Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₃: l0(X₀, X₁) → l1(X₀, X₁)
t₂: l1(X₀, X₁) → l1(X₀, X₁-X₀) :|: X₀+1 ≤ X₁ ∧ 1 ≤ X₀
t₀: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ 0
t₁: l1(X₀, X₁) → l2(X₀, X₁) :|: X₁ ≤ X₀

Preprocessing

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₃: l0(X₀, X₁) → l1(X₀, X₁)
t₂: l1(X₀, X₁) → l1(X₀, X₁-X₀) :|: X₀+1 ≤ X₁ ∧ 1 ≤ X₀
t₀: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ 0
t₁: l1(X₀, X₁) → l2(X₀, X₁) :|: X₁ ≤ X₀

MPRF for transition t₂: l1(X₀, X₁) → l1(X₀, X₁-X₀) :|: X₀+1 ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀+X₁ {O(n)}

All Bounds

Timebounds

Overall timebound:X₀+X₁+3 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀+X₁ {O(n)}
t₃: 1 {O(1)}

Costbounds

Overall costbound: X₀+X₁+3 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀+X₁ {O(n)}
t₃: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₀: 2⋅X₀ {O(n)}
t₁, X₁: 2⋅X₁ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}