YES(?,O(n^1)) * Step 1: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f4(A,B,C,D,E,F,G) -> f4(A + B,B,C,D,E,F,G) [-1 + -1*B >= 0 && A >= 0] (?,1) 1. f4(A,B,C,D,E,F,G) -> f6(A,B,0,0,0,0,0) [-1 + -1*B >= 0 && 0 >= 1 + A] (?,1) 2. f5(A,B,C,D,E,F,G) -> f4(A,B,C,D,E,F,G) [0 >= 1 + B] (1,1) 3. f5(A,B,C,D,E,F,G) -> f6(A,B,0,0,0,0,0) [B >= 0] (1,1) Signature: {(f4,7);(f5,7);(f6,7)} Flow Graph: [0->{0,1},1->{},2->{0,1},3->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f4(A,B,C,D,E,F,G) -> f4(A + B,B,C,D,E,F,G) [-1 + -1*B >= 0 && A >= 0] (?,1) 1. f4(A,B,C,D,E,F,G) -> f6(A,B,0,0,0,0,0) [-1 + -1*B >= 0 && 0 >= 1 + A] (1,1) 2. f5(A,B,C,D,E,F,G) -> f4(A,B,C,D,E,F,G) [0 >= 1 + B] (1,1) 3. f5(A,B,C,D,E,F,G) -> f6(A,B,0,0,0,0,0) [B >= 0] (1,1) Signature: {(f4,7);(f5,7);(f6,7)} Flow Graph: [0->{0,1},1->{},2->{0,1},3->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f4) = 1 + x1 p(f5) = 1 + x1 p(f6) = 1 + x1 Following rules are strictly oriented: [-1 + -1*B >= 0 && A >= 0] ==> f4(A,B,C,D,E,F,G) = 1 + A > 1 + A + B = f4(A + B,B,C,D,E,F,G) Following rules are weakly oriented: [-1 + -1*B >= 0 && 0 >= 1 + A] ==> f4(A,B,C,D,E,F,G) = 1 + A >= 1 + A = f6(A,B,0,0,0,0,0) [0 >= 1 + B] ==> f5(A,B,C,D,E,F,G) = 1 + A >= 1 + A = f4(A,B,C,D,E,F,G) [B >= 0] ==> f5(A,B,C,D,E,F,G) = 1 + A >= 1 + A = f6(A,B,0,0,0,0,0) * Step 3: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f4(A,B,C,D,E,F,G) -> f4(A + B,B,C,D,E,F,G) [-1 + -1*B >= 0 && A >= 0] (1 + A,1) 1. f4(A,B,C,D,E,F,G) -> f6(A,B,0,0,0,0,0) [-1 + -1*B >= 0 && 0 >= 1 + A] (1,1) 2. f5(A,B,C,D,E,F,G) -> f4(A,B,C,D,E,F,G) [0 >= 1 + B] (1,1) 3. f5(A,B,C,D,E,F,G) -> f6(A,B,0,0,0,0,0) [B >= 0] (1,1) Signature: {(f4,7);(f5,7);(f6,7)} Flow Graph: [0->{0,1},1->{},2->{0,1},3->{}] + Applied Processor: KnowledgePropagation + Details: The problem is already solved. YES(?,O(n^1))