WORST_CASE(?,O(n^1)) * Step 1: RestrictVarsProcessor WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f300(A,B,C) -> f300(-99 + A,0,C) [0 >= 1 + A && 1 + B = 0] (?,1) 1. f300(A,B,C) -> f300(1 + A,1 + B,C) [0 >= 1 + A && B >= 0] (?,1) 2. f300(A,B,C) -> f300(1 + A,1 + B,C) [0 >= 1 + A && 0 >= 2 + B] (?,1) 3. f300(A,B,C) -> f1(A,B,D) [A >= 0] (?,1) 4. f2(A,B,C) -> f300(A,B,C) True (1,1) Signature: {(f1,3);(f2,3);(f300,3)} Flow Graph: [0->{0,1,2,3},1->{0,1,2,3},2->{0,1,2,3},3->{},4->{0,1,2,3}] + Applied Processor: RestrictVarsProcessor + Details: We removed the arguments [C] . * Step 2: LocalSizeboundsProc WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f300(A,B) -> f300(-99 + A,0) [0 >= 1 + A && 1 + B = 0] (?,1) 1. f300(A,B) -> f300(1 + A,1 + B) [0 >= 1 + A && B >= 0] (?,1) 2. f300(A,B) -> f300(1 + A,1 + B) [0 >= 1 + A && 0 >= 2 + B] (?,1) 3. f300(A,B) -> f1(A,B) [A >= 0] (?,1) 4. f2(A,B) -> f300(A,B) True (1,1) Signature: {(f1,2);(f2,2);(f300,2)} Flow Graph: [0->{0,1,2,3},1->{0,1,2,3},2->{0,1,2,3},3->{},4->{0,1,2,3}] + Applied Processor: LocalSizeboundsProc + Details: LocalSizebounds generated; rvgraph (<0,0,A>, 99 + A, .+ 99) (<0,0,B>, 0, .= 0) (<1,0,A>, 1 + A, .+ 1) (<1,0,B>, 1 + B, .+ 1) (<2,0,A>, 1 + A, .+ 1) (<2,0,B>, 1 + B, .+ 1) (<3,0,A>, A, .= 0) (<3,0,B>, B, .= 0) (<4,0,A>, A, .= 0) (<4,0,B>, B, .= 0) * Step 3: SizeboundsProc WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f300(A,B) -> f300(-99 + A,0) [0 >= 1 + A && 1 + B = 0] (?,1) 1. f300(A,B) -> f300(1 + A,1 + B) [0 >= 1 + A && B >= 0] (?,1) 2. f300(A,B) -> f300(1 + A,1 + B) [0 >= 1 + A && 0 >= 2 + B] (?,1) 3. f300(A,B) -> f1(A,B) [A >= 0] (?,1) 4. f2(A,B) -> f300(A,B) True (1,1) Signature: {(f1,2);(f2,2);(f300,2)} Flow Graph: [0->{0,1,2,3},1->{0,1,2,3},2->{0,1,2,3},3->{},4->{0,1,2,3}] Sizebounds: (<0,0,A>, ?) (<0,0,B>, ?) (<1,0,A>, ?) (<1,0,B>, ?) (<2,0,A>, ?) (<2,0,B>, ?) (<3,0,A>, ?) (<3,0,B>, ?) (<4,0,A>, ?) (<4,0,B>, ?) + Applied Processor: SizeboundsProc + Details: Sizebounds computed: (<0,0,A>, 0) (<0,0,B>, 0) (<1,0,A>, 0) (<1,0,B>, ?) (<2,0,A>, 0) (<2,0,B>, 0) (<3,0,A>, A) (<3,0,B>, ?) (<4,0,A>, A) (<4,0,B>, B) * Step 4: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f300(A,B) -> f300(-99 + A,0) [0 >= 1 + A && 1 + B = 0] (?,1) 1. f300(A,B) -> f300(1 + A,1 + B) [0 >= 1 + A && B >= 0] (?,1) 2. f300(A,B) -> f300(1 + A,1 + B) [0 >= 1 + A && 0 >= 2 + B] (?,1) 3. f300(A,B) -> f1(A,B) [A >= 0] (?,1) 4. f2(A,B) -> f300(A,B) True (1,1) Signature: {(f1,2);(f2,2);(f300,2)} Flow Graph: [0->{0,1,2,3},1->{0,1,2,3},2->{0,1,2,3},3->{},4->{0,1,2,3}] Sizebounds: (<0,0,A>, 0) (<0,0,B>, 0) (<1,0,A>, 0) (<1,0,B>, ?) (<2,0,A>, 0) (<2,0,B>, 0) (<3,0,A>, A) (<3,0,B>, ?) (<4,0,A>, A) (<4,0,B>, B) + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,0),(0,2),(0,3),(1,0),(1,2),(2,1)] * Step 5: LeafRules WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f300(A,B) -> f300(-99 + A,0) [0 >= 1 + A && 1 + B = 0] (?,1) 1. f300(A,B) -> f300(1 + A,1 + B) [0 >= 1 + A && B >= 0] (?,1) 2. f300(A,B) -> f300(1 + A,1 + B) [0 >= 1 + A && 0 >= 2 + B] (?,1) 3. f300(A,B) -> f1(A,B) [A >= 0] (?,1) 4. f2(A,B) -> f300(A,B) True (1,1) Signature: {(f1,2);(f2,2);(f300,2)} Flow Graph: [0->{1},1->{1,3},2->{0,2,3},3->{},4->{0,1,2,3}] Sizebounds: (<0,0,A>, 0) (<0,0,B>, 0) (<1,0,A>, 0) (<1,0,B>, ?) (<2,0,A>, 0) (<2,0,B>, 0) (<3,0,A>, A) (<3,0,B>, ?) (<4,0,A>, A) (<4,0,B>, B) + Applied Processor: LeafRules + Details: The following transitions are estimated by its predecessors and are removed [3] * Step 6: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f300(A,B) -> f300(-99 + A,0) [0 >= 1 + A && 1 + B = 0] (?,1) 1. f300(A,B) -> f300(1 + A,1 + B) [0 >= 1 + A && B >= 0] (?,1) 2. f300(A,B) -> f300(1 + A,1 + B) [0 >= 1 + A && 0 >= 2 + B] (?,1) 4. f2(A,B) -> f300(A,B) True (1,1) Signature: {(f1,2);(f2,2);(f300,2)} Flow Graph: [0->{1},1->{1},2->{0,2},4->{0,1,2}] Sizebounds: (<0,0,A>, 0) (<0,0,B>, 0) (<1,0,A>, 0) (<1,0,B>, ?) (<2,0,A>, 0) (<2,0,B>, 0) (<4,0,A>, A) (<4,0,B>, B) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f2) = -1*x2 p(f300) = -1*x2 The following rules are strictly oriented: [0 >= 1 + A && 0 >= 2 + B] ==> f300(A,B) = -1*B > -1 + -1*B = f300(1 + A,1 + B) The following rules are weakly oriented: [0 >= 1 + A && 1 + B = 0] ==> f300(A,B) = -1*B >= 0 = f300(-99 + A,0) [0 >= 1 + A && B >= 0] ==> f300(A,B) = -1*B >= -1 + -1*B = f300(1 + A,1 + B) True ==> f2(A,B) = -1*B >= -1*B = f300(A,B) * Step 7: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f300(A,B) -> f300(-99 + A,0) [0 >= 1 + A && 1 + B = 0] (?,1) 1. f300(A,B) -> f300(1 + A,1 + B) [0 >= 1 + A && B >= 0] (?,1) 2. f300(A,B) -> f300(1 + A,1 + B) [0 >= 1 + A && 0 >= 2 + B] (B,1) 4. f2(A,B) -> f300(A,B) True (1,1) Signature: {(f1,2);(f2,2);(f300,2)} Flow Graph: [0->{1},1->{1},2->{0,2},4->{0,1,2}] Sizebounds: (<0,0,A>, 0) (<0,0,B>, 0) (<1,0,A>, 0) (<1,0,B>, ?) (<2,0,A>, 0) (<2,0,B>, 0) (<4,0,A>, A) (<4,0,B>, B) + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 8: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f300(A,B) -> f300(-99 + A,0) [0 >= 1 + A && 1 + B = 0] (1 + B,1) 1. f300(A,B) -> f300(1 + A,1 + B) [0 >= 1 + A && B >= 0] (?,1) 2. f300(A,B) -> f300(1 + A,1 + B) [0 >= 1 + A && 0 >= 2 + B] (B,1) 4. f2(A,B) -> f300(A,B) True (1,1) Signature: {(f1,2);(f2,2);(f300,2)} Flow Graph: [0->{1},1->{1},2->{0,2},4->{0,1,2}] Sizebounds: (<0,0,A>, 0) (<0,0,B>, 0) (<1,0,A>, 0) (<1,0,B>, ?) (<2,0,A>, 0) (<2,0,B>, 0) (<4,0,A>, A) (<4,0,B>, B) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [1], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f300) = -1*x1 The following rules are strictly oriented: [0 >= 1 + A && B >= 0] ==> f300(A,B) = -1*A > -1 + -1*A = f300(1 + A,1 + B) The following rules are weakly oriented: We use the following global sizebounds: (<0,0,A>, 0) (<0,0,B>, 0) (<1,0,A>, 0) (<1,0,B>, ?) (<2,0,A>, 0) (<2,0,B>, 0) (<4,0,A>, A) (<4,0,B>, B) * Step 9: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f300(A,B) -> f300(-99 + A,0) [0 >= 1 + A && 1 + B = 0] (1 + B,1) 1. f300(A,B) -> f300(1 + A,1 + B) [0 >= 1 + A && B >= 0] (A,1) 2. f300(A,B) -> f300(1 + A,1 + B) [0 >= 1 + A && 0 >= 2 + B] (B,1) 4. f2(A,B) -> f300(A,B) True (1,1) Signature: {(f1,2);(f2,2);(f300,2)} Flow Graph: [0->{1},1->{1},2->{0,2},4->{0,1,2}] Sizebounds: (<0,0,A>, 0) (<0,0,B>, 0) (<1,0,A>, 0) (<1,0,B>, ?) (<2,0,A>, 0) (<2,0,B>, 0) (<4,0,A>, A) (<4,0,B>, B) + Applied Processor: KnowledgePropagation + Details: The problem is already solved. WORST_CASE(?,O(n^1))