Initial Problem

Start: eval_non_linear01_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: eval_non_linear01_bb0_in, eval_non_linear01_bb1_in, eval_non_linear01_bb2_in, eval_non_linear01_bb3_in, eval_non_linear01_start, eval_non_linear01_stop
Transitions:
t₁: eval_non_linear01_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear01_bb1_in(X₅, X₆, X₂, X₃, X₄, X₅, X₆)
t₂: eval_non_linear01_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear01_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₀ ≤ 0 ∧ 1+(X₀)² ≤ X₁+(X₄)⁵
t₃: eval_non_linear01_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear01_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₀ ∧ 1+(X₀)² ≤ X₁+(X₄)⁵
t₄: eval_non_linear01_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear01_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₁+(X₄)⁵ ≤ (X₀)²
t₅: eval_non_linear01_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear01_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 ≤ X₀ ∧ X₀ ≤ 0
t₆: eval_non_linear01_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear01_bb1_in(-2⋅X₀, 3⋅X₁+(X₄)², X₂, X₃, X₄, X₅, X₆)
t₇: eval_non_linear01_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear01_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₀: eval_non_linear01_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_non_linear01_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆)

Preprocessing

Eliminate variables [X₂; X₃] that do not contribute to the problem

Problem after Preprocessing

Start: eval_non_linear01_start
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: eval_non_linear01_bb0_in, eval_non_linear01_bb1_in, eval_non_linear01_bb2_in, eval_non_linear01_bb3_in, eval_non_linear01_start, eval_non_linear01_stop
Transitions:
t₁₅: eval_non_linear01_bb0_in(X₀, X₁, X₂, X₃, X₄) → eval_non_linear01_bb1_in(X₃, X₄, X₂, X₃, X₄)
t₁₆: eval_non_linear01_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_non_linear01_bb2_in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ 0 ∧ 1+(X₀)² ≤ X₁+(X₂)⁵
t₁₇: eval_non_linear01_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_non_linear01_bb2_in(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₀ ∧ 1+(X₀)² ≤ X₁+(X₂)⁵
t₁₈: eval_non_linear01_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_non_linear01_bb3_in(X₀, X₁, X₂, X₃, X₄) :|: X₁+(X₂)⁵ ≤ (X₀)²
t₁₉: eval_non_linear01_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_non_linear01_bb3_in(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₀ ∧ X₀ ≤ 0
t₂₀: eval_non_linear01_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_non_linear01_bb1_in(-2⋅X₀, 3⋅X₁+(X₂)², X₂, X₃, X₄)
t₂₁: eval_non_linear01_bb3_in(X₀, X₁, X₂, X₃, X₄) → eval_non_linear01_stop(X₀, X₁, X₂, X₃, X₄)
t₂₂: eval_non_linear01_start(X₀, X₁, X₂, X₃, X₄) → eval_non_linear01_bb0_in(X₀, X₁, X₂, X₃, X₄)

TWN: t₁₆: eval_non_linear01_bb1_in→eval_non_linear01_bb2_in

Show Graph

Termination: true
Formula:

TWN - Lifting for [16: eval_non_linear01_bb1_in->eval_non_linear01_bb2_in; 17: eval_non_linear01_bb1_in->eval_non_linear01_bb2_in; 20: eval_non_linear01_bb2_in->eval_non_linear01_bb1_in] of 16⋅X₂⋅X₂⋅X₂⋅X₂⋅X₂+16⋅X₂⋅X₂+32⋅X₁+13 {O(n^5)}

Found invariant X₃ ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀ for location eval_non_linear01_bb2_in_v1

Found invariant X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ for location eval_non_linear01_bb1_in

Found invariant 2+X₃ ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₀ for location eval_non_linear01_bb1_in_v1

Found invariant 1+X₀+X₃ ≤ 0 ∧ X₀ ≤ X₃ ∧ 1+X₀ ≤ 0 for location eval_non_linear01_bb2_in_v2

Found invariant 1+X₀+X₃ ≤ 0 ∧ 2+X₀ ≤ X₃ ∧ 2+X₀ ≤ 0 for location eval_non_linear01_bb1_in_v2

All Bounds

Timebounds

Overall timebound:48⋅X₂⋅X₂⋅X₂⋅X₂⋅X₂+48⋅X₂⋅X₂+96⋅X₄+44 {O(n^5)}
t₁₅: 1 {O(1)}
t₁₆: 16⋅X₂⋅X₂⋅X₂⋅X₂⋅X₂+16⋅X₂⋅X₂+32⋅X₄+13 {O(n^5)}
t₁₇: 16⋅X₂⋅X₂⋅X₂⋅X₂⋅X₂+16⋅X₂⋅X₂+32⋅X₄+13 {O(n^5)}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}
t₂₀: 16⋅X₂⋅X₂⋅X₂⋅X₂⋅X₂+16⋅X₂⋅X₂+32⋅X₄+13 {O(n^5)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}

Costbounds

Overall costbound: 48⋅X₂⋅X₂⋅X₂⋅X₂⋅X₂+48⋅X₂⋅X₂+96⋅X₄+44 {O(n^5)}
t₁₅: 1 {O(1)}
t₁₆: 16⋅X₂⋅X₂⋅X₂⋅X₂⋅X₂+16⋅X₂⋅X₂+32⋅X₄+13 {O(n^5)}
t₁₇: 16⋅X₂⋅X₂⋅X₂⋅X₂⋅X₂+16⋅X₂⋅X₂+32⋅X₄+13 {O(n^5)}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}
t₂₀: 16⋅X₂⋅X₂⋅X₂⋅X₂⋅X₂+16⋅X₂⋅X₂+32⋅X₄+13 {O(n^5)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}

Sizebounds

t₁₅, X₀: X₃ {O(n)}
t₁₅, X₁: X₄ {O(n)}
t₁₅, X₂: X₂ {O(n)}
t₁₅, X₃: X₃ {O(n)}
t₁₅, X₄: X₄ {O(n)}
t₁₆, X₀: 2^(16⋅X₂⋅X₂)⋅2^(16⋅X₂⋅X₂⋅X₂⋅X₂⋅X₂)⋅2^(32⋅X₄)⋅8192⋅X₃ {O(EXP)}
t₁₆, X₁: 3^(48⋅X₂⋅X₂)⋅3^(48⋅X₂⋅X₂⋅X₂⋅X₂⋅X₂)⋅3^(96⋅X₄)⋅4052555153018976267⋅X₂⋅X₂+3^(48⋅X₂⋅X₂)⋅3^(48⋅X₂⋅X₂⋅X₂⋅X₂⋅X₂)⋅3^(96⋅X₄)⋅4052555153018976267⋅X₄+X₂⋅X₂ {O(EXP)}
t₁₆, X₂: X₂ {O(n)}
t₁₆, X₃: X₃ {O(n)}
t₁₆, X₄: X₄ {O(n)}
t₁₇, X₀: 2^(16⋅X₂⋅X₂)⋅2^(16⋅X₂⋅X₂⋅X₂⋅X₂⋅X₂)⋅2^(32⋅X₄)⋅8192⋅X₃ {O(EXP)}
t₁₇, X₁: 3^(48⋅X₂⋅X₂)⋅3^(48⋅X₂⋅X₂⋅X₂⋅X₂⋅X₂)⋅3^(96⋅X₄)⋅4052555153018976267⋅X₂⋅X₂+3^(48⋅X₂⋅X₂)⋅3^(48⋅X₂⋅X₂⋅X₂⋅X₂⋅X₂)⋅3^(96⋅X₄)⋅4052555153018976267⋅X₄+X₂⋅X₂ {O(EXP)}
t₁₇, X₂: X₂ {O(n)}
t₁₇, X₃: X₃ {O(n)}
t₁₇, X₄: X₄ {O(n)}
t₁₈, X₀: 2^(16⋅X₂⋅X₂)⋅2^(16⋅X₂⋅X₂⋅X₂⋅X₂⋅X₂)⋅2^(32⋅X₄)⋅8192⋅X₃+X₃ {O(EXP)}
t₁₈, X₁: 3^(48⋅X₂⋅X₂)⋅3^(48⋅X₂⋅X₂⋅X₂⋅X₂⋅X₂)⋅3^(96⋅X₄)⋅4052555153018976267⋅X₂⋅X₂+3^(48⋅X₂⋅X₂)⋅3^(48⋅X₂⋅X₂⋅X₂⋅X₂⋅X₂)⋅3^(96⋅X₄)⋅4052555153018976267⋅X₄+X₂⋅X₂+X₄ {O(EXP)}
t₁₈, X₂: 2⋅X₂ {O(n)}
t₁₈, X₃: 2⋅X₃ {O(n)}
t₁₈, X₄: 2⋅X₄ {O(n)}
t₁₉, X₀: 0 {O(1)}
t₁₉, X₁: 3^(48⋅X₂⋅X₂)⋅3^(48⋅X₂⋅X₂⋅X₂⋅X₂⋅X₂)⋅3^(96⋅X₄)⋅4052555153018976267⋅X₂⋅X₂+3^(48⋅X₂⋅X₂)⋅3^(48⋅X₂⋅X₂⋅X₂⋅X₂⋅X₂)⋅3^(96⋅X₄)⋅4052555153018976267⋅X₄+X₂⋅X₂+X₄ {O(EXP)}
t₁₉, X₂: 2⋅X₂ {O(n)}
t₁₉, X₃: 2⋅X₃ {O(n)}
t₁₉, X₄: 2⋅X₄ {O(n)}
t₂₀, X₀: 2^(16⋅X₂⋅X₂)⋅2^(16⋅X₂⋅X₂⋅X₂⋅X₂⋅X₂)⋅2^(32⋅X₄)⋅8192⋅X₃ {O(EXP)}
t₂₀, X₁: 3^(48⋅X₂⋅X₂)⋅3^(48⋅X₂⋅X₂⋅X₂⋅X₂⋅X₂)⋅3^(96⋅X₄)⋅4052555153018976267⋅X₂⋅X₂+3^(48⋅X₂⋅X₂)⋅3^(48⋅X₂⋅X₂⋅X₂⋅X₂⋅X₂)⋅3^(96⋅X₄)⋅4052555153018976267⋅X₄+X₂⋅X₂ {O(EXP)}
t₂₀, X₂: X₂ {O(n)}
t₂₀, X₃: X₃ {O(n)}
t₂₀, X₄: X₄ {O(n)}
t₂₁, X₀: 2^(16⋅X₂⋅X₂)⋅2^(16⋅X₂⋅X₂⋅X₂⋅X₂⋅X₂)⋅2^(32⋅X₄)⋅8192⋅X₃+X₃ {O(EXP)}
t₂₁, X₁: 3^(48⋅X₂⋅X₂)⋅3^(48⋅X₂⋅X₂⋅X₂⋅X₂⋅X₂)⋅3^(96⋅X₄)⋅8105110306037952534⋅X₂⋅X₂+3^(48⋅X₂⋅X₂)⋅3^(48⋅X₂⋅X₂⋅X₂⋅X₂⋅X₂)⋅3^(96⋅X₄)⋅8105110306037952534⋅X₄+2⋅X₂⋅X₂+2⋅X₄ {O(EXP)}
t₂₁, X₂: 4⋅X₂ {O(n)}
t₂₁, X₃: 4⋅X₃ {O(n)}
t₂₁, X₄: 4⋅X₄ {O(n)}
t₂₂, X₀: X₀ {O(n)}
t₂₂, X₁: X₁ {O(n)}
t₂₂, X₂: X₂ {O(n)}
t₂₂, X₃: X₃ {O(n)}
t₂₂, X₄: X₄ {O(n)}