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