Inferring Expected Runtimes Using Sizes

KoAT2 Proof WORST_CASE( ?, 43/3+43/3*Arg_2+43/3*Arg_3 {O(n)})

Initial Complexity Problem (after preprocessing)

Start:f
Program_Vars:Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
Temp_Vars:
Locations:f, g, h
Transitions:
f(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -{0}> g(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
g(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -{0}> h(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) :|: Arg_2<Arg_3
h(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> 1/4:g(Arg_0+2,Arg_1,Arg_2+2,Arg_3,Arg_4) :+: 1/4:g(Arg_0,Arg_1+2,Arg_2+2,Arg_3,Arg_4) :+: 1/4:g(Arg_0-1,Arg_1,Arg_2-1,Arg_3,Arg_4) :+: 1/4:g(Arg_0,Arg_1-1,Arg_2-1,Arg_3,Arg_4) :|: 0<Arg_0 && 0<Arg_1 && 1+Arg_2<=Arg_3
h(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> 1/4:g(Arg_0+2,Arg_1,Arg_2+2,Arg_3,Arg_4) :+: 1/4:g(Arg_0,Arg_1+1,Arg_2-1,Arg_3,Arg_4) :+: 1/4:g(Arg_0-1,Arg_1,Arg_2-1,Arg_3,Arg_4) :+: 1/4:g(Arg_0,Arg_1-2,Arg_2+2,Arg_3,Arg_4) :|: 0<Arg_0 && Arg_1<0 && 1+Arg_2<=Arg_3
h(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> 1/4:g(Arg_0+2,Arg_1,Arg_2+2,Arg_3,Arg_4) :+: 1/4:g(Arg_0,Arg_1+1,Arg_2+1,Arg_3,Arg_4) :+: 1/4:g(Arg_0-1,Arg_1,Arg_2-1,Arg_3,Arg_4) :+: 1/4:g(Arg_0,Arg_1-1,Arg_2+1,Arg_3,Arg_4) :|: 0<Arg_0 && Arg_1<=0 && 0<=Arg_1 && 1+Arg_2<=Arg_3
h(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> 1/4:g(Arg_0+1,Arg_1,Arg_2-1,Arg_3,Arg_4) :+: 1/4:g(Arg_0,Arg_1+2,Arg_2+2,Arg_3,Arg_4) :+: 1/4:g(Arg_0-2,Arg_1,Arg_2+2,Arg_3,Arg_4) :+: 1/4:g(Arg_0,Arg_1-1,Arg_2-1,Arg_3,Arg_4) :|: Arg_0<0 && 0<Arg_1 && 1+Arg_2<=Arg_3
h(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> 1/4:g(Arg_0+1,Arg_1,Arg_2-1,Arg_3,Arg_4) :+: 1/4:g(Arg_0,Arg_1+1,Arg_2-1,Arg_3,Arg_4) :+: 1/4:g(Arg_0-2,Arg_1,Arg_2+2,Arg_3,Arg_4) :+: 1/4:g(Arg_0,Arg_1-2,Arg_2+2,Arg_3,Arg_4) :|: Arg_0<0 && Arg_1<0 && 1+Arg_2<=Arg_3
h(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> 1/4:g(Arg_0+1,Arg_1,Arg_2-1,Arg_3,Arg_4) :+: 1/4:g(Arg_0,Arg_1+1,Arg_2+1,Arg_3,Arg_4) :+: 1/4:g(Arg_0-2,Arg_1,Arg_2+2,Arg_3,Arg_4) :+: 1/4:g(Arg_0,Arg_1-1,Arg_2+1,Arg_3,Arg_4) :|: Arg_0<0 && Arg_1<=0 && 0<=Arg_1 && 1+Arg_2<=Arg_3
h(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> 1/4:g(Arg_0+1,Arg_1,Arg_2+1,Arg_3,Arg_4) :+: 1/4:g(Arg_0,Arg_1+2,Arg_2+2,Arg_3,Arg_4) :+: 1/4:g(Arg_0-1,Arg_1,Arg_2+1,Arg_3,Arg_4) :+: 1/4:g(Arg_0,Arg_1-1,Arg_2-1,Arg_3,Arg_4) :|: Arg_0<=0 && 0<=Arg_0 && 0<Arg_1 && 1+Arg_2<=Arg_3
h(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> 1/4:g(Arg_0+1,Arg_1,Arg_2+1,Arg_3,Arg_4) :+: 1/4:g(Arg_0,Arg_1+1,Arg_2-1,Arg_3,Arg_4) :+: 1/4:g(Arg_0-1,Arg_1,Arg_2+1,Arg_3,Arg_4) :+: 1/4:g(Arg_0,Arg_1-2,Arg_2+2,Arg_3,Arg_4) :|: Arg_0<=0 && 0<=Arg_0 && Arg_1<0 && 1+Arg_2<=Arg_3
h(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> 1/4:g(Arg_0+1,Arg_1,Arg_2+1,Arg_3,Arg_4) :+: 1/4:g(Arg_0,Arg_1+1,Arg_2+1,Arg_3,Arg_4) :+: 1/4:g(Arg_0-1,Arg_1,Arg_2+1,Arg_3,Arg_4) :+: 1/4:g(Arg_0,Arg_1-1,Arg_2+1,Arg_3,Arg_4) :|: Arg_0<=0 && 0<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 1+Arg_2<=Arg_3

G f f g g f->g t₀ ∈ g₀ {0} h h g->h t₁ ∈ g₁ τ = Arg_2<Arg_3 {0} h->g t₂ ∈ g₂ p = 1/4 η (Arg_0) = Arg_0+2 η (Arg_2) = Arg_2+2 τ = 0<Arg_0 && 0<Arg_1 h->g t₃ ∈ g₂ p = 1/4 η (Arg_1) = Arg_1+2 η (Arg_2) = Arg_2+2 τ = 0<Arg_0 && 0<Arg_1 h->g t₄ ∈ g₂ p = 1/4 η (Arg_0) = Arg_0-1 η (Arg_2) = Arg_2-1 τ = 0<Arg_0 && 0<Arg_1 h->g t₅ ∈ g₂ p = 1/4 η (Arg_1) = Arg_1-1 η (Arg_2) = Arg_2-1 τ = 0<Arg_0 && 0<Arg_1 h->g t₆ ∈ g₃ p = 1/4 η (Arg_0) = Arg_0+2 η (Arg_2) = Arg_2+2 τ = 0<Arg_0 && Arg_1<0 h->g t₇ ∈ g₃ p = 1/4 η (Arg_1) = Arg_1+1 η (Arg_2) = Arg_2-1 τ = 0<Arg_0 && Arg_1<0 h->g t₈ ∈ g₃ p = 1/4 η (Arg_0) = Arg_0-1 η (Arg_2) = Arg_2-1 τ = 0<Arg_0 && Arg_1<0 h->g t₉ ∈ g₃ p = 1/4 η (Arg_1) = Arg_1-2 η (Arg_2) = Arg_2+2 τ = 0<Arg_0 && Arg_1<0 h->g t₁₀ ∈ g₄ p = 1/4 η (Arg_0) = Arg_0+2 η (Arg_2) = Arg_2+2 τ = 0<Arg_0 && Arg_1<=0 && 0<=Arg_1 h->g t₁₁ ∈ g₄ p = 1/4 η (Arg_1) = Arg_1+1 η (Arg_2) = Arg_2+1 τ = 0<Arg_0 && Arg_1<=0 && 0<=Arg_1 h->g t₁₂ ∈ g₄ p = 1/4 η (Arg_0) = Arg_0-1 η (Arg_2) = Arg_2-1 τ = 0<Arg_0 && Arg_1<=0 && 0<=Arg_1 h->g t₁₃ ∈ g₄ p = 1/4 η (Arg_1) = Arg_1-1 η (Arg_2) = Arg_2+1 τ = 0<Arg_0 && Arg_1<=0 && 0<=Arg_1 h->g t₁₄ ∈ g₅ p = 1/4 η (Arg_0) = Arg_0+1 η (Arg_2) = Arg_2-1 τ = Arg_0<0 && 0<Arg_1 h->g t₁₅ ∈ g₅ p = 1/4 η (Arg_1) = Arg_1+2 η (Arg_2) = Arg_2+2 τ = Arg_0<0 && 0<Arg_1 h->g t₁₆ ∈ g₅ p = 1/4 η (Arg_0) = Arg_0-2 η (Arg_2) = Arg_2+2 τ = Arg_0<0 && 0<Arg_1 h->g t₁₇ ∈ g₅ p = 1/4 η (Arg_1) = Arg_1-1 η (Arg_2) = Arg_2-1 τ = Arg_0<0 && 0<Arg_1 h->g t₁₈ ∈ g₆ p = 1/4 η (Arg_0) = Arg_0+1 η (Arg_2) = Arg_2-1 τ = Arg_0<0 && Arg_1<0 h->g t₁₉ ∈ g₆ p = 1/4 η (Arg_1) = Arg_1+1 η (Arg_2) = Arg_2-1 τ = Arg_0<0 && Arg_1<0 h->g t₂₀ ∈ g₆ p = 1/4 η (Arg_0) = Arg_0-2 η (Arg_2) = Arg_2+2 τ = Arg_0<0 && Arg_1<0 h->g t₂₁ ∈ g₆ p = 1/4 η (Arg_1) = Arg_1-2 η (Arg_2) = Arg_2+2 τ = Arg_0<0 && Arg_1<0 h->g t₂₂ ∈ g₇ p = 1/4 η (Arg_0) = Arg_0+1 η (Arg_2) = Arg_2-1 τ = Arg_0<0 && Arg_1<=0 && 0<=Arg_1 h->g t₂₃ ∈ g₇ p = 1/4 η (Arg_1) = Arg_1+1 η (Arg_2) = Arg_2+1 τ = Arg_0<0 && Arg_1<=0 && 0<=Arg_1 h->g t₂₄ ∈ g₇ p = 1/4 η (Arg_0) = Arg_0-2 η (Arg_2) = Arg_2+2 τ = Arg_0<0 && Arg_1<=0 && 0<=Arg_1 h->g t₂₅ ∈ g₇ p = 1/4 η (Arg_1) = Arg_1-1 η (Arg_2) = Arg_2+1 τ = Arg_0<0 && Arg_1<=0 && 0<=Arg_1 h->g t₂₆ ∈ g₈ p = 1/4 η (Arg_0) = Arg_0+1 η (Arg_2) = Arg_2+1 τ = Arg_0<=0 && 0<=Arg_0 && 0<Arg_1 h->g t₂₇ ∈ g₈ p = 1/4 η (Arg_1) = Arg_1+2 η (Arg_2) = Arg_2+2 τ = Arg_0<=0 && 0<=Arg_0 && 0<Arg_1 h->g t₂₈ ∈ g₈ p = 1/4 η (Arg_0) = Arg_0-1 η (Arg_2) = Arg_2+1 τ = Arg_0<=0 && 0<=Arg_0 && 0<Arg_1 h->g t₂₉ ∈ g₈ p = 1/4 η (Arg_1) = Arg_1-1 η (Arg_2) = Arg_2-1 τ = Arg_0<=0 && 0<=Arg_0 && 0<Arg_1 h->g t₃₀ ∈ g₉ p = 1/4 η (Arg_0) = Arg_0+1 η (Arg_2) = Arg_2+1 τ = Arg_0<=0 && 0<=Arg_0 && Arg_1<0 h->g t₃₁ ∈ g₉ p = 1/4 η (Arg_1) = Arg_1+1 η (Arg_2) = Arg_2-1 τ = Arg_0<=0 && 0<=Arg_0 && Arg_1<0 h->g t₃₂ ∈ g₉ p = 1/4 η (Arg_0) = Arg_0-1 η (Arg_2) = Arg_2+1 τ = Arg_0<=0 && 0<=Arg_0 && Arg_1<0 h->g t₃₃ ∈ g₉ p = 1/4 η (Arg_1) = Arg_1-2 η (Arg_2) = Arg_2+2 τ = Arg_0<=0 && 0<=Arg_0 && Arg_1<0 h->g t₃₄ ∈ g₁₀ p = 1/4 η (Arg_0) = Arg_0+1 η (Arg_2) = Arg_2+1 τ = Arg_0<=0 && 0<=Arg_0 && Arg_1<=0 && 0<=Arg_1 h->g t₃₅ ∈ g₁₀ p = 1/4 η (Arg_1) = Arg_1+1 η (Arg_2) = Arg_2+1 τ = Arg_0<=0 && 0<=Arg_0 && Arg_1<=0 && 0<=Arg_1 h->g t₃₆ ∈ g₁₀ p = 1/4 η (Arg_0) = Arg_0-1 η (Arg_2) = Arg_2+1 τ = Arg_0<=0 && 0<=Arg_0 && Arg_1<=0 && 0<=Arg_1 h->g t₃₇ ∈ g₁₀ p = 1/4 η (Arg_1) = Arg_1-1 η (Arg_2) = Arg_2+1 τ = Arg_0<=0 && 0<=Arg_0 && Arg_1<=0 && 0<=Arg_1

Timebounds:

Overall timebound:inf {Infinity}
0,0: f->g: 1 {O(1)}
1,1: g->h: inf {Infinity}
2,2: h->g: inf {Infinity}
3,2: h->g: inf {Infinity}
4,2: h->g: inf {Infinity}
5,2: h->g: inf {Infinity}
6,3: h->g: inf {Infinity}
7,3: h->g: inf {Infinity}
8,3: h->g: inf {Infinity}
9,3: h->g: inf {Infinity}
10,4: h->g: inf {Infinity}
11,4: h->g: inf {Infinity}
12,4: h->g: inf {Infinity}
13,4: h->g: inf {Infinity}
14,5: h->g: inf {Infinity}
15,5: h->g: inf {Infinity}
16,5: h->g: inf {Infinity}
17,5: h->g: inf {Infinity}
18,6: h->g: inf {Infinity}
19,6: h->g: inf {Infinity}
20,6: h->g: inf {Infinity}
21,6: h->g: inf {Infinity}
22,7: h->g: inf {Infinity}
23,7: h->g: inf {Infinity}
24,7: h->g: inf {Infinity}
25,7: h->g: inf {Infinity}
26,8: h->g: inf {Infinity}
27,8: h->g: inf {Infinity}
28,8: h->g: inf {Infinity}
29,8: h->g: inf {Infinity}
30,9: h->g: inf {Infinity}
31,9: h->g: inf {Infinity}
32,9: h->g: inf {Infinity}
33,9: h->g: inf {Infinity}
34,10: h->g: inf {Infinity}
35,10: h->g: inf {Infinity}
36,10: h->g: inf {Infinity}
37,10: h->g: inf {Infinity}

Expected Timebounds:

Overall expected timebound: 49/3*Arg_2+52/3+49/3*Arg_3 {O(n)}
0: f->[1:g]: 1 {O(1)}
1: g->[1:h]: 2+2*Arg_2+2*Arg_3 {O(n)}
2: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g]: 2+2*Arg_2+2*Arg_3 {O(n)}
3: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g]: 2+2*Arg_2+2*Arg_3 {O(n)}
4: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g]: 4/3+4/3*Arg_2+4/3*Arg_3 {O(n)}
5: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g]: 2+2*Arg_2+2*Arg_3 {O(n)}
6: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g]: 2+2*Arg_2+2*Arg_3 {O(n)}
7: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g]: 4/3+4/3*Arg_2+4/3*Arg_3 {O(n)}
8: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g]: 4/3+4/3*Arg_2+4/3*Arg_3 {O(n)}
9: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g]: 4/3+4/3*Arg_2+4/3*Arg_3 {O(n)}
10: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g]: 1+Arg_2+Arg_3 {O(n)}

Costbounds:

Overall costbound: inf {Infinity}
0,0: f->g: inf {Infinity}
1,1: g->h: inf {Infinity}
2,2: h->g: inf {Infinity}
3,2: h->g: inf {Infinity}
4,2: h->g: inf {Infinity}
5,2: h->g: inf {Infinity}
6,3: h->g: inf {Infinity}
7,3: h->g: inf {Infinity}
8,3: h->g: inf {Infinity}
9,3: h->g: inf {Infinity}
10,4: h->g: inf {Infinity}
11,4: h->g: inf {Infinity}
12,4: h->g: inf {Infinity}
13,4: h->g: inf {Infinity}
14,5: h->g: inf {Infinity}
15,5: h->g: inf {Infinity}
16,5: h->g: inf {Infinity}
17,5: h->g: inf {Infinity}
18,6: h->g: inf {Infinity}
19,6: h->g: inf {Infinity}
20,6: h->g: inf {Infinity}
21,6: h->g: inf {Infinity}
22,7: h->g: inf {Infinity}
23,7: h->g: inf {Infinity}
24,7: h->g: inf {Infinity}
25,7: h->g: inf {Infinity}
26,8: h->g: inf {Infinity}
27,8: h->g: inf {Infinity}
28,8: h->g: inf {Infinity}
29,8: h->g: inf {Infinity}
30,9: h->g: inf {Infinity}
31,9: h->g: inf {Infinity}
32,9: h->g: inf {Infinity}
33,9: h->g: inf {Infinity}
34,10: h->g: inf {Infinity}
35,10: h->g: inf {Infinity}
36,10: h->g: inf {Infinity}
37,10: h->g: inf {Infinity}

Expected Costbounds:

Overall expected costbound: 43/3+43/3*Arg_2+43/3*Arg_3 {O(n)}
0: f->[1:g]: 0 {O(1)}
1: g->[1:h]: 0 {O(1)}
2: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g]: 2+2*Arg_2+2*Arg_3 {O(n)}
3: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g]: 2+2*Arg_2+2*Arg_3 {O(n)}
4: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g]: 4/3+4/3*Arg_2+4/3*Arg_3 {O(n)}
5: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g]: 2+2*Arg_2+2*Arg_3 {O(n)}
6: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g]: 2+2*Arg_2+2*Arg_3 {O(n)}
7: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g]: 4/3+4/3*Arg_2+4/3*Arg_3 {O(n)}
8: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g]: 4/3+4/3*Arg_2+4/3*Arg_3 {O(n)}
9: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g]: 4/3+4/3*Arg_2+4/3*Arg_3 {O(n)}
10: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g]: 1+Arg_2+Arg_3 {O(n)}

Sizebounds:

0,0: f->g, Arg_0: Arg_0 {O(n)}
0,0: f->g, Arg_1: Arg_1 {O(n)}
0,0: f->g, Arg_2: Arg_2 {O(n)}
0,0: f->g, Arg_3: Arg_3 {O(n)}
0,0: f->g, Arg_4: Arg_4 {O(n)}
1,1: g->h, Arg_3: Arg_3 {O(n)}
1,1: g->h, Arg_4: Arg_4 {O(n)}
2,2: h->g, Arg_3: Arg_3 {O(n)}
2,2: h->g, Arg_4: Arg_4 {O(n)}
3,2: h->g, Arg_3: Arg_3 {O(n)}
3,2: h->g, Arg_4: Arg_4 {O(n)}
4,2: h->g, Arg_3: Arg_3 {O(n)}
4,2: h->g, Arg_4: Arg_4 {O(n)}
5,2: h->g, Arg_3: Arg_3 {O(n)}
5,2: h->g, Arg_4: Arg_4 {O(n)}
6,3: h->g, Arg_1: (-1) {O(1)}
6,3: h->g, Arg_3: Arg_3 {O(n)}
6,3: h->g, Arg_4: Arg_4 {O(n)}
7,3: h->g, Arg_1: 0 {O(1)}
7,3: h->g, Arg_3: Arg_3 {O(n)}
7,3: h->g, Arg_4: Arg_4 {O(n)}
8,3: h->g, Arg_1: (-1) {O(1)}
8,3: h->g, Arg_3: Arg_3 {O(n)}
8,3: h->g, Arg_4: Arg_4 {O(n)}
9,3: h->g, Arg_1: (-3) {O(1)}
9,3: h->g, Arg_3: Arg_3 {O(n)}
9,3: h->g, Arg_4: Arg_4 {O(n)}
10,4: h->g, Arg_1: 0 {O(1)}
10,4: h->g, Arg_3: Arg_3 {O(n)}
10,4: h->g, Arg_4: Arg_4 {O(n)}
11,4: h->g, Arg_1: 1 {O(1)}
11,4: h->g, Arg_3: Arg_3 {O(n)}
11,4: h->g, Arg_4: Arg_4 {O(n)}
12,4: h->g, Arg_1: 0 {O(1)}
12,4: h->g, Arg_3: Arg_3 {O(n)}
12,4: h->g, Arg_4: Arg_4 {O(n)}
13,4: h->g, Arg_1: (-1) {O(1)}
13,4: h->g, Arg_3: Arg_3 {O(n)}
13,4: h->g, Arg_4: Arg_4 {O(n)}
14,5: h->g, Arg_0: 0 {O(1)}
14,5: h->g, Arg_3: Arg_3 {O(n)}
14,5: h->g, Arg_4: Arg_4 {O(n)}
15,5: h->g, Arg_0: (-1) {O(1)}
15,5: h->g, Arg_3: Arg_3 {O(n)}
15,5: h->g, Arg_4: Arg_4 {O(n)}
16,5: h->g, Arg_0: (-3) {O(1)}
16,5: h->g, Arg_3: Arg_3 {O(n)}
16,5: h->g, Arg_4: Arg_4 {O(n)}
17,5: h->g, Arg_0: (-1) {O(1)}
17,5: h->g, Arg_3: Arg_3 {O(n)}
17,5: h->g, Arg_4: Arg_4 {O(n)}
18,6: h->g, Arg_0: 0 {O(1)}
18,6: h->g, Arg_1: (-1) {O(1)}
18,6: h->g, Arg_3: Arg_3 {O(n)}
18,6: h->g, Arg_4: Arg_4 {O(n)}
19,6: h->g, Arg_0: (-1) {O(1)}
19,6: h->g, Arg_1: 0 {O(1)}
19,6: h->g, Arg_3: Arg_3 {O(n)}
19,6: h->g, Arg_4: Arg_4 {O(n)}
20,6: h->g, Arg_0: (-3) {O(1)}
20,6: h->g, Arg_1: (-1) {O(1)}
20,6: h->g, Arg_3: Arg_3 {O(n)}
20,6: h->g, Arg_4: Arg_4 {O(n)}
21,6: h->g, Arg_0: (-1) {O(1)}
21,6: h->g, Arg_1: (-3) {O(1)}
21,6: h->g, Arg_3: Arg_3 {O(n)}
21,6: h->g, Arg_4: Arg_4 {O(n)}
22,7: h->g, Arg_0: 0 {O(1)}
22,7: h->g, Arg_1: 0 {O(1)}
22,7: h->g, Arg_3: Arg_3 {O(n)}
22,7: h->g, Arg_4: Arg_4 {O(n)}
23,7: h->g, Arg_0: (-1) {O(1)}
23,7: h->g, Arg_1: 1 {O(1)}
23,7: h->g, Arg_3: Arg_3 {O(n)}
23,7: h->g, Arg_4: Arg_4 {O(n)}
24,7: h->g, Arg_0: (-3) {O(1)}
24,7: h->g, Arg_1: 0 {O(1)}
24,7: h->g, Arg_3: Arg_3 {O(n)}
24,7: h->g, Arg_4: Arg_4 {O(n)}
25,7: h->g, Arg_0: (-1) {O(1)}
25,7: h->g, Arg_1: (-1) {O(1)}
25,7: h->g, Arg_3: Arg_3 {O(n)}
25,7: h->g, Arg_4: Arg_4 {O(n)}
26,8: h->g, Arg_0: 1 {O(1)}
26,8: h->g, Arg_3: Arg_3 {O(n)}
26,8: h->g, Arg_4: Arg_4 {O(n)}
27,8: h->g, Arg_0: 0 {O(1)}
27,8: h->g, Arg_3: Arg_3 {O(n)}
27,8: h->g, Arg_4: Arg_4 {O(n)}
28,8: h->g, Arg_0: (-1) {O(1)}
28,8: h->g, Arg_3: Arg_3 {O(n)}
28,8: h->g, Arg_4: Arg_4 {O(n)}
29,8: h->g, Arg_0: 0 {O(1)}
29,8: h->g, Arg_3: Arg_3 {O(n)}
29,8: h->g, Arg_4: Arg_4 {O(n)}
30,9: h->g, Arg_0: 1 {O(1)}
30,9: h->g, Arg_1: (-1) {O(1)}
30,9: h->g, Arg_3: Arg_3 {O(n)}
30,9: h->g, Arg_4: Arg_4 {O(n)}
31,9: h->g, Arg_0: 0 {O(1)}
31,9: h->g, Arg_1: 0 {O(1)}
31,9: h->g, Arg_3: Arg_3 {O(n)}
31,9: h->g, Arg_4: Arg_4 {O(n)}
32,9: h->g, Arg_0: (-1) {O(1)}
32,9: h->g, Arg_1: (-1) {O(1)}
32,9: h->g, Arg_3: Arg_3 {O(n)}
32,9: h->g, Arg_4: Arg_4 {O(n)}
33,9: h->g, Arg_0: 0 {O(1)}
33,9: h->g, Arg_1: (-3) {O(1)}
33,9: h->g, Arg_3: Arg_3 {O(n)}
33,9: h->g, Arg_4: Arg_4 {O(n)}
34,10: h->g, Arg_0: 1 {O(1)}
34,10: h->g, Arg_1: 0 {O(1)}
34,10: h->g, Arg_3: Arg_3 {O(n)}
34,10: h->g, Arg_4: Arg_4 {O(n)}
35,10: h->g, Arg_0: 0 {O(1)}
35,10: h->g, Arg_1: 1 {O(1)}
35,10: h->g, Arg_3: Arg_3 {O(n)}
35,10: h->g, Arg_4: Arg_4 {O(n)}
36,10: h->g, Arg_0: (-1) {O(1)}
36,10: h->g, Arg_1: 0 {O(1)}
36,10: h->g, Arg_3: Arg_3 {O(n)}
36,10: h->g, Arg_4: Arg_4 {O(n)}
37,10: h->g, Arg_0: 0 {O(1)}
37,10: h->g, Arg_1: (-1) {O(1)}
37,10: h->g, Arg_3: Arg_3 {O(n)}
37,10: h->g, Arg_4: Arg_4 {O(n)}

ExpSizeBounds:

(0: f->[1:g], g), Arg_0: Arg_0 {O(n)}
(0: f->[1:g], g), Arg_1: Arg_1 {O(n)}
(0: f->[1:g], g), Arg_2: Arg_2 {O(n)}
(0: f->[1:g], g), Arg_3: Arg_3 {O(n)}
(0: f->[1:g], g), Arg_4: Arg_4 {O(n)}
(1: g->[1:h], h), Arg_0: 1/2*(1+Arg_2+Arg_3)+3*(2+2*Arg_2+2*Arg_3)+3/2*(4/3+4/3*Arg_2+4/3*Arg_3)+4/3+4/3*Arg_2+Arg_0+4/3*Arg_3 {O(n)}
(1: g->[1:h], h), Arg_1: 1/2*(1+Arg_2+Arg_3)+3*(2+2*Arg_2+2*Arg_3)+Arg_1+5/2*(4/3+4/3*Arg_2+4/3*Arg_3) {O(n)}
(1: g->[1:h], h), Arg_2: 1+2*Arg_2+5*(4/3+4/3*Arg_2+4/3*Arg_3)+Arg_3+6*(2+2*Arg_2+2*Arg_3) {O(n)}
(1: g->[1:h], h), Arg_3: Arg_3 {O(n)}
(1: g->[1:h], h), Arg_4: Arg_4 {O(n)}
(2: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_0: 1/2*(1+Arg_2+Arg_3)+3*(2+2*Arg_2+2*Arg_3)+3/2*(4/3+4/3*Arg_2+4/3*Arg_3)+4/3+4/3*Arg_2+Arg_0+4/3*Arg_3 {O(n)}
(2: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_1: 1/2*(1+Arg_2+Arg_3)+3*(2+2*Arg_2+2*Arg_3)+Arg_1+5/2*(4/3+4/3*Arg_2+4/3*Arg_3) {O(n)}
(2: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_2: 1+2*Arg_2+5*(4/3+4/3*Arg_2+4/3*Arg_3)+Arg_3+6*(2+2*Arg_2+2*Arg_3) {O(n)}
(2: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_3: Arg_3 {O(n)}
(2: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_4: Arg_4 {O(n)}
(3: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_0: 1/2*(1+Arg_2+Arg_3)+3*(2+2*Arg_2+2*Arg_3)+3/2*(4/3+4/3*Arg_2+4/3*Arg_3)+4/3+4/3*Arg_2+Arg_0+4/3*Arg_3 {O(n)}
(3: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_1: 1/2*(1+Arg_2+Arg_3)+3*(2+2*Arg_2+2*Arg_3)+Arg_1+5/2*(4/3+4/3*Arg_2+4/3*Arg_3) {O(n)}
(3: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_2: 1+2*Arg_2+5*(4/3+4/3*Arg_2+4/3*Arg_3)+Arg_3+6*(2+2*Arg_2+2*Arg_3) {O(n)}
(3: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_3: Arg_3 {O(n)}
(3: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_4: Arg_4 {O(n)}
(4: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_0: 1/2*(1+Arg_2+Arg_3)+3*(2+2*Arg_2+2*Arg_3)+3/2*(4/3+4/3*Arg_2+4/3*Arg_3)+4/3+4/3*Arg_2+Arg_0+4/3*Arg_3 {O(n)}
(4: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_1: 1 {O(1)}
(4: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_2: 1+2*Arg_2+5*(4/3+4/3*Arg_2+4/3*Arg_3)+Arg_3+6*(2+2*Arg_2+2*Arg_3) {O(n)}
(4: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_3: Arg_3 {O(n)}
(4: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_4: Arg_4 {O(n)}
(5: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_0: 1/2*(1+Arg_2+Arg_3)+3*(2+2*Arg_2+2*Arg_3)+3/2*(4/3+4/3*Arg_2+4/3*Arg_3)+4/3+4/3*Arg_2+Arg_0+4/3*Arg_3 {O(n)}
(5: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_1: 1/2*(1+Arg_2+Arg_3)+3*(2+2*Arg_2+2*Arg_3)+Arg_1+5/2*(4/3+4/3*Arg_2+4/3*Arg_3) {O(n)}
(5: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_2: 1+2*Arg_2+5*(4/3+4/3*Arg_2+4/3*Arg_3)+Arg_3+6*(2+2*Arg_2+2*Arg_3) {O(n)}
(5: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_3: Arg_3 {O(n)}
(5: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_4: Arg_4 {O(n)}
(6: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_0: 1/2*(1+Arg_2+Arg_3)+3*(2+2*Arg_2+2*Arg_3)+3/2*(4/3+4/3*Arg_2+4/3*Arg_3)+4/3+4/3*Arg_2+Arg_0+4/3*Arg_3 {O(n)}
(6: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_1: 1/2*(1+Arg_2+Arg_3)+3*(2+2*Arg_2+2*Arg_3)+Arg_1+5/2*(4/3+4/3*Arg_2+4/3*Arg_3) {O(n)}
(6: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_2: 1+2*Arg_2+5*(4/3+4/3*Arg_2+4/3*Arg_3)+Arg_3+6*(2+2*Arg_2+2*Arg_3) {O(n)}
(6: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_3: Arg_3 {O(n)}
(6: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_4: Arg_4 {O(n)}
(7: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_0: 1/2*(1+Arg_2+Arg_3)+3*(2+2*Arg_2+2*Arg_3)+3/2*(4/3+4/3*Arg_2+4/3*Arg_3)+4/3+4/3*Arg_2+Arg_0+4/3*Arg_3 {O(n)}
(7: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_1: 1 {O(1)}
(7: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_2: 1+2*Arg_2+5*(4/3+4/3*Arg_2+4/3*Arg_3)+Arg_3+6*(2+2*Arg_2+2*Arg_3) {O(n)}
(7: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_3: Arg_3 {O(n)}
(7: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_4: Arg_4 {O(n)}
(8: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_0: 1 {O(1)}
(8: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_1: 1/2*(1+Arg_2+Arg_3)+3*(2+2*Arg_2+2*Arg_3)+Arg_1+5/2*(4/3+4/3*Arg_2+4/3*Arg_3) {O(n)}
(8: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_2: 1+2*Arg_2+5*(4/3+4/3*Arg_2+4/3*Arg_3)+Arg_3+6*(2+2*Arg_2+2*Arg_3) {O(n)}
(8: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_3: Arg_3 {O(n)}
(8: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_4: Arg_4 {O(n)}
(9: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_0: 1 {O(1)}
(9: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_1: 1/2*(1+Arg_2+Arg_3)+3*(2+2*Arg_2+2*Arg_3)+Arg_1+5/2*(4/3+4/3*Arg_2+4/3*Arg_3) {O(n)}
(9: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_2: 1+2*Arg_2+5*(4/3+4/3*Arg_2+4/3*Arg_3)+Arg_3+6*(2+2*Arg_2+2*Arg_3) {O(n)}
(9: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_3: Arg_3 {O(n)}
(9: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_4: Arg_4 {O(n)}
(10: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_0: 1 {O(1)}
(10: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_1: 1 {O(1)}
(10: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_2: 1+2*Arg_2+5*(4/3+4/3*Arg_2+4/3*Arg_3)+Arg_3+6*(2+2*Arg_2+2*Arg_3) {O(n)}
(10: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_3: Arg_3 {O(n)}
(10: h->[1/4:g; 1/4:g; 1/4:g; 1/4:g], g), Arg_4: Arg_4 {O(n)}