Initial Problem
Start: evalNestedMultipleDepstart
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
Temp_Vars:
Locations: evalNestedMultipleDepbb1in, evalNestedMultipleDepbb2in, evalNestedMultipleDepbb3in, evalNestedMultipleDepbbin, evalNestedMultipleDepentryin, evalNestedMultipleDepreturnin, evalNestedMultipleDepstart, evalNestedMultipleDepstop
Transitions:
7:evalNestedMultipleDepbb1in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalNestedMultipleDepbb2in(Arg_0,Arg_1,Arg_2,Arg_3+1,Arg_4)
5:evalNestedMultipleDepbb2in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalNestedMultipleDepbb1in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_3+1<=Arg_4
6:evalNestedMultipleDepbb2in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalNestedMultipleDepbb3in(Arg_2,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=Arg_3
2:evalNestedMultipleDepbb3in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalNestedMultipleDepbbin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_0+1<=Arg_1
3:evalNestedMultipleDepbb3in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalNestedMultipleDepreturnin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_1<=Arg_0
4:evalNestedMultipleDepbbin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalNestedMultipleDepbb2in(Arg_0,Arg_1,Arg_0+1,0,Arg_4)
1:evalNestedMultipleDepentryin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalNestedMultipleDepbb3in(0,Arg_1,Arg_2,Arg_3,Arg_4)
8:evalNestedMultipleDepreturnin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalNestedMultipleDepstop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
0:evalNestedMultipleDepstart(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalNestedMultipleDepentryin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
Preprocessing
Found invariant 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 for location evalNestedMultipleDepbb2in
Found invariant 0<=Arg_0 for location evalNestedMultipleDepbb3in
Found invariant 1<=Arg_4 && 1<=Arg_3+Arg_4 && 1+Arg_3<=Arg_4 && 2<=Arg_2+Arg_4 && 2<=Arg_1+Arg_4 && 1<=Arg_0+Arg_4 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 for location evalNestedMultipleDepbb1in
Found invariant Arg_1<=Arg_0 && 0<=Arg_0 for location evalNestedMultipleDepreturnin
Found invariant Arg_1<=Arg_0 && 0<=Arg_0 for location evalNestedMultipleDepstop
Found invariant 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 for location evalNestedMultipleDepbbin
Problem after Preprocessing
Start: evalNestedMultipleDepstart
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
Temp_Vars:
Locations: evalNestedMultipleDepbb1in, evalNestedMultipleDepbb2in, evalNestedMultipleDepbb3in, evalNestedMultipleDepbbin, evalNestedMultipleDepentryin, evalNestedMultipleDepreturnin, evalNestedMultipleDepstart, evalNestedMultipleDepstop
Transitions:
7:evalNestedMultipleDepbb1in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalNestedMultipleDepbb2in(Arg_0,Arg_1,Arg_2,Arg_3+1,Arg_4):|:1<=Arg_4 && 1<=Arg_3+Arg_4 && 1+Arg_3<=Arg_4 && 2<=Arg_2+Arg_4 && 2<=Arg_1+Arg_4 && 1<=Arg_0+Arg_4 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0
5:evalNestedMultipleDepbb2in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalNestedMultipleDepbb1in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && Arg_3+1<=Arg_4
6:evalNestedMultipleDepbb2in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalNestedMultipleDepbb3in(Arg_2,Arg_1,Arg_2,Arg_3,Arg_4):|:0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && Arg_4<=Arg_3
2:evalNestedMultipleDepbb3in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalNestedMultipleDepbbin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:0<=Arg_0 && Arg_0+1<=Arg_1
3:evalNestedMultipleDepbb3in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalNestedMultipleDepreturnin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:0<=Arg_0 && Arg_1<=Arg_0
4:evalNestedMultipleDepbbin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalNestedMultipleDepbb2in(Arg_0,Arg_1,Arg_0+1,0,Arg_4):|:1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0
1:evalNestedMultipleDepentryin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalNestedMultipleDepbb3in(0,Arg_1,Arg_2,Arg_3,Arg_4)
8:evalNestedMultipleDepreturnin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalNestedMultipleDepstop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_1<=Arg_0 && 0<=Arg_0
0:evalNestedMultipleDepstart(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalNestedMultipleDepentryin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
MPRF for transition 6:evalNestedMultipleDepbb2in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalNestedMultipleDepbb3in(Arg_2,Arg_1,Arg_2,Arg_3,Arg_4):|:0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && Arg_4<=Arg_3 of depth 1:
new bound:
Arg_1 {O(n)}
MPRF:
evalNestedMultipleDepbb1in [Arg_1-Arg_0 ]
evalNestedMultipleDepbb3in [Arg_1-Arg_0 ]
evalNestedMultipleDepbbin [Arg_1-Arg_0 ]
evalNestedMultipleDepbb2in [Arg_1+1-Arg_2 ]
MPRF for transition 2:evalNestedMultipleDepbb3in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalNestedMultipleDepbbin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:0<=Arg_0 && Arg_0+1<=Arg_1 of depth 1:
new bound:
Arg_1 {O(n)}
MPRF:
evalNestedMultipleDepbb1in [Arg_1-Arg_2 ]
evalNestedMultipleDepbb3in [Arg_1-Arg_0 ]
evalNestedMultipleDepbbin [Arg_1-Arg_0-1 ]
evalNestedMultipleDepbb2in [Arg_1-Arg_2 ]
MPRF for transition 4:evalNestedMultipleDepbbin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalNestedMultipleDepbb2in(Arg_0,Arg_1,Arg_0+1,0,Arg_4):|:1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 of depth 1:
new bound:
Arg_1 {O(n)}
MPRF:
evalNestedMultipleDepbb1in [Arg_1-Arg_2 ]
evalNestedMultipleDepbb3in [Arg_1-Arg_0 ]
evalNestedMultipleDepbbin [Arg_1-Arg_0 ]
evalNestedMultipleDepbb2in [Arg_1-Arg_0-1 ]
MPRF for transition 7:evalNestedMultipleDepbb1in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalNestedMultipleDepbb2in(Arg_0,Arg_1,Arg_2,Arg_3+1,Arg_4):|:1<=Arg_4 && 1<=Arg_3+Arg_4 && 1+Arg_3<=Arg_4 && 2<=Arg_2+Arg_4 && 2<=Arg_1+Arg_4 && 1<=Arg_0+Arg_4 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 of depth 1:
new bound:
Arg_1*Arg_4+Arg_3+Arg_4 {O(n^2)}
MPRF:
evalNestedMultipleDepbb1in [Arg_4-Arg_3 ]
evalNestedMultipleDepbb2in [Arg_4-Arg_3 ]
evalNestedMultipleDepbb3in [Arg_4-Arg_3 ]
evalNestedMultipleDepbbin [Arg_4-Arg_3 ]
MPRF for transition 5:evalNestedMultipleDepbb2in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalNestedMultipleDepbb1in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:0<=Arg_3 && 1<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 0<=Arg_0+Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && Arg_3+1<=Arg_4 of depth 1:
new bound:
Arg_1*Arg_4+Arg_3+Arg_4 {O(n^2)}
MPRF:
evalNestedMultipleDepbb1in [Arg_4-Arg_3-1 ]
evalNestedMultipleDepbb2in [Arg_4-Arg_3 ]
evalNestedMultipleDepbb3in [Arg_4-Arg_3 ]
evalNestedMultipleDepbbin [Arg_4-Arg_3 ]
All Bounds
Timebounds
Overall timebound:2*Arg_1*Arg_4+2*Arg_3+2*Arg_4+3*Arg_1+4 {O(n^2)}
7: evalNestedMultipleDepbb1in->evalNestedMultipleDepbb2in: Arg_1*Arg_4+Arg_3+Arg_4 {O(n^2)}
5: evalNestedMultipleDepbb2in->evalNestedMultipleDepbb1in: Arg_1*Arg_4+Arg_3+Arg_4 {O(n^2)}
6: evalNestedMultipleDepbb2in->evalNestedMultipleDepbb3in: Arg_1 {O(n)}
2: evalNestedMultipleDepbb3in->evalNestedMultipleDepbbin: Arg_1 {O(n)}
3: evalNestedMultipleDepbb3in->evalNestedMultipleDepreturnin: 1 {O(1)}
4: evalNestedMultipleDepbbin->evalNestedMultipleDepbb2in: Arg_1 {O(n)}
1: evalNestedMultipleDepentryin->evalNestedMultipleDepbb3in: 1 {O(1)}
8: evalNestedMultipleDepreturnin->evalNestedMultipleDepstop: 1 {O(1)}
0: evalNestedMultipleDepstart->evalNestedMultipleDepentryin: 1 {O(1)}
Costbounds
Overall costbound: 2*Arg_1*Arg_4+2*Arg_3+2*Arg_4+3*Arg_1+4 {O(n^2)}
7: evalNestedMultipleDepbb1in->evalNestedMultipleDepbb2in: Arg_1*Arg_4+Arg_3+Arg_4 {O(n^2)}
5: evalNestedMultipleDepbb2in->evalNestedMultipleDepbb1in: Arg_1*Arg_4+Arg_3+Arg_4 {O(n^2)}
6: evalNestedMultipleDepbb2in->evalNestedMultipleDepbb3in: Arg_1 {O(n)}
2: evalNestedMultipleDepbb3in->evalNestedMultipleDepbbin: Arg_1 {O(n)}
3: evalNestedMultipleDepbb3in->evalNestedMultipleDepreturnin: 1 {O(1)}
4: evalNestedMultipleDepbbin->evalNestedMultipleDepbb2in: Arg_1 {O(n)}
1: evalNestedMultipleDepentryin->evalNestedMultipleDepbb3in: 1 {O(1)}
8: evalNestedMultipleDepreturnin->evalNestedMultipleDepstop: 1 {O(1)}
0: evalNestedMultipleDepstart->evalNestedMultipleDepentryin: 1 {O(1)}
Sizebounds
7: evalNestedMultipleDepbb1in->evalNestedMultipleDepbb2in, Arg_0: Arg_1 {O(n)}
7: evalNestedMultipleDepbb1in->evalNestedMultipleDepbb2in, Arg_1: Arg_1 {O(n)}
7: evalNestedMultipleDepbb1in->evalNestedMultipleDepbb2in, Arg_2: Arg_1+1 {O(n)}
7: evalNestedMultipleDepbb1in->evalNestedMultipleDepbb2in, Arg_3: Arg_1*Arg_4+Arg_3+Arg_4 {O(n^2)}
7: evalNestedMultipleDepbb1in->evalNestedMultipleDepbb2in, Arg_4: Arg_4 {O(n)}
5: evalNestedMultipleDepbb2in->evalNestedMultipleDepbb1in, Arg_0: Arg_1 {O(n)}
5: evalNestedMultipleDepbb2in->evalNestedMultipleDepbb1in, Arg_1: Arg_1 {O(n)}
5: evalNestedMultipleDepbb2in->evalNestedMultipleDepbb1in, Arg_2: Arg_1+1 {O(n)}
5: evalNestedMultipleDepbb2in->evalNestedMultipleDepbb1in, Arg_3: Arg_1*Arg_4+Arg_3+Arg_4 {O(n^2)}
5: evalNestedMultipleDepbb2in->evalNestedMultipleDepbb1in, Arg_4: Arg_4 {O(n)}
6: evalNestedMultipleDepbb2in->evalNestedMultipleDepbb3in, Arg_0: Arg_1 {O(n)}
6: evalNestedMultipleDepbb2in->evalNestedMultipleDepbb3in, Arg_1: Arg_1 {O(n)}
6: evalNestedMultipleDepbb2in->evalNestedMultipleDepbb3in, Arg_2: 2*Arg_1+2 {O(n)}
6: evalNestedMultipleDepbb2in->evalNestedMultipleDepbb3in, Arg_3: Arg_1*Arg_4+Arg_3+Arg_4 {O(n^2)}
6: evalNestedMultipleDepbb2in->evalNestedMultipleDepbb3in, Arg_4: Arg_4 {O(n)}
2: evalNestedMultipleDepbb3in->evalNestedMultipleDepbbin, Arg_0: Arg_1 {O(n)}
2: evalNestedMultipleDepbb3in->evalNestedMultipleDepbbin, Arg_1: Arg_1 {O(n)}
2: evalNestedMultipleDepbb3in->evalNestedMultipleDepbbin, Arg_2: 2*Arg_1+Arg_2+2 {O(n)}
2: evalNestedMultipleDepbb3in->evalNestedMultipleDepbbin, Arg_3: Arg_1*Arg_4+2*Arg_3+Arg_4 {O(n^2)}
2: evalNestedMultipleDepbb3in->evalNestedMultipleDepbbin, Arg_4: Arg_4 {O(n)}
3: evalNestedMultipleDepbb3in->evalNestedMultipleDepreturnin, Arg_0: Arg_1 {O(n)}
3: evalNestedMultipleDepbb3in->evalNestedMultipleDepreturnin, Arg_1: 2*Arg_1 {O(n)}
3: evalNestedMultipleDepbb3in->evalNestedMultipleDepreturnin, Arg_2: 2*Arg_1+Arg_2+2 {O(n)}
3: evalNestedMultipleDepbb3in->evalNestedMultipleDepreturnin, Arg_3: Arg_1*Arg_4+2*Arg_3+Arg_4 {O(n^2)}
3: evalNestedMultipleDepbb3in->evalNestedMultipleDepreturnin, Arg_4: 2*Arg_4 {O(n)}
4: evalNestedMultipleDepbbin->evalNestedMultipleDepbb2in, Arg_0: Arg_1 {O(n)}
4: evalNestedMultipleDepbbin->evalNestedMultipleDepbb2in, Arg_1: Arg_1 {O(n)}
4: evalNestedMultipleDepbbin->evalNestedMultipleDepbb2in, Arg_2: Arg_1+1 {O(n)}
4: evalNestedMultipleDepbbin->evalNestedMultipleDepbb2in, Arg_3: 0 {O(1)}
4: evalNestedMultipleDepbbin->evalNestedMultipleDepbb2in, Arg_4: Arg_4 {O(n)}
1: evalNestedMultipleDepentryin->evalNestedMultipleDepbb3in, Arg_0: 0 {O(1)}
1: evalNestedMultipleDepentryin->evalNestedMultipleDepbb3in, Arg_1: Arg_1 {O(n)}
1: evalNestedMultipleDepentryin->evalNestedMultipleDepbb3in, Arg_2: Arg_2 {O(n)}
1: evalNestedMultipleDepentryin->evalNestedMultipleDepbb3in, Arg_3: Arg_3 {O(n)}
1: evalNestedMultipleDepentryin->evalNestedMultipleDepbb3in, Arg_4: Arg_4 {O(n)}
8: evalNestedMultipleDepreturnin->evalNestedMultipleDepstop, Arg_0: Arg_1 {O(n)}
8: evalNestedMultipleDepreturnin->evalNestedMultipleDepstop, Arg_1: 2*Arg_1 {O(n)}
8: evalNestedMultipleDepreturnin->evalNestedMultipleDepstop, Arg_2: 2*Arg_1+Arg_2+2 {O(n)}
8: evalNestedMultipleDepreturnin->evalNestedMultipleDepstop, Arg_3: Arg_1*Arg_4+2*Arg_3+Arg_4 {O(n^2)}
8: evalNestedMultipleDepreturnin->evalNestedMultipleDepstop, Arg_4: 2*Arg_4 {O(n)}
0: evalNestedMultipleDepstart->evalNestedMultipleDepentryin, Arg_0: Arg_0 {O(n)}
0: evalNestedMultipleDepstart->evalNestedMultipleDepentryin, Arg_1: Arg_1 {O(n)}
0: evalNestedMultipleDepstart->evalNestedMultipleDepentryin, Arg_2: Arg_2 {O(n)}
0: evalNestedMultipleDepstart->evalNestedMultipleDepentryin, Arg_3: Arg_3 {O(n)}
0: evalNestedMultipleDepstart->evalNestedMultipleDepentryin, Arg_4: Arg_4 {O(n)}