WORST_CASE(?,O(1)) * Step 1: LocalSizeboundsProc WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A) -> f3(0) True (1,1) 1. f3(A) -> f3(1 + A) [9 >= A] (?,1) 2. f3(A) -> f11(A) [A >= 10 && 0 >= 1 + B] (?,1) 3. f3(A) -> f11(A) [A >= 10] (?,1) Signature: {(f0,1);(f11,1);(f3,1)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{},3->{}] + Applied Processor: LocalSizeboundsProc + Details: LocalSizebounds generated; rvgraph (<0,0,A>, 0, .= 0) (<1,0,A>, 1 + A, .+ 1) (<2,0,A>, A, .= 0) (<3,0,A>, A, .= 0) * Step 2: SizeboundsProc WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A) -> f3(0) True (1,1) 1. f3(A) -> f3(1 + A) [9 >= A] (?,1) 2. f3(A) -> f11(A) [A >= 10 && 0 >= 1 + B] (?,1) 3. f3(A) -> f11(A) [A >= 10] (?,1) Signature: {(f0,1);(f11,1);(f3,1)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{},3->{}] Sizebounds: (<0,0,A>, ?) (<1,0,A>, ?) (<2,0,A>, ?) (<3,0,A>, ?) + Applied Processor: SizeboundsProc + Details: Sizebounds computed: (<0,0,A>, 0) (<1,0,A>, 10) (<2,0,A>, 10) (<3,0,A>, 10) * Step 3: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A) -> f3(0) True (1,1) 1. f3(A) -> f3(1 + A) [9 >= A] (?,1) 2. f3(A) -> f11(A) [A >= 10 && 0 >= 1 + B] (?,1) 3. f3(A) -> f11(A) [A >= 10] (?,1) Signature: {(f0,1);(f11,1);(f3,1)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{},3->{}] Sizebounds: (<0,0,A>, 0) (<1,0,A>, 10) (<2,0,A>, 10) (<3,0,A>, 10) + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,2),(0,3)] * Step 4: LeafRules WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A) -> f3(0) True (1,1) 1. f3(A) -> f3(1 + A) [9 >= A] (?,1) 2. f3(A) -> f11(A) [A >= 10 && 0 >= 1 + B] (?,1) 3. f3(A) -> f11(A) [A >= 10] (?,1) Signature: {(f0,1);(f11,1);(f3,1)} Flow Graph: [0->{1},1->{1,2,3},2->{},3->{}] Sizebounds: (<0,0,A>, 0) (<1,0,A>, 10) (<2,0,A>, 10) (<3,0,A>, 10) + Applied Processor: LeafRules + Details: The following transitions are estimated by its predecessors and are removed [2,3] * Step 5: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A) -> f3(0) True (1,1) 1. f3(A) -> f3(1 + A) [9 >= A] (?,1) Signature: {(f0,1);(f11,1);(f3,1)} Flow Graph: [0->{1},1->{1}] Sizebounds: (<0,0,A>, 0) (<1,0,A>, 10) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 10 p(f3) = 10 + -1*x1 The following rules are strictly oriented: [9 >= A] ==> f3(A) = 10 + -1*A > 9 + -1*A = f3(1 + A) The following rules are weakly oriented: True ==> f0(A) = 10 >= 10 = f3(0) * Step 6: KnowledgePropagation WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A) -> f3(0) True (1,1) 1. f3(A) -> f3(1 + A) [9 >= A] (10,1) Signature: {(f0,1);(f11,1);(f3,1)} Flow Graph: [0->{1},1->{1}] Sizebounds: (<0,0,A>, 0) (<1,0,A>, 10) + Applied Processor: KnowledgePropagation + Details: The problem is already solved. WORST_CASE(?,O(1))