WORST_CASE(?,O(1)) * Step 1: RestrictVarsProcessor WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B) -> f6(C,0) True (1,1) 1. f6(A,B) -> f6(A,1 + B) [9 >= B] (?,1) 2. f6(A,B) -> f15(A,B) [B >= 10] (?,1) Signature: {(f0,2);(f15,2);(f6,2)} Flow Graph: [0->{1,2},1->{1,2},2->{}] + Applied Processor: RestrictVarsProcessor + Details: We removed the arguments [A] . * Step 2: LocalSizeboundsProc WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(B) -> f6(0) True (1,1) 1. f6(B) -> f6(1 + B) [9 >= B] (?,1) 2. f6(B) -> f15(B) [B >= 10] (?,1) Signature: {(f0,1);(f15,1);(f6,1)} Flow Graph: [0->{1,2},1->{1,2},2->{}] + Applied Processor: LocalSizeboundsProc + Details: LocalSizebounds generated; rvgraph (<0,0,B>, 0, .= 0) (<1,0,B>, 1 + B, .+ 1) (<2,0,B>, B, .= 0) * Step 3: SizeboundsProc WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(B) -> f6(0) True (1,1) 1. f6(B) -> f6(1 + B) [9 >= B] (?,1) 2. f6(B) -> f15(B) [B >= 10] (?,1) Signature: {(f0,1);(f15,1);(f6,1)} Flow Graph: [0->{1,2},1->{1,2},2->{}] Sizebounds: (<0,0,B>, ?) (<1,0,B>, ?) (<2,0,B>, ?) + Applied Processor: SizeboundsProc + Details: Sizebounds computed: (<0,0,B>, 0) (<1,0,B>, 10) (<2,0,B>, 10) * Step 4: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(B) -> f6(0) True (1,1) 1. f6(B) -> f6(1 + B) [9 >= B] (?,1) 2. f6(B) -> f15(B) [B >= 10] (?,1) Signature: {(f0,1);(f15,1);(f6,1)} Flow Graph: [0->{1,2},1->{1,2},2->{}] Sizebounds: (<0,0,B>, 0) (<1,0,B>, 10) (<2,0,B>, 10) + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,2)] * Step 5: LeafRules WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(B) -> f6(0) True (1,1) 1. f6(B) -> f6(1 + B) [9 >= B] (?,1) 2. f6(B) -> f15(B) [B >= 10] (?,1) Signature: {(f0,1);(f15,1);(f6,1)} Flow Graph: [0->{1},1->{1,2},2->{}] Sizebounds: (<0,0,B>, 0) (<1,0,B>, 10) (<2,0,B>, 10) + Applied Processor: LeafRules + Details: The following transitions are estimated by its predecessors and are removed [2] * Step 6: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(B) -> f6(0) True (1,1) 1. f6(B) -> f6(1 + B) [9 >= B] (?,1) Signature: {(f0,1);(f15,1);(f6,1)} Flow Graph: [0->{1},1->{1}] Sizebounds: (<0,0,B>, 0) (<1,0,B>, 10) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 10 p(f6) = 10 + -1*x1 The following rules are strictly oriented: [9 >= B] ==> f6(B) = 10 + -1*B > 9 + -1*B = f6(1 + B) The following rules are weakly oriented: True ==> f0(B) = 10 >= 10 = f6(0) * Step 7: KnowledgePropagation WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(B) -> f6(0) True (1,1) 1. f6(B) -> f6(1 + B) [9 >= B] (10,1) Signature: {(f0,1);(f15,1);(f6,1)} Flow Graph: [0->{1},1->{1}] Sizebounds: (<0,0,B>, 0) (<1,0,B>, 10) + Applied Processor: KnowledgePropagation + Details: The problem is already solved. WORST_CASE(?,O(1))