Preprocessing

Found invariant 0 ≤ X₀ for location l1

Found invariant 1 ≤ X₀ for location l2

Probabilistic Analysis

Probabilistic Program after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
g₀:l0(X₀,X₁) → t₁:l1(1,X₁) :|:
g₂:l1(X₀,X₁) → t₃:l2(X₀,X₁) :|: 1 ≤ X₀ ∧ 0 ≤ X₀
g₄:l2(X₀,X₁) → t₅:l1(X₀-1,X₁-10) :|: 101 ≤ X₁ ∧ 1 ≤ X₀
g₆:l2(X₀,X₁) → t₇:l1(1+X₀,11+X₁) :|: X₁ ≤ 100 ∧ 1 ≤ X₀

Run classical analysis on SCC: [l0]

Classical Approximation after Lifting Classical Results

All Bounds
Timebounds

Overall timebound:inf {Infinity}
g₀: 1 {O(1)}
g₂: inf {Infinity}
g₄: inf {Infinity}
g₆: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₂: inf {Infinity}
g₄: inf {Infinity}
g₆: inf {Infinity}

Sizebounds

(g₀,l1), X₀: 1 {O(1)}
(g₀,l1), X₁: X₁ {O(n)}

Run probabilistic analysis on SCC: [l0]

Run classical analysis on SCC: [l1; l2]

MPRF for transition t₇: l2(X₀,X₁) → l1(1+X₀,11+X₁) :|: 1 ≤ X₀ ∧ X₁ ≤ 100 of depth 1:

new bound:

X₁+101 {O(n)}

MPRF:

• l1: [91+10⋅X₀-X₁]
• l2: [91+10⋅X₀-X₁]

MPRF for transition t₃: l1(X₀,X₁) → l2(X₀,X₁) :|: 0 ≤ X₀ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁⋅X₁+204⋅X₁+10405 {O(n^2)}

MPRF:

• l1: [1+X₀]
• l2: [X₀]

MPRF for transition t₅: l2(X₀,X₁) → l1(X₀-1,X₁-10) :|: 1 ≤ X₀ ∧ 101 ≤ X₁ of depth 1:

new bound:

X₁⋅X₁+203⋅X₁+10303 {O(n^2)}

MPRF:

• l1: [X₀]
• l2: [X₀]

Classical Approximation after Lifting Classical Results

All Bounds
Timebounds

Overall timebound:2⋅X₁⋅X₁+408⋅X₁+20810 {O(n^2)}
g₀: 1 {O(1)}
g₂: X₁⋅X₁+204⋅X₁+10405 {O(n^2)}
g₄: X₁⋅X₁+203⋅X₁+10303 {O(n^2)}
g₆: X₁+101 {O(n)}

Costbounds

Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₂: inf {Infinity}
g₄: inf {Infinity}
g₆: inf {Infinity}

Sizebounds

(g₀,l1), X₀: 1 {O(1)}
(g₀,l1), X₁: X₁ {O(n)}
(g₂,l2), X₀: X₁+102 {O(n)}
(g₂,l2), X₁: 12⋅X₁+1111 {O(n)}
(g₄,l1), X₀: X₁+102 {O(n)}
(g₄,l1), X₁: 12⋅X₁+1111 {O(n)}
(g₆,l1), X₀: X₁+102 {O(n)}
(g₆,l1), X₁: 12⋅X₁+1111 {O(n)}

Run probabilistic analysis on SCC: [l1; l2]

Analysing control-flow refined program

Run classical analysis on SCC: [l1]

Classical Approximation after Lifting Classical Results

All Bounds
Timebounds

Overall timebound:inf {Infinity}
g₀: 1 {O(1)}
g₉: 1 {O(1)}
g₁₁: 1 {O(1)}
g₁₃: 1 {O(1)}
g₁₅: inf {Infinity}
g₁₇: 1 {O(1)}
g₁₉: inf {Infinity}
g₂₁: inf {Infinity}
g₂₃: inf {Infinity}
g₂₅: inf {Infinity}
g₂₇: inf {Infinity}
g₂₉: inf {Infinity}
g₃₁: inf {Infinity}
g₃₃: inf {Infinity}
g₃₅: inf {Infinity}
g₃₇: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₉: inf {Infinity}
g₁₁: inf {Infinity}
g₁₃: inf {Infinity}
g₁₅: inf {Infinity}
g₁₇: inf {Infinity}
g₁₉: inf {Infinity}
g₂₁: inf {Infinity}
g₂₃: inf {Infinity}
g₂₅: inf {Infinity}
g₂₇: inf {Infinity}
g₂₉: inf {Infinity}
g₃₁: inf {Infinity}
g₃₃: inf {Infinity}
g₃₅: inf {Infinity}
g₃₇: inf {Infinity}

Sizebounds

(g₀,l1), X₀: 1 {O(1)}
(g₀,l1), X₁: X₁ {O(n)}
(g₉,l2_v1), X₀: 1 {O(1)}
(g₉,l2_v1), X₁: X₁ {O(n)}

Run probabilistic analysis on SCC: [l1]

Run classical analysis on SCC: [l2_v1]

Classical Approximation after Lifting Classical Results

All Bounds
Timebounds

Overall timebound:inf {Infinity}
g₀: 1 {O(1)}
g₉: 1 {O(1)}
g₁₁: 1 {O(1)}
g₁₃: 1 {O(1)}
g₁₅: inf {Infinity}
g₁₇: 1 {O(1)}
g₁₉: inf {Infinity}
g₂₁: inf {Infinity}
g₂₃: inf {Infinity}
g₂₅: inf {Infinity}
g₂₇: inf {Infinity}
g₂₉: inf {Infinity}
g₃₁: inf {Infinity}
g₃₃: inf {Infinity}
g₃₅: inf {Infinity}
g₃₇: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₉: inf {Infinity}
g₁₁: inf {Infinity}
g₁₃: inf {Infinity}
g₁₅: inf {Infinity}
g₁₇: inf {Infinity}
g₁₉: inf {Infinity}
g₂₁: inf {Infinity}
g₂₃: inf {Infinity}
g₂₅: inf {Infinity}
g₂₇: inf {Infinity}
g₂₉: inf {Infinity}
g₃₁: inf {Infinity}
g₃₃: inf {Infinity}
g₃₅: inf {Infinity}
g₃₇: inf {Infinity}

Sizebounds

(g₀,l1), X₀: 1 {O(1)}
(g₀,l1), X₁: X₁ {O(n)}
(g₉,l2_v1), X₀: 1 {O(1)}
(g₉,l2_v1), X₁: X₁ {O(n)}
(g₁₁,l1_v1), X₀: 1 {O(1)}
(g₁₁,l1_v1), X₁: X₁ {O(n)}
(g₁₃,l1_v2), X₀: 2 {O(1)}
(g₁₃,l1_v2), X₁: X₁+11 {O(n)}

Run probabilistic analysis on SCC: [l2_v1]

Run classical analysis on SCC: [l1_v1; l2_v5]

MPRF for transition t₃₂: l1_v1(X₀,X₁) → l2_v5(X₀,X₁) :|: 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀ of depth 1:

new bound:

2 {O(1)}

MPRF:

• l1_v1: [1+X₀]
• l2_v5: [X₀]

MPRF for transition t₃₄: l2_v5(X₀,X₁) → l1_v1(X₀-1,X₁-10) :|: 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ of depth 1:

new bound:

1 {O(1)}

MPRF:

• l1_v1: [X₀]
• l2_v5: [X₀]

Classical Approximation after Lifting Classical Results

All Bounds
Timebounds

Overall timebound:inf {Infinity}
g₀: 1 {O(1)}
g₉: 1 {O(1)}
g₁₁: 1 {O(1)}
g₁₃: 1 {O(1)}
g₁₅: inf {Infinity}
g₁₇: 1 {O(1)}
g₁₉: inf {Infinity}
g₂₁: inf {Infinity}
g₂₃: inf {Infinity}
g₂₅: inf {Infinity}
g₂₇: inf {Infinity}
g₂₉: inf {Infinity}
g₃₁: inf {Infinity}
g₃₃: 2 {O(1)}
g₃₅: 1 {O(1)}
g₃₇: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₉: inf {Infinity}
g₁₁: inf {Infinity}
g₁₃: inf {Infinity}
g₁₅: inf {Infinity}
g₁₇: inf {Infinity}
g₁₉: inf {Infinity}
g₂₁: inf {Infinity}
g₂₃: inf {Infinity}
g₂₅: inf {Infinity}
g₂₇: inf {Infinity}
g₂₉: inf {Infinity}
g₃₁: inf {Infinity}
g₃₃: inf {Infinity}
g₃₅: inf {Infinity}
g₃₇: inf {Infinity}

Sizebounds

(g₀,l1), X₀: 1 {O(1)}
(g₀,l1), X₁: X₁ {O(n)}
(g₉,l2_v1), X₀: 1 {O(1)}
(g₉,l2_v1), X₁: X₁ {O(n)}
(g₁₁,l1_v1), X₀: 1 {O(1)}
(g₁₁,l1_v1), X₁: X₁ {O(n)}
(g₁₃,l1_v2), X₀: 2 {O(1)}
(g₁₃,l1_v2), X₁: X₁+11 {O(n)}
(g₃₃,l2_v5), X₀: 1 {O(1)}
(g₃₃,l2_v5), X₁: X₁ {O(n)}
(g₃₅,l1_v1), X₀: 1 {O(1)}
(g₃₅,l1_v1), X₁: X₁ {O(n)}
(g₃₇,l1_v5), X₀: 2 {O(1)}
(g₃₇,l1_v5), X₁: 111 {O(1)}

Run probabilistic analysis on SCC: [l1_v1; l2_v5]

Run classical analysis on SCC: [l1_v2; l2_v2]

MPRF for transition t₁₄: l1_v2(X₀,X₁) → l2_v2(X₀,X₁) :|: X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁+123 {O(n)}

MPRF:

• l1_v2: [112-X₁]
• l2_v2: [101-X₁]

MPRF for transition t₁₈: l2_v2(X₀,X₁) → l1_v2(1+X₀,11+X₁) :|: X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100 of depth 1:

new bound:

X₁+123 {O(n)}

MPRF:

• l1_v2: [112-X₁]
• l2_v2: [112-X₁]

Classical Approximation after Lifting Classical Results

All Bounds
Timebounds

Overall timebound:inf {Infinity}
g₀: 1 {O(1)}
g₉: 1 {O(1)}
g₁₁: 1 {O(1)}
g₁₃: 1 {O(1)}
g₁₅: X₁+123 {O(n)}
g₁₇: 1 {O(1)}
g₁₉: X₁+123 {O(n)}
g₂₁: inf {Infinity}
g₂₃: inf {Infinity}
g₂₅: inf {Infinity}
g₂₇: inf {Infinity}
g₂₉: inf {Infinity}
g₃₁: inf {Infinity}
g₃₃: 2 {O(1)}
g₃₅: 1 {O(1)}
g₃₇: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₉: inf {Infinity}
g₁₁: inf {Infinity}
g₁₃: inf {Infinity}
g₁₅: inf {Infinity}
g₁₇: inf {Infinity}
g₁₉: inf {Infinity}
g₂₁: inf {Infinity}
g₂₃: inf {Infinity}
g₂₅: inf {Infinity}
g₂₇: inf {Infinity}
g₂₉: inf {Infinity}
g₃₁: inf {Infinity}
g₃₃: inf {Infinity}
g₃₅: inf {Infinity}
g₃₇: inf {Infinity}

Sizebounds

(g₀,l1), X₀: 1 {O(1)}
(g₀,l1), X₁: X₁ {O(n)}
(g₉,l2_v1), X₀: 1 {O(1)}
(g₉,l2_v1), X₁: X₁ {O(n)}
(g₁₁,l1_v1), X₀: 1 {O(1)}
(g₁₁,l1_v1), X₁: X₁ {O(n)}
(g₁₃,l1_v2), X₀: 2 {O(1)}
(g₁₃,l1_v2), X₁: X₁+11 {O(n)}
(g₁₅,l2_v2), X₀: X₁+125 {O(n)}
(g₁₅,l2_v2), X₁: 12⋅X₁+1364 {O(n)}
(g₁₇,l1_v3), X₀: X₁+125 {O(n)}
(g₁₇,l1_v3), X₁: 101 {O(1)}
(g₁₉,l1_v2), X₀: X₁+125 {O(n)}
(g₁₉,l1_v2), X₁: 12⋅X₁+1364 {O(n)}
(g₃₃,l2_v5), X₀: 1 {O(1)}
(g₃₃,l2_v5), X₁: X₁ {O(n)}
(g₃₅,l1_v1), X₀: 1 {O(1)}
(g₃₅,l1_v1), X₁: X₁ {O(n)}
(g₃₇,l1_v5), X₀: 2 {O(1)}
(g₃₇,l1_v5), X₁: 111 {O(1)}

Run probabilistic analysis on SCC: [l1_v2; l2_v2]

Run classical analysis on SCC: [l1_v3; l1_v4; l1_v5; l2_v3; l2_v4]

MPRF for transition t₂₀: l1_v3(X₀,X₁) → l2_v3(X₀,X₁) :|: X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀ of depth 1:

new bound:

10⋅X₁+1686 {O(n)}

MPRF:

• l1_v3: [102+10⋅X₀-X₁]
• l1_v4: [101+10⋅X₀-X₁]
• l1_v5: [102+10⋅X₀-X₁]
• l2_v3: [101+10⋅X₀-X₁]
• l2_v4: [102+10⋅X₀-X₁]

MPRF for transition t₂₂: l2_v3(X₀,X₁) → l1_v4(X₀-1,X₁-10) :|: X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ of depth 1:

new bound:

X₁+128 {O(n)}

MPRF:

• l1_v3: [X₀]
• l1_v4: [X₀]
• l1_v5: [X₀-1]
• l2_v3: [X₀]
• l2_v4: [X₀-1]

MPRF for transition t₂₄: l2_v3(X₀,X₁) → l1_v5(1+X₀,11+X₁) :|: X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100 of depth 1:

new bound:

10⋅X₁+1664 {O(n)}

MPRF:

• l1_v3: [91+10⋅X₀-X₁]
• l1_v4: [91+10⋅X₀-X₁]
• l1_v5: [91+10⋅X₀-X₁]
• l2_v3: [91+10⋅X₀-X₁]
• l2_v4: [91+10⋅X₀-X₁]

MPRF for transition t₂₆: l1_v5(X₀,X₁) → l2_v4(X₀,X₁) :|: X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀ of depth 1:

new bound:

10⋅X₁+1665 {O(n)}

MPRF:

• l1_v3: [91+10⋅X₀-X₁]
• l1_v4: [91+10⋅X₀-X₁]
• l1_v5: [92+10⋅X₀-X₁]
• l2_v3: [91+10⋅X₀-X₁]
• l2_v4: [91+10⋅X₀-X₁]

MPRF for transition t₂₈: l2_v4(X₀,X₁) → l1_v3(X₀-1,X₁-10) :|: X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁ of depth 1:

new bound:

10⋅X₁+1685 {O(n)}

MPRF:

• l1_v3: [101+10⋅X₀-X₁]
• l1_v4: [101+10⋅X₀-X₁]
• l1_v5: [102+10⋅X₀-X₁]
• l2_v3: [101+10⋅X₀-X₁]
• l2_v4: [102+10⋅X₀-X₁]

MPRF for transition t₃₀: l1_v4(X₀,X₁) → l2_v3(X₀,X₁) :|: X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁+128 {O(n)}

MPRF:

• l1_v3: [X₀]
• l1_v4: [1+X₀]
• l1_v5: [X₀-1]
• l2_v3: [X₀]
• l2_v4: [X₀-1]

Classical Approximation after Lifting Classical Results

All Bounds
Timebounds

Overall timebound:44⋅X₁+7211 {O(n)}
g₀: 1 {O(1)}
g₉: 1 {O(1)}
g₁₁: 1 {O(1)}
g₁₃: 1 {O(1)}
g₁₅: X₁+123 {O(n)}
g₁₇: 1 {O(1)}
g₁₉: X₁+123 {O(n)}
g₂₁: 10⋅X₁+1686 {O(n)}
g₂₃: X₁+128 {O(n)}
g₂₅: 10⋅X₁+1664 {O(n)}
g₂₇: 10⋅X₁+1665 {O(n)}
g₂₉: 10⋅X₁+1685 {O(n)}
g₃₁: X₁+128 {O(n)}
g₃₃: 2 {O(1)}
g₃₅: 1 {O(1)}
g₃₇: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₉: inf {Infinity}
g₁₁: inf {Infinity}
g₁₃: inf {Infinity}
g₁₅: inf {Infinity}
g₁₇: inf {Infinity}
g₁₉: inf {Infinity}
g₂₁: inf {Infinity}
g₂₃: inf {Infinity}
g₂₅: inf {Infinity}
g₂₇: inf {Infinity}
g₂₉: inf {Infinity}
g₃₁: inf {Infinity}
g₃₃: inf {Infinity}
g₃₅: inf {Infinity}
g₃₇: inf {Infinity}

Sizebounds

(g₀,l1), X₀: 1 {O(1)}
(g₀,l1), X₁: X₁ {O(n)}
(g₉,l2_v1), X₀: 1 {O(1)}
(g₉,l2_v1), X₁: X₁ {O(n)}
(g₁₁,l1_v1), X₀: 1 {O(1)}
(g₁₁,l1_v1), X₁: X₁ {O(n)}
(g₁₃,l1_v2), X₀: 2 {O(1)}
(g₁₃,l1_v2), X₁: X₁+11 {O(n)}
(g₁₅,l2_v2), X₀: X₁+125 {O(n)}
(g₁₅,l2_v2), X₁: 12⋅X₁+1364 {O(n)}
(g₁₇,l1_v3), X₀: X₁+125 {O(n)}
(g₁₇,l1_v3), X₁: 101 {O(1)}
(g₁₉,l1_v2), X₀: X₁+125 {O(n)}
(g₁₉,l1_v2), X₁: 12⋅X₁+1364 {O(n)}
(g₂₁,l2_v3), X₀: 11⋅X₁+1791 {O(n)}
(g₂₁,l2_v3), X₁: 111 {O(1)}
(g₂₃,l1_v4), X₀: 11⋅X₁+1791 {O(n)}
(g₂₃,l1_v4), X₁: 101 {O(1)}
(g₂₅,l1_v5), X₀: 11⋅X₁+1791 {O(n)}
(g₂₅,l1_v5), X₁: 111 {O(1)}
(g₂₇,l2_v4), X₀: 11⋅X₁+1791 {O(n)}
(g₂₇,l2_v4), X₁: 111 {O(1)}
(g₂₉,l1_v3), X₀: 11⋅X₁+1791 {O(n)}
(g₂₉,l1_v3), X₁: 101 {O(1)}
(g₃₁,l2_v3), X₀: 11⋅X₁+1791 {O(n)}
(g₃₁,l2_v3), X₁: 111 {O(1)}
(g₃₃,l2_v5), X₀: 1 {O(1)}
(g₃₃,l2_v5), X₁: X₁ {O(n)}
(g₃₅,l1_v1), X₀: 1 {O(1)}
(g₃₅,l1_v1), X₁: X₁ {O(n)}
(g₃₇,l1_v5), X₀: 2 {O(1)}
(g₃₇,l1_v5), X₁: 111 {O(1)}

Run probabilistic analysis on SCC: [l1_v3; l1_v4; l1_v5; l2_v3; l2_v4]

CFR: Improvement to new bound with the following program:

method: PartialEvaluationProbabilistic new bound:

O(n)

cfr-program:

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l1_v1, l1_v2, l1_v3, l1_v4, l1_v5, l2_v1, l2_v2, l2_v3, l2_v4, l2_v5
Transitions:
g₀:l0(X₀,X₁) → t₁:l1(1,X₁) :|:
g₉:l1(X₀,X₁) → t₈:l2_v1(X₀,X₁) :|: 1 ≤ X₀ ∧ 0 ≤ X₀
g₁₁:l2_v1(X₀,X₁) → t₁₀:l1_v1(X₀-1,X₁-10) :|: 101 ≤ X₁ ∧ 1 ≤ X₀
g₁₃:l2_v1(X₀,X₁) → t₁₂:l1_v2(1+X₀,11+X₁) :|: X₁ ≤ 100 ∧ 1 ≤ X₀
g₁₅:l1_v2(X₀,X₁) → t₁₄:l2_v2(X₀,X₁) :|: 1 ≤ X₀ ∧ X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀
g₁₇:l2_v2(X₀,X₁) → t₁₆:l1_v3(X₀-1,X₁-10) :|: 101 ≤ X₁ ∧ X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀
g₁₉:l2_v2(X₀,X₁) → t₁₈:l1_v2(1+X₀,11+X₁) :|: X₁ ≤ 100 ∧ X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀
g₂₁:l1_v3(X₀,X₁) → t₂₀:l2_v3(X₀,X₁) :|: 1 ≤ X₀ ∧ X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀
g₂₃:l2_v3(X₀,X₁) → t₂₂:l1_v4(X₀-1,X₁-10) :|: 101 ≤ X₁ ∧ X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁
g₂₅:l2_v3(X₀,X₁) → t₂₄:l1_v5(1+X₀,11+X₁) :|: X₁ ≤ 100 ∧ X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁
g₂₇:l1_v5(X₀,X₁) → t₂₆:l2_v4(X₀,X₁) :|: 1 ≤ X₀ ∧ X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀
g₂₉:l2_v4(X₀,X₁) → t₂₈:l1_v3(X₀-1,X₁-10) :|: 101 ≤ X₁ ∧ X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀
g₃₁:l1_v4(X₀,X₁) → t₃₀:l2_v3(X₀,X₁) :|: 1 ≤ X₀ ∧ X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀
g₃₃:l1_v1(X₀,X₁) → t₃₂:l2_v5(X₀,X₁) :|: 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 0 ≤ X₀
g₃₅:l2_v5(X₀,X₁) → t₃₄:l1_v1(X₀-1,X₁-10) :|: 101 ≤ X₁ ∧ 1 ≤ X₀ ∧ 91 ≤ X₁
g₃₇:l2_v5(X₀,X₁) → t₃₆:l1_v5(1+X₀,11+X₁) :|: X₁ ≤ 100 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁

Results of Probabilistic Analysis

All Bounds

Timebounds

Overall timebound:44⋅X₁+7211 {O(n)}
g₀: 1 {O(1)}
g₉: 1 {O(1)}
g₁₁: 1 {O(1)}
g₁₃: 1 {O(1)}
g₁₅: X₁+123 {O(n)}
g₁₇: 1 {O(1)}
g₁₉: X₁+123 {O(n)}
g₂₁: 10⋅X₁+1686 {O(n)}
g₂₃: X₁+128 {O(n)}
g₂₅: 10⋅X₁+1664 {O(n)}
g₂₇: 10⋅X₁+1665 {O(n)}
g₂₉: 10⋅X₁+1685 {O(n)}
g₃₁: X₁+128 {O(n)}
g₃₃: 2 {O(1)}
g₃₅: 1 {O(1)}
g₃₇: 1 {O(1)}

Costbounds

Overall costbound: 44⋅X₁+7211 {O(n)}
g₀: 1 {O(1)}
g₉: 1 {O(1)}
g₁₁: 1 {O(1)}
g₁₃: 1 {O(1)}
g₁₅: X₁+123 {O(n)}
g₁₇: 1 {O(1)}
g₁₉: X₁+123 {O(n)}
g₂₁: 10⋅X₁+1686 {O(n)}
g₂₃: X₁+128 {O(n)}
g₂₅: 10⋅X₁+1664 {O(n)}
g₂₇: 10⋅X₁+1665 {O(n)}
g₂₉: 10⋅X₁+1685 {O(n)}
g₃₁: X₁+128 {O(n)}
g₃₃: 2 {O(1)}
g₃₅: 1 {O(1)}
g₃₇: 1 {O(1)}

Sizebounds

(g₀,l1), X₀: 1 {O(1)}
(g₀,l1), X₁: X₁ {O(n)}
(g₉,l2_v1), X₀: 1 {O(1)}
(g₉,l2_v1), X₁: X₁ {O(n)}
(g₁₁,l1_v1), X₀: 1 {O(1)}
(g₁₁,l1_v1), X₁: X₁ {O(n)}
(g₁₃,l1_v2), X₀: 2 {O(1)}
(g₁₃,l1_v2), X₁: X₁+11 {O(n)}
(g₁₅,l2_v2), X₀: X₁+125 {O(n)}
(g₁₅,l2_v2), X₁: 12⋅X₁+1364 {O(n)}
(g₁₇,l1_v3), X₀: X₁+125 {O(n)}
(g₁₇,l1_v3), X₁: 101 {O(1)}
(g₁₉,l1_v2), X₀: X₁+125 {O(n)}
(g₁₉,l1_v2), X₁: 12⋅X₁+1364 {O(n)}
(g₂₁,l2_v3), X₀: 11⋅X₁+1791 {O(n)}
(g₂₁,l2_v3), X₁: 111 {O(1)}
(g₂₃,l1_v4), X₀: 11⋅X₁+1791 {O(n)}
(g₂₃,l1_v4), X₁: 101 {O(1)}
(g₂₅,l1_v5), X₀: 11⋅X₁+1791 {O(n)}
(g₂₅,l1_v5), X₁: 111 {O(1)}
(g₂₇,l2_v4), X₀: 11⋅X₁+1791 {O(n)}
(g₂₇,l2_v4), X₁: 111 {O(1)}
(g₂₉,l1_v3), X₀: 11⋅X₁+1791 {O(n)}
(g₂₉,l1_v3), X₁: 101 {O(1)}
(g₃₁,l2_v3), X₀: 11⋅X₁+1791 {O(n)}
(g₃₁,l2_v3), X₁: 111 {O(1)}
(g₃₃,l2_v5), X₀: 1 {O(1)}
(g₃₃,l2_v5), X₁: X₁ {O(n)}
(g₃₅,l1_v1), X₀: 1 {O(1)}
(g₃₅,l1_v1), X₁: X₁ {O(n)}
(g₃₇,l1_v5), X₀: 2 {O(1)}
(g₃₇,l1_v5), X₁: 111 {O(1)}