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_0,1):|: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)
Preprocessing
Found invariant 1<=Arg_1 && 1<=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_0,1):|: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)
MPRF for transition 0:eval1(Arg_0,Arg_1) -> eval2(Arg_0,1):|: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):|:1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 1<=Arg_1 && 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_0,2*Arg_1):|:1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 1<=Arg_1 && Arg_1+1<=Arg_0 of depth 1:
new bound:
Arg_0*Arg_0+3*Arg_0+1 {O(n^2)}
MPRF:
eval1 [Arg_0 ]
eval2 [Arg_0-Arg_1 ]
Analysing control-flow refined program
Found invariant Arg_1<=1 && Arg_1<=2+Arg_0 && Arg_0+Arg_1<=1 && 1<=Arg_1 && 0<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=1+Arg_0 for location n_eval1___4
Found invariant Arg_1<=1 && Arg_1<=1+Arg_0 && Arg_0+Arg_1<=1 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_eval2___2
Found invariant 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 for location n_eval1___1
Found invariant Arg_1<=1 && Arg_1<=1+Arg_0 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 for location n_eval2___5
Found invariant 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 for location n_eval2___3
MPRF for transition 39:n_eval1___1(Arg_0,Arg_1) -> n_eval2___5(Arg_0,1):|:2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 0<=1+Arg_0 && 1<=Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 of depth 1:
new bound:
Arg_0 {O(n)}
MPRF:
n_eval1___1 [Arg_0+1 ]
n_eval2___5 [Arg_0 ]
n_eval2___3 [Arg_0 ]
MPRF for transition 43:n_eval2___3(Arg_0,Arg_1) -> n_eval1___1(Arg_0-1,Arg_1):|:2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 && 0<=Arg_0 && 1<=Arg_1 && 2<=Arg_1 && 2+Arg_1<=2*Arg_0 && 0<=Arg_0 && 1<=Arg_1 && Arg_0<=Arg_1 of depth 1:
new bound:
Arg_0+1 {O(n)}
MPRF:
n_eval1___1 [Arg_0+1 ]
n_eval2___5 [Arg_0+Arg_1 ]
n_eval2___3 [Arg_0+1 ]
MPRF for transition 46:n_eval2___5(Arg_0,Arg_1) -> n_eval2___3(Arg_0,2*Arg_1):|:Arg_1<=1 && Arg_1<=1+Arg_0 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 1<=Arg_1 && Arg_1<=1 && 1<=Arg_1 && 0<=Arg_0 && 1+Arg_1<=Arg_0 && 1<=Arg_1 of depth 1:
new bound:
Arg_0+1 {O(n)}
MPRF:
n_eval1___1 [Arg_0+1 ]
n_eval2___5 [Arg_0+1 ]
n_eval2___3 [Arg_0 ]
MPRF for transition 44:n_eval2___3(Arg_0,Arg_1) -> n_eval2___3(Arg_0,2*Arg_1):|:2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 && 0<=Arg_0 && 1<=Arg_1 && 2<=Arg_1 && 2+Arg_1<=2*Arg_0 && 1+Arg_1<=Arg_0 && 1<=Arg_1 of depth 1:
new bound:
4*Arg_0*Arg_0+6*Arg_0+2 {O(n^2)}
MPRF:
n_eval2___5 [2*Arg_0 ]
n_eval1___1 [2*Arg_0 ]
n_eval2___3 [4*Arg_0-Arg_1 ]
knowledge_propagation leads to new time bound 1 {O(1)} for transition 40:n_eval1___4(Arg_0,Arg_1) -> n_eval2___2(Arg_0,1):|:Arg_1<=1 && Arg_1<=2+Arg_0 && Arg_0+Arg_1<=1 && 1<=Arg_1 && 0<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=1+Arg_0 && Arg_0<=1 && 0<=1+Arg_0 && 1<=Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0
knowledge_propagation leads to new time bound 1 {O(1)} for transition 42:n_eval2___2(Arg_0,Arg_1) -> n_eval1___4(Arg_0-1,Arg_1):|:Arg_1<=1 && Arg_1<=1+Arg_0 && Arg_0+Arg_1<=1 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=Arg_1 && 0<=Arg_0 && 1<=Arg_1 && Arg_1<=1 && 1<=Arg_1 && 0<=Arg_0 && 0<=Arg_0 && Arg_0<=Arg_1 && 1<=Arg_1 && 0<=Arg_0 && 1<=Arg_1 && Arg_0<=Arg_1
CFR did not improve the program. Rolling back
All Bounds
Timebounds
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)}
Costbounds
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)}
Sizebounds
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)}