WORST_CASE(?,O(n^1)) * Step 1: RestrictVarsProcessor WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B,C,D) -> f300(A,B,C,D) True (1,1) 1. f300(A,B,C,D) -> f300(1 + A,B,E,D) [E >= 1 && B >= 1 + A] (?,1) 2. f300(A,B,C,D) -> f300(1 + A,B,E,D) [0 >= 1 + E && B >= 1 + A] (?,1) 3. f300(A,B,C,D) -> f300(A,-1 + B,0,D) [B >= 1 + A] (?,1) 4. f300(A,B,C,D) -> f1(A,B,C,E) [A >= B] (?,1) Signature: {(f1,4);(f2,4);(f300,4)} Flow Graph: [0->{1,2,3,4},1->{1,2,3,4},2->{1,2,3,4},3->{1,2,3,4},4->{}] + Applied Processor: RestrictVarsProcessor + Details: We removed the arguments [C,D] . * Step 2: LocalSizeboundsProc WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B) -> f300(A,B) True (1,1) 1. f300(A,B) -> f300(1 + A,B) [E >= 1 && B >= 1 + A] (?,1) 2. f300(A,B) -> f300(1 + A,B) [0 >= 1 + E && B >= 1 + A] (?,1) 3. f300(A,B) -> f300(A,-1 + B) [B >= 1 + A] (?,1) 4. f300(A,B) -> f1(A,B) [A >= B] (?,1) Signature: {(f1,2);(f2,2);(f300,2)} Flow Graph: [0->{1,2,3,4},1->{1,2,3,4},2->{1,2,3,4},3->{1,2,3,4},4->{}] + Applied Processor: LocalSizeboundsProc + Details: LocalSizebounds generated; rvgraph (<0,0,A>, A, .= 0) (<0,0,B>, B, .= 0) (<1,0,A>, 1 + A, .+ 1) (<1,0,B>, B, .= 0) (<2,0,A>, 1 + A, .+ 1) (<2,0,B>, B, .= 0) (<3,0,A>, A, .= 0) (<3,0,B>, 1 + B, .+ 1) (<4,0,A>, A, .= 0) (<4,0,B>, B, .= 0) * Step 3: SizeboundsProc WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B) -> f300(A,B) True (1,1) 1. f300(A,B) -> f300(1 + A,B) [E >= 1 && B >= 1 + A] (?,1) 2. f300(A,B) -> f300(1 + A,B) [0 >= 1 + E && B >= 1 + A] (?,1) 3. f300(A,B) -> f300(A,-1 + B) [B >= 1 + A] (?,1) 4. f300(A,B) -> f1(A,B) [A >= B] (?,1) Signature: {(f1,2);(f2,2);(f300,2)} Flow Graph: [0->{1,2,3,4},1->{1,2,3,4},2->{1,2,3,4},3->{1,2,3,4},4->{}] 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>, ?) (<4,0,A>, ?) (<4,0,B>, ?) + Applied Processor: SizeboundsProc + Details: Sizebounds computed: (<0,0,A>, A) (<0,0,B>, B) (<1,0,A>, ?) (<1,0,B>, ?) (<2,0,A>, ?) (<2,0,B>, ?) (<3,0,A>, ?) (<3,0,B>, ?) (<4,0,A>, ?) (<4,0,B>, ?) * Step 4: LeafRules WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B) -> f300(A,B) True (1,1) 1. f300(A,B) -> f300(1 + A,B) [E >= 1 && B >= 1 + A] (?,1) 2. f300(A,B) -> f300(1 + A,B) [0 >= 1 + E && B >= 1 + A] (?,1) 3. f300(A,B) -> f300(A,-1 + B) [B >= 1 + A] (?,1) 4. f300(A,B) -> f1(A,B) [A >= B] (?,1) Signature: {(f1,2);(f2,2);(f300,2)} Flow Graph: [0->{1,2,3,4},1->{1,2,3,4},2->{1,2,3,4},3->{1,2,3,4},4->{}] Sizebounds: (<0,0,A>, A) (<0,0,B>, B) (<1,0,A>, ?) (<1,0,B>, ?) (<2,0,A>, ?) (<2,0,B>, ?) (<3,0,A>, ?) (<3,0,B>, ?) (<4,0,A>, ?) (<4,0,B>, ?) + Applied Processor: LeafRules + Details: The following transitions are estimated by its predecessors and are removed [4] * Step 5: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B) -> f300(A,B) True (1,1) 1. f300(A,B) -> f300(1 + A,B) [E >= 1 && B >= 1 + A] (?,1) 2. f300(A,B) -> f300(1 + A,B) [0 >= 1 + E && B >= 1 + A] (?,1) 3. f300(A,B) -> f300(A,-1 + B) [B >= 1 + A] (?,1) Signature: {(f1,2);(f2,2);(f300,2)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{1,2,3},3->{1,2,3}] Sizebounds: (<0,0,A>, A) (<0,0,B>, B) (<1,0,A>, ?) (<1,0,B>, ?) (<2,0,A>, ?) (<2,0,B>, ?) (<3,0,A>, ?) (<3,0,B>, ?) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f2) = -1*x1 + x2 p(f300) = -1*x1 + x2 The following rules are strictly oriented: [B >= 1 + A] ==> f300(A,B) = -1*A + B > -1 + -1*A + B = f300(A,-1 + B) The following rules are weakly oriented: True ==> f2(A,B) = -1*A + B >= -1*A + B = f300(A,B) [E >= 1 && B >= 1 + A] ==> f300(A,B) = -1*A + B >= -1 + -1*A + B = f300(1 + A,B) [0 >= 1 + E && B >= 1 + A] ==> f300(A,B) = -1*A + B >= -1 + -1*A + B = f300(1 + A,B) * Step 6: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B) -> f300(A,B) True (1,1) 1. f300(A,B) -> f300(1 + A,B) [E >= 1 && B >= 1 + A] (?,1) 2. f300(A,B) -> f300(1 + A,B) [0 >= 1 + E && B >= 1 + A] (?,1) 3. f300(A,B) -> f300(A,-1 + B) [B >= 1 + A] (A + B,1) Signature: {(f1,2);(f2,2);(f300,2)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{1,2,3},3->{1,2,3}] Sizebounds: (<0,0,A>, A) (<0,0,B>, B) (<1,0,A>, ?) (<1,0,B>, ?) (<2,0,A>, ?) (<2,0,B>, ?) (<3,0,A>, ?) (<3,0,B>, ?) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f2) = -1*x1 + x2 p(f300) = -1*x1 + x2 The following rules are strictly oriented: [0 >= 1 + E && B >= 1 + A] ==> f300(A,B) = -1*A + B > -1 + -1*A + B = f300(1 + A,B) [B >= 1 + A] ==> f300(A,B) = -1*A + B > -1 + -1*A + B = f300(A,-1 + B) The following rules are weakly oriented: True ==> f2(A,B) = -1*A + B >= -1*A + B = f300(A,B) [E >= 1 && B >= 1 + A] ==> f300(A,B) = -1*A + B >= -1 + -1*A + B = f300(1 + A,B) * Step 7: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B) -> f300(A,B) True (1,1) 1. f300(A,B) -> f300(1 + A,B) [E >= 1 && B >= 1 + A] (?,1) 2. f300(A,B) -> f300(1 + A,B) [0 >= 1 + E && B >= 1 + A] (A + B,1) 3. f300(A,B) -> f300(A,-1 + B) [B >= 1 + A] (A + B,1) Signature: {(f1,2);(f2,2);(f300,2)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{1,2,3},3->{1,2,3}] Sizebounds: (<0,0,A>, A) (<0,0,B>, B) (<1,0,A>, ?) (<1,0,B>, ?) (<2,0,A>, ?) (<2,0,B>, ?) (<3,0,A>, ?) (<3,0,B>, ?) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f2) = -1*x1 + x2 p(f300) = -1*x1 + x2 The following rules are strictly oriented: [E >= 1 && B >= 1 + A] ==> f300(A,B) = -1*A + B > -1 + -1*A + B = f300(1 + A,B) [0 >= 1 + E && B >= 1 + A] ==> f300(A,B) = -1*A + B > -1 + -1*A + B = f300(1 + A,B) [B >= 1 + A] ==> f300(A,B) = -1*A + B > -1 + -1*A + B = f300(A,-1 + B) The following rules are weakly oriented: True ==> f2(A,B) = -1*A + B >= -1*A + B = f300(A,B) * Step 8: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B) -> f300(A,B) True (1,1) 1. f300(A,B) -> f300(1 + A,B) [E >= 1 && B >= 1 + A] (A + B,1) 2. f300(A,B) -> f300(1 + A,B) [0 >= 1 + E && B >= 1 + A] (A + B,1) 3. f300(A,B) -> f300(A,-1 + B) [B >= 1 + A] (A + B,1) Signature: {(f1,2);(f2,2);(f300,2)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{1,2,3},3->{1,2,3}] Sizebounds: (<0,0,A>, A) (<0,0,B>, B) (<1,0,A>, ?) (<1,0,B>, ?) (<2,0,A>, ?) (<2,0,B>, ?) (<3,0,A>, ?) (<3,0,B>, ?) + Applied Processor: KnowledgePropagation + Details: The problem is already solved. WORST_CASE(?,O(n^1))