Initial Problem

Start: eval_t10_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
Temp_Vars: nondef.0
Locations: eval_t10_0, eval_t10_1, eval_t10_bb0_in, eval_t10_bb1_in, eval_t10_bb2_in, eval_t10_bb3_in, eval_t10_start, eval_t10_stop
Transitions:
6:eval_t10_0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t10_1(Arg_0,Arg_1,nondef.0,Arg_3,Arg_4)
7:eval_t10_1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t10_bb1_in(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4):|:0<Arg_2 && 0<Arg_2
8:eval_t10_1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t10_bb1_in(Arg_0-1,Arg_1+1,Arg_2,Arg_3,Arg_4):|:0<Arg_2 && Arg_2<=0
9:eval_t10_1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t10_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_2<=0 && 0<Arg_2
10:eval_t10_1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t10_bb1_in(Arg_0-1,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_2<=0 && Arg_2<=0
1:eval_t10_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t10_bb1_in(Arg_3,Arg_4,Arg_2,Arg_3,Arg_4)
2:eval_t10_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t10_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_1<Arg_0
3:eval_t10_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t10_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_0<=Arg_1
4:eval_t10_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t10_0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
11:eval_t10_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t10_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
0:eval_t10_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t10_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)

Preprocessing

Cut unsatisfiable transition 8: eval_t10_1->eval_t10_bb1_in

Cut unsatisfiable transition 9: eval_t10_1->eval_t10_bb1_in

Found invariant 1+Arg_4<=Arg_3 && Arg_4<=Arg_1 && 1+Arg_4<=Arg_0 && 1+Arg_1<=Arg_3 && Arg_0<=Arg_3 && 1+Arg_1<=Arg_0 for location eval_t10_0

Found invariant Arg_4<=Arg_1 && Arg_0<=Arg_3 && Arg_0<=Arg_1 for location eval_t10_bb3_in

Found invariant Arg_4<=Arg_1 && Arg_0<=Arg_3 && Arg_0<=Arg_1 for location eval_t10_stop

Found invariant Arg_4<=Arg_1 && Arg_0<=Arg_3 for location eval_t10_bb1_in

Found invariant 1+Arg_4<=Arg_3 && Arg_4<=Arg_1 && 1+Arg_4<=Arg_0 && 1+Arg_1<=Arg_3 && Arg_0<=Arg_3 && 1+Arg_1<=Arg_0 for location eval_t10_bb2_in

Found invariant 1+Arg_4<=Arg_3 && Arg_4<=Arg_1 && 1+Arg_4<=Arg_0 && 1+Arg_1<=Arg_3 && Arg_0<=Arg_3 && 1+Arg_1<=Arg_0 for location eval_t10_1

Problem after Preprocessing

Start: eval_t10_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
Temp_Vars: nondef.0
Locations: eval_t10_0, eval_t10_1, eval_t10_bb0_in, eval_t10_bb1_in, eval_t10_bb2_in, eval_t10_bb3_in, eval_t10_start, eval_t10_stop
Transitions:
6:eval_t10_0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t10_1(Arg_0,Arg_1,nondef.0,Arg_3,Arg_4):|:1+Arg_4<=Arg_3 && Arg_4<=Arg_1 && 1+Arg_4<=Arg_0 && 1+Arg_1<=Arg_3 && Arg_0<=Arg_3 && 1+Arg_1<=Arg_0
7:eval_t10_1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t10_bb1_in(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4):|:1+Arg_4<=Arg_3 && Arg_4<=Arg_1 && 1+Arg_4<=Arg_0 && 1+Arg_1<=Arg_3 && Arg_0<=Arg_3 && 1+Arg_1<=Arg_0 && 0<Arg_2 && 0<Arg_2
10:eval_t10_1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t10_bb1_in(Arg_0-1,Arg_1,Arg_2,Arg_3,Arg_4):|:1+Arg_4<=Arg_3 && Arg_4<=Arg_1 && 1+Arg_4<=Arg_0 && 1+Arg_1<=Arg_3 && Arg_0<=Arg_3 && 1+Arg_1<=Arg_0 && Arg_2<=0 && Arg_2<=0
1:eval_t10_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t10_bb1_in(Arg_3,Arg_4,Arg_2,Arg_3,Arg_4)
2:eval_t10_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t10_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=Arg_1 && Arg_0<=Arg_3 && Arg_1<Arg_0
3:eval_t10_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t10_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=Arg_1 && Arg_0<=Arg_3 && Arg_0<=Arg_1
4:eval_t10_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t10_0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1+Arg_4<=Arg_3 && Arg_4<=Arg_1 && 1+Arg_4<=Arg_0 && 1+Arg_1<=Arg_3 && Arg_0<=Arg_3 && 1+Arg_1<=Arg_0
11:eval_t10_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t10_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=Arg_1 && Arg_0<=Arg_3 && Arg_0<=Arg_1
0:eval_t10_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t10_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)

MPRF for transition 6:eval_t10_0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t10_1(Arg_0,Arg_1,nondef.0,Arg_3,Arg_4):|:1+Arg_4<=Arg_3 && Arg_4<=Arg_1 && 1+Arg_4<=Arg_0 && 1+Arg_1<=Arg_3 && Arg_0<=Arg_3 && 1+Arg_1<=Arg_0 of depth 1:

new bound:

Arg_3+Arg_4 {O(n)}

MPRF:

eval_t10_1 [Arg_0-Arg_1-1 ]
eval_t10_bb1_in [Arg_0-Arg_1 ]
eval_t10_bb2_in [Arg_0-Arg_1 ]
eval_t10_0 [Arg_0-Arg_1 ]

MPRF for transition 7:eval_t10_1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t10_bb1_in(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4):|:1+Arg_4<=Arg_3 && Arg_4<=Arg_1 && 1+Arg_4<=Arg_0 && 1+Arg_1<=Arg_3 && Arg_0<=Arg_3 && 1+Arg_1<=Arg_0 && 0<Arg_2 && 0<Arg_2 of depth 1:

new bound:

Arg_3+Arg_4 {O(n)}

MPRF:

eval_t10_1 [Arg_3-Arg_1 ]
eval_t10_bb1_in [Arg_3-Arg_1 ]
eval_t10_bb2_in [Arg_3-Arg_1 ]
eval_t10_0 [Arg_3-Arg_1 ]

MPRF for transition 10:eval_t10_1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t10_bb1_in(Arg_0-1,Arg_1,Arg_2,Arg_3,Arg_4):|:1+Arg_4<=Arg_3 && Arg_4<=Arg_1 && 1+Arg_4<=Arg_0 && 1+Arg_1<=Arg_3 && Arg_0<=Arg_3 && 1+Arg_1<=Arg_0 && Arg_2<=0 && Arg_2<=0 of depth 1:

new bound:

Arg_3+Arg_4 {O(n)}

MPRF:

eval_t10_1 [Arg_0-Arg_1 ]
eval_t10_bb1_in [Arg_0-Arg_1 ]
eval_t10_bb2_in [Arg_0-Arg_1 ]
eval_t10_0 [Arg_0-Arg_1 ]

MPRF for transition 2:eval_t10_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t10_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=Arg_1 && Arg_0<=Arg_3 && Arg_1<Arg_0 of depth 1:

new bound:

Arg_3+Arg_4 {O(n)}

MPRF:

eval_t10_1 [Arg_0-Arg_1-1 ]
eval_t10_bb1_in [Arg_0-Arg_1 ]
eval_t10_bb2_in [Arg_0-Arg_1-1 ]
eval_t10_0 [Arg_0-Arg_1-1 ]

MPRF for transition 4:eval_t10_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_t10_0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1+Arg_4<=Arg_3 && Arg_4<=Arg_1 && 1+Arg_4<=Arg_0 && 1+Arg_1<=Arg_3 && Arg_0<=Arg_3 && 1+Arg_1<=Arg_0 of depth 1:

new bound:

Arg_3+Arg_4 {O(n)}

MPRF:

eval_t10_1 [Arg_0-Arg_1-1 ]
eval_t10_bb1_in [Arg_0-Arg_1 ]
eval_t10_bb2_in [Arg_0-Arg_1 ]
eval_t10_0 [Arg_0-Arg_1-1 ]

All Bounds

Timebounds

Overall timebound:5*Arg_3+5*Arg_4+4 {O(n)}
6: eval_t10_0->eval_t10_1: Arg_3+Arg_4 {O(n)}
7: eval_t10_1->eval_t10_bb1_in: Arg_3+Arg_4 {O(n)}
10: eval_t10_1->eval_t10_bb1_in: Arg_3+Arg_4 {O(n)}
1: eval_t10_bb0_in->eval_t10_bb1_in: 1 {O(1)}
2: eval_t10_bb1_in->eval_t10_bb2_in: Arg_3+Arg_4 {O(n)}
3: eval_t10_bb1_in->eval_t10_bb3_in: 1 {O(1)}
4: eval_t10_bb2_in->eval_t10_0: Arg_3+Arg_4 {O(n)}
11: eval_t10_bb3_in->eval_t10_stop: 1 {O(1)}
0: eval_t10_start->eval_t10_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 5*Arg_3+5*Arg_4+4 {O(n)}
6: eval_t10_0->eval_t10_1: Arg_3+Arg_4 {O(n)}
7: eval_t10_1->eval_t10_bb1_in: Arg_3+Arg_4 {O(n)}
10: eval_t10_1->eval_t10_bb1_in: Arg_3+Arg_4 {O(n)}
1: eval_t10_bb0_in->eval_t10_bb1_in: 1 {O(1)}
2: eval_t10_bb1_in->eval_t10_bb2_in: Arg_3+Arg_4 {O(n)}
3: eval_t10_bb1_in->eval_t10_bb3_in: 1 {O(1)}
4: eval_t10_bb2_in->eval_t10_0: Arg_3+Arg_4 {O(n)}
11: eval_t10_bb3_in->eval_t10_stop: 1 {O(1)}
0: eval_t10_start->eval_t10_bb0_in: 1 {O(1)}

Sizebounds

6: eval_t10_0->eval_t10_1, Arg_0: 2*Arg_3+Arg_4 {O(n)}
6: eval_t10_0->eval_t10_1, Arg_1: 2*Arg_4+Arg_3 {O(n)}
6: eval_t10_0->eval_t10_1, Arg_3: Arg_3 {O(n)}
6: eval_t10_0->eval_t10_1, Arg_4: Arg_4 {O(n)}
7: eval_t10_1->eval_t10_bb1_in, Arg_0: 2*Arg_3+Arg_4 {O(n)}
7: eval_t10_1->eval_t10_bb1_in, Arg_1: 2*Arg_4+Arg_3 {O(n)}
7: eval_t10_1->eval_t10_bb1_in, Arg_3: Arg_3 {O(n)}
7: eval_t10_1->eval_t10_bb1_in, Arg_4: Arg_4 {O(n)}
10: eval_t10_1->eval_t10_bb1_in, Arg_0: 2*Arg_3+Arg_4 {O(n)}
10: eval_t10_1->eval_t10_bb1_in, Arg_1: 2*Arg_4+Arg_3 {O(n)}
10: eval_t10_1->eval_t10_bb1_in, Arg_3: Arg_3 {O(n)}
10: eval_t10_1->eval_t10_bb1_in, Arg_4: Arg_4 {O(n)}
1: eval_t10_bb0_in->eval_t10_bb1_in, Arg_0: Arg_3 {O(n)}
1: eval_t10_bb0_in->eval_t10_bb1_in, Arg_1: Arg_4 {O(n)}
1: eval_t10_bb0_in->eval_t10_bb1_in, Arg_2: Arg_2 {O(n)}
1: eval_t10_bb0_in->eval_t10_bb1_in, Arg_3: Arg_3 {O(n)}
1: eval_t10_bb0_in->eval_t10_bb1_in, Arg_4: Arg_4 {O(n)}
2: eval_t10_bb1_in->eval_t10_bb2_in, Arg_0: 2*Arg_3+Arg_4 {O(n)}
2: eval_t10_bb1_in->eval_t10_bb2_in, Arg_1: 2*Arg_4+Arg_3 {O(n)}
2: eval_t10_bb1_in->eval_t10_bb2_in, Arg_3: Arg_3 {O(n)}
2: eval_t10_bb1_in->eval_t10_bb2_in, Arg_4: Arg_4 {O(n)}
3: eval_t10_bb1_in->eval_t10_bb3_in, Arg_0: 2*Arg_4+5*Arg_3 {O(n)}
3: eval_t10_bb1_in->eval_t10_bb3_in, Arg_1: 2*Arg_3+5*Arg_4 {O(n)}
3: eval_t10_bb1_in->eval_t10_bb3_in, Arg_3: 3*Arg_3 {O(n)}
3: eval_t10_bb1_in->eval_t10_bb3_in, Arg_4: 3*Arg_4 {O(n)}
4: eval_t10_bb2_in->eval_t10_0, Arg_0: 2*Arg_3+Arg_4 {O(n)}
4: eval_t10_bb2_in->eval_t10_0, Arg_1: 2*Arg_4+Arg_3 {O(n)}
4: eval_t10_bb2_in->eval_t10_0, Arg_3: Arg_3 {O(n)}
4: eval_t10_bb2_in->eval_t10_0, Arg_4: Arg_4 {O(n)}
11: eval_t10_bb3_in->eval_t10_stop, Arg_0: 2*Arg_4+5*Arg_3 {O(n)}
11: eval_t10_bb3_in->eval_t10_stop, Arg_1: 2*Arg_3+5*Arg_4 {O(n)}
11: eval_t10_bb3_in->eval_t10_stop, Arg_3: 3*Arg_3 {O(n)}
11: eval_t10_bb3_in->eval_t10_stop, Arg_4: 3*Arg_4 {O(n)}
0: eval_t10_start->eval_t10_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_t10_start->eval_t10_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_t10_start->eval_t10_bb0_in, Arg_2: Arg_2 {O(n)}
0: eval_t10_start->eval_t10_bb0_in, Arg_3: Arg_3 {O(n)}
0: eval_t10_start->eval_t10_bb0_in, Arg_4: Arg_4 {O(n)}