NO * Step 1: TrivialSCCs NO + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f10(F,0,F,D,0) True (1,1) 1. f10(A,B,C,D,E) -> f25(A,B,C,D,E) [-1*E >= 0 (?,1) && B + -1*E >= 0 && -1*B + -1*E >= 0 && E >= 0 && B + E >= 0 && -1*B + E >= 0 && -1*B >= 0 && B >= 0 && A >= 1] 2. f10(A,B,C,D,E) -> f16(A,0,F,F,E) [-1*E >= 0 (?,1) && B + -1*E >= 0 && -1*B + -1*E >= 0 && E >= 0 && B + E >= 0 && -1*B + E >= 0 && -1*B >= 0 && B >= 0 && 0 >= A] 3. f25(A,B,C,D,E) -> f25(A,B,C,D,E) [-1*E >= 0 (?,1) && B + -1*E >= 0 && -1*B + -1*E >= 0 && -1 + A + -1*E >= 0 && E >= 0 && B + E >= 0 && -1*B + E >= 0 && -1 + A + E >= 0 && -1*B >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0] 4. f16(A,B,C,D,E) -> f10(F,B,F,D,0) [-1*E >= 0 (?,1) && B + -1*E >= 0 && -1*B + -1*E >= 0 && -1*A + -1*E >= 0 && E >= 0 && B + E >= 0 && -1*B + E >= 0 && -1*A + E >= 0 && -1*B >= 0 && -1*A + -1*B >= 0 && B >= 0 && -1*A + B >= 0 && -1*A >= 0 && 0 >= D] 5. f16(A,B,C,D,E) -> f16(A,B,C,D,E) [-1*E >= 0 (?,1) && B + -1*E >= 0 && -1*B + -1*E >= 0 && -1*A + -1*E >= 0 && E >= 0 && B + E >= 0 && -1*B + E >= 0 && -1*A + E >= 0 && -1*B >= 0 && -1*A + -1*B >= 0 && B >= 0 && -1*A + B >= 0 && -1*A >= 0 && D >= 1] Signature: {(f0,5);(f10,5);(f16,5);(f25,5)} Flow Graph: [0->{1,2},1->{3},2->{4,5},3->{3},4->{1,2},5->{4,5}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths NO + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f10(F,0,F,D,0) True (1,1) 1. f10(A,B,C,D,E) -> f25(A,B,C,D,E) [-1*E >= 0 (1,1) && B + -1*E >= 0 && -1*B + -1*E >= 0 && E >= 0 && B + E >= 0 && -1*B + E >= 0 && -1*B >= 0 && B >= 0 && A >= 1] 2. f10(A,B,C,D,E) -> f16(A,0,F,F,E) [-1*E >= 0 (?,1) && B + -1*E >= 0 && -1*B + -1*E >= 0 && E >= 0 && B + E >= 0 && -1*B + E >= 0 && -1*B >= 0 && B >= 0 && 0 >= A] 3. f25(A,B,C,D,E) -> f25(A,B,C,D,E) [-1*E >= 0 (?,1) && B + -1*E >= 0 && -1*B + -1*E >= 0 && -1 + A + -1*E >= 0 && E >= 0 && B + E >= 0 && -1*B + E >= 0 && -1 + A + E >= 0 && -1*B >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0] 4. f16(A,B,C,D,E) -> f10(F,B,F,D,0) [-1*E >= 0 (?,1) && B + -1*E >= 0 && -1*B + -1*E >= 0 && -1*A + -1*E >= 0 && E >= 0 && B + E >= 0 && -1*B + E >= 0 && -1*A + E >= 0 && -1*B >= 0 && -1*A + -1*B >= 0 && B >= 0 && -1*A + B >= 0 && -1*A >= 0 && 0 >= D] 5. f16(A,B,C,D,E) -> f16(A,B,C,D,E) [-1*E >= 0 (?,1) && B + -1*E >= 0 && -1*B + -1*E >= 0 && -1*A + -1*E >= 0 && E >= 0 && B + E >= 0 && -1*B + E >= 0 && -1*A + E >= 0 && -1*B >= 0 && -1*A + -1*B >= 0 && B >= 0 && -1*A + B >= 0 && -1*A >= 0 && D >= 1] Signature: {(f0,5);(f10,5);(f16,5);(f25,5)} Flow Graph: [0->{1,2},1->{3},2->{4,5},3->{3},4->{1,2},5->{4,5}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(5,4)] * Step 3: Looptree NO + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f10(F,0,F,D,0) True (1,1) 1. f10(A,B,C,D,E) -> f25(A,B,C,D,E) [-1*E >= 0 (1,1) && B + -1*E >= 0 && -1*B + -1*E >= 0 && E >= 0 && B + E >= 0 && -1*B + E >= 0 && -1*B >= 0 && B >= 0 && A >= 1] 2. f10(A,B,C,D,E) -> f16(A,0,F,F,E) [-1*E >= 0 (?,1) && B + -1*E >= 0 && -1*B + -1*E >= 0 && E >= 0 && B + E >= 0 && -1*B + E >= 0 && -1*B >= 0 && B >= 0 && 0 >= A] 3. f25(A,B,C,D,E) -> f25(A,B,C,D,E) [-1*E >= 0 (?,1) && B + -1*E >= 0 && -1*B + -1*E >= 0 && -1 + A + -1*E >= 0 && E >= 0 && B + E >= 0 && -1*B + E >= 0 && -1 + A + E >= 0 && -1*B >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0] 4. f16(A,B,C,D,E) -> f10(F,B,F,D,0) [-1*E >= 0 (?,1) && B + -1*E >= 0 && -1*B + -1*E >= 0 && -1*A + -1*E >= 0 && E >= 0 && B + E >= 0 && -1*B + E >= 0 && -1*A + E >= 0 && -1*B >= 0 && -1*A + -1*B >= 0 && B >= 0 && -1*A + B >= 0 && -1*A >= 0 && 0 >= D] 5. f16(A,B,C,D,E) -> f16(A,B,C,D,E) [-1*E >= 0 (?,1) && B + -1*E >= 0 && -1*B + -1*E >= 0 && -1*A + -1*E >= 0 && E >= 0 && B + E >= 0 && -1*B + E >= 0 && -1*A + E >= 0 && -1*B >= 0 && -1*A + -1*B >= 0 && B >= 0 && -1*A + B >= 0 && -1*A >= 0 && D >= 1] Signature: {(f0,5);(f10,5);(f16,5);(f25,5)} Flow Graph: [0->{1,2},1->{3},2->{4,5},3->{3},4->{1,2},5->{5}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5] | +- p:[2,4] c: [] | +- p:[5] c: [] | `- p:[3] c: [] NO