YES * Step 1: FromIts YES + Considered Problem: Rules: 0. evalsipmabubblestart(A,B) -> evalsipmabubbleentryin(A,B) True (1,1) 1. evalsipmabubbleentryin(A,B) -> evalsipmabubblebb6in(A,B) True (?,1) 2. evalsipmabubblebb6in(A,B) -> evalsipmabubblebb4in(A,0) [A >= 0] (?,1) 3. evalsipmabubblebb6in(A,B) -> evalsipmabubblereturnin(A,B) [0 >= 1 + A] (?,1) 4. evalsipmabubblebb4in(A,B) -> evalsipmabubblebb1in(A,B) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 1 + B] (?,1) 5. evalsipmabubblebb4in(A,B) -> evalsipmabubblebb5in(A,B) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && B >= A] (?,1) 6. evalsipmabubblebb1in(A,B) -> evalsipmabubblebb2in(A,B) [-1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && C >= 1 + D] (?,1) 7. evalsipmabubblebb1in(A,B) -> evalsipmabubblebb3in(A,B) [-1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && D >= C] (?,1) 8. evalsipmabubblebb2in(A,B) -> evalsipmabubblebb3in(A,B) [-1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0] (?,1) 9. evalsipmabubblebb3in(A,B) -> evalsipmabubblebb4in(A,1 + B) [-1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0] (?,1) 10. evalsipmabubblebb5in(A,B) -> evalsipmabubblebb6in(-1 + A,B) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0] (?,1) 11. evalsipmabubblereturnin(A,B) -> evalsipmabubblestop(A,B) [-1 + -1*A >= 0] (?,1) Signature: {(evalsipmabubblebb1in,2) ;(evalsipmabubblebb2in,2) ;(evalsipmabubblebb3in,2) ;(evalsipmabubblebb4in,2) ;(evalsipmabubblebb5in,2) ;(evalsipmabubblebb6in,2) ;(evalsipmabubbleentryin,2) ;(evalsipmabubblereturnin,2) ;(evalsipmabubblestart,2) ;(evalsipmabubblestop,2)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{11},4->{6,7},5->{10},6->{8},7->{9},8->{9},9->{4,5},10->{2,3},11->{}] + Applied Processor: FromIts + Details: () * Step 2: Decompose YES + Considered Problem: Rules: evalsipmabubblestart(A,B) -> evalsipmabubbleentryin(A,B) True evalsipmabubbleentryin(A,B) -> evalsipmabubblebb6in(A,B) True evalsipmabubblebb6in(A,B) -> evalsipmabubblebb4in(A,0) [A >= 0] evalsipmabubblebb6in(A,B) -> evalsipmabubblereturnin(A,B) [0 >= 1 + A] evalsipmabubblebb4in(A,B) -> evalsipmabubblebb1in(A,B) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 1 + B] evalsipmabubblebb4in(A,B) -> evalsipmabubblebb5in(A,B) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && B >= A] evalsipmabubblebb1in(A,B) -> evalsipmabubblebb2in(A,B) [-1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && C >= 1 + D] evalsipmabubblebb1in(A,B) -> evalsipmabubblebb3in(A,B) [-1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && D >= C] evalsipmabubblebb2in(A,B) -> evalsipmabubblebb3in(A,B) [-1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0] evalsipmabubblebb3in(A,B) -> evalsipmabubblebb4in(A,1 + B) [-1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0] evalsipmabubblebb5in(A,B) -> evalsipmabubblebb6in(-1 + A,B) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0] evalsipmabubblereturnin(A,B) -> evalsipmabubblestop(A,B) [-1 + -1*A >= 0] Signature: {(evalsipmabubblebb1in,2) ;(evalsipmabubblebb2in,2) ;(evalsipmabubblebb3in,2) ;(evalsipmabubblebb4in,2) ;(evalsipmabubblebb5in,2) ;(evalsipmabubblebb6in,2) ;(evalsipmabubbleentryin,2) ;(evalsipmabubblereturnin,2) ;(evalsipmabubblestart,2) ;(evalsipmabubblestop,2)} Rule Graph: [0->{1},1->{2,3},2->{4,5},3->{11},4->{6,7},5->{10},6->{8},7->{9},8->{9},9->{4,5},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:[2,10,5,9,7,4,8,6] c: [2,5,10] | `- p:[4,9,7,8,6] c: [4,6,7,8,9] * Step 3: CloseWith YES + Considered Problem: (Rules: evalsipmabubblestart(A,B) -> evalsipmabubbleentryin(A,B) True evalsipmabubbleentryin(A,B) -> evalsipmabubblebb6in(A,B) True evalsipmabubblebb6in(A,B) -> evalsipmabubblebb4in(A,0) [A >= 0] evalsipmabubblebb6in(A,B) -> evalsipmabubblereturnin(A,B) [0 >= 1 + A] evalsipmabubblebb4in(A,B) -> evalsipmabubblebb1in(A,B) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 1 + B] evalsipmabubblebb4in(A,B) -> evalsipmabubblebb5in(A,B) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && B >= A] evalsipmabubblebb1in(A,B) -> evalsipmabubblebb2in(A,B) [-1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && C >= 1 + D] evalsipmabubblebb1in(A,B) -> evalsipmabubblebb3in(A,B) [-1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && D >= C] evalsipmabubblebb2in(A,B) -> evalsipmabubblebb3in(A,B) [-1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0] evalsipmabubblebb3in(A,B) -> evalsipmabubblebb4in(A,1 + B) [-1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0] evalsipmabubblebb5in(A,B) -> evalsipmabubblebb6in(-1 + A,B) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0] evalsipmabubblereturnin(A,B) -> evalsipmabubblestop(A,B) [-1 + -1*A >= 0] Signature: {(evalsipmabubblebb1in,2) ;(evalsipmabubblebb2in,2) ;(evalsipmabubblebb3in,2) ;(evalsipmabubblebb4in,2) ;(evalsipmabubblebb5in,2) ;(evalsipmabubblebb6in,2) ;(evalsipmabubbleentryin,2) ;(evalsipmabubblereturnin,2) ;(evalsipmabubblestart,2) ;(evalsipmabubblestop,2)} Rule Graph: [0->{1},1->{2,3},2->{4,5},3->{11},4->{6,7},5->{10},6->{8},7->{9},8->{9},9->{4,5},10->{2,3},11->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11] | `- p:[2,10,5,9,7,4,8,6] c: [2,5,10] | `- p:[4,9,7,8,6] c: [4,6,7,8,9]) + Applied Processor: CloseWith True + Details: () YES