WORST_CASE(?,O(1)) * Step 1: LocalSizeboundsProc WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C) -> f8(0,10,0) True (1,1) 1. f8(A,B,C) -> f8(2 + A,B,1 + C) [B >= 1 + C] (?,1) 2. f8(A,B,C) -> f6(A,B,C) [2*B >= 1 + A && C >= B] (?,1) 3. f8(A,B,C) -> f6(A,B,C) [A >= 2*B && C >= B] (?,1) Signature: {(f0,3);(f6,3);(f8,3)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{},3->{}] + Applied Processor: LocalSizeboundsProc + Details: LocalSizebounds generated; rvgraph (<0,0,A>, 0, .= 0) (<0,0,B>, 10, .= 10) (<0,0,C>, 0, .= 0) (<1,0,A>, 2 + A, .+ 2) (<1,0,B>, B, .= 0) (<1,0,C>, 1 + C, .+ 1) (<2,0,A>, A, .= 0) (<2,0,B>, B, .= 0) (<2,0,C>, C, .= 0) (<3,0,A>, A, .= 0) (<3,0,B>, B, .= 0) (<3,0,C>, C, .= 0) * Step 2: SizeboundsProc WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C) -> f8(0,10,0) True (1,1) 1. f8(A,B,C) -> f8(2 + A,B,1 + C) [B >= 1 + C] (?,1) 2. f8(A,B,C) -> f6(A,B,C) [2*B >= 1 + A && C >= B] (?,1) 3. f8(A,B,C) -> f6(A,B,C) [A >= 2*B && C >= B] (?,1) Signature: {(f0,3);(f6,3);(f8,3)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{},3->{}] Sizebounds: (<0,0,A>, ?) (<0,0,B>, ?) (<0,0,C>, ?) (<1,0,A>, ?) (<1,0,B>, ?) (<1,0,C>, ?) (<2,0,A>, ?) (<2,0,B>, ?) (<2,0,C>, ?) (<3,0,A>, ?) (<3,0,B>, ?) (<3,0,C>, ?) + Applied Processor: SizeboundsProc + Details: Sizebounds computed: (<0,0,A>, 0) (<0,0,B>, 10) (<0,0,C>, 0) (<1,0,A>, ?) (<1,0,B>, 10) (<1,0,C>, 10) (<2,0,A>, ?) (<2,0,B>, 10) (<2,0,C>, 10) (<3,0,A>, ?) (<3,0,B>, 10) (<3,0,C>, 10) * Step 3: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C) -> f8(0,10,0) True (1,1) 1. f8(A,B,C) -> f8(2 + A,B,1 + C) [B >= 1 + C] (?,1) 2. f8(A,B,C) -> f6(A,B,C) [2*B >= 1 + A && C >= B] (?,1) 3. f8(A,B,C) -> f6(A,B,C) [A >= 2*B && C >= B] (?,1) Signature: {(f0,3);(f6,3);(f8,3)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{},3->{}] Sizebounds: (<0,0,A>, 0) (<0,0,B>, 10) (<0,0,C>, 0) (<1,0,A>, ?) (<1,0,B>, 10) (<1,0,C>, 10) (<2,0,A>, ?) (<2,0,B>, 10) (<2,0,C>, 10) (<3,0,A>, ?) (<3,0,B>, 10) (<3,0,C>, 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,B,C) -> f8(0,10,0) True (1,1) 1. f8(A,B,C) -> f8(2 + A,B,1 + C) [B >= 1 + C] (?,1) 2. f8(A,B,C) -> f6(A,B,C) [2*B >= 1 + A && C >= B] (?,1) 3. f8(A,B,C) -> f6(A,B,C) [A >= 2*B && C >= B] (?,1) Signature: {(f0,3);(f6,3);(f8,3)} Flow Graph: [0->{1},1->{1,2,3},2->{},3->{}] Sizebounds: (<0,0,A>, 0) (<0,0,B>, 10) (<0,0,C>, 0) (<1,0,A>, ?) (<1,0,B>, 10) (<1,0,C>, 10) (<2,0,A>, ?) (<2,0,B>, 10) (<2,0,C>, 10) (<3,0,A>, ?) (<3,0,B>, 10) (<3,0,C>, 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,B,C) -> f8(0,10,0) True (1,1) 1. f8(A,B,C) -> f8(2 + A,B,1 + C) [B >= 1 + C] (?,1) Signature: {(f0,3);(f6,3);(f8,3)} Flow Graph: [0->{1},1->{1}] Sizebounds: (<0,0,A>, 0) (<0,0,B>, 10) (<0,0,C>, 0) (<1,0,A>, ?) (<1,0,B>, 10) (<1,0,C>, 10) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 10 p(f8) = x2 + -1*x3 The following rules are strictly oriented: [B >= 1 + C] ==> f8(A,B,C) = B + -1*C > -1 + B + -1*C = f8(2 + A,B,1 + C) The following rules are weakly oriented: True ==> f0(A,B,C) = 10 >= 10 = f8(0,10,0) * Step 6: KnowledgePropagation WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C) -> f8(0,10,0) True (1,1) 1. f8(A,B,C) -> f8(2 + A,B,1 + C) [B >= 1 + C] (10,1) Signature: {(f0,3);(f6,3);(f8,3)} Flow Graph: [0->{1},1->{1}] Sizebounds: (<0,0,A>, 0) (<0,0,B>, 10) (<0,0,C>, 0) (<1,0,A>, ?) (<1,0,B>, 10) (<1,0,C>, 10) + Applied Processor: KnowledgePropagation + Details: The problem is already solved. WORST_CASE(?,O(1))