Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, 0, X₂) :|: 128 ≤ X₀
t₁: l0(X₀, X₁, X₂) → l2(X₀, 0, D) :|: X₀ ≤ 127
t₃: l2(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: 36 ≤ X₁
t₂: l2(X₀, X₁, X₂) → l2(X₀, X₁+1, X₂+1) :|: X₁ ≤ 35

Preprocessing

Eliminate variables {D,X₂} that do not contribute to the problem

Found invariant X₁ ≤ 36 ∧ X₀+X₁ ≤ 163 ∧ 0 ≤ X₁ ∧ X₀ ≤ 127+X₁ ∧ X₀ ≤ 127 for location l2

Found invariant X₁ ≤ 36 ∧ 0 ≤ X₁ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₇: l0(X₀, X₁) → l1(X₀, 0) :|: 128 ≤ X₀
t₈: l0(X₀, X₁) → l2(X₀, 0) :|: X₀ ≤ 127
t₉: l2(X₀, X₁) → l1(X₀, X₁) :|: 36 ≤ X₁ ∧ X₁ ≤ 36 ∧ X₀+X₁ ≤ 163 ∧ 0 ≤ X₁ ∧ X₀ ≤ 127+X₁ ∧ X₀ ≤ 127
t₁₀: l2(X₀, X₁) → l2(X₀, X₁+1) :|: X₁ ≤ 35 ∧ X₁ ≤ 36 ∧ X₀+X₁ ≤ 163 ∧ 0 ≤ X₁ ∧ X₀ ≤ 127+X₁ ∧ X₀ ≤ 127

MPRF for transition t₁₀: l2(X₀, X₁) → l2(X₀, X₁+1) :|: X₁ ≤ 35 ∧ X₁ ≤ 36 ∧ X₀+X₁ ≤ 163 ∧ 0 ≤ X₁ ∧ X₀ ≤ 127+X₁ ∧ X₀ ≤ 127 of depth 1:

new bound:

36 {O(1)}

All Bounds

Timebounds

Overall timebound:39 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 36 {O(1)}

Costbounds

Overall costbound: 39 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 36 {O(1)}

Sizebounds

t₇, X₀: X₀ {O(n)}
t₇, X₁: 0 {O(1)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: 0 {O(1)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: 36 {O(1)}
t₁₀, X₀: X₀ {O(n)}
t₁₀, X₁: 36 {O(1)}