YES(?,O(1)) * Step 1: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f11(A,B,C,D,E,F,G,H,I,J,K) -> f54(A,B,A + B,D,E,F,G,H,I,J,K) [A >= B] (?,1) 1. f11(A,B,C,D,E,F,G,H,I,J,K) -> f54(A,B,-1*A + B,D,E,F,G,H,I,J,K) [B >= 1 + A] (?,1) 2. f38(A,B,C,D,E,F,G,H,I,J,K) -> f11(L,B,C,D,E,D,D,H,I,J,K) [D >= 1 + E] (?,1) 3. f38(A,B,C,D,E,F,G,H,I,J,K) -> f11(L,B,C,D,E,D,D,M,I,J,K) [E >= D] (?,1) 4. f0(A,B,C,D,E,F,G,H,I,J,K) -> f38(1,2,C,1,10,F,G,H,10,2,L) True (1,1) Signature: {(f0,11);(f11,11);(f38,11);(f54,11)} Flow Graph: [0->{},1->{},2->{0,1},3->{0,1},4->{2,3}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(4,2)] * Step 2: UnreachableRules WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f11(A,B,C,D,E,F,G,H,I,J,K) -> f54(A,B,A + B,D,E,F,G,H,I,J,K) [A >= B] (?,1) 1. f11(A,B,C,D,E,F,G,H,I,J,K) -> f54(A,B,-1*A + B,D,E,F,G,H,I,J,K) [B >= 1 + A] (?,1) 2. f38(A,B,C,D,E,F,G,H,I,J,K) -> f11(L,B,C,D,E,D,D,H,I,J,K) [D >= 1 + E] (?,1) 3. f38(A,B,C,D,E,F,G,H,I,J,K) -> f11(L,B,C,D,E,D,D,M,I,J,K) [E >= D] (?,1) 4. f0(A,B,C,D,E,F,G,H,I,J,K) -> f38(1,2,C,1,10,F,G,H,10,2,L) True (1,1) Signature: {(f0,11);(f11,11);(f38,11);(f54,11)} Flow Graph: [0->{},1->{},2->{0,1},3->{0,1},4->{3}] + Applied Processor: UnreachableRules + Details: Following transitions are not reachable from the starting states and are revomed: [2] * Step 3: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f11(A,B,C,D,E,F,G,H,I,J,K) -> f54(A,B,A + B,D,E,F,G,H,I,J,K) [A >= B] (?,1) 1. f11(A,B,C,D,E,F,G,H,I,J,K) -> f54(A,B,-1*A + B,D,E,F,G,H,I,J,K) [B >= 1 + A] (?,1) 3. f38(A,B,C,D,E,F,G,H,I,J,K) -> f11(L,B,C,D,E,D,D,M,I,J,K) [E >= D] (?,1) 4. f0(A,B,C,D,E,F,G,H,I,J,K) -> f38(1,2,C,1,10,F,G,H,10,2,L) True (1,1) Signature: {(f0,11);(f11,11);(f38,11);(f54,11)} Flow Graph: [0->{},1->{},3->{0,1},4->{3}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 4: KnowledgePropagation WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f11(A,B,C,D,E,F,G,H,I,J,K) -> f54(A,B,A + B,D,E,F,G,H,I,J,K) [A >= B] (1,1) 1. f11(A,B,C,D,E,F,G,H,I,J,K) -> f54(A,B,-1*A + B,D,E,F,G,H,I,J,K) [B >= 1 + A] (1,1) 3. f38(A,B,C,D,E,F,G,H,I,J,K) -> f11(L,B,C,D,E,D,D,M,I,J,K) [E >= D] (1,1) 4. f0(A,B,C,D,E,F,G,H,I,J,K) -> f38(1,2,C,1,10,F,G,H,10,2,L) True (1,1) Signature: {(f0,11);(f11,11);(f38,11);(f54,11)} Flow Graph: [0->{},1->{},3->{0,1},4->{3}] + Applied Processor: KnowledgePropagation + Details: The problem is already solved. YES(?,O(1))