YES * Step 1: TrivialSCCs 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) -> f6(0,0,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) True (1,1) 1. f6(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f6(U,1 + B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [B >= 0 && 63 >= B] (?,1) 2. f14(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f14(A,B,-1 + C,U + V,W,X + Y,Z,A1 + B1,C1,D1 + E1,F1,D1 + E1 + U + V,-1*D1 + -1*E1 + U + V[7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && C >= 0] (?,1) ,A1 + B1 + X + Y,-1*A1 + -1*B1 + X + Y,G1,H1,I1 + J1,J1 + K1,J1) 3. f57(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f57(A,B,-1 + C,U + V,W,X + Y,Z,A1 + B1,C1,D1 + E1,F1,D1 + E1 + U + V,-1*D1 + -1*E1 + U + V[7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && C >= 0] (?,1) ,A1 + B1 + X + Y,-1*A1 + -1*B1 + X + Y,G1,H1,I1 + J1,J1 + K1,J1) 4. f57(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f101(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && 0 >= 1 + C] (?,1) 5. f14(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f57(A,B,7,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && 0 >= 1 + C] (?,1) 6. f6(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f14(A,B,7,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [B >= 0 && B >= 64] (?,1) Signature: {(f0,20);(f101,20);(f14,20);(f57,20);(f6,20)} Flow Graph: [0->{1,6},1->{1,6},2->{2,5},3->{3,4},4->{},5->{3,4},6->{2,5}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: 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) -> f6(0,0,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) True (1,1) 1. f6(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f6(U,1 + B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [B >= 0 && 63 >= B] (?,1) 2. f14(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f14(A,B,-1 + C,U + V,W,X + Y,Z,A1 + B1,C1,D1 + E1,F1,D1 + E1 + U + V,-1*D1 + -1*E1 + U + V[7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && C >= 0] (?,1) ,A1 + B1 + X + Y,-1*A1 + -1*B1 + X + Y,G1,H1,I1 + J1,J1 + K1,J1) 3. f57(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f57(A,B,-1 + C,U + V,W,X + Y,Z,A1 + B1,C1,D1 + E1,F1,D1 + E1 + U + V,-1*D1 + -1*E1 + U + V[7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && C >= 0] (?,1) ,A1 + B1 + X + Y,-1*A1 + -1*B1 + X + Y,G1,H1,I1 + J1,J1 + K1,J1) 4. f57(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f101(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && 0 >= 1 + C] (1,1) 5. f14(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f57(A,B,7,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && 0 >= 1 + C] (1,1) 6. f6(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f14(A,B,7,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [B >= 0 && B >= 64] (1,1) Signature: {(f0,20);(f101,20);(f14,20);(f57,20);(f6,20)} Flow Graph: [0->{1,6},1->{1,6},2->{2,5},3->{3,4},4->{},5->{3,4},6->{2,5}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,6),(5,4),(6,5)] * Step 3: Looptree 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) -> f6(0,0,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) True (1,1) 1. f6(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f6(U,1 + B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [B >= 0 && 63 >= B] (?,1) 2. f14(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f14(A,B,-1 + C,U + V,W,X + Y,Z,A1 + B1,C1,D1 + E1,F1,D1 + E1 + U + V,-1*D1 + -1*E1 + U + V[7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && C >= 0] (?,1) ,A1 + B1 + X + Y,-1*A1 + -1*B1 + X + Y,G1,H1,I1 + J1,J1 + K1,J1) 3. f57(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f57(A,B,-1 + C,U + V,W,X + Y,Z,A1 + B1,C1,D1 + E1,F1,D1 + E1 + U + V,-1*D1 + -1*E1 + U + V[7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && C >= 0] (?,1) ,A1 + B1 + X + Y,-1*A1 + -1*B1 + X + Y,G1,H1,I1 + J1,J1 + K1,J1) 4. f57(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f101(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && 0 >= 1 + C] (1,1) 5. f14(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f57(A,B,7,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && 0 >= 1 + C] (1,1) 6. f6(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f14(A,B,7,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [B >= 0 && B >= 64] (1,1) Signature: {(f0,20);(f101,20);(f14,20);(f57,20);(f6,20)} Flow Graph: [0->{1},1->{1,6},2->{2,5},3->{3,4},4->{},5->{3},6->{2}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6] | +- p:[1] c: [1] | +- p:[2] c: [2] | `- p:[3] c: [3] YES