Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: F
Locations: f0, f10, f20, f22, f25
Transitions:
t₅: f0(X₀, X₁, X₂, X₃, X₄) → f10(8, F, 0, X₃, 8) :|: 1 ≤ F
t₀: f10(X₀, X₁, X₂, X₃, X₄) → f10(X₀-1, X₁-1, 1+X₂, F, X₄) :|: 1 ≤ F ∧ 1 ≤ X₀
t₁: f10(X₀, X₁, X₂, X₃, X₄) → f10(X₀-1, X₁, X₂, F, X₄) :|: 1 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ F ≤ 0
t₄: f10(X₀, X₁, X₂, X₃, X₄) → f20(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0
t₂: f20(X₀, X₁, X₂, X₃, X₄) → f20(X₀, X₁, X₂, X₃, X₄)
t₃: f22(X₀, X₁, X₂, X₃, X₄) → f25(X₀, X₁, X₂, X₃, X₄)

Preprocessing

Cut unreachable locations [f22; f25] from the program graph

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

Found invariant 0 ≤ 7+X₁ ∧ 0 ≤ 7+X₀+X₁ ∧ X₀ ≤ 7+X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location f20

Found invariant 0 ≤ 7+X₁ ∧ 0 ≤ 7+X₀+X₁ ∧ X₀ ≤ 7+X₁ ∧ X₀ ≤ 8 ∧ 0 ≤ X₀ for location f10

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁
Temp_Vars: F
Locations: f0, f10, f20
Transitions:
t₁₂: f0(X₀, X₁) → f10(8, F) :|: 1 ≤ F
t₁₃: f10(X₀, X₁) → f10(X₀-1, X₁-1) :|: 1 ≤ F ∧ 1 ≤ X₀ ∧ X₀ ≤ 8 ∧ 0 ≤ 7+X₀+X₁ ∧ X₀ ≤ 7+X₁ ∧ 0 ≤ 7+X₁ ∧ 0 ≤ X₀
t₁₄: f10(X₀, X₁) → f10(X₀-1, X₁) :|: 1 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ F ≤ 0 ∧ X₀ ≤ 8 ∧ 0 ≤ 7+X₀+X₁ ∧ X₀ ≤ 7+X₁ ∧ 0 ≤ 7+X₁ ∧ 0 ≤ X₀
t₁₅: f10(X₀, X₁) → f20(X₀, X₁) :|: X₀ ≤ 0 ∧ X₀ ≤ 8 ∧ 0 ≤ 7+X₀+X₁ ∧ X₀ ≤ 7+X₁ ∧ 0 ≤ 7+X₁ ∧ 0 ≤ X₀
t₁₆: f20(X₀, X₁) → f20(X₀, X₁) :|: 0 ≤ 7+X₀+X₁ ∧ X₀ ≤ 7+X₁ ∧ 0 ≤ 7+X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0

MPRF for transition t₁₃: f10(X₀, X₁) → f10(X₀-1, X₁-1) :|: 1 ≤ F ∧ 1 ≤ X₀ ∧ X₀ ≤ 8 ∧ 0 ≤ 7+X₀+X₁ ∧ X₀ ≤ 7+X₁ ∧ 0 ≤ 7+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

9 {O(1)}

MPRF:

• f10: [1+X₀]

MPRF for transition t₁₄: f10(X₀, X₁) → f10(X₀-1, X₁) :|: 1 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ F ≤ 0 ∧ X₀ ≤ 8 ∧ 0 ≤ 7+X₀+X₁ ∧ X₀ ≤ 7+X₁ ∧ 0 ≤ 7+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

9 {O(1)}

MPRF:

• f10: [1+X₀]

Found invariant 0 ≤ 7+X₁ ∧ 0 ≤ 7+X₀+X₁ ∧ X₀ ≤ 7+X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location f20

Found invariant 0 ≤ 7+X₁ ∧ 0 ≤ 7+X₀+X₁ ∧ X₀ ≤ 7+X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location f20_v1

Found invariant 0 ≤ 7+X₁ ∧ 0 ≤ 7+X₀+X₁ ∧ X₀ ≤ 7+X₁ ∧ X₀ ≤ 8 ∧ 0 ≤ X₀ for location f10

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₂: 1 {O(1)}
t₁₃: 9 {O(1)}
t₁₄: 9 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₁₂: 1 {O(1)}
t₁₃: 9 {O(1)}
t₁₄: 9 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: inf {Infinity}

Sizebounds

t₁₂, X₀: 8 {O(1)}
t₁₃, X₀: 7 {O(1)}
t₁₄, X₀: 7 {O(1)}
t₁₄, X₁: 7 {O(1)}
t₁₅, X₀: 0 {O(1)}
t₁₆, X₀: 0 {O(1)}