KoAT2 Proof Output

Initial Problem

Start: eval_complex_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: eval_complex_bb0_in, eval_complex_bb1_in, eval_complex_bb2_in, eval_complex_bb3_in, eval_complex_bb4_in, eval_complex_bb5_in, eval_complex_start, eval_complex_stop
Transitions:
t₁: eval_complex_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_complex_bb1_in(X₄, X₅, X₂, X₃, X₄, X₅)
t₂: eval_complex_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_complex_bb2_in(X₀, X₁, X₀, X₁, X₄, X₅) :|: X₀ ≤ 29
t₃: eval_complex_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_complex_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 30 ≤ X₀
t₄: eval_complex_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_complex_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₃ ≤ X₂
t₅: eval_complex_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_complex_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ X₃
t₆: eval_complex_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_complex_bb2_in(X₀, X₁, 10+X₂, 7+X₃, X₄, X₅) :|: X₃ ≤ 5 ∧ 3 ≤ X₃ ∧ 6 ≤ X₃
t₇: eval_complex_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_complex_bb2_in(X₀, X₁, 1+X₂, 7+X₃, X₄, X₅) :|: X₃ ≤ 2 ∧ 6 ≤ X₃
t₈: eval_complex_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_complex_bb2_in(X₀, X₁, 1+X₂, 7+X₃, X₄, X₅) :|: 6 ≤ X₃
t₉: eval_complex_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_complex_bb2_in(X₀, X₁, 10+X₂, 2+X₃, X₄, X₅) :|: X₃ ≤ 10 ∧ X₃ ≤ 5 ∧ 8 ≤ X₃
t₁₀: eval_complex_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_complex_bb2_in(X₀, X₁, 1+X₂, 2+X₃, X₄, X₅) :|: X₃ ≤ 7 ∧ X₃ ≤ 5
t₁₁: eval_complex_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_complex_bb2_in(X₀, X₁, 1+X₂, 2+X₃, X₄, X₅) :|: X₃ ≤ 5 ∧ 11 ≤ X₃
t₁₂: eval_complex_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_complex_bb1_in(2+X₂, X₃-10, X₂, X₃, X₄, X₅)
t₁₃: eval_complex_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_complex_stop(X₀, X₁, X₂, X₃, X₄, X₅)
t₀: eval_complex_start(X₀, X₁, X₂, X₃, X₄, X₅) → eval_complex_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅)

Preprocessing

Cut unsatisfiable transition [t₆: eval_complex_bb3_in→eval_complex_bb2_in; t₇: eval_complex_bb3_in→eval_complex_bb2_in; t₉: eval_complex_bb3_in→eval_complex_bb2_in; t₁₁: eval_complex_bb3_in→eval_complex_bb2_in]

Found invariant X₄ ≤ X₀ for location eval_complex_bb1_in

Found invariant X₄ ≤ X₀ ∧ 30 ≤ X₀ for location eval_complex_bb5_in

Found invariant X₄ ≤ 29 ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₀ ∧ X₀+X₄ ≤ 58 ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 29 for location eval_complex_bb2_in

Found invariant X₄ ≤ 29 ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₀ ∧ X₀+X₄ ≤ 58 ∧ 1+X₃ ≤ X₂ ∧ X₁ ≤ X₃ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 29 for location eval_complex_bb3_in

Found invariant X₄ ≤ X₀ ∧ 30 ≤ X₀ for location eval_complex_stop

Found invariant X₄ ≤ 29 ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₀ ∧ X₀+X₄ ≤ 58 ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 29 for location eval_complex_bb4_in

Problem after Preprocessing

Start: eval_complex_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: eval_complex_bb0_in, eval_complex_bb1_in, eval_complex_bb2_in, eval_complex_bb3_in, eval_complex_bb4_in, eval_complex_bb5_in, eval_complex_start, eval_complex_stop
Transitions:
t₁: eval_complex_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_complex_bb1_in(X₄, X₅, X₂, X₃, X₄, X₅)
t₂: eval_complex_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_complex_bb2_in(X₀, X₁, X₀, X₁, X₄, X₅) :|: X₀ ≤ 29 ∧ X₄ ≤ X₀
t₃: eval_complex_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_complex_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 30 ≤ X₀ ∧ X₄ ≤ X₀
t₄: eval_complex_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_complex_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₃ ≤ X₂ ∧ X₀+X₄ ≤ 58 ∧ X₀ ≤ 29 ∧ X₄ ≤ 29 ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₄ ≤ X₂
t₅: eval_complex_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_complex_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ X₃ ∧ X₀+X₄ ≤ 58 ∧ X₀ ≤ 29 ∧ X₄ ≤ 29 ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₄ ≤ X₂
t₈: eval_complex_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_complex_bb2_in(X₀, X₁, 1+X₂, 7+X₃, X₄, X₅) :|: 6 ≤ X₃ ∧ X₀+X₄ ≤ 58 ∧ X₀ ≤ 29 ∧ X₄ ≤ 29 ∧ 1+X₁ ≤ X₂ ∧ 1+X₃ ≤ X₂ ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₄ ≤ X₂
t₁₀: eval_complex_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_complex_bb2_in(X₀, X₁, 1+X₂, 2+X₃, X₄, X₅) :|: X₃ ≤ 7 ∧ X₃ ≤ 5 ∧ X₀+X₄ ≤ 58 ∧ X₀ ≤ 29 ∧ X₄ ≤ 29 ∧ 1+X₁ ≤ X₂ ∧ 1+X₃ ≤ X₂ ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₄ ≤ X₂
t₁₂: eval_complex_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_complex_bb1_in(2+X₂, X₃-10, X₂, X₃, X₄, X₅) :|: X₀+X₄ ≤ 58 ∧ X₀ ≤ 29 ∧ X₄ ≤ 29 ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₄ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₄ ≤ X₃
t₁₃: eval_complex_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_complex_stop(X₀, X₁, X₂, X₃, X₄, X₅) :|: 30 ≤ X₀ ∧ X₄ ≤ X₀
t₀: eval_complex_start(X₀, X₁, X₂, X₃, X₄, X₅) → eval_complex_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅)

MPRF for transition t₂: eval_complex_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_complex_bb2_in(X₀, X₁, X₀, X₁, X₄, X₅) :|: X₀ ≤ 29 ∧ X₄ ≤ X₀ of depth 1:

new bound:

X₄+30 {O(n)}

MPRF:

• eval_complex_bb1_in: [30-X₀]
• eval_complex_bb2_in: [29-X₀]
• eval_complex_bb3_in: [29-X₀]
• eval_complex_bb4_in: [28-X₀]

MPRF for transition t₄: eval_complex_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_complex_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₃ ≤ X₂ ∧ X₀+X₄ ≤ 58 ∧ X₀ ≤ 29 ∧ X₄ ≤ 29 ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₄ ≤ X₂ of depth 1:

new bound:

5⋅X₄+X₅+174 {O(n)}

MPRF:

• eval_complex_bb1_in: [174-5⋅X₀-X₁]
• eval_complex_bb2_in: [174+X₂-6⋅X₀-X₃]
• eval_complex_bb3_in: [173+X₂-6⋅X₀-X₃]
• eval_complex_bb4_in: [174-5⋅X₂-X₃]

MPRF for transition t₅: eval_complex_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_complex_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ X₃ ∧ X₀+X₄ ≤ 58 ∧ X₀ ≤ 29 ∧ X₄ ≤ 29 ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₄ ≤ X₂ of depth 1:

new bound:

2⋅X₄+60 {O(n)}

MPRF:

• eval_complex_bb1_in: [60-X₀-X₄]
• eval_complex_bb2_in: [59-X₀-X₄]
• eval_complex_bb3_in: [59-X₀-X₄]
• eval_complex_bb4_in: [58-X₀-X₄]

MPRF for transition t₈: eval_complex_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_complex_bb2_in(X₀, X₁, 1+X₂, 7+X₃, X₄, X₅) :|: 6 ≤ X₃ ∧ X₀+X₄ ≤ 58 ∧ X₀ ≤ 29 ∧ X₄ ≤ 29 ∧ 1+X₁ ≤ X₂ ∧ 1+X₃ ≤ X₂ ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₄ ≤ X₂ of depth 1:

new bound:

5⋅X₄+X₅+175 {O(n)}

MPRF:

• eval_complex_bb1_in: [175-5⋅X₀-X₁]
• eval_complex_bb2_in: [175+X₂-6⋅X₀-X₃]
• eval_complex_bb3_in: [174+X₂-6⋅X₀-X₃]
• eval_complex_bb4_in: [175+X₂-6⋅X₀-X₃]

MPRF for transition t₁₀: eval_complex_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_complex_bb2_in(X₀, X₁, 1+X₂, 2+X₃, X₄, X₅) :|: X₃ ≤ 7 ∧ X₃ ≤ 5 ∧ X₀+X₄ ≤ 58 ∧ X₀ ≤ 29 ∧ X₄ ≤ 29 ∧ 1+X₁ ≤ X₂ ∧ 1+X₃ ≤ X₂ ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₄ ≤ X₂ of depth 1:

new bound:

10⋅X₄+2⋅X₅+326 {O(n)}

MPRF:

• eval_complex_bb1_in: [326-10⋅X₀-2⋅X₁]
• eval_complex_bb2_in: [326+X₂-11⋅X₀-X₁-X₃]
• eval_complex_bb3_in: [326+X₂-11⋅X₀-X₁-X₃]
• eval_complex_bb4_in: [326-X₁-10⋅X₂-X₃]

MPRF for transition t₁₂: eval_complex_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_complex_bb1_in(2+X₂, X₃-10, X₂, X₃, X₄, X₅) :|: X₀+X₄ ≤ 58 ∧ X₀ ≤ 29 ∧ X₄ ≤ 29 ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₄ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₄ ≤ X₃ of depth 1:

new bound:

X₄+31 {O(n)}

MPRF:

• eval_complex_bb1_in: [31-X₀]
• eval_complex_bb2_in: [31-X₀]
• eval_complex_bb3_in: [31-X₀]
• eval_complex_bb4_in: [30-X₀]

All Bounds

Timebounds

Overall timebound:24⋅X₄+4⋅X₅+800 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₄+30 {O(n)}
t₃: 1 {O(1)}
t₄: 5⋅X₄+X₅+174 {O(n)}
t₅: 2⋅X₄+60 {O(n)}
t₈: 5⋅X₄+X₅+175 {O(n)}
t₁₀: 10⋅X₄+2⋅X₅+326 {O(n)}
t₁₂: X₄+31 {O(n)}
t₁₃: 1 {O(1)}

Costbounds

Overall costbound: 24⋅X₄+4⋅X₅+800 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₄+30 {O(n)}
t₃: 1 {O(1)}
t₄: 5⋅X₄+X₅+174 {O(n)}
t₅: 2⋅X₄+60 {O(n)}
t₈: 5⋅X₄+X₅+175 {O(n)}
t₁₀: 10⋅X₄+2⋅X₅+326 {O(n)}
t₁₂: X₄+31 {O(n)}
t₁₃: 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)}
t₁, X₀: X₄ {O(n)}
t₁, X₁: X₅ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₂, X₀: 19⋅X₄+3⋅X₅+563 {O(n)}
t₂, X₁: 13⋅X₅+65⋅X₄+2187 {O(n)}
t₂, X₂: 18⋅X₄+3⋅X₅+563 {O(n)}
t₂, X₃: 12⋅X₅+65⋅X₄+2187 {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₃, X₀: 19⋅X₄+3⋅X₅+563 {O(n)}
t₃, X₁: 13⋅X₅+65⋅X₄+2187 {O(n)}
t₃, X₂: 18⋅X₄+3⋅X₅+X₂+563 {O(n)}
t₃, X₃: 12⋅X₅+65⋅X₄+X₃+2187 {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₃, X₅: 2⋅X₅ {O(n)}
t₄, X₀: 19⋅X₄+3⋅X₅+563 {O(n)}
t₄, X₁: 13⋅X₅+65⋅X₄+2187 {O(n)}
t₄, X₂: 18⋅X₄+3⋅X₅+563 {O(n)}
t₄, X₃: 12⋅X₅+65⋅X₄+2187 {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: X₅ {O(n)}
t₅, X₀: 57⋅X₄+9⋅X₅+1689 {O(n)}
t₅, X₁: 195⋅X₄+39⋅X₅+6561 {O(n)}
t₅, X₂: 18⋅X₄+3⋅X₅+563 {O(n)}
t₅, X₃: 12⋅X₅+65⋅X₄+2187 {O(n)}
t₅, X₄: X₄ {O(n)}
t₅, X₅: X₅ {O(n)}
t₈, X₀: 19⋅X₄+3⋅X₅+563 {O(n)}
t₈, X₁: 13⋅X₅+65⋅X₄+2187 {O(n)}
t₈, X₂: 18⋅X₄+3⋅X₅+563 {O(n)}
t₈, X₃: 12⋅X₅+65⋅X₄+2187 {O(n)}
t₈, X₄: X₄ {O(n)}
t₈, X₅: X₅ {O(n)}
t₁₀, X₀: 19⋅X₄+3⋅X₅+563 {O(n)}
t₁₀, X₁: 13⋅X₅+65⋅X₄+2187 {O(n)}
t₁₀, X₂: 18⋅X₄+3⋅X₅+563 {O(n)}
t₁₀, X₃: 12⋅X₅+65⋅X₄+2187 {O(n)}
t₁₀, X₄: X₄ {O(n)}
t₁₀, X₅: X₅ {O(n)}
t₁₂, X₀: 18⋅X₄+3⋅X₅+563 {O(n)}
t₁₂, X₁: 12⋅X₅+65⋅X₄+2187 {O(n)}
t₁₂, X₂: 18⋅X₄+3⋅X₅+563 {O(n)}
t₁₂, X₃: 12⋅X₅+65⋅X₄+2187 {O(n)}
t₁₂, X₄: X₄ {O(n)}
t₁₂, X₅: X₅ {O(n)}
t₁₃, X₀: 19⋅X₄+3⋅X₅+563 {O(n)}
t₁₃, X₁: 13⋅X₅+65⋅X₄+2187 {O(n)}
t₁₃, X₂: 18⋅X₄+3⋅X₅+X₂+563 {O(n)}
t₁₃, X₃: 12⋅X₅+65⋅X₄+X₃+2187 {O(n)}
t₁₃, X₄: 2⋅X₄ {O(n)}
t₁₃, X₅: 2⋅X₅ {O(n)}