YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. evalterminatestart(A,B,C) -> evalterminateentryin(A,B,C) True (1,1) 1. evalterminateentryin(A,B,C) -> evalterminatebb1in(B,A,C) True (?,1) 2. evalterminatebb1in(A,B,C) -> evalterminatebbin(A,B,C) [100 >= B && A >= C] (?,1) 3. evalterminatebb1in(A,B,C) -> evalterminatereturnin(A,B,C) [B >= 101] (?,1) 4. evalterminatebb1in(A,B,C) -> evalterminatereturnin(A,B,C) [C >= 1 + A] (?,1) 5. evalterminatebbin(A,B,C) -> evalterminatebb1in(-1 + A,C,1 + B) [A + -1*C >= 0 && 100 + -1*B >= 0] (?,1) 6. evalterminatereturnin(A,B,C) -> evalterminatestop(A,B,C) True (?,1) Signature: {(evalterminatebb1in,3) ;(evalterminatebbin,3) ;(evalterminateentryin,3) ;(evalterminatereturnin,3) ;(evalterminatestart,3) ;(evalterminatestop,3)} Flow Graph: [0->{1},1->{2,3,4},2->{5},3->{6},4->{6},5->{2,3,4},6->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: Looptree YES + Considered Problem: Rules: 0. evalterminatestart(A,B,C) -> evalterminateentryin(A,B,C) True (1,1) 1. evalterminateentryin(A,B,C) -> evalterminatebb1in(B,A,C) True (1,1) 2. evalterminatebb1in(A,B,C) -> evalterminatebbin(A,B,C) [100 >= B && A >= C] (?,1) 3. evalterminatebb1in(A,B,C) -> evalterminatereturnin(A,B,C) [B >= 101] (1,1) 4. evalterminatebb1in(A,B,C) -> evalterminatereturnin(A,B,C) [C >= 1 + A] (1,1) 5. evalterminatebbin(A,B,C) -> evalterminatebb1in(-1 + A,C,1 + B) [A + -1*C >= 0 && 100 + -1*B >= 0] (?,1) 6. evalterminatereturnin(A,B,C) -> evalterminatestop(A,B,C) True (1,1) Signature: {(evalterminatebb1in,3) ;(evalterminatebbin,3) ;(evalterminateentryin,3) ;(evalterminatereturnin,3) ;(evalterminatestart,3) ;(evalterminatestop,3)} Flow Graph: [0->{1},1->{2,3,4},2->{5},3->{6},4->{6},5->{2,3,4},6->{}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6] | `- p:[2,5] c: [5] YES