Initial Problem

Start: f0
Program_Vars: X₀, X₁
Temp_Vars: C
Locations: f0, f14, f6
Transitions:
t₀: f0(X₀, X₁) → f6(0, C)
t₂: f6(X₀, X₁) → f14(X₀, X₁) :|: 50 ≤ X₀
t₁: f6(X₀, X₁) → f6(1+X₀, X₁) :|: X₀ ≤ 49

Preprocessing

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

Found invariant X₀ ≤ 50 ∧ 50 ≤ X₀ for location f14

Found invariant X₀ ≤ 50 ∧ 0 ≤ X₀ for location f6

Problem after Preprocessing

Start: f0
Program_Vars: X₀
Temp_Vars:
Locations: f0, f14, f6
Transitions:
t₆: f0(X₀) → f6(0)
t₇: f6(X₀) → f14(X₀) :|: 50 ≤ X₀ ∧ X₀ ≤ 50 ∧ 0 ≤ X₀
t₈: f6(X₀) → f6(1+X₀) :|: X₀ ≤ 49 ∧ X₀ ≤ 50 ∧ 0 ≤ X₀

MPRF for transition t₈: f6(X₀) → f6(1+X₀) :|: X₀ ≤ 49 ∧ X₀ ≤ 50 ∧ 0 ≤ X₀ of depth 1:

new bound:

51 {O(1)}

• f6: [51-X₀]

All Bounds

Timebounds

Overall timebound:53 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 51 {O(1)}

Costbounds

Overall costbound: 53 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 51 {O(1)}

Sizebounds

t₆, X₀: 0 {O(1)}
t₇, X₀: 50 {O(1)}
t₈, X₀: 50 {O(1)}