Initial Problem

Start: evalfstart
Program_Vars: X₀, X₁
Temp_Vars:
Locations: evalfbb1in, evalfbbin, evalfentryin, evalfreturnin, evalfstart, evalfstop
Transitions:
t₂: evalfbb1in(X₀, X₁) → evalfbbin(X₀, X₁) :|: X₁ ≤ X₀
t₃: evalfbb1in(X₀, X₁) → evalfreturnin(X₀, X₁) :|: 1+X₀ ≤ X₁
t₄: evalfbbin(X₀, X₁) → evalfbb1in(X₀, 1+X₁)
t₁: evalfentryin(X₀, X₁) → evalfbb1in(X₁, X₀)
t₅: evalfreturnin(X₀, X₁) → evalfstop(X₀, X₁)
t₀: evalfstart(X₀, X₁) → evalfentryin(X₀, X₁)

Preprocessing

Found invariant 1+X₀ ≤ X₁ for location evalfreturnin

Found invariant X₁ ≤ X₀ for location evalfbbin

Found invariant 1+X₀ ≤ X₁ for location evalfstop

Problem after Preprocessing

Start: evalfstart
Program_Vars: X₀, X₁
Temp_Vars:
Locations: evalfbb1in, evalfbbin, evalfentryin, evalfreturnin, evalfstart, evalfstop
Transitions:
t₂: evalfbb1in(X₀, X₁) → evalfbbin(X₀, X₁) :|: X₁ ≤ X₀
t₃: evalfbb1in(X₀, X₁) → evalfreturnin(X₀, X₁) :|: 1+X₀ ≤ X₁
t₄: evalfbbin(X₀, X₁) → evalfbb1in(X₀, 1+X₁) :|: X₁ ≤ X₀
t₁: evalfentryin(X₀, X₁) → evalfbb1in(X₁, X₀)
t₅: evalfreturnin(X₀, X₁) → evalfstop(X₀, X₁) :|: 1+X₀ ≤ X₁
t₀: evalfstart(X₀, X₁) → evalfentryin(X₀, X₁)

MPRF for transition t₂: evalfbb1in(X₀, X₁) → evalfbbin(X₀, X₁) :|: X₁ ≤ X₀ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

• evalfbb1in: [1+X₀-X₁]
• evalfbbin: [X₀-X₁]

MPRF for transition t₄: evalfbbin(X₀, X₁) → evalfbb1in(X₀, 1+X₁) :|: X₁ ≤ X₀ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

• evalfbb1in: [1+X₀-X₁]
• evalfbbin: [1+X₀-X₁]

All Bounds

Timebounds

Overall timebound:2⋅X₀+2⋅X₁+6 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀+X₁+1 {O(n)}
t₃: 1 {O(1)}
t₄: X₀+X₁+1 {O(n)}
t₅: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₀+2⋅X₁+6 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀+X₁+1 {O(n)}
t₃: 1 {O(1)}
t₄: X₀+X₁+1 {O(n)}
t₅: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₀ {O(n)}
t₂, X₀: X₁ {O(n)}
t₂, X₁: 2⋅X₀+X₁+1 {O(n)}
t₃, X₀: 2⋅X₁ {O(n)}
t₃, X₁: 3⋅X₀+X₁+1 {O(n)}
t₄, X₀: X₁ {O(n)}
t₄, X₁: 2⋅X₀+X₁+1 {O(n)}
t₅, X₀: 2⋅X₁ {O(n)}
t₅, X₁: 3⋅X₀+X₁+1 {O(n)}