Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: F, G
Locations: f0, f12, f25, f36
Transitions:
t₄: f0(X₀, X₁, X₂, X₃, X₄) → f12(0, X₁, X₂, F, G)
t₀: f12(X₀, X₁, X₂, X₃, X₄) → f12(1+X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 9
t₃: f12(X₀, X₁, X₂, X₃, X₄) → f25(X₀, 0, F, X₃, X₄) :|: 10 ≤ X₀
t₁: f25(X₀, X₁, X₂, X₃, X₄) → f25(X₀, 1+X₁, X₂, X₃, X₄) :|: X₁ ≤ 9
t₂: f25(X₀, X₁, X₂, X₃, X₄) → f36(X₀, X₁, X₂, X₃, X₄) :|: 10 ≤ X₁

Preprocessing

Eliminate variables [F; G; X₂; X₃; X₄] that do not contribute to the problem

Found invariant X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ 10 ≤ X₁ ∧ 20 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ for location f36

Found invariant X₀ ≤ 10 ∧ 0 ≤ X₀ for location f12

Found invariant X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ for location f25

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f0, f12, f25, f36
Transitions:
t₁₁: f0(X₀, X₁) → f12(0, X₁)
t₁₂: f12(X₀, X₁) → f12(1+X₀, X₁) :|: X₀ ≤ 9 ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
t₁₃: f12(X₀, X₁) → f25(X₀, 0) :|: 10 ≤ X₀ ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
t₁₄: f25(X₀, X₁) → f25(X₀, 1+X₁) :|: X₁ ≤ 9 ∧ X₀+X₁ ≤ 20 ∧ X₀ ≤ 10 ∧ X₀ ≤ 10+X₁ ∧ X₁ ≤ 10 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁
t₁₅: f25(X₀, X₁) → f36(X₀, X₁) :|: 10 ≤ X₁ ∧ X₀+X₁ ≤ 20 ∧ X₀ ≤ 10 ∧ X₀ ≤ 10+X₁ ∧ X₁ ≤ 10 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁

MPRF for transition t₁₂: f12(X₀, X₁) → f12(1+X₀, X₁) :|: X₀ ≤ 9 ∧ X₀ ≤ 10 ∧ 0 ≤ X₀ of depth 1:

new bound:

11 {O(1)}

MPRF:

• f12: [11-X₀]

MPRF for transition t₁₄: f25(X₀, X₁) → f25(X₀, 1+X₁) :|: X₁ ≤ 9 ∧ X₀+X₁ ≤ 20 ∧ X₀ ≤ 10 ∧ X₀ ≤ 10+X₁ ∧ X₁ ≤ 10 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ of depth 1:

new bound:

11 {O(1)}

MPRF:

• f25: [1+X₀-X₁]

All Bounds

Timebounds

Overall timebound:25 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: 11 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 11 {O(1)}
t₁₅: 1 {O(1)}

Costbounds

Overall costbound: 25 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: 11 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 11 {O(1)}
t₁₅: 1 {O(1)}

Sizebounds

t₁₁, X₀: 0 {O(1)}
t₁₁, X₁: X₁ {O(n)}
t₁₂, X₀: 10 {O(1)}
t₁₂, X₁: X₁ {O(n)}
t₁₃, X₀: 10 {O(1)}
t₁₃, X₁: 0 {O(1)}
t₁₄, X₀: 10 {O(1)}
t₁₄, X₁: 10 {O(1)}
t₁₅, X₀: 10 {O(1)}
t₁₅, X₁: 10 {O(1)}