WORST_CASE(?,O(n^1)) * Step 1: UnreachableRules WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eq(A,B,C,D) -> eq(-1 + A,-1 + B,C,D) [A >= 1 && B >= 1] (?,1) 1. nub0(A,B,C,D) -> remove(A,-1 + B,C,D) True (?,1) 2. nub1(A,B,C,D) -> nub(C,D,C,D) True (?,1) 3. nub(A,B,C,D) -> c2(nub0(F,A,E,B),nub1(F,A,E,B)) [A >= 1 && A >= 1 + E] (?,1) 4. remove0(A,B,C,D) -> eq(A,B,C,D) True (?,1) 5. remove1(A,B,C,D) -> remove(A,-1 + D,C,B) True (?,1) 6. remove(A,B,C,D) -> c2(remove0(A,D,C,B),remove1(A,D,C,B)) [B >= 1] (?,1) 7. remove(A,B,C,D) -> remove(A,-1 + B,C,D) [B >= 1] (?,1) 8. start(A,B,C,D) -> eq(A,B,C,D) True (1,1) Signature: {(eq,4);(nub,4);(nub0,4);(nub1,4);(remove,4);(remove0,4);(remove1,4);(start,4)} Flow Graph: [0->{0},1->{6,7},2->{3},3->{1,2},4->{0},5->{6,7},6->{4,5},7->{6,7},8->{0}] + Applied Processor: UnreachableRules + Details: The following transitions are not reachable from the starting states and are removed: [1,2,3,4,5,6,7] * Step 2: LocalSizeboundsProc WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eq(A,B,C,D) -> eq(-1 + A,-1 + B,C,D) [A >= 1 && B >= 1] (?,1) 8. start(A,B,C,D) -> eq(A,B,C,D) True (1,1) Signature: {(eq,4);(nub,4);(nub0,4);(nub1,4);(remove,4);(remove0,4);(remove1,4);(start,4)} Flow Graph: [0->{0},8->{0}] + Applied Processor: LocalSizeboundsProc + Details: LocalSizebounds generated; rvgraph (<0,0,A>, 1 + A, .+ 1) (<0,0,B>, 1 + B, .+ 1) (<0,0,C>, C, .= 0) (<0,0,D>, D, .= 0) (<8,0,A>, A, .= 0) (<8,0,B>, B, .= 0) (<8,0,C>, C, .= 0) (<8,0,D>, D, .= 0) * Step 3: SizeboundsProc WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eq(A,B,C,D) -> eq(-1 + A,-1 + B,C,D) [A >= 1 && B >= 1] (?,1) 8. start(A,B,C,D) -> eq(A,B,C,D) True (1,1) Signature: {(eq,4);(nub,4);(nub0,4);(nub1,4);(remove,4);(remove0,4);(remove1,4);(start,4)} Flow Graph: [0->{0},8->{0}] Sizebounds: (<0,0,A>, ?) (<0,0,B>, ?) (<0,0,C>, ?) (<0,0,D>, ?) (<8,0,A>, ?) (<8,0,B>, ?) (<8,0,C>, ?) (<8,0,D>, ?) + Applied Processor: SizeboundsProc + Details: Sizebounds computed: (<0,0,A>, ?) (<0,0,B>, ?) (<0,0,C>, C) (<0,0,D>, D) (<8,0,A>, A) (<8,0,B>, B) (<8,0,C>, C) (<8,0,D>, D) * Step 4: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eq(A,B,C,D) -> eq(-1 + A,-1 + B,C,D) [A >= 1 && B >= 1] (?,1) 8. start(A,B,C,D) -> eq(A,B,C,D) True (1,1) Signature: {(eq,4);(nub,4);(nub0,4);(nub1,4);(remove,4);(remove0,4);(remove1,4);(start,4)} Flow Graph: [0->{0},8->{0}] Sizebounds: (<0,0,A>, ?) (<0,0,B>, ?) (<0,0,C>, C) (<0,0,D>, D) (<8,0,A>, A) (<8,0,B>, B) (<8,0,C>, C) (<8,0,D>, D) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eq) = x2 p(start) = x2 The following rules are strictly oriented: [A >= 1 && B >= 1] ==> eq(A,B,C,D) = B > -1 + B = eq(-1 + A,-1 + B,C,D) The following rules are weakly oriented: True ==> start(A,B,C,D) = B >= B = eq(A,B,C,D) * Step 5: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eq(A,B,C,D) -> eq(-1 + A,-1 + B,C,D) [A >= 1 && B >= 1] (B,1) 8. start(A,B,C,D) -> eq(A,B,C,D) True (1,1) Signature: {(eq,4);(nub,4);(nub0,4);(nub1,4);(remove,4);(remove0,4);(remove1,4);(start,4)} Flow Graph: [0->{0},8->{0}] Sizebounds: (<0,0,A>, ?) (<0,0,B>, ?) (<0,0,C>, C) (<0,0,D>, D) (<8,0,A>, A) (<8,0,B>, B) (<8,0,C>, C) (<8,0,D>, D) + Applied Processor: KnowledgePropagation + Details: The problem is already solved. WORST_CASE(?,O(n^1))