Initial Problem

Start: eval_ndecr_start
Program_Vars: X₀, X₁
Temp_Vars:
Locations: eval_ndecr_bb0_in, eval_ndecr_bb1_in, eval_ndecr_bb2_in, eval_ndecr_bb3_in, eval_ndecr_start, eval_ndecr_stop
Transitions:
t₁: eval_ndecr_bb0_in(X₀, X₁) → eval_ndecr_bb1_in(X₁-1, X₁)
t₂: eval_ndecr_bb1_in(X₀, X₁) → eval_ndecr_bb2_in(X₀, X₁) :|: 2 ≤ X₀
t₃: eval_ndecr_bb1_in(X₀, X₁) → eval_ndecr_bb3_in(X₀, X₁) :|: X₀ ≤ 1
t₄: eval_ndecr_bb2_in(X₀, X₁) → eval_ndecr_bb1_in(X₀-1, X₁)
t₅: eval_ndecr_bb3_in(X₀, X₁) → eval_ndecr_stop(X₀, X₁)
t₀: eval_ndecr_start(X₀, X₁) → eval_ndecr_bb0_in(X₀, X₁)

Preprocessing

Found invariant 1+X₀ ≤ X₁ for location eval_ndecr_bb1_in

Found invariant 1+X₀ ≤ X₁ ∧ X₀ ≤ 1 for location eval_ndecr_bb3_in

Found invariant 1+X₀ ≤ X₁ ∧ X₀ ≤ 1 for location eval_ndecr_stop

Found invariant 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location eval_ndecr_bb2_in

Problem after Preprocessing

Start: eval_ndecr_start
Program_Vars: X₀, X₁
Temp_Vars:
Locations: eval_ndecr_bb0_in, eval_ndecr_bb1_in, eval_ndecr_bb2_in, eval_ndecr_bb3_in, eval_ndecr_start, eval_ndecr_stop
Transitions:
t₁: eval_ndecr_bb0_in(X₀, X₁) → eval_ndecr_bb1_in(X₁-1, X₁)
t₂: eval_ndecr_bb1_in(X₀, X₁) → eval_ndecr_bb2_in(X₀, X₁) :|: 2 ≤ X₀ ∧ 1+X₀ ≤ X₁
t₃: eval_ndecr_bb1_in(X₀, X₁) → eval_ndecr_bb3_in(X₀, X₁) :|: X₀ ≤ 1 ∧ 1+X₀ ≤ X₁
t₄: eval_ndecr_bb2_in(X₀, X₁) → eval_ndecr_bb1_in(X₀-1, X₁) :|: 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁
t₅: eval_ndecr_bb3_in(X₀, X₁) → eval_ndecr_stop(X₀, X₁) :|: X₀ ≤ 1 ∧ 1+X₀ ≤ X₁
t₀: eval_ndecr_start(X₀, X₁) → eval_ndecr_bb0_in(X₀, X₁)

MPRF for transition t₂: eval_ndecr_bb1_in(X₀, X₁) → eval_ndecr_bb2_in(X₀, X₁) :|: 2 ≤ X₀ ∧ 1+X₀ ≤ X₁ of depth 1:

new bound:

X₁+2 {O(n)}

• eval_ndecr_bb1_in: [X₀-1]
• eval_ndecr_bb2_in: [X₀-2]

MPRF for transition t₄: eval_ndecr_bb2_in(X₀, X₁) → eval_ndecr_bb1_in(X₀-1, X₁) :|: 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ of depth 1:

new bound:

X₁+2 {O(n)}

• eval_ndecr_bb1_in: [X₀-1]
• eval_ndecr_bb2_in: [X₀-1]

All Bounds

Timebounds

Overall timebound:2⋅X₁+8 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁+2 {O(n)}
t₃: 1 {O(1)}
t₄: X₁+2 {O(n)}
t₅: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₁+8 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁+2 {O(n)}
t₃: 1 {O(1)}
t₄: X₁+2 {O(n)}
t₅: 1 {O(1)}

Sizebounds

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