WORST_CASE(?,O(1)) * Step 1: LocalSizeboundsProc WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f4(A) -> f5(A) [0 >= 1 + B] (?,1) 1. f4(A) -> f5(A) True (?,1) 2. f0(A) -> f4(0) True (1,1) 3. f5(A) -> f11(A) [A >= 3] (?,1) 4. f4(A) -> f11(A) True (?,1) 5. f5(A) -> f4(1 + A) [2 >= A] (?,1) 6. f11(A) -> f14(A) [1 >= A] (?,1) 7. f11(A) -> f14(A) [A >= 2] (?,1) Signature: {(f0,1);(f11,1);(f14,1);(f4,1);(f5,1)} Flow Graph: [0->{3,5},1->{3,5},2->{0,1,4},3->{6,7},4->{6,7},5->{0,1,4},6->{},7->{}] + Applied Processor: LocalSizeboundsProc + Details: LocalSizebounds generated; rvgraph (<0,0,A>, A, .= 0) (<1,0,A>, A, .= 0) (<2,0,A>, 0, .= 0) (<3,0,A>, A, .= 0) (<4,0,A>, A, .= 0) (<5,0,A>, 1 + A, .+ 1) (<6,0,A>, A, .= 0) (<7,0,A>, A, .= 0) * Step 2: SizeboundsProc WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f4(A) -> f5(A) [0 >= 1 + B] (?,1) 1. f4(A) -> f5(A) True (?,1) 2. f0(A) -> f4(0) True (1,1) 3. f5(A) -> f11(A) [A >= 3] (?,1) 4. f4(A) -> f11(A) True (?,1) 5. f5(A) -> f4(1 + A) [2 >= A] (?,1) 6. f11(A) -> f14(A) [1 >= A] (?,1) 7. f11(A) -> f14(A) [A >= 2] (?,1) Signature: {(f0,1);(f11,1);(f14,1);(f4,1);(f5,1)} Flow Graph: [0->{3,5},1->{3,5},2->{0,1,4},3->{6,7},4->{6,7},5->{0,1,4},6->{},7->{}] Sizebounds: (<0,0,A>, ?) (<1,0,A>, ?) (<2,0,A>, ?) (<3,0,A>, ?) (<4,0,A>, ?) (<5,0,A>, ?) (<6,0,A>, ?) (<7,0,A>, ?) + Applied Processor: SizeboundsProc + Details: Sizebounds computed: (<0,0,A>, 3) (<1,0,A>, 3) (<2,0,A>, 0) (<3,0,A>, 3) (<4,0,A>, 3) (<5,0,A>, 3) (<6,0,A>, 3) (<7,0,A>, 3) * Step 3: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f4(A) -> f5(A) [0 >= 1 + B] (?,1) 1. f4(A) -> f5(A) True (?,1) 2. f0(A) -> f4(0) True (1,1) 3. f5(A) -> f11(A) [A >= 3] (?,1) 4. f4(A) -> f11(A) True (?,1) 5. f5(A) -> f4(1 + A) [2 >= A] (?,1) 6. f11(A) -> f14(A) [1 >= A] (?,1) 7. f11(A) -> f14(A) [A >= 2] (?,1) Signature: {(f0,1);(f11,1);(f14,1);(f4,1);(f5,1)} Flow Graph: [0->{3,5},1->{3,5},2->{0,1,4},3->{6,7},4->{6,7},5->{0,1,4},6->{},7->{}] Sizebounds: (<0,0,A>, 3) (<1,0,A>, 3) (<2,0,A>, 0) (<3,0,A>, 3) (<4,0,A>, 3) (<5,0,A>, 3) (<6,0,A>, 3) (<7,0,A>, 3) + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(3,6)] * Step 4: LeafRules WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f4(A) -> f5(A) [0 >= 1 + B] (?,1) 1. f4(A) -> f5(A) True (?,1) 2. f0(A) -> f4(0) True (1,1) 3. f5(A) -> f11(A) [A >= 3] (?,1) 4. f4(A) -> f11(A) True (?,1) 5. f5(A) -> f4(1 + A) [2 >= A] (?,1) 6. f11(A) -> f14(A) [1 >= A] (?,1) 7. f11(A) -> f14(A) [A >= 2] (?,1) Signature: {(f0,1);(f11,1);(f14,1);(f4,1);(f5,1)} Flow Graph: [0->{3,5},1->{3,5},2->{0,1,4},3->{7},4->{6,7},5->{0,1,4},6->{},7->{}] Sizebounds: (<0,0,A>, 3) (<1,0,A>, 3) (<2,0,A>, 0) (<3,0,A>, 3) (<4,0,A>, 3) (<5,0,A>, 3) (<6,0,A>, 3) (<7,0,A>, 3) + Applied Processor: LeafRules + Details: The following transitions are estimated by its predecessors and are removed [3,4,6,7] * Step 5: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f4(A) -> f5(A) [0 >= 1 + B] (?,1) 1. f4(A) -> f5(A) True (?,1) 2. f0(A) -> f4(0) True (1,1) 5. f5(A) -> f4(1 + A) [2 >= A] (?,1) Signature: {(f0,1);(f11,1);(f14,1);(f4,1);(f5,1)} Flow Graph: [0->{5},1->{5},2->{0,1},5->{0,1}] Sizebounds: (<0,0,A>, 3) (<1,0,A>, 3) (<2,0,A>, 0) (<5,0,A>, 3) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 3 p(f4) = 3 + -1*x1 p(f5) = 3 + -1*x1 The following rules are strictly oriented: [2 >= A] ==> f5(A) = 3 + -1*A > 2 + -1*A = f4(1 + A) The following rules are weakly oriented: [0 >= 1 + B] ==> f4(A) = 3 + -1*A >= 3 + -1*A = f5(A) True ==> f4(A) = 3 + -1*A >= 3 + -1*A = f5(A) True ==> f0(A) = 3 >= 3 = f4(0) * Step 6: KnowledgePropagation WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f4(A) -> f5(A) [0 >= 1 + B] (?,1) 1. f4(A) -> f5(A) True (?,1) 2. f0(A) -> f4(0) True (1,1) 5. f5(A) -> f4(1 + A) [2 >= A] (3,1) Signature: {(f0,1);(f11,1);(f14,1);(f4,1);(f5,1)} Flow Graph: [0->{5},1->{5},2->{0,1},5->{0,1}] Sizebounds: (<0,0,A>, 3) (<1,0,A>, 3) (<2,0,A>, 0) (<5,0,A>, 3) + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 7: LocalSizeboundsProc WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f4(A) -> f5(A) [0 >= 1 + B] (4,1) 1. f4(A) -> f5(A) True (4,1) 2. f0(A) -> f4(0) True (1,1) 5. f5(A) -> f4(1 + A) [2 >= A] (3,1) Signature: {(f0,1);(f11,1);(f14,1);(f4,1);(f5,1)} Flow Graph: [0->{5},1->{5},2->{0,1},5->{0,1}] Sizebounds: (<0,0,A>, 3) (<1,0,A>, 3) (<2,0,A>, 0) (<5,0,A>, 3) + Applied Processor: LocalSizeboundsProc + Details: The problem is already solved. WORST_CASE(?,O(1))