YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. evalinsertsortstart(A,B,C,D) -> evalinsertsortentryin(A,B,C,D) True (1,1) 1. evalinsertsortentryin(A,B,C,D) -> evalinsertsortbb5in(1,B,C,D) True (?,1) 2. evalinsertsortbb5in(A,B,C,D) -> evalinsertsortbbin(A,B,C,D) [-1 + A >= 0 && B >= 1 + A] (?,1) 3. evalinsertsortbb5in(A,B,C,D) -> evalinsertsortreturnin(A,B,C,D) [-1 + A >= 0 && A >= B] (?,1) 4. evalinsertsortbbin(A,B,C,D) -> evalinsertsortbb2in(A,B,E,-1 + A) [-2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] (?,1) 5. evalinsertsortbb2in(A,B,C,D) -> evalinsertsortbb4in(A,B,C,D) [-2 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && 0 >= 1 + D] 6. evalinsertsortbb2in(A,B,C,D) -> evalinsertsortbb3in(A,B,C,D) [-2 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && D >= 0] 7. evalinsertsortbb3in(A,B,C,D) -> evalinsertsortbb1in(A,B,C,D) [-2 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && E >= 1 + C] 8. evalinsertsortbb3in(A,B,C,D) -> evalinsertsortbb4in(A,B,C,D) [-2 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && C >= E] 9. evalinsertsortbb1in(A,B,C,D) -> evalinsertsortbb2in(A,B,C,-1 + D) [-2 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] 10. evalinsertsortbb4in(A,B,C,D) -> evalinsertsortbb5in(1 + A,B,C,D) [-2 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] 11. evalinsertsortreturnin(A,B,C,D) -> evalinsertsortstop(A,B,C,D) [A + -1*B >= 0 && -1 + A >= 0] (?,1) Signature: {(evalinsertsortbb1in,4) ;(evalinsertsortbb2in,4) ;(evalinsertsortbb3in,4) ;(evalinsertsortbb4in,4) ;(evalinsertsortbb5in,4) ;(evalinsertsortbbin,4) ;(evalinsertsortentryin,4) ;(evalinsertsortreturnin,4) ;(evalinsertsortstart,4) ;(evalinsertsortstop,4)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{11},4->{5,6},5->{10},6->{7,8},7->{9},8->{10},9->{5,6},10->{2,3},11->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths YES + Considered Problem: Rules: 0. evalinsertsortstart(A,B,C,D) -> evalinsertsortentryin(A,B,C,D) True (1,1) 1. evalinsertsortentryin(A,B,C,D) -> evalinsertsortbb5in(1,B,C,D) True (1,1) 2. evalinsertsortbb5in(A,B,C,D) -> evalinsertsortbbin(A,B,C,D) [-1 + A >= 0 && B >= 1 + A] (?,1) 3. evalinsertsortbb5in(A,B,C,D) -> evalinsertsortreturnin(A,B,C,D) [-1 + A >= 0 && A >= B] (1,1) 4. evalinsertsortbbin(A,B,C,D) -> evalinsertsortbb2in(A,B,E,-1 + A) [-2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] (?,1) 5. evalinsertsortbb2in(A,B,C,D) -> evalinsertsortbb4in(A,B,C,D) [-2 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && 0 >= 1 + D] 6. evalinsertsortbb2in(A,B,C,D) -> evalinsertsortbb3in(A,B,C,D) [-2 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && D >= 0] 7. evalinsertsortbb3in(A,B,C,D) -> evalinsertsortbb1in(A,B,C,D) [-2 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && E >= 1 + C] 8. evalinsertsortbb3in(A,B,C,D) -> evalinsertsortbb4in(A,B,C,D) [-2 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && C >= E] 9. evalinsertsortbb1in(A,B,C,D) -> evalinsertsortbb2in(A,B,C,-1 + D) [-2 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] 10. evalinsertsortbb4in(A,B,C,D) -> evalinsertsortbb5in(1 + A,B,C,D) [-2 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] 11. evalinsertsortreturnin(A,B,C,D) -> evalinsertsortstop(A,B,C,D) [A + -1*B >= 0 && -1 + A >= 0] (1,1) Signature: {(evalinsertsortbb1in,4) ;(evalinsertsortbb2in,4) ;(evalinsertsortbb3in,4) ;(evalinsertsortbb4in,4) ;(evalinsertsortbb5in,4) ;(evalinsertsortbbin,4) ;(evalinsertsortentryin,4) ;(evalinsertsortreturnin,4) ;(evalinsertsortstart,4) ;(evalinsertsortstop,4)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{11},4->{5,6},5->{10},6->{7,8},7->{9},8->{10},9->{5,6},10->{2,3},11->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(4,5)] * Step 3: Looptree YES + Considered Problem: Rules: 0. evalinsertsortstart(A,B,C,D) -> evalinsertsortentryin(A,B,C,D) True (1,1) 1. evalinsertsortentryin(A,B,C,D) -> evalinsertsortbb5in(1,B,C,D) True (1,1) 2. evalinsertsortbb5in(A,B,C,D) -> evalinsertsortbbin(A,B,C,D) [-1 + A >= 0 && B >= 1 + A] (?,1) 3. evalinsertsortbb5in(A,B,C,D) -> evalinsertsortreturnin(A,B,C,D) [-1 + A >= 0 && A >= B] (1,1) 4. evalinsertsortbbin(A,B,C,D) -> evalinsertsortbb2in(A,B,E,-1 + A) [-2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] (?,1) 5. evalinsertsortbb2in(A,B,C,D) -> evalinsertsortbb4in(A,B,C,D) [-2 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && 0 >= 1 + D] 6. evalinsertsortbb2in(A,B,C,D) -> evalinsertsortbb3in(A,B,C,D) [-2 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && D >= 0] 7. evalinsertsortbb3in(A,B,C,D) -> evalinsertsortbb1in(A,B,C,D) [-2 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && E >= 1 + C] 8. evalinsertsortbb3in(A,B,C,D) -> evalinsertsortbb4in(A,B,C,D) [-2 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && C >= E] 9. evalinsertsortbb1in(A,B,C,D) -> evalinsertsortbb2in(A,B,C,-1 + D) [-2 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] 10. evalinsertsortbb4in(A,B,C,D) -> evalinsertsortbb5in(1 + A,B,C,D) [-2 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] 11. evalinsertsortreturnin(A,B,C,D) -> evalinsertsortstop(A,B,C,D) [A + -1*B >= 0 && -1 + A >= 0] (1,1) Signature: {(evalinsertsortbb1in,4) ;(evalinsertsortbb2in,4) ;(evalinsertsortbb3in,4) ;(evalinsertsortbb4in,4) ;(evalinsertsortbb5in,4) ;(evalinsertsortbbin,4) ;(evalinsertsortentryin,4) ;(evalinsertsortreturnin,4) ;(evalinsertsortstart,4) ;(evalinsertsortstop,4)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{11},4->{6},5->{10},6->{7,8},7->{9},8->{10},9->{5,6},10->{2,3},11->{}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11] | `- p:[2,10,5,9,7,6,4,8] c: [10] | `- p:[6,9,7] c: [9] YES