YES * Step 1: UnsatPaths YES + 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 YES + 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: FromIts YES + 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: FromIts + Details: () * Step 4: Decompose YES + Considered Problem: Rules: 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] 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] 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] 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 Signature: {(f0,11);(f11,11);(f38,11);(f54,11)} Rule Graph: [0->{},1->{},3->{0,1},4->{3}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,3,4] * Step 5: CloseWith YES + Considered Problem: (Rules: 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] 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] 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] 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 Signature: {(f0,11);(f11,11);(f38,11);(f54,11)} Rule Graph: [0->{},1->{},3->{0,1},4->{3}] ,We construct a looptree: P: [0,1,3,4]) + Applied Processor: CloseWith True + Details: () YES