YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. evalfstart(A,B,C,D) -> evalfentryin(A,B,C,D) True (1,1) 1. evalfentryin(A,B,C,D) -> evalfbb6in(0,B,C,D) True (?,1) 2. evalfbb6in(A,B,C,D) -> evalfbbin(A,B,C,D) [A >= 0 && B >= 1 + A] (?,1) 3. evalfbb6in(A,B,C,D) -> evalfreturnin(A,B,C,D) [A >= 0 && A >= B] (?,1) 4. evalfbbin(A,B,C,D) -> evalfbb2in(A,B,0,1 + A) [-1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] (?,1) 5. evalfbb2in(A,B,C,D) -> evalfbb4in(A,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && D >= B] 6. evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && B >= 1 + D] 7. evalfbb3in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && 0 >= 1 + E] 8. evalfbb3in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && E >= 1] 9. evalfbb3in(A,B,C,D) -> evalfbb4in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0] 10. evalfbb1in(A,B,C,D) -> evalfbb2in(A,B,1 + C,1 + D) [-1 + B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0] 11. evalfbb4in(A,B,C,D) -> evalfbb6in(-1 + D,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && C >= 1] 12. evalfbb4in(A,B,C,D) -> evalfbb6in(D,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && 0 >= C] 13. evalfreturnin(A,B,C,D) -> evalfstop(A,B,C,D) [A + -1*B >= 0 && A >= 0] (?,1) Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfbb6in,4) ;(evalfbbin,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{13},4->{5,6},5->{11,12},6->{7,8,9},7->{10},8->{10},9->{11,12},10->{5,6},11->{2 ,3},12->{2,3},13->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(11,3)] * Step 2: FromIts YES + Considered Problem: Rules: 0. evalfstart(A,B,C,D) -> evalfentryin(A,B,C,D) True (1,1) 1. evalfentryin(A,B,C,D) -> evalfbb6in(0,B,C,D) True (?,1) 2. evalfbb6in(A,B,C,D) -> evalfbbin(A,B,C,D) [A >= 0 && B >= 1 + A] (?,1) 3. evalfbb6in(A,B,C,D) -> evalfreturnin(A,B,C,D) [A >= 0 && A >= B] (?,1) 4. evalfbbin(A,B,C,D) -> evalfbb2in(A,B,0,1 + A) [-1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] (?,1) 5. evalfbb2in(A,B,C,D) -> evalfbb4in(A,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && D >= B] 6. evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && B >= 1 + D] 7. evalfbb3in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && 0 >= 1 + E] 8. evalfbb3in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && E >= 1] 9. evalfbb3in(A,B,C,D) -> evalfbb4in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0] 10. evalfbb1in(A,B,C,D) -> evalfbb2in(A,B,1 + C,1 + D) [-1 + B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0] 11. evalfbb4in(A,B,C,D) -> evalfbb6in(-1 + D,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && C >= 1] 12. evalfbb4in(A,B,C,D) -> evalfbb6in(D,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && 0 >= C] 13. evalfreturnin(A,B,C,D) -> evalfstop(A,B,C,D) [A + -1*B >= 0 && A >= 0] (?,1) Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfbb6in,4) ;(evalfbbin,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{13},4->{5,6},5->{11,12},6->{7,8,9},7->{10},8->{10},9->{11,12},10->{5,6} ,11->{2},12->{2,3},13->{}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: evalfstart(A,B,C,D) -> evalfentryin(A,B,C,D) True evalfentryin(A,B,C,D) -> evalfbb6in(0,B,C,D) True evalfbb6in(A,B,C,D) -> evalfbbin(A,B,C,D) [A >= 0 && B >= 1 + A] evalfbb6in(A,B,C,D) -> evalfreturnin(A,B,C,D) [A >= 0 && A >= B] evalfbbin(A,B,C,D) -> evalfbb2in(A,B,0,1 + A) [-1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] evalfbb2in(A,B,C,D) -> evalfbb4in(A,B,C,D) [B + -1*D >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && D >= B] evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,C,D) [B + -1*D >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && B >= 1 + D] evalfbb3in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + B + -1*D >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && 0 >= 1 + E] evalfbb3in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + B + -1*D >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && E >= 1] evalfbb3in(A,B,C,D) -> evalfbb4in(A,B,C,D) [-1 + B + -1*D >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0] evalfbb1in(A,B,C,D) -> evalfbb2in(A,B,1 + C,1 + D) [-1 + B + -1*D >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0] evalfbb4in(A,B,C,D) -> evalfbb6in(-1 + D,B,C,D) [B + -1*D >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && C >= 1] evalfbb4in(A,B,C,D) -> evalfbb6in(D,B,C,D) [B + -1*D >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && 0 >= C] evalfreturnin(A,B,C,D) -> evalfstop(A,B,C,D) [A + -1*B >= 0 && A >= 0] Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfbb6in,4) ;(evalfbbin,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4)} Rule Graph: [0->{1},1->{2,3},2->{4},3->{13},4->{5,6},5->{11,12},6->{7,8,9},7->{10},8->{10},9->{11,12},10->{5,6} ,11->{2},12->{2,3},13->{}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13] | `- p:[2,11,5,4,10,7,6,8,9,12] c: [12] | `- p:[2,11,5,4,10,7,6,8,9] c: [2,4,5,9,11] | `- p:[6,10,7,8] c: [6,7,8,10] * Step 4: CloseWith YES + Considered Problem: (Rules: evalfstart(A,B,C,D) -> evalfentryin(A,B,C,D) True evalfentryin(A,B,C,D) -> evalfbb6in(0,B,C,D) True evalfbb6in(A,B,C,D) -> evalfbbin(A,B,C,D) [A >= 0 && B >= 1 + A] evalfbb6in(A,B,C,D) -> evalfreturnin(A,B,C,D) [A >= 0 && A >= B] evalfbbin(A,B,C,D) -> evalfbb2in(A,B,0,1 + A) [-1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] evalfbb2in(A,B,C,D) -> evalfbb4in(A,B,C,D) [B + -1*D >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && D >= B] evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,C,D) [B + -1*D >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && B >= 1 + D] evalfbb3in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + B + -1*D >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && 0 >= 1 + E] evalfbb3in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + B + -1*D >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && E >= 1] evalfbb3in(A,B,C,D) -> evalfbb4in(A,B,C,D) [-1 + B + -1*D >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0] evalfbb1in(A,B,C,D) -> evalfbb2in(A,B,1 + C,1 + D) [-1 + B + -1*D >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0] evalfbb4in(A,B,C,D) -> evalfbb6in(-1 + D,B,C,D) [B + -1*D >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && C >= 1] evalfbb4in(A,B,C,D) -> evalfbb6in(D,B,C,D) [B + -1*D >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && 0 >= C] evalfreturnin(A,B,C,D) -> evalfstop(A,B,C,D) [A + -1*B >= 0 && A >= 0] Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfbb6in,4) ;(evalfbbin,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4)} Rule Graph: [0->{1},1->{2,3},2->{4},3->{13},4->{5,6},5->{11,12},6->{7,8,9},7->{10},8->{10},9->{11,12},10->{5,6} ,11->{2},12->{2,3},13->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13] | `- p:[2,11,5,4,10,7,6,8,9,12] c: [12] | `- p:[2,11,5,4,10,7,6,8,9] c: [2,4,5,9,11] | `- p:[6,10,7,8] c: [6,7,8,10]) + Applied Processor: CloseWith True + Details: () YES