NO * Step 1: UnsatPaths NO + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f1(A,B,C,D,E,F,G) [A >= 0 && 3 >= A && B >= 0 && 3 >= B && 3 >= C && D >= 0 && 3 >= E && E >= 0] (1,1) 1. f1(A,B,C,D,E,F,G) -> f2(A,B,C,D,E,1 + D,G) [1 + B >= 2*D] (?,1) 2. f1(A,B,C,D,E,F,G) -> f2(A,B,C,D,E,-1 + D,G) [2*D >= 4 + B] (?,1) 3. f1(A,B,C,D,E,F,G) -> f2(A,B,C,D,E,D,G) [2 + B = 2*D] (?,1) 4. f1(A,B,C,D,E,F,G) -> f2(A,B,C,D,E,D,G) [3 + B = 2*D] (?,1) 5. f2(A,B,C,D,E,F,G) -> f3(A,B,C,D,E,F,1 + E) [A + D >= 1 + 2*E] (?,1) 6. f2(A,B,C,D,E,F,G) -> f3(A,B,C,D,E,F,-1 + E) [2*E >= 2 + A + D] (?,1) 7. f2(A,B,C,D,E,F,G) -> f3(A,B,C,D,E,F,E) [A + D = 2*E] (?,1) 8. f2(A,B,C,D,E,F,G) -> f3(A,B,C,D,E,F,E) [1 + A + D = 2*E] (?,1) 9. f3(A,B,C,D,E,F,G) -> f1(A,B,C,F,G,F,G) [D >= 1 + F] (?,1) 10. f3(A,B,C,D,E,F,G) -> f1(A,B,C,F,G,F,G) [F >= 1 + D] (?,1) 11. f3(A,B,C,D,E,F,G) -> f1(A,B,C,F,G,F,G) [E >= 1 + G] (?,1) 12. f3(A,B,C,D,E,F,G) -> f1(A,B,C,F,G,F,G) [G >= 1 + E] (?,1) Signature: {(f0,7);(f1,7);(f2,7);(f3,7)} Flow Graph: [0->{1,2,3,4},1->{5,6,7,8},2->{5,6,7,8},3->{5,6,7,8},4->{5,6,7,8},5->{9,10,11,12},6->{9,10,11,12},7->{9,10 ,11,12},8->{9,10,11,12},9->{1,2,3,4},10->{1,2,3,4},11->{1,2,3,4},12->{1,2,3,4}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(5,11),(6,12),(7,11),(7,12),(8,11),(8,12)] * Step 2: FromIts NO + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f1(A,B,C,D,E,F,G) [A >= 0 && 3 >= A && B >= 0 && 3 >= B && 3 >= C && D >= 0 && 3 >= E && E >= 0] (1,1) 1. f1(A,B,C,D,E,F,G) -> f2(A,B,C,D,E,1 + D,G) [1 + B >= 2*D] (?,1) 2. f1(A,B,C,D,E,F,G) -> f2(A,B,C,D,E,-1 + D,G) [2*D >= 4 + B] (?,1) 3. f1(A,B,C,D,E,F,G) -> f2(A,B,C,D,E,D,G) [2 + B = 2*D] (?,1) 4. f1(A,B,C,D,E,F,G) -> f2(A,B,C,D,E,D,G) [3 + B = 2*D] (?,1) 5. f2(A,B,C,D,E,F,G) -> f3(A,B,C,D,E,F,1 + E) [A + D >= 1 + 2*E] (?,1) 6. f2(A,B,C,D,E,F,G) -> f3(A,B,C,D,E,F,-1 + E) [2*E >= 2 + A + D] (?,1) 7. f2(A,B,C,D,E,F,G) -> f3(A,B,C,D,E,F,E) [A + D = 2*E] (?,1) 8. f2(A,B,C,D,E,F,G) -> f3(A,B,C,D,E,F,E) [1 + A + D = 2*E] (?,1) 9. f3(A,B,C,D,E,F,G) -> f1(A,B,C,F,G,F,G) [D >= 1 + F] (?,1) 10. f3(A,B,C,D,E,F,G) -> f1(A,B,C,F,G,F,G) [F >= 1 + D] (?,1) 11. f3(A,B,C,D,E,F,G) -> f1(A,B,C,F,G,F,G) [E >= 1 + G] (?,1) 12. f3(A,B,C,D,E,F,G) -> f1(A,B,C,F,G,F,G) [G >= 1 + E] (?,1) Signature: {(f0,7);(f1,7);(f2,7);(f3,7)} Flow Graph: [0->{1,2,3,4},1->{5,6,7,8},2->{5,6,7,8},3->{5,6,7,8},4->{5,6,7,8},5->{9,10,12},6->{9,10,11},7->{9,10} ,8->{9,10},9->{1,2,3,4},10->{1,2,3,4},11->{1,2,3,4},12->{1,2,3,4}] + Applied Processor: FromIts + Details: () * Step 3: CloseWith NO + Considered Problem: Rules: f0(A,B,C,D,E,F,G) -> f1(A,B,C,D,E,F,G) [A >= 0 && 3 >= A && B >= 0 && 3 >= B && 3 >= C && D >= 0 && 3 >= E && E >= 0] f1(A,B,C,D,E,F,G) -> f2(A,B,C,D,E,1 + D,G) [1 + B >= 2*D] f1(A,B,C,D,E,F,G) -> f2(A,B,C,D,E,-1 + D,G) [2*D >= 4 + B] f1(A,B,C,D,E,F,G) -> f2(A,B,C,D,E,D,G) [2 + B = 2*D] f1(A,B,C,D,E,F,G) -> f2(A,B,C,D,E,D,G) [3 + B = 2*D] f2(A,B,C,D,E,F,G) -> f3(A,B,C,D,E,F,1 + E) [A + D >= 1 + 2*E] f2(A,B,C,D,E,F,G) -> f3(A,B,C,D,E,F,-1 + E) [2*E >= 2 + A + D] f2(A,B,C,D,E,F,G) -> f3(A,B,C,D,E,F,E) [A + D = 2*E] f2(A,B,C,D,E,F,G) -> f3(A,B,C,D,E,F,E) [1 + A + D = 2*E] f3(A,B,C,D,E,F,G) -> f1(A,B,C,F,G,F,G) [D >= 1 + F] f3(A,B,C,D,E,F,G) -> f1(A,B,C,F,G,F,G) [F >= 1 + D] f3(A,B,C,D,E,F,G) -> f1(A,B,C,F,G,F,G) [E >= 1 + G] f3(A,B,C,D,E,F,G) -> f1(A,B,C,F,G,F,G) [G >= 1 + E] Signature: {(f0,7);(f1,7);(f2,7);(f3,7)} Rule Graph: [0->{1,2,3,4},1->{5,6,7,8},2->{5,6,7,8},3->{5,6,7,8},4->{5,6,7,8},5->{9,10,12},6->{9,10,11},7->{9,10} ,8->{9,10},9->{1,2,3,4},10->{1,2,3,4},11->{1,2,3,4},12->{1,2,3,4}] + Applied Processor: CloseWith False + Details: () NO