WORST_CASE(?,O(n^1)) * Step 1: UnsatRules WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval(A,B) -> eval(-1 + A,B) [A >= 1] (?,1) 1. eval(A,B) -> eval(-1 + A,B) [B >= 1 && A >= 1] (?,1) 2. eval(A,B) -> eval(A,-1 + B) [A >= 1 && 0 >= A && B >= 1] (?,1) 3. eval(A,B) -> eval(A,-1 + B) [B >= 1 && 0 >= A] (?,1) 4. eval(A,B) -> eval(A,B) [A >= 1 && 0 >= A && 0 >= B] (?,1) 5. eval(A,B) -> eval(A,B) [B >= 1 && 0 >= A && 0 >= B] (?,1) 6. start(A,B) -> eval(A,B) True (1,1) Signature: {(eval,2);(start,2)} Flow Graph: [0->{0,1,2,3,4,5},1->{0,1,2,3,4,5},2->{0,1,2,3,4,5},3->{0,1,2,3,4,5},4->{0,1,2,3,4,5},5->{0,1,2,3,4,5} ,6->{0,1,2,3,4,5}] + Applied Processor: UnsatRules + Details: The following transitions have unsatisfiable constraints and are removed: [2,4,5] * Step 2: LocalSizeboundsProc WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval(A,B) -> eval(-1 + A,B) [A >= 1] (?,1) 1. eval(A,B) -> eval(-1 + A,B) [B >= 1 && A >= 1] (?,1) 3. eval(A,B) -> eval(A,-1 + B) [B >= 1 && 0 >= A] (?,1) 6. start(A,B) -> eval(A,B) True (1,1) Signature: {(eval,2);(start,2)} Flow Graph: [0->{0,1,3},1->{0,1,3},3->{0,1,3},6->{0,1,3}] + Applied Processor: LocalSizeboundsProc + Details: LocalSizebounds generated; rvgraph (<0,0,A>, 1 + A, .+ 1) (<0,0,B>, B, .= 0) (<1,0,A>, 1 + A, .+ 1) (<1,0,B>, B, .= 0) (<3,0,A>, A, .= 0) (<3,0,B>, 1 + B, .+ 1) (<6,0,A>, A, .= 0) (<6,0,B>, B, .= 0) * Step 3: SizeboundsProc WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval(A,B) -> eval(-1 + A,B) [A >= 1] (?,1) 1. eval(A,B) -> eval(-1 + A,B) [B >= 1 && A >= 1] (?,1) 3. eval(A,B) -> eval(A,-1 + B) [B >= 1 && 0 >= A] (?,1) 6. start(A,B) -> eval(A,B) True (1,1) Signature: {(eval,2);(start,2)} Flow Graph: [0->{0,1,3},1->{0,1,3},3->{0,1,3},6->{0,1,3}] Sizebounds: (<0,0,A>, ?) (<0,0,B>, ?) (<1,0,A>, ?) (<1,0,B>, ?) (<3,0,A>, ?) (<3,0,B>, ?) (<6,0,A>, ?) (<6,0,B>, ?) + Applied Processor: SizeboundsProc + Details: Sizebounds computed: (<0,0,A>, ?) (<0,0,B>, ?) (<1,0,A>, ?) (<1,0,B>, ?) (<3,0,A>, 0) (<3,0,B>, ?) (<6,0,A>, A) (<6,0,B>, B) * Step 4: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval(A,B) -> eval(-1 + A,B) [A >= 1] (?,1) 1. eval(A,B) -> eval(-1 + A,B) [B >= 1 && A >= 1] (?,1) 3. eval(A,B) -> eval(A,-1 + B) [B >= 1 && 0 >= A] (?,1) 6. start(A,B) -> eval(A,B) True (1,1) Signature: {(eval,2);(start,2)} Flow Graph: [0->{0,1,3},1->{0,1,3},3->{0,1,3},6->{0,1,3}] Sizebounds: (<0,0,A>, ?) (<0,0,B>, ?) (<1,0,A>, ?) (<1,0,B>, ?) (<3,0,A>, 0) (<3,0,B>, ?) (<6,0,A>, A) (<6,0,B>, B) + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(3,0),(3,1)] * Step 5: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval(A,B) -> eval(-1 + A,B) [A >= 1] (?,1) 1. eval(A,B) -> eval(-1 + A,B) [B >= 1 && A >= 1] (?,1) 3. eval(A,B) -> eval(A,-1 + B) [B >= 1 && 0 >= A] (?,1) 6. start(A,B) -> eval(A,B) True (1,1) Signature: {(eval,2);(start,2)} Flow Graph: [0->{0,1,3},1->{0,1,3},3->{3},6->{0,1,3}] Sizebounds: (<0,0,A>, ?) (<0,0,B>, ?) (<1,0,A>, ?) (<1,0,B>, ?) (<3,0,A>, 0) (<3,0,B>, ?) (<6,0,A>, A) (<6,0,B>, B) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval) = x2 p(start) = x2 The following rules are strictly oriented: [B >= 1 && 0 >= A] ==> eval(A,B) = B > -1 + B = eval(A,-1 + B) The following rules are weakly oriented: [A >= 1] ==> eval(A,B) = B >= B = eval(-1 + A,B) [B >= 1 && A >= 1] ==> eval(A,B) = B >= B = eval(-1 + A,B) True ==> start(A,B) = B >= B = eval(A,B) * Step 6: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval(A,B) -> eval(-1 + A,B) [A >= 1] (?,1) 1. eval(A,B) -> eval(-1 + A,B) [B >= 1 && A >= 1] (?,1) 3. eval(A,B) -> eval(A,-1 + B) [B >= 1 && 0 >= A] (B,1) 6. start(A,B) -> eval(A,B) True (1,1) Signature: {(eval,2);(start,2)} Flow Graph: [0->{0,1,3},1->{0,1,3},3->{3},6->{0,1,3}] Sizebounds: (<0,0,A>, ?) (<0,0,B>, ?) (<1,0,A>, ?) (<1,0,B>, ?) (<3,0,A>, 0) (<3,0,B>, ?) (<6,0,A>, A) (<6,0,B>, B) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval) = x1 p(start) = x1 The following rules are strictly oriented: [B >= 1 && A >= 1] ==> eval(A,B) = A > -1 + A = eval(-1 + A,B) The following rules are weakly oriented: [A >= 1] ==> eval(A,B) = A >= -1 + A = eval(-1 + A,B) [B >= 1 && 0 >= A] ==> eval(A,B) = A >= A = eval(A,-1 + B) True ==> start(A,B) = A >= A = eval(A,B) * Step 7: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval(A,B) -> eval(-1 + A,B) [A >= 1] (?,1) 1. eval(A,B) -> eval(-1 + A,B) [B >= 1 && A >= 1] (A,1) 3. eval(A,B) -> eval(A,-1 + B) [B >= 1 && 0 >= A] (B,1) 6. start(A,B) -> eval(A,B) True (1,1) Signature: {(eval,2);(start,2)} Flow Graph: [0->{0,1,3},1->{0,1,3},3->{3},6->{0,1,3}] Sizebounds: (<0,0,A>, ?) (<0,0,B>, ?) (<1,0,A>, ?) (<1,0,B>, ?) (<3,0,A>, 0) (<3,0,B>, ?) (<6,0,A>, A) (<6,0,B>, B) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval) = x1 p(start) = x1 The following rules are strictly oriented: [A >= 1] ==> eval(A,B) = A > -1 + A = eval(-1 + A,B) [B >= 1 && A >= 1] ==> eval(A,B) = A > -1 + A = eval(-1 + A,B) The following rules are weakly oriented: [B >= 1 && 0 >= A] ==> eval(A,B) = A >= A = eval(A,-1 + B) True ==> start(A,B) = A >= A = eval(A,B) * Step 8: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval(A,B) -> eval(-1 + A,B) [A >= 1] (A,1) 1. eval(A,B) -> eval(-1 + A,B) [B >= 1 && A >= 1] (A,1) 3. eval(A,B) -> eval(A,-1 + B) [B >= 1 && 0 >= A] (B,1) 6. start(A,B) -> eval(A,B) True (1,1) Signature: {(eval,2);(start,2)} Flow Graph: [0->{0,1,3},1->{0,1,3},3->{3},6->{0,1,3}] Sizebounds: (<0,0,A>, ?) (<0,0,B>, ?) (<1,0,A>, ?) (<1,0,B>, ?) (<3,0,A>, 0) (<3,0,B>, ?) (<6,0,A>, A) (<6,0,B>, B) + Applied Processor: KnowledgePropagation + Details: The problem is already solved. WORST_CASE(?,O(n^1))