arg16Parg16P ≤ 0arg16 + arg16 ≤ 0arg16arg16 ≤ 0arg15P + arg15P ≤ 0arg15Parg15P ≤ 0arg15 + arg15 ≤ 0arg15arg15 ≤ 0arg14P + arg14P ≤ 0arg14Parg14P ≤ 0arg14 + arg14 ≤ 0arg14arg14 ≤ 0arg13P + arg13P ≤ 0arg13Parg13P ≤ 0arg13 + arg13 ≤ 0arg13arg13 ≤ 0arg12P + arg12P ≤ 0arg12Parg12P ≤ 0arg12 + arg12 ≤ 0arg12arg12 ≤ 0arg11P + arg11P ≤ 0arg11Parg11P ≤ 0arg11 + arg11 ≤ 0arg11arg11 ≤ 0arg10P + arg10P ≤ 0arg10Parg10P ≤ 0arg10 + arg10 ≤ 0arg10arg10 ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

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

9 15 9_var_snapshot: x67 + x67 ≤ 0x67x67 ≤ 0x66 + x66 ≤ 0x66x66 ≤ 0x65 + x65 ≤ 0x65x65 ≤ 0x51 + x51 ≤ 0x51x51 ≤ 0x50 + x50 ≤ 0x50x50 ≤ 0x49 + x49 ≤ 0x49x49 ≤ 0x25 + x25 ≤ 0x25x25 ≤ 0x247 + x247 ≤ 0x247x247 ≤ 0x212 + x212 ≤ 0x212x212 ≤ 0x211 + x211 ≤ 0x211x211 ≤ 0x170 + x170 ≤ 0x170x170 ≤ 0arg9P + arg9P ≤ 0arg9Parg9P ≤ 0arg9 + arg9 ≤ 0arg9arg9 ≤ 0arg8P + arg8P ≤ 0arg8Parg8P ≤ 0arg8 + arg8 ≤ 0arg8arg8 ≤ 0arg7P + arg7P ≤ 0arg7Parg7P ≤ 0arg7 + arg7 ≤ 0arg7arg7 ≤ 0arg6P + arg6P ≤ 0arg6Parg6P ≤ 0arg6 + arg6 ≤ 0arg6arg6 ≤ 0arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg25P + arg25P ≤ 0arg25Parg25P ≤ 0arg25 + arg25 ≤ 0arg25arg25 ≤ 0arg24P + arg24P ≤ 0arg24Parg24P ≤ 0arg24 + arg24 ≤ 0arg24arg24 ≤ 0arg23P + arg23P ≤ 0arg23Parg23P ≤ 0arg23 + arg23 ≤ 0arg23arg23 ≤ 0arg22P + arg22P ≤ 0arg22Parg22P ≤ 0arg22 + arg22 ≤ 0arg22arg22 ≤ 0arg21P + arg21P ≤ 0arg21Parg21P ≤ 0arg21 + arg21 ≤ 0arg21arg21 ≤ 0arg20P + arg20P ≤ 0arg20Parg20P ≤ 0arg20 + arg20 ≤ 0arg20arg20 ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg19P + arg19P ≤ 0arg19Parg19P ≤ 0arg19 + arg19 ≤ 0arg19arg19 ≤ 0arg18P + arg18P ≤ 0arg18Parg18P ≤ 0arg18 + arg18 ≤ 0arg18arg18 ≤ 0arg17P + arg17P ≤ 0arg17Parg17P ≤ 0arg17 + arg17 ≤ 0arg17arg17 ≤ 0arg16P + arg16P ≤ 0arg16Parg16P ≤ 0arg16 + arg16 ≤ 0arg16arg16 ≤ 0arg15P + arg15P ≤ 0arg15Parg15P ≤ 0arg15 + arg15 ≤ 0arg15arg15 ≤ 0arg14P + arg14P ≤ 0arg14Parg14P ≤ 0arg14 + arg14 ≤ 0arg14arg14 ≤ 0arg13P + arg13P ≤ 0arg13Parg13P ≤ 0arg13 + arg13 ≤ 0arg13arg13 ≤ 0arg12P + arg12P ≤ 0arg12Parg12P ≤ 0arg12 + arg12 ≤ 0arg12arg12 ≤ 0arg11P + arg11P ≤ 0arg11Parg11P ≤ 0arg11 + arg11 ≤ 0arg11arg11 ≤ 0arg10P + arg10P ≤ 0arg10Parg10P ≤ 0arg10 + arg10 ≤ 0arg10arg10 ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 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 { 9, 9_var_snapshot, 9* }.

6.1.1 Transition Removal

We remove transitions 17, 11, 12 using the following ranking functions, which are bounded by −3.

 9: −1 9_var_snapshot: −2 9*: 0

6.1.2 Transition Removal

We remove transition 15 using the following ranking functions, which are bounded by 0.

 9: arg1P 9_var_snapshot: 0 9*: 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 14.

6.1.3.1.1 Splitting Cut-Point Transitions

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

T2Cert

• version: 1.0