Initial Problem
Start: l0
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: l0, l1, l2
Transitions:
0:l0(Arg_0,Arg_1,Arg_2,Arg_3) -> l1(Arg_0,Arg_1,Arg_2,Arg_3)
1:l1(Arg_0,Arg_1,Arg_2,Arg_3) -> l1(Arg_0+Arg_1,Arg_1+Arg_2,Arg_2-1,Arg_3):|:1<=Arg_0
2:l1(Arg_0,Arg_1,Arg_2,Arg_3) -> l2(Arg_0,Arg_1,Arg_2,Arg_3-1):|:Arg_0<=0
3:l2(Arg_0,Arg_1,Arg_2,Arg_3) -> l1(Arg_3,Arg_3,Arg_3,Arg_3):|:1<=Arg_3
Preprocessing
Found invariant Arg_0<=0 for location l2
Problem after Preprocessing
Start: l0
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: l0, l1, l2
Transitions:
0:l0(Arg_0,Arg_1,Arg_2,Arg_3) -> l1(Arg_0,Arg_1,Arg_2,Arg_3)
1:l1(Arg_0,Arg_1,Arg_2,Arg_3) -> l1(Arg_0+Arg_1,Arg_1+Arg_2,Arg_2-1,Arg_3):|:1<=Arg_0
2:l1(Arg_0,Arg_1,Arg_2,Arg_3) -> l2(Arg_0,Arg_1,Arg_2,Arg_3-1):|:Arg_0<=0
3:l2(Arg_0,Arg_1,Arg_2,Arg_3) -> l1(Arg_3,Arg_3,Arg_3,Arg_3):|:Arg_0<=0 && 1<=Arg_3
MPRF for transition 3:l2(Arg_0,Arg_1,Arg_2,Arg_3) -> l1(Arg_3,Arg_3,Arg_3,Arg_3):|:Arg_0<=0 && 1<=Arg_3 of depth 1:
new bound:
Arg_3+1 {O(n)}
MPRF:
l2 [Arg_3 ]
l1 [Arg_3-1 ]
MPRF for transition 2:l1(Arg_0,Arg_1,Arg_2,Arg_3) -> l2(Arg_0,Arg_1,Arg_2,Arg_3-1):|:Arg_0<=0 of depth 1:
new bound:
Arg_3+2 {O(n)}
MPRF:
l1 [1 ]
l2 [0 ]
MPRF for transition 1:l1(Arg_0,Arg_1,Arg_2,Arg_3) -> l1(Arg_0+Arg_1,Arg_1+Arg_2,Arg_2-1,Arg_3):|:1<=Arg_0 of depth 3:
new bound:
243*Arg_3*Arg_3+27*Arg_0+27*Arg_1+27*Arg_2+460*Arg_3+272 {O(n^2)}
MPRF:
l1 [Arg_2+1 ; Arg_1+1 ; Arg_0 ]
l2 [Arg_2 ; Arg_1 ; Arg_0 ]
Analysing control-flow refined program
Found invariant Arg_3<=Arg_2 && Arg_3<=Arg_1 && Arg_3<=Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 for location n_l1___2
Found invariant Arg_0<=0 for location n_l2___3
Found invariant Arg_3<=1+Arg_2 && 1+Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 1<=Arg_3 && 1<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 3<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 2+Arg_2<=Arg_1 && 2+Arg_2<=Arg_0 && 0<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 for location n_l1___1
Found invariant Arg_0<=0 for location n_l2___4
MPRF for transition 43:n_l1___1(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___5(Arg_0+Arg_1,Arg_1+Arg_2,Arg_2-1,Arg_3):|:Arg_3<=1+Arg_2 && 1+Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 1<=Arg_3 && 1<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 3<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 2+Arg_2<=Arg_1 && 2+Arg_2<=Arg_0 && 0<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<=Arg_0+Arg_2 && 1<=Arg_0 of depth 1:
new bound:
2*Arg_3+2 {O(n)}
MPRF:
n_l1___1 [Arg_3 ]
n_l1___5 [Arg_3-1 ]
n_l2___3 [Arg_3 ]
n_l1___2 [Arg_1 ]
MPRF for transition 44:n_l1___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___1(Arg_0+Arg_1,Arg_1+Arg_2,Arg_2-1,Arg_3):|:Arg_3<=Arg_2 && Arg_3<=Arg_1 && Arg_3<=Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_2<=Arg_0 && Arg_0<=Arg_3 && Arg_3<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 of depth 1:
new bound:
2*Arg_3+2 {O(n)}
MPRF:
n_l1___1 [Arg_3-1 ]
n_l1___5 [Arg_3-1 ]
n_l2___3 [Arg_3 ]
n_l1___2 [Arg_2 ]
MPRF for transition 49:n_l2___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___2(Arg_3,Arg_3,Arg_3,Arg_3):|:Arg_0<=0 && Arg_0<=0 && Arg_1<=Arg_0+Arg_2 && 1<=Arg_3 && Arg_0<=0 of depth 1:
new bound:
2*Arg_3+3 {O(n)}
MPRF:
n_l1___1 [Arg_3-1 ]
n_l1___5 [Arg_3-1 ]
n_l2___3 [Arg_3 ]
n_l1___2 [Arg_0-1 ]
MPRF for transition 46:n_l1___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l2___3(Arg_0,Arg_1,Arg_2,Arg_3-1):|:Arg_1<=Arg_0+Arg_2 && Arg_0<=0 of depth 1:
new bound:
2*Arg_3+5 {O(n)}
MPRF:
n_l1___2 [1 ]
n_l1___1 [1 ]
n_l1___5 [1 ]
n_l2___3 [0 ]
MPRF for transition 45:n_l1___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___5(Arg_0+Arg_1,Arg_1+Arg_2,Arg_2-1,Arg_3):|:Arg_1<=Arg_0+Arg_2 && 1<=Arg_0 of depth 3:
new bound:
2160*Arg_3*Arg_3+27*Arg_0+54*Arg_1+54*Arg_2+6050*Arg_3+4190 {O(n^2)}
MPRF:
n_l1___2 [Arg_2 ; 3*Arg_1 ; 2*Arg_0+2*Arg_1 ]
n_l1___1 [Arg_2 ; Arg_1+Arg_2+1 ; Arg_0+Arg_1 ]
n_l1___5 [Arg_2+1 ; Arg_1+1 ; Arg_0 ]
n_l2___3 [Arg_2 ; Arg_1 ; Arg_0 ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:243*Arg_3*Arg_3+27*Arg_0+27*Arg_1+27*Arg_2+462*Arg_3+276 {O(n^2)}
0: l0->l1: 1 {O(1)}
1: l1->l1: 243*Arg_3*Arg_3+27*Arg_0+27*Arg_1+27*Arg_2+460*Arg_3+272 {O(n^2)}
2: l1->l2: Arg_3+2 {O(n)}
3: l2->l1: Arg_3+1 {O(n)}
Costbounds
Overall costbound: 243*Arg_3*Arg_3+27*Arg_0+27*Arg_1+27*Arg_2+462*Arg_3+276 {O(n^2)}
0: l0->l1: 1 {O(1)}
1: l1->l1: 243*Arg_3*Arg_3+27*Arg_0+27*Arg_1+27*Arg_2+460*Arg_3+272 {O(n^2)}
2: l1->l2: Arg_3+2 {O(n)}
3: l2->l1: Arg_3+1 {O(n)}
Sizebounds
0: l0->l1, Arg_0: Arg_0 {O(n)}
0: l0->l1, Arg_1: Arg_1 {O(n)}
0: l0->l1, Arg_2: Arg_2 {O(n)}
0: l0->l1, Arg_3: Arg_3 {O(n)}
1: l1->l1, Arg_0: 14348907*Arg_3*Arg_3*Arg_3*Arg_3*Arg_3*Arg_3+4782969*Arg_0*Arg_3*Arg_3*Arg_3*Arg_3+4782969*Arg_1*Arg_3*Arg_3*Arg_3*Arg_3+4901067*Arg_2*Arg_3*Arg_3*Arg_3*Arg_3+81841914*Arg_3*Arg_3*Arg_3*Arg_3*Arg_3+1062882*Arg_0*Arg_1*Arg_3*Arg_3+1089126*Arg_0*Arg_2*Arg_3*Arg_3+1089126*Arg_1*Arg_2*Arg_3*Arg_3+18187092*Arg_0*Arg_3*Arg_3*Arg_3+18187092*Arg_1*Arg_3*Arg_3*Arg_3+18634212*Arg_2*Arg_3*Arg_3*Arg_3+204136038*Arg_3*Arg_3*Arg_3*Arg_3+531441*Arg_0*Arg_0*Arg_3*Arg_3+531441*Arg_1*Arg_1*Arg_3*Arg_3+557685*Arg_2*Arg_2*Arg_3*Arg_3+1010394*Arg_0*Arg_0*Arg_3+1010394*Arg_1*Arg_1*Arg_3+1060074*Arg_2*Arg_2*Arg_3+121014*Arg_0*Arg_1*Arg_2+19683*Arg_0*Arg_0*Arg_0+19683*Arg_1*Arg_1*Arg_1+2020788*Arg_0*Arg_1*Arg_3+2070468*Arg_0*Arg_2*Arg_3+2070468*Arg_1*Arg_2*Arg_3+21141*Arg_2*Arg_2*Arg_2+28074924*Arg_0*Arg_3*Arg_3+28075410*Arg_1*Arg_3*Arg_3+283169446*Arg_3*Arg_3*Arg_3+28763480*Arg_2*Arg_3*Arg_3+59049*Arg_0*Arg_0*Arg_1+59049*Arg_0*Arg_1*Arg_1+60507*Arg_0*Arg_0*Arg_2+60507*Arg_1*Arg_1*Arg_2+61965*Arg_0*Arg_2*Arg_2+61965*Arg_1*Arg_2*Arg_2+1198530*Arg_0*Arg_1+1227960*Arg_0*Arg_2+1228014*Arg_1*Arg_2+20507094*Arg_0*Arg_3+20508014*Arg_1*Arg_3+21009414*Arg_2*Arg_3+230175567*Arg_3*Arg_3+599238*Arg_0*Arg_0+599292*Arg_1*Arg_1+628722*Arg_2*Arg_2+104054155*Arg_3+6081184*Arg_0+6081729*Arg_1+6230241*Arg_2+20571098 {O(n^6)}
1: l1->l1, Arg_1: 59049*Arg_3*Arg_3*Arg_3*Arg_3+13122*Arg_0*Arg_3*Arg_3+13122*Arg_1*Arg_3*Arg_3+13608*Arg_2*Arg_3*Arg_3+225018*Arg_3*Arg_3*Arg_3+1458*Arg_0*Arg_1+1512*Arg_0*Arg_2+1512*Arg_1*Arg_2+25002*Arg_0*Arg_3+25002*Arg_1*Arg_3+25922*Arg_2*Arg_3+347767*Arg_3*Arg_3+729*Arg_0*Arg_0+729*Arg_1*Arg_1+783*Arg_2*Arg_2+14823*Arg_0+14824*Arg_1+15369*Arg_2+254181*Arg_3+75350 {O(n^4)}
1: l1->l1, Arg_2: 243*Arg_3*Arg_3+27*Arg_0+27*Arg_1+28*Arg_2+463*Arg_3+274 {O(n^2)}
1: l1->l1, Arg_3: 3*Arg_3+2 {O(n)}
2: l1->l2, Arg_0: 14348907*Arg_3*Arg_3*Arg_3*Arg_3*Arg_3*Arg_3+4782969*Arg_0*Arg_3*Arg_3*Arg_3*Arg_3+4782969*Arg_1*Arg_3*Arg_3*Arg_3*Arg_3+4901067*Arg_2*Arg_3*Arg_3*Arg_3*Arg_3+81841914*Arg_3*Arg_3*Arg_3*Arg_3*Arg_3+1062882*Arg_0*Arg_1*Arg_3*Arg_3+1089126*Arg_0*Arg_2*Arg_3*Arg_3+1089126*Arg_1*Arg_2*Arg_3*Arg_3+18187092*Arg_0*Arg_3*Arg_3*Arg_3+18187092*Arg_1*Arg_3*Arg_3*Arg_3+18634212*Arg_2*Arg_3*Arg_3*Arg_3+204136038*Arg_3*Arg_3*Arg_3*Arg_3+531441*Arg_0*Arg_0*Arg_3*Arg_3+531441*Arg_1*Arg_1*Arg_3*Arg_3+557685*Arg_2*Arg_2*Arg_3*Arg_3+1010394*Arg_0*Arg_0*Arg_3+1010394*Arg_1*Arg_1*Arg_3+1060074*Arg_2*Arg_2*Arg_3+121014*Arg_0*Arg_1*Arg_2+19683*Arg_0*Arg_0*Arg_0+19683*Arg_1*Arg_1*Arg_1+2020788*Arg_0*Arg_1*Arg_3+2070468*Arg_0*Arg_2*Arg_3+2070468*Arg_1*Arg_2*Arg_3+21141*Arg_2*Arg_2*Arg_2+28074924*Arg_0*Arg_3*Arg_3+28075410*Arg_1*Arg_3*Arg_3+283169446*Arg_3*Arg_3*Arg_3+28763480*Arg_2*Arg_3*Arg_3+59049*Arg_0*Arg_0*Arg_1+59049*Arg_0*Arg_1*Arg_1+60507*Arg_0*Arg_0*Arg_2+60507*Arg_1*Arg_1*Arg_2+61965*Arg_0*Arg_2*Arg_2+61965*Arg_1*Arg_2*Arg_2+1198530*Arg_0*Arg_1+1227960*Arg_0*Arg_2+1228014*Arg_1*Arg_2+20507094*Arg_0*Arg_3+20508014*Arg_1*Arg_3+21009414*Arg_2*Arg_3+230175567*Arg_3*Arg_3+599238*Arg_0*Arg_0+599292*Arg_1*Arg_1+628722*Arg_2*Arg_2+104054155*Arg_3+6081185*Arg_0+6081729*Arg_1+6230241*Arg_2+20571098 {O(n^6)}
2: l1->l2, Arg_1: 59049*Arg_3*Arg_3*Arg_3*Arg_3+13122*Arg_0*Arg_3*Arg_3+13122*Arg_1*Arg_3*Arg_3+13608*Arg_2*Arg_3*Arg_3+225018*Arg_3*Arg_3*Arg_3+1458*Arg_0*Arg_1+1512*Arg_0*Arg_2+1512*Arg_1*Arg_2+25002*Arg_0*Arg_3+25002*Arg_1*Arg_3+25922*Arg_2*Arg_3+347767*Arg_3*Arg_3+729*Arg_0*Arg_0+729*Arg_1*Arg_1+783*Arg_2*Arg_2+14823*Arg_0+14825*Arg_1+15369*Arg_2+254181*Arg_3+75350 {O(n^4)}
2: l1->l2, Arg_2: 243*Arg_3*Arg_3+27*Arg_0+27*Arg_1+29*Arg_2+463*Arg_3+274 {O(n^2)}
2: l1->l2, Arg_3: 3*Arg_3+2 {O(n)}
3: l2->l1, Arg_0: 3*Arg_3+2 {O(n)}
3: l2->l1, Arg_1: 3*Arg_3+2 {O(n)}
3: l2->l1, Arg_2: 3*Arg_3+2 {O(n)}
3: l2->l1, Arg_3: 3*Arg_3+2 {O(n)}