Initial Problem

Start: start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval1, eval2, start
Transitions:
0:eval1(Arg_0,Arg_1,Arg_2) -> eval2(Arg_0,Arg_1,Arg_2):|:Arg_1+1<=Arg_0 && Arg_2<=Arg_0 && Arg_0<=Arg_2
2:eval2(Arg_0,Arg_1,Arg_2) -> eval1(Arg_0,Arg_1,Arg_2):|:Arg_0<=Arg_1
1:eval2(Arg_0,Arg_1,Arg_2) -> eval2(Arg_0-1,Arg_1,Arg_2-1):|:Arg_1+1<=Arg_0
3:start(Arg_0,Arg_1,Arg_2) -> eval1(Arg_0,Arg_1,Arg_2)

Preprocessing

Found invariant Arg_2<=Arg_0 && Arg_1<=Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 for location eval2

Problem after Preprocessing

Start: start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval1, eval2, start
Transitions:
0:eval1(Arg_0,Arg_1,Arg_2) -> eval2(Arg_0,Arg_1,Arg_2):|:Arg_1+1<=Arg_0 && Arg_2<=Arg_0 && Arg_0<=Arg_2
2:eval2(Arg_0,Arg_1,Arg_2) -> eval1(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && Arg_1<=Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && Arg_0<=Arg_1
1:eval2(Arg_0,Arg_1,Arg_2) -> eval2(Arg_0-1,Arg_1,Arg_2-1):|:Arg_2<=Arg_0 && Arg_1<=Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && Arg_1+1<=Arg_0
3:start(Arg_0,Arg_1,Arg_2) -> eval1(Arg_0,Arg_1,Arg_2)

knowledge_propagation leads to new time bound 1 {O(1)} for transition 0:eval1(Arg_0,Arg_1,Arg_2) -> eval2(Arg_0,Arg_1,Arg_2):|:Arg_1+1<=Arg_0 && Arg_2<=Arg_0 && Arg_0<=Arg_2

MPRF for transition 1:eval2(Arg_0,Arg_1,Arg_2) -> eval2(Arg_0-1,Arg_1,Arg_2-1):|:Arg_2<=Arg_0 && Arg_1<=Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && Arg_1+1<=Arg_0 of depth 1:

new bound:

Arg_1+Arg_2+1 {O(n)}

MPRF:

eval2 [Arg_2+1-Arg_1 ]
eval1 [Arg_2+1-Arg_1 ]

MPRF for transition 2:eval2(Arg_0,Arg_1,Arg_2) -> eval1(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && Arg_1<=Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && Arg_0<=Arg_1 of depth 1:

new bound:

Arg_0+Arg_1 {O(n)}

MPRF:

eval2 [1 ]
eval1 [Arg_0-Arg_1 ]

All Bounds

Timebounds

Overall timebound:2*Arg_1+Arg_0+Arg_2+3 {O(n)}
0: eval1->eval2: 1 {O(1)}
1: eval2->eval2: Arg_1+Arg_2+1 {O(n)}
2: eval2->eval1: Arg_0+Arg_1 {O(n)}
3: start->eval1: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_1+Arg_0+Arg_2+3 {O(n)}
0: eval1->eval2: 1 {O(1)}
1: eval2->eval2: Arg_1+Arg_2+1 {O(n)}
2: eval2->eval1: Arg_0+Arg_1 {O(n)}
3: start->eval1: 1 {O(1)}

Sizebounds

0: eval1->eval2, Arg_0: Arg_0 {O(n)}
0: eval1->eval2, Arg_1: Arg_1 {O(n)}
0: eval1->eval2, Arg_2: Arg_2 {O(n)}
1: eval2->eval2, Arg_0: Arg_0+Arg_1+Arg_2+1 {O(n)}
1: eval2->eval2, Arg_1: Arg_1 {O(n)}
1: eval2->eval2, Arg_2: 2*Arg_2+Arg_1+1 {O(n)}
2: eval2->eval1, Arg_0: Arg_0+Arg_1+Arg_2+1 {O(n)}
2: eval2->eval1, Arg_1: Arg_1 {O(n)}
2: eval2->eval1, Arg_2: 2*Arg_2+Arg_1+1 {O(n)}
3: start->eval1, Arg_0: Arg_0 {O(n)}
3: start->eval1, Arg_1: Arg_1 {O(n)}
3: start->eval1, Arg_2: Arg_2 {O(n)}