WORST_CASE(?,O(1)) * Step 1: LocalSizeboundsProc WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(400,0,C,D,E) True (1,1) 1. f7(A,B,C,D,E) -> f10(A,B,0,D,E) [4 >= B] (?,1) 2. f10(A,B,C,D,E) -> f13(A,B,C,0,E) [4 >= C] (?,1) 3. f13(A,B,C,D,E) -> f16(A,B,C,D,0) [4 >= D] (?,1) 4. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E && A >= 1 + F] (?,1) 5. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E] (?,1) 6. f16(A,B,C,D,E) -> f31(A,B,C,D,E) [4 >= E] (?,1) 7. f16(A,B,C,D,E) -> f13(A,B,C,1 + D,E) [E >= 5] (?,1) 8. f13(A,B,C,D,E) -> f10(A,B,1 + C,D,E) [D >= 5] (?,1) 9. f10(A,B,C,D,E) -> f7(A,1 + B,C,D,E) [C >= 5] (?,1) 10. f7(A,B,C,D,E) -> f31(A,B,C,D,E) [B >= 5] (?,1) Signature: {(f0,5);(f10,5);(f13,5);(f16,5);(f31,5);(f7,5)} Flow Graph: [0->{1,10},1->{2,9},2->{3,8},3->{4,5,6,7},4->{4,5,6,7},5->{4,5,6,7},6->{},7->{3,8},8->{2,9},9->{1,10} ,10->{}] + Applied Processor: LocalSizeboundsProc + Details: LocalSizebounds generated; rvgraph (< 0,0,A>, 400, .= 400) (< 0,0,B>, 0, .= 0) (< 0,0,C>, C, .= 0) (< 0,0,D>, D, .= 0) (< 0,0,E>, E, .= 0) (< 1,0,A>, A, .= 0) (< 1,0,B>, B, .= 0) (< 1,0,C>, 0, .= 0) (< 1,0,D>, D, .= 0) (< 1,0,E>, E, .= 0) (< 2,0,A>, A, .= 0) (< 2,0,B>, B, .= 0) (< 2,0,C>, C, .= 0) (< 2,0,D>, 0, .= 0) (< 2,0,E>, E, .= 0) (< 3,0,A>, A, .= 0) (< 3,0,B>, B, .= 0) (< 3,0,C>, C, .= 0) (< 3,0,D>, D, .= 0) (< 3,0,E>, 0, .= 0) (< 4,0,A>, A, .= 0) (< 4,0,B>, B, .= 0) (< 4,0,C>, C, .= 0) (< 4,0,D>, D, .= 0) (< 4,0,E>, 1 + E, .+ 1) (< 5,0,A>, A, .= 0) (< 5,0,B>, B, .= 0) (< 5,0,C>, C, .= 0) (< 5,0,D>, D, .= 0) (< 5,0,E>, 1 + E, .+ 1) (< 6,0,A>, A, .= 0) (< 6,0,B>, B, .= 0) (< 6,0,C>, C, .= 0) (< 6,0,D>, D, .= 0) (< 6,0,E>, E, .= 0) (< 7,0,A>, A, .= 0) (< 7,0,B>, B, .= 0) (< 7,0,C>, C, .= 0) (< 7,0,D>, 1 + D, .+ 1) (< 7,0,E>, E, .= 0) (< 8,0,A>, A, .= 0) (< 8,0,B>, B, .= 0) (< 8,0,C>, 1 + C, .+ 1) (< 8,0,D>, D, .= 0) (< 8,0,E>, E, .= 0) (< 9,0,A>, A, .= 0) (< 9,0,B>, 1 + B, .+ 1) (< 9,0,C>, C, .= 0) (< 9,0,D>, D, .= 0) (< 9,0,E>, E, .= 0) (<10,0,A>, A, .= 0) (<10,0,B>, B, .= 0) (<10,0,C>, C, .= 0) (<10,0,D>, D, .= 0) (<10,0,E>, E, .= 0) * Step 2: SizeboundsProc WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(400,0,C,D,E) True (1,1) 1. f7(A,B,C,D,E) -> f10(A,B,0,D,E) [4 >= B] (?,1) 2. f10(A,B,C,D,E) -> f13(A,B,C,0,E) [4 >= C] (?,1) 3. f13(A,B,C,D,E) -> f16(A,B,C,D,0) [4 >= D] (?,1) 4. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E && A >= 1 + F] (?,1) 5. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E] (?,1) 6. f16(A,B,C,D,E) -> f31(A,B,C,D,E) [4 >= E] (?,1) 7. f16(A,B,C,D,E) -> f13(A,B,C,1 + D,E) [E >= 5] (?,1) 8. f13(A,B,C,D,E) -> f10(A,B,1 + C,D,E) [D >= 5] (?,1) 9. f10(A,B,C,D,E) -> f7(A,1 + B,C,D,E) [C >= 5] (?,1) 10. f7(A,B,C,D,E) -> f31(A,B,C,D,E) [B >= 5] (?,1) Signature: {(f0,5);(f10,5);(f13,5);(f16,5);(f31,5);(f7,5)} Flow Graph: [0->{1,10},1->{2,9},2->{3,8},3->{4,5,6,7},4->{4,5,6,7},5->{4,5,6,7},6->{},7->{3,8},8->{2,9},9->{1,10} ,10->{}] Sizebounds: (< 0,0,A>, ?) (< 0,0,B>, ?) (< 0,0,C>, ?) (< 0,0,D>, ?) (< 0,0,E>, ?) (< 1,0,A>, ?) (< 1,0,B>, ?) (< 1,0,C>, ?) (< 1,0,D>, ?) (< 1,0,E>, ?) (< 2,0,A>, ?) (< 2,0,B>, ?) (< 2,0,C>, ?) (< 2,0,D>, ?) (< 2,0,E>, ?) (< 3,0,A>, ?) (< 3,0,B>, ?) (< 3,0,C>, ?) (< 3,0,D>, ?) (< 3,0,E>, ?) (< 4,0,A>, ?) (< 4,0,B>, ?) (< 4,0,C>, ?) (< 4,0,D>, ?) (< 4,0,E>, ?) (< 5,0,A>, ?) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?) (< 6,0,A>, ?) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, ?) (< 7,0,A>, ?) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?) (< 8,0,A>, ?) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?) (< 9,0,A>, ?) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?) (<10,0,A>, ?) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?) + Applied Processor: SizeboundsProc + Details: Sizebounds computed: (< 0,0,A>, 400) (< 0,0,B>, 0) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E) (< 1,0,A>, 400) (< 1,0,B>, 4) (< 1,0,C>, 0) (< 1,0,D>, ?) (< 1,0,E>, ?) (< 2,0,A>, 400) (< 2,0,B>, ?) (< 2,0,C>, 4) (< 2,0,D>, 0) (< 2,0,E>, ?) (< 3,0,A>, 400) (< 3,0,B>, ?) (< 3,0,C>, ?) (< 3,0,D>, 4) (< 3,0,E>, 0) (< 4,0,A>, 400) (< 4,0,B>, ?) (< 4,0,C>, ?) (< 4,0,D>, ?) (< 4,0,E>, 5) (< 5,0,A>, 400) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, 5) (< 6,0,A>, 400) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, 5) (< 7,0,A>, 400) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, 5) (< 8,0,A>, 400) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?) (< 9,0,A>, 400) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?) (<10,0,A>, 400) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?) * Step 3: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(400,0,C,D,E) True (1,1) 1. f7(A,B,C,D,E) -> f10(A,B,0,D,E) [4 >= B] (?,1) 2. f10(A,B,C,D,E) -> f13(A,B,C,0,E) [4 >= C] (?,1) 3. f13(A,B,C,D,E) -> f16(A,B,C,D,0) [4 >= D] (?,1) 4. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E && A >= 1 + F] (?,1) 5. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E] (?,1) 6. f16(A,B,C,D,E) -> f31(A,B,C,D,E) [4 >= E] (?,1) 7. f16(A,B,C,D,E) -> f13(A,B,C,1 + D,E) [E >= 5] (?,1) 8. f13(A,B,C,D,E) -> f10(A,B,1 + C,D,E) [D >= 5] (?,1) 9. f10(A,B,C,D,E) -> f7(A,1 + B,C,D,E) [C >= 5] (?,1) 10. f7(A,B,C,D,E) -> f31(A,B,C,D,E) [B >= 5] (?,1) Signature: {(f0,5);(f10,5);(f13,5);(f16,5);(f31,5);(f7,5)} Flow Graph: [0->{1,10},1->{2,9},2->{3,8},3->{4,5,6,7},4->{4,5,6,7},5->{4,5,6,7},6->{},7->{3,8},8->{2,9},9->{1,10} ,10->{}] Sizebounds: (< 0,0,A>, 400) (< 0,0,B>, 0) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E) (< 1,0,A>, 400) (< 1,0,B>, 4) (< 1,0,C>, 0) (< 1,0,D>, ?) (< 1,0,E>, ?) (< 2,0,A>, 400) (< 2,0,B>, ?) (< 2,0,C>, 4) (< 2,0,D>, 0) (< 2,0,E>, ?) (< 3,0,A>, 400) (< 3,0,B>, ?) (< 3,0,C>, ?) (< 3,0,D>, 4) (< 3,0,E>, 0) (< 4,0,A>, 400) (< 4,0,B>, ?) (< 4,0,C>, ?) (< 4,0,D>, ?) (< 4,0,E>, 5) (< 5,0,A>, 400) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, 5) (< 6,0,A>, 400) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, 5) (< 7,0,A>, 400) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, 5) (< 8,0,A>, 400) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?) (< 9,0,A>, 400) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?) (<10,0,A>, 400) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?) + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,10),(1,9),(2,8),(3,7)] * Step 4: LeafRules WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(400,0,C,D,E) True (1,1) 1. f7(A,B,C,D,E) -> f10(A,B,0,D,E) [4 >= B] (?,1) 2. f10(A,B,C,D,E) -> f13(A,B,C,0,E) [4 >= C] (?,1) 3. f13(A,B,C,D,E) -> f16(A,B,C,D,0) [4 >= D] (?,1) 4. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E && A >= 1 + F] (?,1) 5. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E] (?,1) 6. f16(A,B,C,D,E) -> f31(A,B,C,D,E) [4 >= E] (?,1) 7. f16(A,B,C,D,E) -> f13(A,B,C,1 + D,E) [E >= 5] (?,1) 8. f13(A,B,C,D,E) -> f10(A,B,1 + C,D,E) [D >= 5] (?,1) 9. f10(A,B,C,D,E) -> f7(A,1 + B,C,D,E) [C >= 5] (?,1) 10. f7(A,B,C,D,E) -> f31(A,B,C,D,E) [B >= 5] (?,1) Signature: {(f0,5);(f10,5);(f13,5);(f16,5);(f31,5);(f7,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5,6},4->{4,5,6,7},5->{4,5,6,7},6->{},7->{3,8},8->{2,9},9->{1,10},10->{}] Sizebounds: (< 0,0,A>, 400) (< 0,0,B>, 0) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E) (< 1,0,A>, 400) (< 1,0,B>, 4) (< 1,0,C>, 0) (< 1,0,D>, ?) (< 1,0,E>, ?) (< 2,0,A>, 400) (< 2,0,B>, ?) (< 2,0,C>, 4) (< 2,0,D>, 0) (< 2,0,E>, ?) (< 3,0,A>, 400) (< 3,0,B>, ?) (< 3,0,C>, ?) (< 3,0,D>, 4) (< 3,0,E>, 0) (< 4,0,A>, 400) (< 4,0,B>, ?) (< 4,0,C>, ?) (< 4,0,D>, ?) (< 4,0,E>, 5) (< 5,0,A>, 400) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, 5) (< 6,0,A>, 400) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, 5) (< 7,0,A>, 400) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, 5) (< 8,0,A>, 400) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?) (< 9,0,A>, 400) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?) (<10,0,A>, 400) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?) + Applied Processor: LeafRules + Details: The following transitions are estimated by its predecessors and are removed [6,10] * Step 5: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(400,0,C,D,E) True (1,1) 1. f7(A,B,C,D,E) -> f10(A,B,0,D,E) [4 >= B] (?,1) 2. f10(A,B,C,D,E) -> f13(A,B,C,0,E) [4 >= C] (?,1) 3. f13(A,B,C,D,E) -> f16(A,B,C,D,0) [4 >= D] (?,1) 4. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E && A >= 1 + F] (?,1) 5. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E] (?,1) 7. f16(A,B,C,D,E) -> f13(A,B,C,1 + D,E) [E >= 5] (?,1) 8. f13(A,B,C,D,E) -> f10(A,B,1 + C,D,E) [D >= 5] (?,1) 9. f10(A,B,C,D,E) -> f7(A,1 + B,C,D,E) [C >= 5] (?,1) Signature: {(f0,5);(f10,5);(f13,5);(f16,5);(f31,5);(f7,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5},4->{4,5,7},5->{4,5,7},7->{3,8},8->{2,9},9->{1}] Sizebounds: (<0,0,A>, 400) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<1,0,A>, 400) (<1,0,B>, 4) (<1,0,C>, 0) (<1,0,D>, ?) (<1,0,E>, ?) (<2,0,A>, 400) (<2,0,B>, ?) (<2,0,C>, 4) (<2,0,D>, 0) (<2,0,E>, ?) (<3,0,A>, 400) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 4) (<3,0,E>, 0) (<4,0,A>, 400) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, ?) (<4,0,E>, 5) (<5,0,A>, 400) (<5,0,B>, ?) (<5,0,C>, ?) (<5,0,D>, ?) (<5,0,E>, 5) (<7,0,A>, 400) (<7,0,B>, ?) (<7,0,C>, ?) (<7,0,D>, ?) (<7,0,E>, 5) (<8,0,A>, 400) (<8,0,B>, ?) (<8,0,C>, ?) (<8,0,D>, ?) (<8,0,E>, ?) (<9,0,A>, 400) (<9,0,B>, ?) (<9,0,C>, ?) (<9,0,D>, ?) (<9,0,E>, ?) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 5 p(f10) = 4 + -1*x2 p(f13) = 4 + -1*x2 p(f16) = 4 + -1*x2 p(f7) = 5 + -1*x2 The following rules are strictly oriented: [4 >= B] ==> f7(A,B,C,D,E) = 5 + -1*B > 4 + -1*B = f10(A,B,0,D,E) The following rules are weakly oriented: True ==> f0(A,B,C,D,E) = 5 >= 5 = f7(400,0,C,D,E) [4 >= C] ==> f10(A,B,C,D,E) = 4 + -1*B >= 4 + -1*B = f13(A,B,C,0,E) [4 >= D] ==> f13(A,B,C,D,E) = 4 + -1*B >= 4 + -1*B = f16(A,B,C,D,0) [4 >= E && A >= 1 + F] ==> f16(A,B,C,D,E) = 4 + -1*B >= 4 + -1*B = f16(A,B,C,D,1 + E) [4 >= E] ==> f16(A,B,C,D,E) = 4 + -1*B >= 4 + -1*B = f16(A,B,C,D,1 + E) [E >= 5] ==> f16(A,B,C,D,E) = 4 + -1*B >= 4 + -1*B = f13(A,B,C,1 + D,E) [D >= 5] ==> f13(A,B,C,D,E) = 4 + -1*B >= 4 + -1*B = f10(A,B,1 + C,D,E) [C >= 5] ==> f10(A,B,C,D,E) = 4 + -1*B >= 4 + -1*B = f7(A,1 + B,C,D,E) * Step 6: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(400,0,C,D,E) True (1,1) 1. f7(A,B,C,D,E) -> f10(A,B,0,D,E) [4 >= B] (5,1) 2. f10(A,B,C,D,E) -> f13(A,B,C,0,E) [4 >= C] (?,1) 3. f13(A,B,C,D,E) -> f16(A,B,C,D,0) [4 >= D] (?,1) 4. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E && A >= 1 + F] (?,1) 5. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E] (?,1) 7. f16(A,B,C,D,E) -> f13(A,B,C,1 + D,E) [E >= 5] (?,1) 8. f13(A,B,C,D,E) -> f10(A,B,1 + C,D,E) [D >= 5] (?,1) 9. f10(A,B,C,D,E) -> f7(A,1 + B,C,D,E) [C >= 5] (?,1) Signature: {(f0,5);(f10,5);(f13,5);(f16,5);(f31,5);(f7,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5},4->{4,5,7},5->{4,5,7},7->{3,8},8->{2,9},9->{1}] Sizebounds: (<0,0,A>, 400) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<1,0,A>, 400) (<1,0,B>, 4) (<1,0,C>, 0) (<1,0,D>, ?) (<1,0,E>, ?) (<2,0,A>, 400) (<2,0,B>, ?) (<2,0,C>, 4) (<2,0,D>, 0) (<2,0,E>, ?) (<3,0,A>, 400) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 4) (<3,0,E>, 0) (<4,0,A>, 400) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, ?) (<4,0,E>, 5) (<5,0,A>, 400) (<5,0,B>, ?) (<5,0,C>, ?) (<5,0,D>, ?) (<5,0,E>, 5) (<7,0,A>, 400) (<7,0,B>, ?) (<7,0,C>, ?) (<7,0,D>, ?) (<7,0,E>, 5) (<8,0,A>, 400) (<8,0,B>, ?) (<8,0,C>, ?) (<8,0,D>, ?) (<8,0,E>, ?) (<9,0,A>, 400) (<9,0,B>, ?) (<9,0,C>, ?) (<9,0,D>, ?) (<9,0,E>, ?) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [9,8,7,4,3,2,5], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f10) = 1 p(f13) = 1 p(f16) = 1 p(f7) = 0 The following rules are strictly oriented: [C >= 5] ==> f10(A,B,C,D,E) = 1 > 0 = f7(A,1 + B,C,D,E) The following rules are weakly oriented: [4 >= C] ==> f10(A,B,C,D,E) = 1 >= 1 = f13(A,B,C,0,E) [4 >= D] ==> f13(A,B,C,D,E) = 1 >= 1 = f16(A,B,C,D,0) [4 >= E && A >= 1 + F] ==> f16(A,B,C,D,E) = 1 >= 1 = f16(A,B,C,D,1 + E) [4 >= E] ==> f16(A,B,C,D,E) = 1 >= 1 = f16(A,B,C,D,1 + E) [E >= 5] ==> f16(A,B,C,D,E) = 1 >= 1 = f13(A,B,C,1 + D,E) [D >= 5] ==> f13(A,B,C,D,E) = 1 >= 1 = f10(A,B,1 + C,D,E) We use the following global sizebounds: (<0,0,A>, 400) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<1,0,A>, 400) (<1,0,B>, 4) (<1,0,C>, 0) (<1,0,D>, ?) (<1,0,E>, ?) (<2,0,A>, 400) (<2,0,B>, ?) (<2,0,C>, 4) (<2,0,D>, 0) (<2,0,E>, ?) (<3,0,A>, 400) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 4) (<3,0,E>, 0) (<4,0,A>, 400) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, ?) (<4,0,E>, 5) (<5,0,A>, 400) (<5,0,B>, ?) (<5,0,C>, ?) (<5,0,D>, ?) (<5,0,E>, 5) (<7,0,A>, 400) (<7,0,B>, ?) (<7,0,C>, ?) (<7,0,D>, ?) (<7,0,E>, 5) (<8,0,A>, 400) (<8,0,B>, ?) (<8,0,C>, ?) (<8,0,D>, ?) (<8,0,E>, ?) (<9,0,A>, 400) (<9,0,B>, ?) (<9,0,C>, ?) (<9,0,D>, ?) (<9,0,E>, ?) * Step 7: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(400,0,C,D,E) True (1,1) 1. f7(A,B,C,D,E) -> f10(A,B,0,D,E) [4 >= B] (5,1) 2. f10(A,B,C,D,E) -> f13(A,B,C,0,E) [4 >= C] (?,1) 3. f13(A,B,C,D,E) -> f16(A,B,C,D,0) [4 >= D] (?,1) 4. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E && A >= 1 + F] (?,1) 5. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E] (?,1) 7. f16(A,B,C,D,E) -> f13(A,B,C,1 + D,E) [E >= 5] (?,1) 8. f13(A,B,C,D,E) -> f10(A,B,1 + C,D,E) [D >= 5] (?,1) 9. f10(A,B,C,D,E) -> f7(A,1 + B,C,D,E) [C >= 5] (5,1) Signature: {(f0,5);(f10,5);(f13,5);(f16,5);(f31,5);(f7,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5},4->{4,5,7},5->{4,5,7},7->{3,8},8->{2,9},9->{1}] Sizebounds: (<0,0,A>, 400) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<1,0,A>, 400) (<1,0,B>, 4) (<1,0,C>, 0) (<1,0,D>, ?) (<1,0,E>, ?) (<2,0,A>, 400) (<2,0,B>, ?) (<2,0,C>, 4) (<2,0,D>, 0) (<2,0,E>, ?) (<3,0,A>, 400) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 4) (<3,0,E>, 0) (<4,0,A>, 400) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, ?) (<4,0,E>, 5) (<5,0,A>, 400) (<5,0,B>, ?) (<5,0,C>, ?) (<5,0,D>, ?) (<5,0,E>, 5) (<7,0,A>, 400) (<7,0,B>, ?) (<7,0,C>, ?) (<7,0,D>, ?) (<7,0,E>, 5) (<8,0,A>, 400) (<8,0,B>, ?) (<8,0,C>, ?) (<8,0,D>, ?) (<8,0,E>, ?) (<9,0,A>, 400) (<9,0,B>, ?) (<9,0,C>, ?) (<9,0,D>, ?) (<9,0,E>, ?) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [1,8,7,4,3,2,5], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f10) = 5 + -1*x3 p(f13) = 4 + -1*x3 p(f16) = 4 + -1*x3 p(f7) = 5 The following rules are strictly oriented: [4 >= C] ==> f10(A,B,C,D,E) = 5 + -1*C > 4 + -1*C = f13(A,B,C,0,E) The following rules are weakly oriented: [4 >= B] ==> f7(A,B,C,D,E) = 5 >= 5 = f10(A,B,0,D,E) [4 >= D] ==> f13(A,B,C,D,E) = 4 + -1*C >= 4 + -1*C = f16(A,B,C,D,0) [4 >= E && A >= 1 + F] ==> f16(A,B,C,D,E) = 4 + -1*C >= 4 + -1*C = f16(A,B,C,D,1 + E) [4 >= E] ==> f16(A,B,C,D,E) = 4 + -1*C >= 4 + -1*C = f16(A,B,C,D,1 + E) [E >= 5] ==> f16(A,B,C,D,E) = 4 + -1*C >= 4 + -1*C = f13(A,B,C,1 + D,E) [D >= 5] ==> f13(A,B,C,D,E) = 4 + -1*C >= 4 + -1*C = f10(A,B,1 + C,D,E) We use the following global sizebounds: (<0,0,A>, 400) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<1,0,A>, 400) (<1,0,B>, 4) (<1,0,C>, 0) (<1,0,D>, ?) (<1,0,E>, ?) (<2,0,A>, 400) (<2,0,B>, ?) (<2,0,C>, 4) (<2,0,D>, 0) (<2,0,E>, ?) (<3,0,A>, 400) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 4) (<3,0,E>, 0) (<4,0,A>, 400) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, ?) (<4,0,E>, 5) (<5,0,A>, 400) (<5,0,B>, ?) (<5,0,C>, ?) (<5,0,D>, ?) (<5,0,E>, 5) (<7,0,A>, 400) (<7,0,B>, ?) (<7,0,C>, ?) (<7,0,D>, ?) (<7,0,E>, 5) (<8,0,A>, 400) (<8,0,B>, ?) (<8,0,C>, ?) (<8,0,D>, ?) (<8,0,E>, ?) (<9,0,A>, 400) (<9,0,B>, ?) (<9,0,C>, ?) (<9,0,D>, ?) (<9,0,E>, ?) * Step 8: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(400,0,C,D,E) True (1,1) 1. f7(A,B,C,D,E) -> f10(A,B,0,D,E) [4 >= B] (5,1) 2. f10(A,B,C,D,E) -> f13(A,B,C,0,E) [4 >= C] (30,1) 3. f13(A,B,C,D,E) -> f16(A,B,C,D,0) [4 >= D] (?,1) 4. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E && A >= 1 + F] (?,1) 5. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E] (?,1) 7. f16(A,B,C,D,E) -> f13(A,B,C,1 + D,E) [E >= 5] (?,1) 8. f13(A,B,C,D,E) -> f10(A,B,1 + C,D,E) [D >= 5] (?,1) 9. f10(A,B,C,D,E) -> f7(A,1 + B,C,D,E) [C >= 5] (5,1) Signature: {(f0,5);(f10,5);(f13,5);(f16,5);(f31,5);(f7,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5},4->{4,5,7},5->{4,5,7},7->{3,8},8->{2,9},9->{1}] Sizebounds: (<0,0,A>, 400) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<1,0,A>, 400) (<1,0,B>, 4) (<1,0,C>, 0) (<1,0,D>, ?) (<1,0,E>, ?) (<2,0,A>, 400) (<2,0,B>, ?) (<2,0,C>, 4) (<2,0,D>, 0) (<2,0,E>, ?) (<3,0,A>, 400) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 4) (<3,0,E>, 0) (<4,0,A>, 400) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, ?) (<4,0,E>, 5) (<5,0,A>, 400) (<5,0,B>, ?) (<5,0,C>, ?) (<5,0,D>, ?) (<5,0,E>, 5) (<7,0,A>, 400) (<7,0,B>, ?) (<7,0,C>, ?) (<7,0,D>, ?) (<7,0,E>, 5) (<8,0,A>, 400) (<8,0,B>, ?) (<8,0,C>, ?) (<8,0,D>, ?) (<8,0,E>, ?) (<9,0,A>, 400) (<9,0,B>, ?) (<9,0,C>, ?) (<9,0,D>, ?) (<9,0,E>, ?) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [1,9,8,7,4,3,5], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f10) = 0 p(f13) = 1 p(f16) = 1 p(f7) = 0 The following rules are strictly oriented: [D >= 5] ==> f13(A,B,C,D,E) = 1 > 0 = f10(A,B,1 + C,D,E) The following rules are weakly oriented: [4 >= B] ==> f7(A,B,C,D,E) = 0 >= 0 = f10(A,B,0,D,E) [4 >= D] ==> f13(A,B,C,D,E) = 1 >= 1 = f16(A,B,C,D,0) [4 >= E && A >= 1 + F] ==> f16(A,B,C,D,E) = 1 >= 1 = f16(A,B,C,D,1 + E) [4 >= E] ==> f16(A,B,C,D,E) = 1 >= 1 = f16(A,B,C,D,1 + E) [E >= 5] ==> f16(A,B,C,D,E) = 1 >= 1 = f13(A,B,C,1 + D,E) [C >= 5] ==> f10(A,B,C,D,E) = 0 >= 0 = f7(A,1 + B,C,D,E) We use the following global sizebounds: (<0,0,A>, 400) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<1,0,A>, 400) (<1,0,B>, 4) (<1,0,C>, 0) (<1,0,D>, ?) (<1,0,E>, ?) (<2,0,A>, 400) (<2,0,B>, ?) (<2,0,C>, 4) (<2,0,D>, 0) (<2,0,E>, ?) (<3,0,A>, 400) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 4) (<3,0,E>, 0) (<4,0,A>, 400) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, ?) (<4,0,E>, 5) (<5,0,A>, 400) (<5,0,B>, ?) (<5,0,C>, ?) (<5,0,D>, ?) (<5,0,E>, 5) (<7,0,A>, 400) (<7,0,B>, ?) (<7,0,C>, ?) (<7,0,D>, ?) (<7,0,E>, 5) (<8,0,A>, 400) (<8,0,B>, ?) (<8,0,C>, ?) (<8,0,D>, ?) (<8,0,E>, ?) (<9,0,A>, 400) (<9,0,B>, ?) (<9,0,C>, ?) (<9,0,D>, ?) (<9,0,E>, ?) * Step 9: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(400,0,C,D,E) True (1,1) 1. f7(A,B,C,D,E) -> f10(A,B,0,D,E) [4 >= B] (5,1) 2. f10(A,B,C,D,E) -> f13(A,B,C,0,E) [4 >= C] (30,1) 3. f13(A,B,C,D,E) -> f16(A,B,C,D,0) [4 >= D] (?,1) 4. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E && A >= 1 + F] (?,1) 5. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E] (?,1) 7. f16(A,B,C,D,E) -> f13(A,B,C,1 + D,E) [E >= 5] (?,1) 8. f13(A,B,C,D,E) -> f10(A,B,1 + C,D,E) [D >= 5] (30,1) 9. f10(A,B,C,D,E) -> f7(A,1 + B,C,D,E) [C >= 5] (5,1) Signature: {(f0,5);(f10,5);(f13,5);(f16,5);(f31,5);(f7,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5},4->{4,5,7},5->{4,5,7},7->{3,8},8->{2,9},9->{1}] Sizebounds: (<0,0,A>, 400) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<1,0,A>, 400) (<1,0,B>, 4) (<1,0,C>, 0) (<1,0,D>, ?) (<1,0,E>, ?) (<2,0,A>, 400) (<2,0,B>, ?) (<2,0,C>, 4) (<2,0,D>, 0) (<2,0,E>, ?) (<3,0,A>, 400) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 4) (<3,0,E>, 0) (<4,0,A>, 400) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, ?) (<4,0,E>, 5) (<5,0,A>, 400) (<5,0,B>, ?) (<5,0,C>, ?) (<5,0,D>, ?) (<5,0,E>, 5) (<7,0,A>, 400) (<7,0,B>, ?) (<7,0,C>, ?) (<7,0,D>, ?) (<7,0,E>, 5) (<8,0,A>, 400) (<8,0,B>, ?) (<8,0,C>, ?) (<8,0,D>, ?) (<8,0,E>, ?) (<9,0,A>, 400) (<9,0,B>, ?) (<9,0,C>, ?) (<9,0,D>, ?) (<9,0,E>, ?) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [1,9,7,4,3,2,5], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f10) = 5 p(f13) = 5 + -1*x4 p(f16) = 4 + -1*x4 p(f7) = 5 The following rules are strictly oriented: [4 >= D] ==> f13(A,B,C,D,E) = 5 + -1*D > 4 + -1*D = f16(A,B,C,D,0) The following rules are weakly oriented: [4 >= B] ==> f7(A,B,C,D,E) = 5 >= 5 = f10(A,B,0,D,E) [4 >= C] ==> f10(A,B,C,D,E) = 5 >= 5 = f13(A,B,C,0,E) [4 >= E && A >= 1 + F] ==> f16(A,B,C,D,E) = 4 + -1*D >= 4 + -1*D = f16(A,B,C,D,1 + E) [4 >= E] ==> f16(A,B,C,D,E) = 4 + -1*D >= 4 + -1*D = f16(A,B,C,D,1 + E) [E >= 5] ==> f16(A,B,C,D,E) = 4 + -1*D >= 4 + -1*D = f13(A,B,C,1 + D,E) [C >= 5] ==> f10(A,B,C,D,E) = 5 >= 5 = f7(A,1 + B,C,D,E) We use the following global sizebounds: (<0,0,A>, 400) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<1,0,A>, 400) (<1,0,B>, 4) (<1,0,C>, 0) (<1,0,D>, ?) (<1,0,E>, ?) (<2,0,A>, 400) (<2,0,B>, ?) (<2,0,C>, 4) (<2,0,D>, 0) (<2,0,E>, ?) (<3,0,A>, 400) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 4) (<3,0,E>, 0) (<4,0,A>, 400) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, ?) (<4,0,E>, 5) (<5,0,A>, 400) (<5,0,B>, ?) (<5,0,C>, ?) (<5,0,D>, ?) (<5,0,E>, 5) (<7,0,A>, 400) (<7,0,B>, ?) (<7,0,C>, ?) (<7,0,D>, ?) (<7,0,E>, 5) (<8,0,A>, 400) (<8,0,B>, ?) (<8,0,C>, ?) (<8,0,D>, ?) (<8,0,E>, ?) (<9,0,A>, 400) (<9,0,B>, ?) (<9,0,C>, ?) (<9,0,D>, ?) (<9,0,E>, ?) * Step 10: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(400,0,C,D,E) True (1,1) 1. f7(A,B,C,D,E) -> f10(A,B,0,D,E) [4 >= B] (5,1) 2. f10(A,B,C,D,E) -> f13(A,B,C,0,E) [4 >= C] (30,1) 3. f13(A,B,C,D,E) -> f16(A,B,C,D,0) [4 >= D] (155,1) 4. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E && A >= 1 + F] (?,1) 5. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E] (?,1) 7. f16(A,B,C,D,E) -> f13(A,B,C,1 + D,E) [E >= 5] (?,1) 8. f13(A,B,C,D,E) -> f10(A,B,1 + C,D,E) [D >= 5] (30,1) 9. f10(A,B,C,D,E) -> f7(A,1 + B,C,D,E) [C >= 5] (5,1) Signature: {(f0,5);(f10,5);(f13,5);(f16,5);(f31,5);(f7,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5},4->{4,5,7},5->{4,5,7},7->{3,8},8->{2,9},9->{1}] Sizebounds: (<0,0,A>, 400) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<1,0,A>, 400) (<1,0,B>, 4) (<1,0,C>, 0) (<1,0,D>, ?) (<1,0,E>, ?) (<2,0,A>, 400) (<2,0,B>, ?) (<2,0,C>, 4) (<2,0,D>, 0) (<2,0,E>, ?) (<3,0,A>, 400) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 4) (<3,0,E>, 0) (<4,0,A>, 400) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, ?) (<4,0,E>, 5) (<5,0,A>, 400) (<5,0,B>, ?) (<5,0,C>, ?) (<5,0,D>, ?) (<5,0,E>, 5) (<7,0,A>, 400) (<7,0,B>, ?) (<7,0,C>, ?) (<7,0,D>, ?) (<7,0,E>, 5) (<8,0,A>, 400) (<8,0,B>, ?) (<8,0,C>, ?) (<8,0,D>, ?) (<8,0,E>, ?) (<9,0,A>, 400) (<9,0,B>, ?) (<9,0,C>, ?) (<9,0,D>, ?) (<9,0,E>, ?) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [1,9,8,7,4,2,5], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f10) = 0 p(f13) = 0 p(f16) = 1 p(f7) = 0 The following rules are strictly oriented: [E >= 5] ==> f16(A,B,C,D,E) = 1 > 0 = f13(A,B,C,1 + D,E) The following rules are weakly oriented: [4 >= B] ==> f7(A,B,C,D,E) = 0 >= 0 = f10(A,B,0,D,E) [4 >= C] ==> f10(A,B,C,D,E) = 0 >= 0 = f13(A,B,C,0,E) [4 >= E && A >= 1 + F] ==> f16(A,B,C,D,E) = 1 >= 1 = f16(A,B,C,D,1 + E) [4 >= E] ==> f16(A,B,C,D,E) = 1 >= 1 = f16(A,B,C,D,1 + E) [D >= 5] ==> f13(A,B,C,D,E) = 0 >= 0 = f10(A,B,1 + C,D,E) [C >= 5] ==> f10(A,B,C,D,E) = 0 >= 0 = f7(A,1 + B,C,D,E) We use the following global sizebounds: (<0,0,A>, 400) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<1,0,A>, 400) (<1,0,B>, 4) (<1,0,C>, 0) (<1,0,D>, ?) (<1,0,E>, ?) (<2,0,A>, 400) (<2,0,B>, ?) (<2,0,C>, 4) (<2,0,D>, 0) (<2,0,E>, ?) (<3,0,A>, 400) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 4) (<3,0,E>, 0) (<4,0,A>, 400) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, ?) (<4,0,E>, 5) (<5,0,A>, 400) (<5,0,B>, ?) (<5,0,C>, ?) (<5,0,D>, ?) (<5,0,E>, 5) (<7,0,A>, 400) (<7,0,B>, ?) (<7,0,C>, ?) (<7,0,D>, ?) (<7,0,E>, 5) (<8,0,A>, 400) (<8,0,B>, ?) (<8,0,C>, ?) (<8,0,D>, ?) (<8,0,E>, ?) (<9,0,A>, 400) (<9,0,B>, ?) (<9,0,C>, ?) (<9,0,D>, ?) (<9,0,E>, ?) * Step 11: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(400,0,C,D,E) True (1,1) 1. f7(A,B,C,D,E) -> f10(A,B,0,D,E) [4 >= B] (5,1) 2. f10(A,B,C,D,E) -> f13(A,B,C,0,E) [4 >= C] (30,1) 3. f13(A,B,C,D,E) -> f16(A,B,C,D,0) [4 >= D] (155,1) 4. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E && A >= 1 + F] (?,1) 5. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E] (?,1) 7. f16(A,B,C,D,E) -> f13(A,B,C,1 + D,E) [E >= 5] (155,1) 8. f13(A,B,C,D,E) -> f10(A,B,1 + C,D,E) [D >= 5] (30,1) 9. f10(A,B,C,D,E) -> f7(A,1 + B,C,D,E) [C >= 5] (5,1) Signature: {(f0,5);(f10,5);(f13,5);(f16,5);(f31,5);(f7,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5},4->{4,5,7},5->{4,5,7},7->{3,8},8->{2,9},9->{1}] Sizebounds: (<0,0,A>, 400) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<1,0,A>, 400) (<1,0,B>, 4) (<1,0,C>, 0) (<1,0,D>, ?) (<1,0,E>, ?) (<2,0,A>, 400) (<2,0,B>, ?) (<2,0,C>, 4) (<2,0,D>, 0) (<2,0,E>, ?) (<3,0,A>, 400) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 4) (<3,0,E>, 0) (<4,0,A>, 400) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, ?) (<4,0,E>, 5) (<5,0,A>, 400) (<5,0,B>, ?) (<5,0,C>, ?) (<5,0,D>, ?) (<5,0,E>, 5) (<7,0,A>, 400) (<7,0,B>, ?) (<7,0,C>, ?) (<7,0,D>, ?) (<7,0,E>, 5) (<8,0,A>, 400) (<8,0,B>, ?) (<8,0,C>, ?) (<8,0,D>, ?) (<8,0,E>, ?) (<9,0,A>, 400) (<9,0,B>, ?) (<9,0,C>, ?) (<9,0,D>, ?) (<9,0,E>, ?) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [1,9,8,4,3,2,5], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f10) = 5 p(f13) = 5 p(f16) = 5 + -1*x5 p(f7) = 5 The following rules are strictly oriented: [4 >= E] ==> f16(A,B,C,D,E) = 5 + -1*E > 4 + -1*E = f16(A,B,C,D,1 + E) The following rules are weakly oriented: [4 >= B] ==> f7(A,B,C,D,E) = 5 >= 5 = f10(A,B,0,D,E) [4 >= C] ==> f10(A,B,C,D,E) = 5 >= 5 = f13(A,B,C,0,E) [4 >= D] ==> f13(A,B,C,D,E) = 5 >= 5 = f16(A,B,C,D,0) [4 >= E && A >= 1 + F] ==> f16(A,B,C,D,E) = 5 + -1*E >= 4 + -1*E = f16(A,B,C,D,1 + E) [D >= 5] ==> f13(A,B,C,D,E) = 5 >= 5 = f10(A,B,1 + C,D,E) [C >= 5] ==> f10(A,B,C,D,E) = 5 >= 5 = f7(A,1 + B,C,D,E) We use the following global sizebounds: (<0,0,A>, 400) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<1,0,A>, 400) (<1,0,B>, 4) (<1,0,C>, 0) (<1,0,D>, ?) (<1,0,E>, ?) (<2,0,A>, 400) (<2,0,B>, ?) (<2,0,C>, 4) (<2,0,D>, 0) (<2,0,E>, ?) (<3,0,A>, 400) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 4) (<3,0,E>, 0) (<4,0,A>, 400) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, ?) (<4,0,E>, 5) (<5,0,A>, 400) (<5,0,B>, ?) (<5,0,C>, ?) (<5,0,D>, ?) (<5,0,E>, 5) (<7,0,A>, 400) (<7,0,B>, ?) (<7,0,C>, ?) (<7,0,D>, ?) (<7,0,E>, 5) (<8,0,A>, 400) (<8,0,B>, ?) (<8,0,C>, ?) (<8,0,D>, ?) (<8,0,E>, ?) (<9,0,A>, 400) (<9,0,B>, ?) (<9,0,C>, ?) (<9,0,D>, ?) (<9,0,E>, ?) * Step 12: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(400,0,C,D,E) True (1,1) 1. f7(A,B,C,D,E) -> f10(A,B,0,D,E) [4 >= B] (5,1) 2. f10(A,B,C,D,E) -> f13(A,B,C,0,E) [4 >= C] (30,1) 3. f13(A,B,C,D,E) -> f16(A,B,C,D,0) [4 >= D] (155,1) 4. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E && A >= 1 + F] (?,1) 5. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E] (780,1) 7. f16(A,B,C,D,E) -> f13(A,B,C,1 + D,E) [E >= 5] (155,1) 8. f13(A,B,C,D,E) -> f10(A,B,1 + C,D,E) [D >= 5] (30,1) 9. f10(A,B,C,D,E) -> f7(A,1 + B,C,D,E) [C >= 5] (5,1) Signature: {(f0,5);(f10,5);(f13,5);(f16,5);(f31,5);(f7,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5},4->{4,5,7},5->{4,5,7},7->{3,8},8->{2,9},9->{1}] Sizebounds: (<0,0,A>, 400) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<1,0,A>, 400) (<1,0,B>, 4) (<1,0,C>, 0) (<1,0,D>, ?) (<1,0,E>, ?) (<2,0,A>, 400) (<2,0,B>, ?) (<2,0,C>, 4) (<2,0,D>, 0) (<2,0,E>, ?) (<3,0,A>, 400) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 4) (<3,0,E>, 0) (<4,0,A>, 400) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, ?) (<4,0,E>, 5) (<5,0,A>, 400) (<5,0,B>, ?) (<5,0,C>, ?) (<5,0,D>, ?) (<5,0,E>, 5) (<7,0,A>, 400) (<7,0,B>, ?) (<7,0,C>, ?) (<7,0,D>, ?) (<7,0,E>, 5) (<8,0,A>, 400) (<8,0,B>, ?) (<8,0,C>, ?) (<8,0,D>, ?) (<8,0,E>, ?) (<9,0,A>, 400) (<9,0,B>, ?) (<9,0,C>, ?) (<9,0,D>, ?) (<9,0,E>, ?) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [1,9,8,4,3,2,5], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f10) = 5 p(f13) = 5 p(f16) = 5 + -1*x5 p(f7) = 5 The following rules are strictly oriented: [4 >= E && A >= 1 + F] ==> f16(A,B,C,D,E) = 5 + -1*E > 4 + -1*E = f16(A,B,C,D,1 + E) [4 >= E] ==> f16(A,B,C,D,E) = 5 + -1*E > 4 + -1*E = f16(A,B,C,D,1 + E) The following rules are weakly oriented: [4 >= B] ==> f7(A,B,C,D,E) = 5 >= 5 = f10(A,B,0,D,E) [4 >= C] ==> f10(A,B,C,D,E) = 5 >= 5 = f13(A,B,C,0,E) [4 >= D] ==> f13(A,B,C,D,E) = 5 >= 5 = f16(A,B,C,D,0) [D >= 5] ==> f13(A,B,C,D,E) = 5 >= 5 = f10(A,B,1 + C,D,E) [C >= 5] ==> f10(A,B,C,D,E) = 5 >= 5 = f7(A,1 + B,C,D,E) We use the following global sizebounds: (<0,0,A>, 400) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<1,0,A>, 400) (<1,0,B>, 4) (<1,0,C>, 0) (<1,0,D>, ?) (<1,0,E>, ?) (<2,0,A>, 400) (<2,0,B>, ?) (<2,0,C>, 4) (<2,0,D>, 0) (<2,0,E>, ?) (<3,0,A>, 400) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 4) (<3,0,E>, 0) (<4,0,A>, 400) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, ?) (<4,0,E>, 5) (<5,0,A>, 400) (<5,0,B>, ?) (<5,0,C>, ?) (<5,0,D>, ?) (<5,0,E>, 5) (<7,0,A>, 400) (<7,0,B>, ?) (<7,0,C>, ?) (<7,0,D>, ?) (<7,0,E>, 5) (<8,0,A>, 400) (<8,0,B>, ?) (<8,0,C>, ?) (<8,0,D>, ?) (<8,0,E>, ?) (<9,0,A>, 400) (<9,0,B>, ?) (<9,0,C>, ?) (<9,0,D>, ?) (<9,0,E>, ?) * Step 13: KnowledgePropagation WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(400,0,C,D,E) True (1,1) 1. f7(A,B,C,D,E) -> f10(A,B,0,D,E) [4 >= B] (5,1) 2. f10(A,B,C,D,E) -> f13(A,B,C,0,E) [4 >= C] (30,1) 3. f13(A,B,C,D,E) -> f16(A,B,C,D,0) [4 >= D] (155,1) 4. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E && A >= 1 + F] (780,1) 5. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E] (780,1) 7. f16(A,B,C,D,E) -> f13(A,B,C,1 + D,E) [E >= 5] (155,1) 8. f13(A,B,C,D,E) -> f10(A,B,1 + C,D,E) [D >= 5] (30,1) 9. f10(A,B,C,D,E) -> f7(A,1 + B,C,D,E) [C >= 5] (5,1) Signature: {(f0,5);(f10,5);(f13,5);(f16,5);(f31,5);(f7,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5},4->{4,5,7},5->{4,5,7},7->{3,8},8->{2,9},9->{1}] Sizebounds: (<0,0,A>, 400) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<1,0,A>, 400) (<1,0,B>, 4) (<1,0,C>, 0) (<1,0,D>, ?) (<1,0,E>, ?) (<2,0,A>, 400) (<2,0,B>, ?) (<2,0,C>, 4) (<2,0,D>, 0) (<2,0,E>, ?) (<3,0,A>, 400) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 4) (<3,0,E>, 0) (<4,0,A>, 400) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, ?) (<4,0,E>, 5) (<5,0,A>, 400) (<5,0,B>, ?) (<5,0,C>, ?) (<5,0,D>, ?) (<5,0,E>, 5) (<7,0,A>, 400) (<7,0,B>, ?) (<7,0,C>, ?) (<7,0,D>, ?) (<7,0,E>, 5) (<8,0,A>, 400) (<8,0,B>, ?) (<8,0,C>, ?) (<8,0,D>, ?) (<8,0,E>, ?) (<9,0,A>, 400) (<9,0,B>, ?) (<9,0,C>, ?) (<9,0,D>, ?) (<9,0,E>, ?) + Applied Processor: KnowledgePropagation + Details: The problem is already solved. WORST_CASE(?,O(1))