Initial Problem

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

Preprocessing

Found invariant Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location eval2

Problem after Preprocessing

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

MPRF for transition 0:eval1(Arg_0,Arg_1) -> eval2(Arg_0,0):|:0<=Arg_0 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

eval2 [Arg_0 ]
eval1 [Arg_0+1 ]

MPRF for transition 2:eval2(Arg_0,Arg_1) -> eval1(Arg_0-1,Arg_1):|:Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_0<=Arg_1 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

eval2 [Arg_0+1 ]
eval1 [Arg_0+1 ]

MPRF for transition 1:eval2(Arg_0,Arg_1) -> eval2(Arg_0,Arg_1+1):|:Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && 1+Arg_1<=Arg_0 of depth 1:

new bound:

Arg_0*Arg_0+4*Arg_0+3 {O(n^2)}

MPRF:

eval1 [Arg_0+1 ]
eval2 [Arg_0+1-Arg_1 ]

All Bounds

Timebounds

Overall timebound:Arg_0*Arg_0+6*Arg_0+6 {O(n^2)}
0: eval1->eval2: Arg_0+1 {O(n)}
1: eval2->eval2: Arg_0*Arg_0+4*Arg_0+3 {O(n^2)}
2: eval2->eval1: Arg_0+1 {O(n)}
3: start->eval1: 1 {O(1)}

Costbounds

Overall costbound: Arg_0*Arg_0+6*Arg_0+6 {O(n^2)}
0: eval1->eval2: Arg_0+1 {O(n)}
1: eval2->eval2: Arg_0*Arg_0+4*Arg_0+3 {O(n^2)}
2: eval2->eval1: Arg_0+1 {O(n)}
3: start->eval1: 1 {O(1)}

Sizebounds

0: eval1->eval2, Arg_0: Arg_0+1 {O(n)}
0: eval1->eval2, Arg_1: 0 {O(1)}
1: eval2->eval2, Arg_0: Arg_0+1 {O(n)}
1: eval2->eval2, Arg_1: Arg_0*Arg_0+4*Arg_0+3 {O(n^2)}
2: eval2->eval1, Arg_0: Arg_0+1 {O(n)}
2: eval2->eval1, Arg_1: Arg_0*Arg_0+4*Arg_0+3 {O(n^2)}
3: start->eval1, Arg_0: Arg_0 {O(n)}
3: start->eval1, Arg_1: Arg_1 {O(n)}