Initial Problem

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5, Arg_6
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_start, eval_foo_stop
Transitions:
1:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb1_in(Arg_3,Arg_4,Arg_6,Arg_3,Arg_4,Arg_5,Arg_6)
2:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:0<Arg_2
3:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_2<=0
4:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb1_in(3*Arg_0-4*Arg_1,4*Arg_0+3*Arg_1,Arg_2+Arg_0-1,Arg_3,Arg_4,Arg_5,Arg_6)
5:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6)
0:eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6)

Preprocessing

Eliminate variables {Arg_5} that do not contribute to the problem

Found invariant Arg_2<=0 for location eval_foo_stop

Found invariant Arg_2<=0 for location eval_foo_bb3_in

Found invariant 1<=Arg_2 for location eval_foo_bb2_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_6
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_start, eval_foo_stop
Transitions:
12:eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_6) -> eval_foo_bb1_in(Arg_3,Arg_4,Arg_6,Arg_3,Arg_4,Arg_6)
13:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_6) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_6):|:0<Arg_2
14:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_6) -> eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_6):|:Arg_2<=0
15:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_6) -> eval_foo_bb1_in(3*Arg_0-4*Arg_1,4*Arg_0+3*Arg_1,Arg_2+Arg_0-1,Arg_3,Arg_4,Arg_6):|:1<=Arg_2
16:eval_foo_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_6) -> eval_foo_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_6):|:Arg_2<=0
17:eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_6) -> eval_foo_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_6)

MPRF for transition 13:eval_foo_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_6) -> eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_6):|:0<Arg_2 of depth 4:

new bound:

1246*Arg_3+2136*Arg_4+9078*Arg_6+8901 {O(n)}

MPRF:

eval_foo_bb2_in [100*Arg_2-10*Arg_0-20*Arg_1-199 ; -7*Arg_0-24*Arg_1 ; 4*Arg_0+Arg_2-4*Arg_1-2 ; Arg_0+2*Arg_2-2 ]
eval_foo_bb1_in [100*Arg_2-10*Arg_0-20*Arg_1-99 ; 3*Arg_0-4*Arg_1 ; Arg_0+Arg_2-1 ; Arg_2 ]

MPRF for transition 15:eval_foo_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_6) -> eval_foo_bb1_in(3*Arg_0-4*Arg_1,4*Arg_0+3*Arg_1,Arg_2+Arg_0-1,Arg_3,Arg_4,Arg_6):|:1<=Arg_2 of depth 4:

new bound:

1246*Arg_3+2136*Arg_4+9078*Arg_6+8901 {O(n)}

MPRF:

eval_foo_bb2_in [100*Arg_2-10*Arg_0-20*Arg_1-99 ; 3*Arg_0-4*Arg_1 ; Arg_0+Arg_2-1 ; Arg_2 ]
eval_foo_bb1_in [100*Arg_2-10*Arg_0-20*Arg_1-99 ; 3*Arg_0-4*Arg_1 ; Arg_0+Arg_2-1 ; Arg_2 ]

All Bounds

Timebounds

Overall timebound:18156*Arg_6+2492*Arg_3+4272*Arg_4+17806 {O(n)}
12: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
13: eval_foo_bb1_in->eval_foo_bb2_in: 1246*Arg_3+2136*Arg_4+9078*Arg_6+8901 {O(n)}
14: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
15: eval_foo_bb2_in->eval_foo_bb1_in: 1246*Arg_3+2136*Arg_4+9078*Arg_6+8901 {O(n)}
16: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
17: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 18156*Arg_6+2492*Arg_3+4272*Arg_4+17806 {O(n)}
12: eval_foo_bb0_in->eval_foo_bb1_in: 1 {O(1)}
13: eval_foo_bb1_in->eval_foo_bb2_in: 1246*Arg_3+2136*Arg_4+9078*Arg_6+8901 {O(n)}
14: eval_foo_bb1_in->eval_foo_bb3_in: 1 {O(1)}
15: eval_foo_bb2_in->eval_foo_bb1_in: 1246*Arg_3+2136*Arg_4+9078*Arg_6+8901 {O(n)}
16: eval_foo_bb3_in->eval_foo_stop: 1 {O(1)}
17: eval_foo_start->eval_foo_bb0_in: 1 {O(1)}

Sizebounds

12: eval_foo_bb0_in->eval_foo_bb1_in, Arg_0: Arg_3 {O(n)}
12: eval_foo_bb0_in->eval_foo_bb1_in, Arg_1: Arg_4 {O(n)}
12: eval_foo_bb0_in->eval_foo_bb1_in, Arg_2: Arg_6 {O(n)}
12: eval_foo_bb0_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
12: eval_foo_bb0_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
12: eval_foo_bb0_in->eval_foo_bb1_in, Arg_6: Arg_6 {O(n)}
13: eval_foo_bb1_in->eval_foo_bb2_in, Arg_0: 8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_3+8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_4 {O(EXP)}
13: eval_foo_bb1_in->eval_foo_bb2_in, Arg_1: 8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_3+8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_4 {O(EXP)}
13: eval_foo_bb1_in->eval_foo_bb2_in, Arg_2: 1246*8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_3*Arg_3+2136*8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_4*Arg_4+3382*8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_3*Arg_4+8902*8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_3+8902*8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_4+8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*9078*Arg_3*Arg_6+8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*9078*Arg_4*Arg_6+Arg_6 {O(EXP)}
13: eval_foo_bb1_in->eval_foo_bb2_in, Arg_3: Arg_3 {O(n)}
13: eval_foo_bb1_in->eval_foo_bb2_in, Arg_4: Arg_4 {O(n)}
13: eval_foo_bb1_in->eval_foo_bb2_in, Arg_6: Arg_6 {O(n)}
14: eval_foo_bb1_in->eval_foo_bb3_in, Arg_0: 8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_3+8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_4+Arg_3 {O(EXP)}
14: eval_foo_bb1_in->eval_foo_bb3_in, Arg_1: 8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_3+8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_4+Arg_4 {O(EXP)}
14: eval_foo_bb1_in->eval_foo_bb3_in, Arg_2: 1246*8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_3*Arg_3+2136*8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_4*Arg_4+3382*8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_3*Arg_4+8902*8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_3+8902*8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_4+8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*9078*Arg_3*Arg_6+8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*9078*Arg_4*Arg_6+2*Arg_6 {O(EXP)}
14: eval_foo_bb1_in->eval_foo_bb3_in, Arg_3: 2*Arg_3 {O(n)}
14: eval_foo_bb1_in->eval_foo_bb3_in, Arg_4: 2*Arg_4 {O(n)}
14: eval_foo_bb1_in->eval_foo_bb3_in, Arg_6: 2*Arg_6 {O(n)}
15: eval_foo_bb2_in->eval_foo_bb1_in, Arg_0: 8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_3+8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_4 {O(EXP)}
15: eval_foo_bb2_in->eval_foo_bb1_in, Arg_1: 8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_3+8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_4 {O(EXP)}
15: eval_foo_bb2_in->eval_foo_bb1_in, Arg_2: 1246*8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_3*Arg_3+2136*8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_4*Arg_4+3382*8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_3*Arg_4+8902*8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_3+8902*8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_4+8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*9078*Arg_3*Arg_6+8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*9078*Arg_4*Arg_6+Arg_6 {O(EXP)}
15: eval_foo_bb2_in->eval_foo_bb1_in, Arg_3: Arg_3 {O(n)}
15: eval_foo_bb2_in->eval_foo_bb1_in, Arg_4: Arg_4 {O(n)}
15: eval_foo_bb2_in->eval_foo_bb1_in, Arg_6: Arg_6 {O(n)}
16: eval_foo_bb3_in->eval_foo_stop, Arg_0: 8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_3+8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_4+Arg_3 {O(EXP)}
16: eval_foo_bb3_in->eval_foo_stop, Arg_1: 8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_3+8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_4+Arg_4 {O(EXP)}
16: eval_foo_bb3_in->eval_foo_stop, Arg_2: 1246*8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_3*Arg_3+2136*8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_4*Arg_4+3382*8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_3*Arg_4+8902*8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_3+8902*8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*Arg_4+8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*9078*Arg_3*Arg_6+8^(1246*Arg_3+2136*Arg_4+9078*Arg_6+8901)*9078*Arg_4*Arg_6+2*Arg_6 {O(EXP)}
16: eval_foo_bb3_in->eval_foo_stop, Arg_3: 2*Arg_3 {O(n)}
16: eval_foo_bb3_in->eval_foo_stop, Arg_4: 2*Arg_4 {O(n)}
16: eval_foo_bb3_in->eval_foo_stop, Arg_6: 2*Arg_6 {O(n)}
17: eval_foo_start->eval_foo_bb0_in, Arg_0: Arg_0 {O(n)}
17: eval_foo_start->eval_foo_bb0_in, Arg_1: Arg_1 {O(n)}
17: eval_foo_start->eval_foo_bb0_in, Arg_2: Arg_2 {O(n)}
17: eval_foo_start->eval_foo_bb0_in, Arg_3: Arg_3 {O(n)}
17: eval_foo_start->eval_foo_bb0_in, Arg_4: Arg_4 {O(n)}
17: eval_foo_start->eval_foo_bb0_in, Arg_6: Arg_6 {O(n)}