Initial Problem

Start: evalndloopstart
Program_Vars: X₀
Temp_Vars: B
Locations: evalndloopbbin, evalndloopentryin, evalndloopreturnin, evalndloopstart, evalndloopstop
Transitions:
t₂: evalndloopbbin(X₀) → evalndloopbbin(B) :|: B ≤ 9 ∧ B ≤ 2+X₀ ∧ 1+X₀ ≤ B
t₃: evalndloopbbin(X₀) → evalndloopreturnin(X₀) :|: 3+X₀ ≤ B
t₄: evalndloopbbin(X₀) → evalndloopreturnin(X₀) :|: B ≤ X₀
t₅: evalndloopbbin(X₀) → evalndloopreturnin(X₀) :|: 10 ≤ B
t₁: evalndloopentryin(X₀) → evalndloopbbin(0)
t₆: evalndloopreturnin(X₀) → evalndloopstop(X₀)
t₀: evalndloopstart(X₀) → evalndloopentryin(X₀)

Preprocessing

Found invariant X₀ ≤ 9 ∧ 0 ≤ X₀ for location evalndloopreturnin

Found invariant X₀ ≤ 9 ∧ 0 ≤ X₀ for location evalndloopbbin

Found invariant X₀ ≤ 9 ∧ 0 ≤ X₀ for location evalndloopstop

Problem after Preprocessing

Start: evalndloopstart
Program_Vars: X₀
Temp_Vars: B
Locations: evalndloopbbin, evalndloopentryin, evalndloopreturnin, evalndloopstart, evalndloopstop
Transitions:
t₂: evalndloopbbin(X₀) → evalndloopbbin(B) :|: B ≤ 9 ∧ B ≤ 2+X₀ ∧ 1+X₀ ≤ B ∧ X₀ ≤ 9 ∧ 0 ≤ X₀
t₃: evalndloopbbin(X₀) → evalndloopreturnin(X₀) :|: 3+X₀ ≤ B ∧ X₀ ≤ 9 ∧ 0 ≤ X₀
t₄: evalndloopbbin(X₀) → evalndloopreturnin(X₀) :|: B ≤ X₀ ∧ X₀ ≤ 9 ∧ 0 ≤ X₀
t₅: evalndloopbbin(X₀) → evalndloopreturnin(X₀) :|: 10 ≤ B ∧ X₀ ≤ 9 ∧ 0 ≤ X₀
t₁: evalndloopentryin(X₀) → evalndloopbbin(0)
t₆: evalndloopreturnin(X₀) → evalndloopstop(X₀) :|: X₀ ≤ 9 ∧ 0 ≤ X₀
t₀: evalndloopstart(X₀) → evalndloopentryin(X₀)

MPRF for transition t₂: evalndloopbbin(X₀) → evalndloopbbin(B) :|: B ≤ 9 ∧ B ≤ 2+X₀ ∧ 1+X₀ ≤ B ∧ X₀ ≤ 9 ∧ 0 ≤ X₀ of depth 1:

new bound:

10 {O(1)}

• evalndloopbbin: [10-X₀]

All Bounds

Timebounds

Overall timebound:16 {O(1)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 10 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}

Costbounds

Overall costbound: 16 {O(1)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 10 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₁, X₀: 0 {O(1)}
t₂, X₀: 9 {O(1)}
t₃, X₀: 9 {O(1)}
t₄, X₀: 9 {O(1)}
t₅, X₀: 9 {O(1)}
t₆, X₀: 9 {O(1)}