WORST_CASE(?,O(1)) * Step 1: RestrictVarsProcessor WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f300(A,B,C,D,E) -> f300(-1 + A,B,C,D,E) [A >= 101 && 9 >= B] (?,1) 1. f300(A,B,C,D,E) -> f2(A,B,0,0,0) [100 >= A && 9 >= B] (?,1) 2. f300(A,B,C,D,E) -> f2(A,B,0,0,0) [B >= 10] (?,1) 3. f1(A,B,C,D,E) -> f300(1000,B,C,D,E) True (1,1) Signature: {(f1,5);(f2,5);(f300,5)} Flow Graph: [0->{0,1,2},1->{},2->{},3->{0,1,2}] + Applied Processor: RestrictVarsProcessor + Details: We removed the arguments [C,D,E] . * Step 2: LocalSizeboundsProc WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f300(A,B) -> f300(-1 + A,B) [A >= 101 && 9 >= B] (?,1) 1. f300(A,B) -> f2(A,B) [100 >= A && 9 >= B] (?,1) 2. f300(A,B) -> f2(A,B) [B >= 10] (?,1) 3. f1(A,B) -> f300(1000,B) True (1,1) Signature: {(f1,2);(f2,2);(f300,2)} Flow Graph: [0->{0,1,2},1->{},2->{},3->{0,1,2}] + Applied Processor: LocalSizeboundsProc + Details: LocalSizebounds generated; rvgraph (<0,0,A>, 1 + A, .+ 1) (<0,0,B>, B, .= 0) (<1,0,A>, A, .= 0) (<1,0,B>, B, .= 0) (<2,0,A>, A, .= 0) (<2,0,B>, B, .= 0) (<3,0,A>, 1000, .= 1000) (<3,0,B>, B, .= 0) * Step 3: SizeboundsProc WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f300(A,B) -> f300(-1 + A,B) [A >= 101 && 9 >= B] (?,1) 1. f300(A,B) -> f2(A,B) [100 >= A && 9 >= B] (?,1) 2. f300(A,B) -> f2(A,B) [B >= 10] (?,1) 3. f1(A,B) -> f300(1000,B) True (1,1) Signature: {(f1,2);(f2,2);(f300,2)} Flow Graph: [0->{0,1,2},1->{},2->{},3->{0,1,2}] 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>, ?) + Applied Processor: SizeboundsProc + Details: Sizebounds computed: (<0,0,A>, ?) (<0,0,B>, B) (<1,0,A>, ?) (<1,0,B>, B) (<2,0,A>, ?) (<2,0,B>, B) (<3,0,A>, 1000) (<3,0,B>, B) * Step 4: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f300(A,B) -> f300(-1 + A,B) [A >= 101 && 9 >= B] (?,1) 1. f300(A,B) -> f2(A,B) [100 >= A && 9 >= B] (?,1) 2. f300(A,B) -> f2(A,B) [B >= 10] (?,1) 3. f1(A,B) -> f300(1000,B) True (1,1) Signature: {(f1,2);(f2,2);(f300,2)} Flow Graph: [0->{0,1,2},1->{},2->{},3->{0,1,2}] Sizebounds: (<0,0,A>, ?) (<0,0,B>, B) (<1,0,A>, ?) (<1,0,B>, B) (<2,0,A>, ?) (<2,0,B>, B) (<3,0,A>, 1000) (<3,0,B>, B) + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,2),(3,1)] * Step 5: LeafRules WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f300(A,B) -> f300(-1 + A,B) [A >= 101 && 9 >= B] (?,1) 1. f300(A,B) -> f2(A,B) [100 >= A && 9 >= B] (?,1) 2. f300(A,B) -> f2(A,B) [B >= 10] (?,1) 3. f1(A,B) -> f300(1000,B) True (1,1) Signature: {(f1,2);(f2,2);(f300,2)} Flow Graph: [0->{0,1},1->{},2->{},3->{0,2}] Sizebounds: (<0,0,A>, ?) (<0,0,B>, B) (<1,0,A>, ?) (<1,0,B>, B) (<2,0,A>, ?) (<2,0,B>, B) (<3,0,A>, 1000) (<3,0,B>, B) + Applied Processor: LeafRules + Details: The following transitions are estimated by its predecessors and are removed [1,2] * Step 6: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f300(A,B) -> f300(-1 + A,B) [A >= 101 && 9 >= B] (?,1) 3. f1(A,B) -> f300(1000,B) True (1,1) Signature: {(f1,2);(f2,2);(f300,2)} Flow Graph: [0->{0},3->{0}] Sizebounds: (<0,0,A>, ?) (<0,0,B>, B) (<3,0,A>, 1000) (<3,0,B>, B) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f1) = 900 p(f300) = -100 + x1 The following rules are strictly oriented: [A >= 101 && 9 >= B] ==> f300(A,B) = -100 + A > -101 + A = f300(-1 + A,B) The following rules are weakly oriented: True ==> f1(A,B) = 900 >= 900 = f300(1000,B) * Step 7: KnowledgePropagation WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f300(A,B) -> f300(-1 + A,B) [A >= 101 && 9 >= B] (900,1) 3. f1(A,B) -> f300(1000,B) True (1,1) Signature: {(f1,2);(f2,2);(f300,2)} Flow Graph: [0->{0},3->{0}] Sizebounds: (<0,0,A>, ?) (<0,0,B>, B) (<3,0,A>, 1000) (<3,0,B>, B) + Applied Processor: KnowledgePropagation + Details: The problem is already solved. WORST_CASE(?,O(1))