Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D, E, F
Locations: f0, f15, f18, f28
Transitions:
t₀: f0(X₀, X₁, X₂) → f15(2, X₁, X₂)
t₁: f15(X₀, X₁, X₂) → f18(X₀, X₀, X₂) :|: X₀ ≤ 10
t₄: f15(X₀, X₁, X₂) → f28(X₀, X₁, X₂) :|: 11 ≤ X₀
t₃: f18(X₀, X₁, X₂) → f15(1+X₀, X₁, X₂)
t₂: f18(X₀, X₁, X₂) → f18(X₀, X₁-1, F) :|: 1+E ≤ D

Preprocessing

Eliminate variables [F; X₁; X₂] that do not contribute to the problem

Found invariant 2 ≤ X₀ for location f18

Found invariant 2 ≤ X₀ for location f15

Found invariant 11 ≤ X₀ for location f28

Problem after Preprocessing

Start: f0
Program_Vars: X₀
Temp_Vars: D, E
Locations: f0, f15, f18, f28
Transitions:
t₁₀: f0(X₀) → f15(2)
t₁₁: f15(X₀) → f18(X₀) :|: X₀ ≤ 10 ∧ 2 ≤ X₀
t₁₂: f15(X₀) → f28(X₀) :|: 11 ≤ X₀ ∧ 2 ≤ X₀
t₁₃: f18(X₀) → f15(1+X₀) :|: 2 ≤ X₀
t₁₄: f18(X₀) → f18(X₀) :|: 1+E ≤ D ∧ 2 ≤ X₀

MPRF for transition t₁₁: f15(X₀) → f18(X₀) :|: X₀ ≤ 10 ∧ 2 ≤ X₀ of depth 1:

new bound:

13 {O(1)}

• f15: [11-X₀]
• f18: [10-X₀]

MPRF for transition t₁₃: f18(X₀) → f15(1+X₀) :|: 2 ≤ X₀ of depth 1:

new bound:

13 {O(1)}

• f15: [0]
• f18: [1]

Found invariant X₀ ≤ 10 ∧ 2 ≤ X₀ for location f18

Found invariant X₀ ≤ 10 ∧ 2 ≤ X₀ for location f18_v1

Found invariant 2 ≤ X₀ for location f15

Found invariant 11 ≤ X₀ for location f28

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₀: 1 {O(1)}
t₁₁: 13 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 13 {O(1)}
t₁₄: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₁₀: 1 {O(1)}
t₁₁: 13 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 13 {O(1)}
t₁₄: inf {Infinity}

Sizebounds

t₁₀, X₀: 2 {O(1)}
t₁₁, X₀: 10 {O(1)}
t₁₂, X₀: 22 {O(1)}
t₁₃, X₀: 22 {O(1)}
t₁₄, X₀: 10 {O(1)}