YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f7(8,0,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) True (1,1) 1. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f7(A,1 + B,U + V,W,X + Y,Z,A1 + B1,C1,D1 + E1,F1,D1 + E1 + U + V,-1*D1 + -1*E1 + U + V,A1 + B1 + X + Y [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && 7 >= B] (?,1) ,-1*A1 + -1*B1 + X + Y,-3196,G1,H1,I1 + J1,J1 + K1,J1) 2. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f62(A,1 + B,U + V,W,X + Y,Z,A1 + B1,C1,D1 + E1,F1,D1 + E1 + U + V,-1*D1 + -1*E1 + U + V,A1 + B1 + X + Y[B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && 7 >= B] (?,1) ,-1*A1 + -1*B1 + X + Y,-3196,G1,H1,I1 + J1,J1 + K1,J1) 3. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f118(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && B >= 8] (?,1) 4. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f62(A,0,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && B >= 8] (?,1) Signature: {(f0,20);(f118,20);(f62,20);(f7,20)} Flow Graph: [0->{1,4},1->{1,4},2->{2,3},3->{},4->{2,3}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,4),(4,3)] * Step 2: FromIts YES + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f7(8,0,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) True (1,1) 1. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f7(A,1 + B,U + V,W,X + Y,Z,A1 + B1,C1,D1 + E1,F1,D1 + E1 + U + V,-1*D1 + -1*E1 + U + V,A1 + B1 + X + Y [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && 7 >= B] (?,1) ,-1*A1 + -1*B1 + X + Y,-3196,G1,H1,I1 + J1,J1 + K1,J1) 2. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f62(A,1 + B,U + V,W,X + Y,Z,A1 + B1,C1,D1 + E1,F1,D1 + E1 + U + V,-1*D1 + -1*E1 + U + V,A1 + B1 + X + Y[B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && 7 >= B] (?,1) ,-1*A1 + -1*B1 + X + Y,-3196,G1,H1,I1 + J1,J1 + K1,J1) 3. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f118(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && B >= 8] (?,1) 4. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f62(A,0,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && B >= 8] (?,1) Signature: {(f0,20);(f118,20);(f62,20);(f7,20)} Flow Graph: [0->{1},1->{1,4},2->{2,3},3->{},4->{2}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f7(8,0,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S ,T) True f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f7(A,1 + B,U + V,W,X + Y,Z,A1 + B1,C1,D1 + E1,F1 ,D1 + E1 + U + V,-1*D1 + -1*E1 + U + V,A1 + B1 + X + Y,-1*A1 + -1*B1 + X + Y,-3196,G1,H1,I1 + J1,J1 + K1 ,J1) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && 7 >= B] f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f62(A,1 + B,U + V,W,X + Y,Z,A1 + B1,C1,D1 + E1,F1 ,D1 + E1 + U + V,-1*D1 + -1*E1 + U + V,A1 + B1 + X + Y,-1*A1 + -1*B1 + X + Y,-3196,G1,H1,I1 + J1,J1 + K1 ,J1) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && 7 >= B] f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f118(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S ,T) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && B >= 8] f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f62(A,0,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S ,T) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && B >= 8] Signature: {(f0,20);(f118,20);(f62,20);(f7,20)} Rule Graph: [0->{1},1->{1,4},2->{2,3},3->{},4->{2}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4] | +- p:[1] c: [1] | `- p:[2] c: [2] * Step 4: CloseWith YES + Considered Problem: (Rules: f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f7(8,0,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S ,T) True f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f7(A,1 + B,U + V,W,X + Y,Z,A1 + B1,C1,D1 + E1,F1 ,D1 + E1 + U + V,-1*D1 + -1*E1 + U + V,A1 + B1 + X + Y,-1*A1 + -1*B1 + X + Y,-3196,G1,H1,I1 + J1,J1 + K1 ,J1) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && 7 >= B] f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f62(A,1 + B,U + V,W,X + Y,Z,A1 + B1,C1,D1 + E1,F1 ,D1 + E1 + U + V,-1*D1 + -1*E1 + U + V,A1 + B1 + X + Y,-1*A1 + -1*B1 + X + Y,-3196,G1,H1,I1 + J1,J1 + K1 ,J1) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && 7 >= B] f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f118(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S ,T) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && B >= 8] f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f62(A,0,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S ,T) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && B >= 8] Signature: {(f0,20);(f118,20);(f62,20);(f7,20)} Rule Graph: [0->{1},1->{1,4},2->{2,3},3->{},4->{2}] ,We construct a looptree: P: [0,1,2,3,4] | +- p:[1] c: [1] | `- p:[2] c: [2]) + Applied Processor: CloseWith True + Details: () YES