WORST_CASE(?,O(1)) * Step 1: LocalSizeboundsProc WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A) -> f1(300) True (1,1) 1. f1(A) -> f1(-1 + A) [A >= 102] (?,1) 2. f1(A) -> f1(-1 + A) [100 >= A] (?,1) Signature: {(f0,1);(f1,1)} Flow Graph: [0->{1,2},1->{1,2},2->{1,2}] + Applied Processor: LocalSizeboundsProc + Details: LocalSizebounds generated; rvgraph (<0,0,A>, 300, .= 300) (<1,0,A>, 1 + A, .+ 1) (<2,0,A>, 1 + A, .+ 1) * Step 2: SizeboundsProc WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A) -> f1(300) True (1,1) 1. f1(A) -> f1(-1 + A) [A >= 102] (?,1) 2. f1(A) -> f1(-1 + A) [100 >= A] (?,1) Signature: {(f0,1);(f1,1)} Flow Graph: [0->{1,2},1->{1,2},2->{1,2}] Sizebounds: (<0,0,A>, ?) (<1,0,A>, ?) (<2,0,A>, ?) + Applied Processor: SizeboundsProc + Details: Sizebounds computed: (<0,0,A>, 300) (<1,0,A>, ?) (<2,0,A>, 99) * Step 3: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A) -> f1(300) True (1,1) 1. f1(A) -> f1(-1 + A) [A >= 102] (?,1) 2. f1(A) -> f1(-1 + A) [100 >= A] (?,1) Signature: {(f0,1);(f1,1)} Flow Graph: [0->{1,2},1->{1,2},2->{1,2}] Sizebounds: (<0,0,A>, 300) (<1,0,A>, ?) (<2,0,A>, 99) + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,2),(1,2),(2,1)] * Step 4: UnreachableRules WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A) -> f1(300) True (1,1) 1. f1(A) -> f1(-1 + A) [A >= 102] (?,1) 2. f1(A) -> f1(-1 + A) [100 >= A] (?,1) Signature: {(f0,1);(f1,1)} Flow Graph: [0->{1},1->{1},2->{2}] Sizebounds: (<0,0,A>, 300) (<1,0,A>, ?) (<2,0,A>, 99) + Applied Processor: UnreachableRules + Details: The following transitions are not reachable from the starting states and are removed: [2] * Step 5: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A) -> f1(300) True (1,1) 1. f1(A) -> f1(-1 + A) [A >= 102] (?,1) Signature: {(f0,1);(f1,1)} Flow Graph: [0->{1},1->{1}] Sizebounds: (<0,0,A>, 300) (<1,0,A>, ?) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 199 p(f1) = -101 + x1 The following rules are strictly oriented: [A >= 102] ==> f1(A) = -101 + A > -102 + A = f1(-1 + A) The following rules are weakly oriented: True ==> f0(A) = 199 >= 199 = f1(300) * Step 6: KnowledgePropagation WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A) -> f1(300) True (1,1) 1. f1(A) -> f1(-1 + A) [A >= 102] (199,1) Signature: {(f0,1);(f1,1)} Flow Graph: [0->{1},1->{1}] Sizebounds: (<0,0,A>, 300) (<1,0,A>, ?) + Applied Processor: KnowledgePropagation + Details: The problem is already solved. WORST_CASE(?,O(1))