NO * Step 1: TrivialSCCs NO + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O) -> f41(1,B,C,D,E,F,G,H,P,0,1,Q,Q,Q,Q) [P >= 1 && 0 >= Q] (1,1) 1. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O) -> f21(1,B,C,D,E,F,G,H,P,0,1,Q,Q,Q,Q) [P >= 1 && Q >= 1] (1,1) 2. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O) -> f21(1,B,C,D,E,F,G,H,P,P,K,L,M,N,O) [0 >= P] (1,1) 3. f41(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O) -> f41(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O) [-1*J >= 0 && A + -1*J >= 0 && 1 + -1*A + -1*J >= 0 && 1 + -1*A >= 0 && A >= 0] (?,1) 4. f21(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O) -> f29(0,P,P,D,E,F,0,P,I,J,K,L,M,N,O) [-1*J >= 0 && -1 + A + -1*J >= 0 && 1 + -1*A + -1*J >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && A >= 1] (?,1) 5. f29(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O) -> f41(1,B,P,0,P,P,G,H,I,J,K,L,M,N,O) [-1*G >= 0 (?,1) && -1*G + -1*J >= 0 && A + -1*G >= 0 && -1*A + -1*G >= 0 && G >= 0 && G + -1*J >= 0 && A + G >= 0 && -1*A + G >= 0 && -1*J >= 0 && A + -1*J >= 0 && -1*A + -1*J >= 0 && -1*A >= 0 && A >= 0 && 0 >= A && P >= 1000 + B] 6. f29(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O) -> f41(A,B,P,0,P,P,G,H,I,J,K,L,M,N,O) [-1*G >= 0 (?,1) && -1*G + -1*J >= 0 && A + -1*G >= 0 && -1*A + -1*G >= 0 && G >= 0 && G + -1*J >= 0 && A + G >= 0 && -1*A + G >= 0 && -1*J >= 0 && A + -1*J >= 0 && -1*A + -1*J >= 0 && -1*A >= 0 && A >= 0 && 0 >= A && 999 + B >= P] Signature: {(f0,15);(f21,15);(f29,15);(f41,15)} Flow Graph: [0->{3},1->{4},2->{4},3->{3},4->{5,6},5->{3},6->{3}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: Looptree NO + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O) -> f41(1,B,C,D,E,F,G,H,P,0,1,Q,Q,Q,Q) [P >= 1 && 0 >= Q] (1,1) 1. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O) -> f21(1,B,C,D,E,F,G,H,P,0,1,Q,Q,Q,Q) [P >= 1 && Q >= 1] (1,1) 2. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O) -> f21(1,B,C,D,E,F,G,H,P,P,K,L,M,N,O) [0 >= P] (1,1) 3. f41(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O) -> f41(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O) [-1*J >= 0 && A + -1*J >= 0 && 1 + -1*A + -1*J >= 0 && 1 + -1*A >= 0 && A >= 0] (?,1) 4. f21(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O) -> f29(0,P,P,D,E,F,0,P,I,J,K,L,M,N,O) [-1*J >= 0 && -1 + A + -1*J >= 0 && 1 + -1*A + -1*J >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && A >= 1] (1,1) 5. f29(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O) -> f41(1,B,P,0,P,P,G,H,I,J,K,L,M,N,O) [-1*G >= 0 (1,1) && -1*G + -1*J >= 0 && A + -1*G >= 0 && -1*A + -1*G >= 0 && G >= 0 && G + -1*J >= 0 && A + G >= 0 && -1*A + G >= 0 && -1*J >= 0 && A + -1*J >= 0 && -1*A + -1*J >= 0 && -1*A >= 0 && A >= 0 && 0 >= A && P >= 1000 + B] 6. f29(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O) -> f41(A,B,P,0,P,P,G,H,I,J,K,L,M,N,O) [-1*G >= 0 (1,1) && -1*G + -1*J >= 0 && A + -1*G >= 0 && -1*A + -1*G >= 0 && G >= 0 && G + -1*J >= 0 && A + G >= 0 && -1*A + G >= 0 && -1*J >= 0 && A + -1*J >= 0 && -1*A + -1*J >= 0 && -1*A >= 0 && A >= 0 && 0 >= A && 999 + B >= P] Signature: {(f0,15);(f21,15);(f29,15);(f41,15)} Flow Graph: [0->{3},1->{4},2->{4},3->{3},4->{5,6},5->{3},6->{3}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6] | `- p:[3] c: [] NO