Initial Problem

Start: eval_gcd_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: eval_gcd_bb0_in, eval_gcd_bb1_in, eval_gcd_bb2_in, eval_gcd_bb3_in, eval_gcd_start, eval_gcd_stop
Transitions:
1:eval_gcd_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_gcd_bb1_in(Arg_2,Arg_3,Arg_2,Arg_3)
2:eval_gcd_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_gcd_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:0<Arg_0 && 0<Arg_1
3:eval_gcd_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_gcd_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=0
4:eval_gcd_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_gcd_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<=0
5:eval_gcd_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_gcd_bb1_in(Arg_0-Arg_1,Arg_1,Arg_2,Arg_3):|:Arg_1<Arg_0 && Arg_1<Arg_0
6:eval_gcd_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_gcd_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<Arg_0 && Arg_0<=Arg_1
7:eval_gcd_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_gcd_bb1_in(Arg_0-Arg_1,Arg_1-Arg_0,Arg_2,Arg_3):|:Arg_0<=Arg_1 && Arg_1<Arg_0
8:eval_gcd_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_gcd_bb1_in(Arg_0,Arg_1-Arg_0,Arg_2,Arg_3):|:Arg_0<=Arg_1 && Arg_0<=Arg_1
9:eval_gcd_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_gcd_stop(Arg_0,Arg_1,Arg_2,Arg_3)
0:eval_gcd_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_gcd_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)

Preprocessing

Cut unsatisfiable transition 6: eval_gcd_bb2_in->eval_gcd_bb1_in

Cut unsatisfiable transition 7: eval_gcd_bb2_in->eval_gcd_bb1_in

Found invariant Arg_1<=Arg_3 && Arg_0<=Arg_2 for location eval_gcd_bb1_in

Found invariant Arg_1<=Arg_3 && Arg_0<=Arg_2 for location eval_gcd_bb3_in

Found invariant 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location eval_gcd_bb2_in

Found invariant Arg_1<=Arg_3 && Arg_0<=Arg_2 for location eval_gcd_stop

Problem after Preprocessing

Start: eval_gcd_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: eval_gcd_bb0_in, eval_gcd_bb1_in, eval_gcd_bb2_in, eval_gcd_bb3_in, eval_gcd_start, eval_gcd_stop
Transitions:
1:eval_gcd_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_gcd_bb1_in(Arg_2,Arg_3,Arg_2,Arg_3)
2:eval_gcd_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_gcd_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<=Arg_3 && Arg_0<=Arg_2 && 0<Arg_0 && 0<Arg_1
3:eval_gcd_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_gcd_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<=Arg_3 && Arg_0<=Arg_2 && Arg_0<=0
4:eval_gcd_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_gcd_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<=Arg_3 && Arg_0<=Arg_2 && Arg_1<=0
5:eval_gcd_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_gcd_bb1_in(Arg_0-Arg_1,Arg_1,Arg_2,Arg_3):|:1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_1<Arg_0 && Arg_1<Arg_0
8:eval_gcd_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_gcd_bb1_in(Arg_0,Arg_1-Arg_0,Arg_2,Arg_3):|:1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<=Arg_1 && Arg_0<=Arg_1
9:eval_gcd_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_gcd_stop(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<=Arg_3 && Arg_0<=Arg_2
0:eval_gcd_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_gcd_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)

MPRF for transition 2:eval_gcd_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_gcd_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<=Arg_3 && Arg_0<=Arg_2 && 0<Arg_0 && 0<Arg_1 of depth 1:

new bound:

Arg_2+Arg_3+1 {O(n)}

MPRF:

eval_gcd_bb2_in [Arg_0+Arg_1-2 ]
eval_gcd_bb1_in [Arg_0+Arg_1-1 ]

MPRF for transition 5:eval_gcd_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_gcd_bb1_in(Arg_0-Arg_1,Arg_1,Arg_2,Arg_3):|:1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_1<Arg_0 && Arg_1<Arg_0 of depth 1:

new bound:

Arg_2 {O(n)}

MPRF:

eval_gcd_bb2_in [Arg_0 ]
eval_gcd_bb1_in [Arg_0 ]

MPRF for transition 8:eval_gcd_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_gcd_bb1_in(Arg_0,Arg_1-Arg_0,Arg_2,Arg_3):|:1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_0<=Arg_1 && Arg_0<=Arg_1 of depth 1:

new bound:

Arg_3 {O(n)}

MPRF:

eval_gcd_bb2_in [Arg_1 ]
eval_gcd_bb1_in [Arg_1 ]

All Bounds

Timebounds

Overall timebound:2*Arg_2+2*Arg_3+6 {O(n)}
1: eval_gcd_bb0_in->eval_gcd_bb1_in: 1 {O(1)}
2: eval_gcd_bb1_in->eval_gcd_bb2_in: Arg_2+Arg_3+1 {O(n)}
3: eval_gcd_bb1_in->eval_gcd_bb3_in: 1 {O(1)}
4: eval_gcd_bb1_in->eval_gcd_bb3_in: 1 {O(1)}
5: eval_gcd_bb2_in->eval_gcd_bb1_in: Arg_2 {O(n)}
8: eval_gcd_bb2_in->eval_gcd_bb1_in: Arg_3 {O(n)}
9: eval_gcd_bb3_in->eval_gcd_stop: 1 {O(1)}
0: eval_gcd_start->eval_gcd_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_2+2*Arg_3+6 {O(n)}
1: eval_gcd_bb0_in->eval_gcd_bb1_in: 1 {O(1)}
2: eval_gcd_bb1_in->eval_gcd_bb2_in: Arg_2+Arg_3+1 {O(n)}
3: eval_gcd_bb1_in->eval_gcd_bb3_in: 1 {O(1)}
4: eval_gcd_bb1_in->eval_gcd_bb3_in: 1 {O(1)}
5: eval_gcd_bb2_in->eval_gcd_bb1_in: Arg_2 {O(n)}
8: eval_gcd_bb2_in->eval_gcd_bb1_in: Arg_3 {O(n)}
9: eval_gcd_bb3_in->eval_gcd_stop: 1 {O(1)}
0: eval_gcd_start->eval_gcd_bb0_in: 1 {O(1)}

Sizebounds

1: eval_gcd_bb0_in->eval_gcd_bb1_in, Arg_0: Arg_2 {O(n)}
1: eval_gcd_bb0_in->eval_gcd_bb1_in, Arg_1: Arg_3 {O(n)}
1: eval_gcd_bb0_in->eval_gcd_bb1_in, Arg_2: Arg_2 {O(n)}
1: eval_gcd_bb0_in->eval_gcd_bb1_in, Arg_3: Arg_3 {O(n)}
2: eval_gcd_bb1_in->eval_gcd_bb2_in, Arg_0: Arg_2 {O(n)}
2: eval_gcd_bb1_in->eval_gcd_bb2_in, Arg_1: Arg_3 {O(n)}
2: eval_gcd_bb1_in->eval_gcd_bb2_in, Arg_2: Arg_2 {O(n)}
2: eval_gcd_bb1_in->eval_gcd_bb2_in, Arg_3: Arg_3 {O(n)}
3: eval_gcd_bb1_in->eval_gcd_bb3_in, Arg_0: Arg_2 {O(n)}
3: eval_gcd_bb1_in->eval_gcd_bb3_in, Arg_1: Arg_3 {O(n)}
3: eval_gcd_bb1_in->eval_gcd_bb3_in, Arg_2: Arg_2 {O(n)}
3: eval_gcd_bb1_in->eval_gcd_bb3_in, Arg_3: Arg_3 {O(n)}
4: eval_gcd_bb1_in->eval_gcd_bb3_in, Arg_0: 2*Arg_2 {O(n)}
4: eval_gcd_bb1_in->eval_gcd_bb3_in, Arg_1: 2*Arg_3 {O(n)}
4: eval_gcd_bb1_in->eval_gcd_bb3_in, Arg_2: 2*Arg_2 {O(n)}
4: eval_gcd_bb1_in->eval_gcd_bb3_in, Arg_3: 2*Arg_3 {O(n)}
5: eval_gcd_bb2_in->eval_gcd_bb1_in, Arg_0: Arg_2 {O(n)}
5: eval_gcd_bb2_in->eval_gcd_bb1_in, Arg_1: Arg_3 {O(n)}
5: eval_gcd_bb2_in->eval_gcd_bb1_in, Arg_2: Arg_2 {O(n)}
5: eval_gcd_bb2_in->eval_gcd_bb1_in, Arg_3: Arg_3 {O(n)}
8: eval_gcd_bb2_in->eval_gcd_bb1_in, Arg_0: Arg_2 {O(n)}
8: eval_gcd_bb2_in->eval_gcd_bb1_in, Arg_1: Arg_3 {O(n)}
8: eval_gcd_bb2_in->eval_gcd_bb1_in, Arg_2: Arg_2 {O(n)}
8: eval_gcd_bb2_in->eval_gcd_bb1_in, Arg_3: Arg_3 {O(n)}
9: eval_gcd_bb3_in->eval_gcd_stop, Arg_0: 3*Arg_2 {O(n)}
9: eval_gcd_bb3_in->eval_gcd_stop, Arg_1: 3*Arg_3 {O(n)}
9: eval_gcd_bb3_in->eval_gcd_stop, Arg_2: 3*Arg_2 {O(n)}
9: eval_gcd_bb3_in->eval_gcd_stop, Arg_3: 3*Arg_3 {O(n)}
0: eval_gcd_start->eval_gcd_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_gcd_start->eval_gcd_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_gcd_start->eval_gcd_bb0_in, Arg_2: Arg_2 {O(n)}
0: eval_gcd_start->eval_gcd_bb0_in, Arg_3: Arg_3 {O(n)}