Start: start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: eval1, eval2, start
Transitions:
0:eval1(Arg_0,Arg_1) -> eval2(Arg_0,1):|:0<=Arg_0
2:eval2(Arg_0,Arg_1) -> eval1(Arg_0-1,Arg_1):|:0<=Arg_0 && 1<=Arg_1 && Arg_0<=Arg_1
1:eval2(Arg_0,Arg_1) -> eval2(Arg_0,2*Arg_1):|:0<=Arg_0 && 1<=Arg_1 && Arg_1+1<=Arg_0
3:start(Arg_0,Arg_1) -> eval1(Arg_0,Arg_1)
Found invariant 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 for location eval2
Start: start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: eval1, eval2, start
Transitions:
0:eval1(Arg_0,Arg_1) -> eval2(Arg_0,1):|:0<=Arg_0
2:eval2(Arg_0,Arg_1) -> eval1(Arg_0-1,Arg_1):|:1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 1<=Arg_1 && Arg_0<=Arg_1
1:eval2(Arg_0,Arg_1) -> eval2(Arg_0,2*Arg_1):|:1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 1<=Arg_1 && Arg_1+1<=Arg_0
3:start(Arg_0,Arg_1) -> eval1(Arg_0,Arg_1)
new bound:
Arg_0+1 {O(n)}
MPRF:
eval2 [Arg_0 ]
eval1 [Arg_0+1 ]
new bound:
Arg_0+1 {O(n)}
MPRF:
eval2 [Arg_0+1 ]
eval1 [Arg_0+1 ]
new bound:
Arg_0*Arg_0+3*Arg_0+1 {O(n^2)}
MPRF:
eval1 [Arg_0 ]
eval2 [Arg_0-Arg_1 ]
Overall timebound:Arg_0*Arg_0+5*Arg_0+4 {O(n^2)}
0: eval1->eval2: Arg_0+1 {O(n)}
1: eval2->eval2: Arg_0*Arg_0+3*Arg_0+1 {O(n^2)}
2: eval2->eval1: Arg_0+1 {O(n)}
3: start->eval1: 1 {O(1)}
Overall costbound: Arg_0*Arg_0+5*Arg_0+4 {O(n^2)}
0: eval1->eval2: Arg_0+1 {O(n)}
1: eval2->eval2: Arg_0*Arg_0+3*Arg_0+1 {O(n^2)}
2: eval2->eval1: Arg_0+1 {O(n)}
3: start->eval1: 1 {O(1)}
0: eval1->eval2, Arg_0: Arg_0+1 {O(n)}
0: eval1->eval2, Arg_1: 1 {O(1)}
1: eval2->eval2, Arg_0: Arg_0+1 {O(n)}
1: eval2->eval2, Arg_1: 2^(Arg_0*Arg_0+3*Arg_0+1) {O(EXP)}
2: eval2->eval1, Arg_0: Arg_0+1 {O(n)}
2: eval2->eval1, Arg_1: 2^(Arg_0*Arg_0+3*Arg_0+1)+1 {O(EXP)}
3: start->eval1, Arg_0: Arg_0 {O(n)}
3: start->eval1, Arg_1: Arg_1 {O(n)}