Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: f0, f17, f24, f9
Transitions:
t₀: f0(X₀, X₁, X₂) → f9(0, D, 0)
t₂: f17(X₀, X₁, X₂) → f17(1+X₀, X₁, X₂) :|: X₀ ≤ 49
t₃: f17(X₀, X₁, X₂) → f24(X₀, X₁, X₂) :|: 50 ≤ X₀
t₄: f9(X₀, X₁, X₂) → f17(0, X₁, X₂) :|: 50 ≤ X₂
t₁: f9(X₀, X₁, X₂) → f9(X₀, X₁, 1+X₂) :|: X₂ ≤ 49

Preprocessing

Eliminate variables [D; X₁] that do not contribute to the problem

Found invariant X₁ ≤ 50 ∧ X₁ ≤ 50+X₀ ∧ X₀+X₁ ≤ 100 ∧ 50 ≤ X₁ ∧ 50 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 50 ∧ 0 ≤ X₀ for location f17

Found invariant X₁ ≤ 50 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 100 ∧ 50 ≤ X₁ ∧ 100 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 50 ∧ 50 ≤ X₀ for location f24

Found invariant X₁ ≤ 50 ∧ X₁ ≤ 50+X₀ ∧ X₀+X₁ ≤ 50 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location f9

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f0, f17, f24, f9
Transitions:
t₁₁: f0(X₀, X₁) → f9(0, 0)
t₁₂: f17(X₀, X₁) → f17(1+X₀, X₁) :|: X₀ ≤ 49 ∧ X₀+X₁ ≤ 100 ∧ X₁ ≤ 50+X₀ ∧ X₀ ≤ 50 ∧ X₁ ≤ 50 ∧ 50 ≤ X₀+X₁ ∧ 50 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₁
t₁₃: f17(X₀, X₁) → f24(X₀, X₁) :|: 50 ≤ X₀ ∧ X₀+X₁ ≤ 100 ∧ X₁ ≤ 50+X₀ ∧ X₀ ≤ 50 ∧ X₁ ≤ 50 ∧ 50 ≤ X₀+X₁ ∧ 50 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₁
t₁₄: f9(X₀, X₁) → f17(0, X₁) :|: 50 ≤ X₁ ∧ X₁ ≤ 50+X₀ ∧ X₀+X₁ ≤ 50 ∧ X₁ ≤ 50 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁
t₁₅: f9(X₀, X₁) → f9(X₀, 1+X₁) :|: X₁ ≤ 49 ∧ X₁ ≤ 50+X₀ ∧ X₀+X₁ ≤ 50 ∧ X₁ ≤ 50 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁

MPRF for transition t₁₅: f9(X₀, X₁) → f9(X₀, 1+X₁) :|: X₁ ≤ 49 ∧ X₁ ≤ 50+X₀ ∧ X₀+X₁ ≤ 50 ∧ X₁ ≤ 50 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

50 {O(1)}

• f9: [50-X₁]

MPRF for transition t₁₂: f17(X₀, X₁) → f17(1+X₀, X₁) :|: X₀ ≤ 49 ∧ X₀+X₁ ≤ 100 ∧ X₁ ≤ 50+X₀ ∧ X₀ ≤ 50 ∧ X₁ ≤ 50 ∧ 50 ≤ X₀+X₁ ∧ 50 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₁ of depth 1:

new bound:

51 {O(1)}

• f17: [1+X₁-X₀]

All Bounds

Timebounds

Overall timebound:104 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: 51 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 50 {O(1)}

Costbounds

Overall costbound: 104 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: 51 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 50 {O(1)}

Sizebounds

t₁₁, X₀: 0 {O(1)}
t₁₁, X₁: 0 {O(1)}
t₁₂, X₀: 50 {O(1)}
t₁₂, X₁: 50 {O(1)}
t₁₃, X₀: 50 {O(1)}
t₁₃, X₁: 50 {O(1)}
t₁₄, X₀: 0 {O(1)}
t₁₄, X₁: 50 {O(1)}
t₁₅, X₀: 0 {O(1)}
t₁₅, X₁: 50 {O(1)}