WORST_CASE(?,O(1)) * Step 1: RestrictVarsProcessor WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I,J) -> f5(K,0,0,D,E,F,G,H,I,J) True (1,1) 1. f5(A,B,C,D,E,F,G,H,I,J) -> f5(A,1 + B,1 + C,1,E,F,G,H,I,J) [31 >= C] (?,1) 2. f5(A,B,C,D,E,F,G,H,I,J) -> f5(A,B,1 + C,0,E,F,G,H,I,J) [31 >= C] (?,1) 3. f5(A,B,C,D,E,F,G,H,I,J) -> f28(A,B,C,D,B,B,K,L,L,L) [C >= 32] (?,1) Signature: {(f0,10);(f28,10);(f5,10)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{1,2,3},3->{}] + Applied Processor: RestrictVarsProcessor + Details: We removed the arguments [A,D,E,F,G,H,I,J] . * Step 2: LocalSizeboundsProc WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(B,C) -> f5(0,0) True (1,1) 1. f5(B,C) -> f5(1 + B,1 + C) [31 >= C] (?,1) 2. f5(B,C) -> f5(B,1 + C) [31 >= C] (?,1) 3. f5(B,C) -> f28(B,C) [C >= 32] (?,1) Signature: {(f0,2);(f28,2);(f5,2)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{1,2,3},3->{}] + Applied Processor: LocalSizeboundsProc + Details: LocalSizebounds generated; rvgraph (<0,0,B>, 0, .= 0) (<0,0,C>, 0, .= 0) (<1,0,B>, 1 + B, .+ 1) (<1,0,C>, 1 + C, .+ 1) (<2,0,B>, B, .= 0) (<2,0,C>, 1 + C, .+ 1) (<3,0,B>, B, .= 0) (<3,0,C>, C, .= 0) * Step 3: SizeboundsProc WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(B,C) -> f5(0,0) True (1,1) 1. f5(B,C) -> f5(1 + B,1 + C) [31 >= C] (?,1) 2. f5(B,C) -> f5(B,1 + C) [31 >= C] (?,1) 3. f5(B,C) -> f28(B,C) [C >= 32] (?,1) Signature: {(f0,2);(f28,2);(f5,2)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{1,2,3},3->{}] Sizebounds: (<0,0,B>, ?) (<0,0,C>, ?) (<1,0,B>, ?) (<1,0,C>, ?) (<2,0,B>, ?) (<2,0,C>, ?) (<3,0,B>, ?) (<3,0,C>, ?) + Applied Processor: SizeboundsProc + Details: Sizebounds computed: (<0,0,B>, 0) (<0,0,C>, 0) (<1,0,B>, ?) (<1,0,C>, 32) (<2,0,B>, ?) (<2,0,C>, 32) (<3,0,B>, ?) (<3,0,C>, 32) * Step 4: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(B,C) -> f5(0,0) True (1,1) 1. f5(B,C) -> f5(1 + B,1 + C) [31 >= C] (?,1) 2. f5(B,C) -> f5(B,1 + C) [31 >= C] (?,1) 3. f5(B,C) -> f28(B,C) [C >= 32] (?,1) Signature: {(f0,2);(f28,2);(f5,2)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{1,2,3},3->{}] Sizebounds: (<0,0,B>, 0) (<0,0,C>, 0) (<1,0,B>, ?) (<1,0,C>, 32) (<2,0,B>, ?) (<2,0,C>, 32) (<3,0,B>, ?) (<3,0,C>, 32) + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,3)] * Step 5: LeafRules WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(B,C) -> f5(0,0) True (1,1) 1. f5(B,C) -> f5(1 + B,1 + C) [31 >= C] (?,1) 2. f5(B,C) -> f5(B,1 + C) [31 >= C] (?,1) 3. f5(B,C) -> f28(B,C) [C >= 32] (?,1) Signature: {(f0,2);(f28,2);(f5,2)} Flow Graph: [0->{1,2},1->{1,2,3},2->{1,2,3},3->{}] Sizebounds: (<0,0,B>, 0) (<0,0,C>, 0) (<1,0,B>, ?) (<1,0,C>, 32) (<2,0,B>, ?) (<2,0,C>, 32) (<3,0,B>, ?) (<3,0,C>, 32) + Applied Processor: LeafRules + Details: The following transitions are estimated by its predecessors and are removed [3] * Step 6: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(B,C) -> f5(0,0) True (1,1) 1. f5(B,C) -> f5(1 + B,1 + C) [31 >= C] (?,1) 2. f5(B,C) -> f5(B,1 + C) [31 >= C] (?,1) Signature: {(f0,2);(f28,2);(f5,2)} Flow Graph: [0->{1,2},1->{1,2},2->{1,2}] Sizebounds: (<0,0,B>, 0) (<0,0,C>, 0) (<1,0,B>, ?) (<1,0,C>, 32) (<2,0,B>, ?) (<2,0,C>, 32) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 32 p(f5) = 32 + -1*x2 The following rules are strictly oriented: [31 >= C] ==> f5(B,C) = 32 + -1*C > 31 + -1*C = f5(B,1 + C) The following rules are weakly oriented: True ==> f0(B,C) = 32 >= 32 = f5(0,0) [31 >= C] ==> f5(B,C) = 32 + -1*C >= 31 + -1*C = f5(1 + B,1 + C) * Step 7: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(B,C) -> f5(0,0) True (1,1) 1. f5(B,C) -> f5(1 + B,1 + C) [31 >= C] (?,1) 2. f5(B,C) -> f5(B,1 + C) [31 >= C] (32,1) Signature: {(f0,2);(f28,2);(f5,2)} Flow Graph: [0->{1,2},1->{1,2},2->{1,2}] Sizebounds: (<0,0,B>, 0) (<0,0,C>, 0) (<1,0,B>, ?) (<1,0,C>, 32) (<2,0,B>, ?) (<2,0,C>, 32) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 32 p(f5) = 32 + -1*x2 The following rules are strictly oriented: [31 >= C] ==> f5(B,C) = 32 + -1*C > 31 + -1*C = f5(1 + B,1 + C) [31 >= C] ==> f5(B,C) = 32 + -1*C > 31 + -1*C = f5(B,1 + C) The following rules are weakly oriented: True ==> f0(B,C) = 32 >= 32 = f5(0,0) * Step 8: KnowledgePropagation WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(B,C) -> f5(0,0) True (1,1) 1. f5(B,C) -> f5(1 + B,1 + C) [31 >= C] (32,1) 2. f5(B,C) -> f5(B,1 + C) [31 >= C] (32,1) Signature: {(f0,2);(f28,2);(f5,2)} Flow Graph: [0->{1,2},1->{1,2},2->{1,2}] Sizebounds: (<0,0,B>, 0) (<0,0,C>, 0) (<1,0,B>, ?) (<1,0,C>, 32) (<2,0,B>, ?) (<2,0,C>, 32) + Applied Processor: KnowledgePropagation + Details: The problem is already solved. WORST_CASE(?,O(1))