NO * Step 1: UnsatPaths NO + Considered Problem: Rules: 0. f15(A,B,C,D,E) -> f16(A,B,C,D,E) [100 + -1*C >= 0 && 100 + B + -1*C >= 0 && -1 + C >= 0 && -1 + B + C >= 0 && B >= 0 && A >= 1 + B] (?,1) 1. f15(A,B,C,D,E) -> f16(A,B,C,D,E) [100 + -1*C >= 0 && 100 + B + -1*C >= 0 && -1 + C >= 0 && -1 + B + C >= 0 && B >= 0 && B >= 1 + A] (?,1) 2. f0(A,B,C,D,E) -> f7(F,B,F,D,E) [0 >= F] (1,1) 3. f0(A,B,C,D,E) -> f7(F,B,F,D,E) [F >= 101] (1,1) 4. f0(A,B,C,D,E) -> f15(F,0,F,G,E) [100 >= F && F >= 1] (1,1) 5. f16(A,B,C,D,E) -> f15(A,1 + B,C,D,E) [100 + -1*C >= 0 && 100 + B + -1*C >= 0 && -1 + C >= 0 && -1 + B + C >= 0 && B >= 0] (?,1) 6. f23(A,B,C,D,E) -> f23(A,B,C,D,1 + E) [1 + B + -1*E >= 0 (?,1) && E >= 0 && -1 + C + E >= 0 && 100 + -1*C + E >= 0 && 1 + B + E >= 0 && 100 + -1*C >= 0 && 101 + B + -1*C >= 0 && -1 + C >= 0 && B + C >= 0 && 1 + B >= 0 && B >= 1 + E] 7. f23(A,B,C,D,E) -> f7(A,B,C,D,E) [1 + B + -1*E >= 0 (?,1) && E >= 0 && -1 + C + E >= 0 && 100 + -1*C + E >= 0 && 1 + B + E >= 0 && 100 + -1*C >= 0 && 101 + B + -1*C >= 0 && -1 + C >= 0 && B + C >= 0 && 1 + B >= 0 && E >= B] 8. f15(A,B,C,D,E) -> f23(A,-1 + A,C,D,0) [100 + -1*C >= 0 && 100 + B + -1*C >= 0 && -1 + C >= 0 && -1 + B + C >= 0 && B >= 0 && A = B] (?,1) 9. f16(A,B,C,D,E) -> f23(A,-1 + B,C,D,0) [100 + -1*C >= 0 && 100 + B + -1*C >= 0 && -1 + C >= 0 && -1 + B + C >= 0 && B >= 0] (?,1) Signature: {(f0,5);(f15,5);(f16,5);(f23,5);(f7,5)} Flow Graph: [0->{5,9},1->{5,9},2->{},3->{},4->{0,1,8},5->{0,1,8},6->{6,7},7->{},8->{6,7},9->{6,7}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(4,1),(4,8)] * Step 2: FromIts NO + Considered Problem: Rules: 0. f15(A,B,C,D,E) -> f16(A,B,C,D,E) [100 + -1*C >= 0 && 100 + B + -1*C >= 0 && -1 + C >= 0 && -1 + B + C >= 0 && B >= 0 && A >= 1 + B] (?,1) 1. f15(A,B,C,D,E) -> f16(A,B,C,D,E) [100 + -1*C >= 0 && 100 + B + -1*C >= 0 && -1 + C >= 0 && -1 + B + C >= 0 && B >= 0 && B >= 1 + A] (?,1) 2. f0(A,B,C,D,E) -> f7(F,B,F,D,E) [0 >= F] (1,1) 3. f0(A,B,C,D,E) -> f7(F,B,F,D,E) [F >= 101] (1,1) 4. f0(A,B,C,D,E) -> f15(F,0,F,G,E) [100 >= F && F >= 1] (1,1) 5. f16(A,B,C,D,E) -> f15(A,1 + B,C,D,E) [100 + -1*C >= 0 && 100 + B + -1*C >= 0 && -1 + C >= 0 && -1 + B + C >= 0 && B >= 0] (?,1) 6. f23(A,B,C,D,E) -> f23(A,B,C,D,1 + E) [1 + B + -1*E >= 0 (?,1) && E >= 0 && -1 + C + E >= 0 && 100 + -1*C + E >= 0 && 1 + B + E >= 0 && 100 + -1*C >= 0 && 101 + B + -1*C >= 0 && -1 + C >= 0 && B + C >= 0 && 1 + B >= 0 && B >= 1 + E] 7. f23(A,B,C,D,E) -> f7(A,B,C,D,E) [1 + B + -1*E >= 0 (?,1) && E >= 0 && -1 + C + E >= 0 && 100 + -1*C + E >= 0 && 1 + B + E >= 0 && 100 + -1*C >= 0 && 101 + B + -1*C >= 0 && -1 + C >= 0 && B + C >= 0 && 1 + B >= 0 && E >= B] 8. f15(A,B,C,D,E) -> f23(A,-1 + A,C,D,0) [100 + -1*C >= 0 && 100 + B + -1*C >= 0 && -1 + C >= 0 && -1 + B + C >= 0 && B >= 0 && A = B] (?,1) 9. f16(A,B,C,D,E) -> f23(A,-1 + B,C,D,0) [100 + -1*C >= 0 && 100 + B + -1*C >= 0 && -1 + C >= 0 && -1 + B + C >= 0 && B >= 0] (?,1) Signature: {(f0,5);(f15,5);(f16,5);(f23,5);(f7,5)} Flow Graph: [0->{5,9},1->{5,9},2->{},3->{},4->{0},5->{0,1,8},6->{6,7},7->{},8->{6,7},9->{6,7}] + Applied Processor: FromIts + Details: () * Step 3: CloseWith NO + Considered Problem: Rules: f15(A,B,C,D,E) -> f16(A,B,C,D,E) [100 + -1*C >= 0 && 100 + B + -1*C >= 0 && -1 + C >= 0 && -1 + B + C >= 0 && B >= 0 && A >= 1 + B] f15(A,B,C,D,E) -> f16(A,B,C,D,E) [100 + -1*C >= 0 && 100 + B + -1*C >= 0 && -1 + C >= 0 && -1 + B + C >= 0 && B >= 0 && B >= 1 + A] f0(A,B,C,D,E) -> f7(F,B,F,D,E) [0 >= F] f0(A,B,C,D,E) -> f7(F,B,F,D,E) [F >= 101] f0(A,B,C,D,E) -> f15(F,0,F,G,E) [100 >= F && F >= 1] f16(A,B,C,D,E) -> f15(A,1 + B,C,D,E) [100 + -1*C >= 0 && 100 + B + -1*C >= 0 && -1 + C >= 0 && -1 + B + C >= 0 && B >= 0] f23(A,B,C,D,E) -> f23(A,B,C,D,1 + E) [1 + B + -1*E >= 0 && E >= 0 && -1 + C + E >= 0 && 100 + -1*C + E >= 0 && 1 + B + E >= 0 && 100 + -1*C >= 0 && 101 + B + -1*C >= 0 && -1 + C >= 0 && B + C >= 0 && 1 + B >= 0 && B >= 1 + E] f23(A,B,C,D,E) -> f7(A,B,C,D,E) [1 + B + -1*E >= 0 && E >= 0 && -1 + C + E >= 0 && 100 + -1*C + E >= 0 && 1 + B + E >= 0 && 100 + -1*C >= 0 && 101 + B + -1*C >= 0 && -1 + C >= 0 && B + C >= 0 && 1 + B >= 0 && E >= B] f15(A,B,C,D,E) -> f23(A,-1 + A,C,D,0) [100 + -1*C >= 0 && 100 + B + -1*C >= 0 && -1 + C >= 0 && -1 + B + C >= 0 && B >= 0 && A = B] f16(A,B,C,D,E) -> f23(A,-1 + B,C,D,0) [100 + -1*C >= 0 && 100 + B + -1*C >= 0 && -1 + C >= 0 && -1 + B + C >= 0 && B >= 0] Signature: {(f0,5);(f15,5);(f16,5);(f23,5);(f7,5)} Rule Graph: [0->{5,9},1->{5,9},2->{},3->{},4->{0},5->{0,1,8},6->{6,7},7->{},8->{6,7},9->{6,7}] + Applied Processor: CloseWith False + Details: () NO