KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 3 ≤ X₂+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2 ≤ X₀ for location eval_foo_bb5_in

Found invariant X₀ ≤ X₅ ∧ X₀ ≤ 1 for location eval_foo_stop

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₀ for location eval_foo_bb3_in

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 3 ≤ X₂+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2 ≤ X₀ for location eval_foo_3

Found invariant 2 ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 2 ≤ X₀ for location eval_foo_bb2_in

Found invariant X₀ ≤ X₅ for location eval_foo_bb1_in

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₀ for location eval_foo_.critedge_in

Found invariant X₀ ≤ X₅ ∧ X₀ ≤ 1 for location eval_foo_bb6_in

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 3 ≤ X₂+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2 ≤ X₀ for location eval_foo_4

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 3 ≤ X₂+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2 ≤ X₀ for location eval_foo_bb4_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: nondef.0
Locations: eval_foo_.critedge_in, eval_foo_3, eval_foo_4, eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_bb4_in, eval_foo_bb5_in, eval_foo_bb6_in, eval_foo_start, eval_foo_stop
Transitions:
t₁₄: eval_foo_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb1_in(X₃-1, 1+X₂-X₃, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₀ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₃+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅
t₉: eval_foo_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_4(X₀, X₁, X₂, X₃, nondef.0, X₅, X₆) :|: X₀ ≤ 1+X₂ ∧ X₀ ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₀ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₃+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂
t₁₂: eval_foo_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 ≤ X₄ ∧ X₄ ≤ 0 ∧ X₀ ≤ 1+X₂ ∧ X₀ ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₀ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₃+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂
t₁₀: eval_foo_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₄ ≤ 0 ∧ X₀ ≤ 1+X₂ ∧ X₀ ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₀ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₃+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂
t₁₁: eval_foo_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₄ ∧ X₀ ≤ 1+X₂ ∧ X₀ ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₀ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₃+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂
t₁: eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb1_in(X₅, X₆, X₂, X₃, X₄, X₅, X₆)
t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 2 ≤ X₀ ∧ X₀ ≤ X₅
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 1 ∧ X₀ ≤ X₅
t₄: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb3_in(X₀, X₁, X₀+X₁-1, X₀-1, X₄, X₅, X₆) :|: 2 ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅
t₆: eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₀ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₃+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅
t₅: eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ X₂ ∧ X₀ ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₀ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₃+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅
t₇: eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 1+X₂ ∧ X₀ ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₀ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₃+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂
t₁₃: eval_foo_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb3_in(X₀, X₁, X₂-1, X₃, X₄, X₅, X₆) :|: X₀ ≤ 1+X₂ ∧ X₀ ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₀ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₃+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂
t₁₅: eval_foo_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 1 ∧ X₀ ≤ X₅
t₀: eval_foo_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆)

MPRF for transition t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 2 ≤ X₀ ∧ X₀ ≤ X₅ of depth 1:

new bound:

X₅+2 {O(n)}

MPRF:

• eval_foo_.critedge_in: [1+X₃]
• eval_foo_3: [1+X₃]
• eval_foo_4: [X₀]
• eval_foo_bb1_in: [2+X₀]
• eval_foo_bb2_in: [X₀]
• eval_foo_bb3_in: [1+X₃]
• eval_foo_bb4_in: [1+X₃]
• eval_foo_bb5_in: [X₀]

MPRF for transition t₄: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb3_in(X₀, X₁, X₀+X₁-1, X₀-1, X₄, X₅, X₆) :|: 2 ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

• eval_foo_.critedge_in: [X₃]
• eval_foo_3: [X₃]
• eval_foo_4: [X₃]
• eval_foo_bb1_in: [X₀]
• eval_foo_bb2_in: [X₀]
• eval_foo_bb3_in: [X₃]
• eval_foo_bb4_in: [X₃]
• eval_foo_bb5_in: [X₀-1]

MPRF for transition t₅: eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ X₂ ∧ X₀ ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₀ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₃+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ of depth 1:

new bound:

X₅+X₆+1 {O(n)}

MPRF:

• eval_foo_.critedge_in: [X₂-1]
• eval_foo_3: [X₂-1]
• eval_foo_4: [X₂-1]
• eval_foo_bb1_in: [X₀+X₁-1]
• eval_foo_bb2_in: [X₀+X₁-1]
• eval_foo_bb3_in: [X₂]
• eval_foo_bb4_in: [X₂-1]
• eval_foo_bb5_in: [X₂-1]

MPRF for transition t₆: eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₀ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₃+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ of depth 1:

new bound:

X₅+1 {O(n)}

MPRF:

• eval_foo_.critedge_in: [X₃-2]
• eval_foo_3: [X₃]
• eval_foo_4: [X₃]
• eval_foo_bb1_in: [X₀-1]
• eval_foo_bb2_in: [X₀-1]
• eval_foo_bb3_in: [X₃]
• eval_foo_bb4_in: [X₃]
• eval_foo_bb5_in: [X₃]

MPRF for transition t₇: eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 1+X₂ ∧ X₀ ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₀ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₃+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ of depth 1:

new bound:

X₅+X₆+1 {O(n)}

MPRF:

MPRF for transition t₉: eval_foo_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_4(X₀, X₁, X₂, X₃, nondef.0, X₅, X₆) :|: X₀ ≤ 1+X₂ ∧ X₀ ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₀ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₃+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ of depth 1:

new bound:

X₅+X₆ {O(n)}

MPRF:

• eval_foo_.critedge_in: [X₂]
• eval_foo_3: [1+X₂]
• eval_foo_4: [X₂]
• eval_foo_bb1_in: [X₀+X₁]
• eval_foo_bb2_in: [X₀+X₁]
• eval_foo_bb3_in: [1+X₂]
• eval_foo_bb4_in: [1+X₂]
• eval_foo_bb5_in: [X₂]

MPRF for transition t₁₀: eval_foo_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₄ ≤ 0 ∧ X₀ ≤ 1+X₂ ∧ X₀ ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₀ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₃+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ of depth 1:

new bound:

2⋅X₆+X₅+1 {O(n)}

MPRF:

• eval_foo_.critedge_in: [2+2⋅X₂-X₃]
• eval_foo_3: [2+2⋅X₂-X₃]
• eval_foo_4: [3+2⋅X₂-X₀]
• eval_foo_bb1_in: [1+X₀+2⋅X₁]
• eval_foo_bb2_in: [1+X₀+2⋅X₁]
• eval_foo_bb3_in: [2+2⋅X₂-X₃]
• eval_foo_bb4_in: [3+2⋅X₂-X₀]
• eval_foo_bb5_in: [1+2⋅X₂-X₀]

MPRF for transition t₁₁: eval_foo_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₄ ∧ X₀ ≤ 1+X₂ ∧ X₀ ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₀ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₃+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ of depth 1:

new bound:

X₅+X₆+1 {O(n)}

MPRF:

• eval_foo_.critedge_in: [1+X₂]
• eval_foo_3: [2+X₂]
• eval_foo_4: [2+X₂]
• eval_foo_bb1_in: [1+X₀+X₁]
• eval_foo_bb2_in: [1+X₀+X₁]
• eval_foo_bb3_in: [2+X₂]
• eval_foo_bb4_in: [2+X₂]
• eval_foo_bb5_in: [1+X₂]

MPRF for transition t₁₂: eval_foo_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 ≤ X₄ ∧ X₄ ≤ 0 ∧ X₀ ≤ 1+X₂ ∧ X₀ ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₀ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₃+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ of depth 1:

new bound:

X₅+1 {O(n)}

MPRF:

• eval_foo_.critedge_in: [X₀]
• eval_foo_3: [1+X₀]
• eval_foo_4: [1+X₀]
• eval_foo_bb1_in: [1+X₀]
• eval_foo_bb2_in: [1+X₀]
• eval_foo_bb3_in: [1+X₀]
• eval_foo_bb4_in: [2⋅X₀-X₃]
• eval_foo_bb5_in: [2+X₃]

MPRF for transition t₁₃: eval_foo_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb3_in(X₀, X₁, X₂-1, X₃, X₄, X₅, X₆) :|: X₀ ≤ 1+X₂ ∧ X₀ ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₀ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₃+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ of depth 1:

new bound:

X₅+X₆ {O(n)}

MPRF:

• eval_foo_.critedge_in: [X₂]
• eval_foo_3: [X₂]
• eval_foo_4: [X₂]
• eval_foo_bb1_in: [X₀+X₁]
• eval_foo_bb2_in: [X₀+X₁]
• eval_foo_bb3_in: [X₂]
• eval_foo_bb4_in: [X₂]
• eval_foo_bb5_in: [X₂]

MPRF for transition t₁₄: eval_foo_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb1_in(X₃-1, 1+X₂-X₃, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₀ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₃+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ of depth 1:

new bound:

X₅+1 {O(n)}

MPRF:

• eval_foo_.critedge_in: [1+X₃]
• eval_foo_3: [X₀]
• eval_foo_4: [X₀]
• eval_foo_bb1_in: [1+X₀]
• eval_foo_bb2_in: [X₀]
• eval_foo_bb3_in: [X₀]
• eval_foo_bb4_in: [X₀]
• eval_foo_bb5_in: [X₀]

All Bounds

Timebounds

Overall timebound:11⋅X₅+7⋅X₆+13 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₅+2 {O(n)}
t₃: 1 {O(1)}
t₄: X₅ {O(n)}
t₅: X₅+X₆+1 {O(n)}
t₆: X₅+1 {O(n)}
t₇: X₅+X₆+1 {O(n)}
t₉: X₅+X₆ {O(n)}
t₁₀: 2⋅X₆+X₅+1 {O(n)}
t₁₁: X₅+X₆+1 {O(n)}
t₁₂: X₅+1 {O(n)}
t₁₃: X₅+X₆ {O(n)}
t₁₄: X₅+1 {O(n)}
t₁₅: 1 {O(1)}

Costbounds

Overall costbound: 11⋅X₅+7⋅X₆+13 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₅+2 {O(n)}
t₃: 1 {O(1)}
t₄: X₅ {O(n)}
t₅: X₅+X₆+1 {O(n)}
t₆: X₅+1 {O(n)}
t₇: X₅+X₆+1 {O(n)}
t₉: X₅+X₆ {O(n)}
t₁₀: 2⋅X₆+X₅+1 {O(n)}
t₁₁: X₅+X₆+1 {O(n)}
t₁₂: X₅+1 {O(n)}
t₁₃: X₅+X₆ {O(n)}
t₁₄: X₅+1 {O(n)}
t₁₅: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₀, X₅: X₅ {O(n)}
t₀, X₆: X₆ {O(n)}
t₁, X₀: X₅ {O(n)}
t₁, X₁: X₆ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₁, X₆: X₆ {O(n)}
t₂, X₀: X₅ {O(n)}
t₂, X₁: 4⋅X₅⋅X₅+7⋅X₅+X₆ {O(n^2)}
t₂, X₂: 8⋅X₅⋅X₅+14⋅X₅+2⋅X₆+X₂ {O(n^2)}
t₂, X₃: 3⋅X₅+X₃ {O(n)}
t₂, X₅: X₅ {O(n)}
t₂, X₆: X₆ {O(n)}
t₃, X₀: 2⋅X₅ {O(n)}
t₃, X₁: 4⋅X₅⋅X₅+2⋅X₆+7⋅X₅ {O(n^2)}
t₃, X₂: 8⋅X₅⋅X₅+14⋅X₅+2⋅X₆+X₂ {O(n^2)}
t₃, X₃: 3⋅X₅+X₃ {O(n)}
t₃, X₅: 2⋅X₅ {O(n)}
t₃, X₆: 2⋅X₆ {O(n)}
t₄, X₀: X₅ {O(n)}
t₄, X₁: 4⋅X₅⋅X₅+7⋅X₅+X₆ {O(n^2)}
t₄, X₂: 4⋅X₅⋅X₅+7⋅X₅+X₆ {O(n^2)}
t₄, X₃: X₅ {O(n)}
t₄, X₅: X₅ {O(n)}
t₄, X₆: X₆ {O(n)}
t₅, X₀: X₅ {O(n)}
t₅, X₁: 4⋅X₅⋅X₅+7⋅X₅+X₆ {O(n^2)}
t₅, X₂: 4⋅X₅⋅X₅+7⋅X₅+X₆ {O(n^2)}
t₅, X₃: X₅ {O(n)}
t₅, X₅: X₅ {O(n)}
t₅, X₆: X₆ {O(n)}
t₆, X₀: X₅ {O(n)}
t₆, X₁: 8⋅X₅⋅X₅+14⋅X₅+2⋅X₆ {O(n^2)}
t₆, X₂: 4⋅X₅⋅X₅+7⋅X₅+X₆ {O(n^2)}
t₆, X₃: 2⋅X₅ {O(n)}
t₆, X₅: X₅ {O(n)}
t₆, X₆: X₆ {O(n)}
t₇, X₀: X₅ {O(n)}
t₇, X₁: 4⋅X₅⋅X₅+7⋅X₅+X₆ {O(n^2)}
t₇, X₂: 4⋅X₅⋅X₅+7⋅X₅+X₆ {O(n^2)}
t₇, X₃: X₅ {O(n)}
t₇, X₅: X₅ {O(n)}
t₇, X₆: X₆ {O(n)}
t₉, X₀: X₅ {O(n)}
t₉, X₁: 4⋅X₅⋅X₅+7⋅X₅+X₆ {O(n^2)}
t₉, X₂: 4⋅X₅⋅X₅+7⋅X₅+X₆ {O(n^2)}
t₉, X₃: X₅ {O(n)}
t₉, X₅: X₅ {O(n)}
t₉, X₆: X₆ {O(n)}
t₁₀, X₀: X₅ {O(n)}
t₁₀, X₁: 4⋅X₅⋅X₅+7⋅X₅+X₆ {O(n^2)}
t₁₀, X₂: 4⋅X₅⋅X₅+7⋅X₅+X₆ {O(n^2)}
t₁₀, X₃: X₅ {O(n)}
t₁₀, X₅: X₅ {O(n)}
t₁₀, X₆: X₆ {O(n)}
t₁₁, X₀: X₅ {O(n)}
t₁₁, X₁: 4⋅X₅⋅X₅+7⋅X₅+X₆ {O(n^2)}
t₁₁, X₂: 4⋅X₅⋅X₅+7⋅X₅+X₆ {O(n^2)}
t₁₁, X₃: X₅ {O(n)}
t₁₁, X₅: X₅ {O(n)}
t₁₁, X₆: X₆ {O(n)}
t₁₂, X₀: X₅ {O(n)}
t₁₂, X₁: 4⋅X₅⋅X₅+7⋅X₅+X₆ {O(n^2)}
t₁₂, X₂: 4⋅X₅⋅X₅+7⋅X₅+X₆ {O(n^2)}
t₁₂, X₃: X₅ {O(n)}
t₁₂, X₄: 0 {O(1)}
t₁₂, X₅: X₅ {O(n)}
t₁₂, X₆: X₆ {O(n)}
t₁₃, X₀: X₅ {O(n)}
t₁₃, X₁: 4⋅X₅⋅X₅+7⋅X₅+X₆ {O(n^2)}
t₁₃, X₂: 4⋅X₅⋅X₅+7⋅X₅+X₆ {O(n^2)}
t₁₃, X₃: X₅ {O(n)}
t₁₃, X₅: X₅ {O(n)}
t₁₃, X₆: X₆ {O(n)}
t₁₄, X₀: X₅ {O(n)}
t₁₄, X₁: 4⋅X₅⋅X₅+7⋅X₅+X₆ {O(n^2)}
t₁₄, X₂: 8⋅X₅⋅X₅+14⋅X₅+2⋅X₆ {O(n^2)}
t₁₄, X₃: 3⋅X₅ {O(n)}
t₁₄, X₅: X₅ {O(n)}
t₁₄, X₆: X₆ {O(n)}
t₁₅, X₀: 2⋅X₅ {O(n)}
t₁₅, X₁: 4⋅X₅⋅X₅+2⋅X₆+7⋅X₅ {O(n^2)}
t₁₅, X₂: 8⋅X₅⋅X₅+14⋅X₅+2⋅X₆+X₂ {O(n^2)}
t₁₅, X₃: 3⋅X₅+X₃ {O(n)}
t₁₅, X₅: 2⋅X₅ {O(n)}
t₁₅, X₆: 2⋅X₆ {O(n)}