WORST_CASE(?, O(n^2)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 1: evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ] We thus obtain the following problem: 2: T: (Comp: ?, Cost: 1) evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ] (Comp: ?, Cost: 1) evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (Comp: ?, Cost: 1) evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ] (Comp: ?, Cost: 1) evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ] (Comp: 1, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ] (Comp: 1, Cost: 1) evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalrealheapsortstep2bb7in) = 2 Pol(evalrealheapsortstep2bb9in) = 2 Pol(evalrealheapsortstep2bb6in) = 2 Pol(evalrealheapsortstep2bb5in) = 2 Pol(evalrealheapsortstep2bb3in) = 2 Pol(evalrealheapsortstep2bb4in) = 2 Pol(evalrealheapsortstep2bb10in) = 2 Pol(evalrealheapsortstep2bb11in) = 2 Pol(evalrealheapsortstep2bb2in) = 2 Pol(evalrealheapsortstep2bb1in) = 2 Pol(evalrealheapsortstep2returnin) = 1 Pol(evalrealheapsortstep2stop) = 0 Pol(evalrealheapsortstep2bbin) = 2 Pol(evalrealheapsortstep2entryin) = 2 Pol(evalrealheapsortstep2start) = 2 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3)) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ] strictly and produces the following problem: 4: T: (Comp: ?, Cost: 1) evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3)) (Comp: 2, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ] (Comp: 2, Cost: 1) evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ] (Comp: 1, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ] (Comp: 1, Cost: 1) evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalrealheapsortstep2bb9in) = V_1 - V_2 + 1 Pol(evalrealheapsortstep2bb2in) = V_1 - V_2 + 1 Pol(evalrealheapsortstep2bb10in) = V_1 - V_2 + 1 Pol(evalrealheapsortstep2bb7in) = V_1 - V_2 + 1 Pol(evalrealheapsortstep2bb6in) = V_1 - V_2 + 1 Pol(evalrealheapsortstep2bb5in) = V_1 - V_2 + 1 Pol(evalrealheapsortstep2bb4in) = V_1 - V_2 + 1 Pol(evalrealheapsortstep2bb3in) = V_1 - V_2 + 1 Pol(evalrealheapsortstep2bb1in) = V_1 - V_2 + 1 Pol(evalrealheapsortstep2bb11in) = V_1 - V_2 + 2 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 S("evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ]", 0-0) = Ar_0 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ]", 0-1) = Ar_1 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ]", 0-2) = Ar_2 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ]", 0-3) = Ar_3 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ]", 0-1) = Ar_1 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ]", 0-2) = Ar_2 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ]", 0-3) = Ar_3 S("evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3))", 0-1) = 0 S("evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ]", 0-1) = ? S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ]", 0-2) = ? S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ]", 0-3) = ? S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ]", 0-1) = ? S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ]", 0-2) = ? S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ]", 0-3) = ? S("evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3))", 0-1) = ? S("evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3))", 0-2) = 0 S("evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3))", 0-3) = ? S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ]", 0-1) = ? S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ]", 0-2) = ? S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ]", 0-3) = ? S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ]", 0-1) = ? S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ]", 0-2) = ? S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ]", 0-3) = ? S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ]", 0-1) = ? S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ]", 0-2) = ? S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ]", 0-3) = ? S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ]", 0-1) = ? S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ]", 0-2) = ? S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ]", 0-3) = ? S("evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3))", 0-1) = ? S("evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3))", 0-2) = ? S("evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3))", 0-3) = ? S("evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1))", 0-0) = Ar_0 S("evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1))", 0-1) = ? S("evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1))", 0-2) = ? S("evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1))", 0-3) = ? S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2))", 0-0) = Ar_0 S("evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2))", 0-1) = ? S("evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2))", 0-2) = ? S("evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2))", 0-3) = ? S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3))", 0-1) = ? S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3))", 0-2) = Ar_0 S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3))", 0-3) = ? S("evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3))", 0-1) = ? S("evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3))", 0-2) = ? S("evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3))", 0-3) = ? orients the transitions evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ] evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ] evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ] evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ] evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3)) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ] evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) weakly and the transition evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ] strictly and produces the following problem: 5: T: (Comp: ?, Cost: 1) evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3)) (Comp: 2, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ] (Comp: Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ] (Comp: 2, Cost: 1) evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ] (Comp: 1, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ] (Comp: 1, Cost: 1) evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 5 produces the following problem: 6: T: (Comp: ?, Cost: 1) evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ] (Comp: Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3)) (Comp: 2, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ] (Comp: Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ] (Comp: 2, Cost: 1) evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ] (Comp: 1, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ] (Comp: 1, Cost: 1) evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalrealheapsortstep2bb9in) = 1 Pol(evalrealheapsortstep2bb2in) = 1 Pol(evalrealheapsortstep2bb10in) = 0 Pol(evalrealheapsortstep2bb7in) = 1 Pol(evalrealheapsortstep2bb6in) = 1 Pol(evalrealheapsortstep2bb5in) = 1 Pol(evalrealheapsortstep2bb4in) = 1 Pol(evalrealheapsortstep2bb3in) = 1 Pol(evalrealheapsortstep2bb11in) = -1 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 S("evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ]", 0-0) = Ar_0 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ]", 0-1) = Ar_1 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ]", 0-2) = Ar_2 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ]", 0-3) = Ar_3 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ]", 0-1) = Ar_1 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ]", 0-2) = Ar_2 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ]", 0-3) = Ar_3 S("evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3))", 0-1) = 0 S("evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ]", 0-1) = ? S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ]", 0-2) = ? S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ]", 0-3) = ? S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ]", 0-1) = ? S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ]", 0-2) = ? S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ]", 0-3) = ? S("evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3))", 0-1) = ? S("evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3))", 0-2) = 0 S("evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3))", 0-3) = ? S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ]", 0-1) = ? S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ]", 0-2) = ? S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ]", 0-3) = ? S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ]", 0-1) = ? S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ]", 0-2) = ? S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ]", 0-3) = ? S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ]", 0-1) = ? S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ]", 0-2) = ? S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ]", 0-3) = ? S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ]", 0-1) = ? S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ]", 0-2) = ? S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ]", 0-3) = ? S("evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3))", 0-1) = ? S("evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3))", 0-2) = ? S("evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3))", 0-3) = ? S("evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1))", 0-0) = Ar_0 S("evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1))", 0-1) = ? S("evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1))", 0-2) = ? S("evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1))", 0-3) = ? S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2))", 0-0) = Ar_0 S("evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2))", 0-1) = ? S("evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2))", 0-2) = ? S("evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2))", 0-3) = ? S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3))", 0-1) = ? S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3))", 0-2) = Ar_0 S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3))", 0-3) = ? S("evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3))", 0-1) = ? S("evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3))", 0-2) = ? S("evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3))", 0-3) = ? orients the transitions evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ] evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ] evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ] evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ] evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) weakly and the transition evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ] strictly and produces the following problem: 7: T: (Comp: ?, Cost: 1) evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ] (Comp: Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ] (Comp: Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3)) (Comp: 2, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ] (Comp: Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ] (Comp: 2, Cost: 1) evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ] (Comp: 1, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ] (Comp: 1, Cost: 1) evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 7 produces the following problem: 8: T: (Comp: ?, Cost: 1) evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) (Comp: Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ] (Comp: Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ] (Comp: Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3)) (Comp: 2, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ] (Comp: Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ] (Comp: 2, Cost: 1) evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ] (Comp: 1, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ] (Comp: 1, Cost: 1) evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 8 to obtain the following invariants: For symbol evalrealheapsortstep2bb10in: X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ X_1 - 3 >= 0 For symbol evalrealheapsortstep2bb11in: X_2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ X_1 - 3 >= 0 For symbol evalrealheapsortstep2bb1in: X_1 - X_2 - 2 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ X_1 - 3 >= 0 For symbol evalrealheapsortstep2bb2in: X_1 - X_3 - 3 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ X_1 - X_2 - 3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ X_1 - 3 >= 0 For symbol evalrealheapsortstep2bb3in: X_1 - X_3 - 4 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 - 4 >= 0 /\ X_1 - X_2 - 4 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 - 4 >= 0 /\ X_1 - 4 >= 0 For symbol evalrealheapsortstep2bb4in: X_1 - X_3 - 3 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ X_1 - X_2 - 3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ X_1 - 3 >= 0 For symbol evalrealheapsortstep2bb5in: X_1 - X_3 - 4 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 - 4 >= 0 /\ X_1 - X_2 - 4 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 - 4 >= 0 /\ X_1 - 4 >= 0 For symbol evalrealheapsortstep2bb6in: X_4 - 1 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ -X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 1 >= 0 /\ X_1 + X_4 - 4 >= 0 /\ X_1 - X_3 - 3 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ X_1 - X_2 - 3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ X_1 - 3 >= 0 For symbol evalrealheapsortstep2bb7in: X_4 - 1 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ -X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 1 >= 0 /\ X_1 + X_4 - 4 >= 0 /\ X_1 - X_3 - 3 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ X_1 - X_2 - 3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ X_1 - 3 >= 0 For symbol evalrealheapsortstep2bb9in: X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ X_1 - 3 >= 0 For symbol evalrealheapsortstep2bbin: X_1 - 3 >= 0 This yielded the following problem: 9: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 1, Cost: 1) evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ] (Comp: 1, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ] (Comp: 1, Cost: 1) evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3)) [ Ar_0 - 3 >= 0 ] (Comp: 2, Cost: 1) evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ Ar_0 >= Ar_1 + 2 ] (Comp: 2, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ Ar_1 + 1 >= Ar_0 ] (Comp: Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 - Ar_1 - 2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ] (Comp: Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ Ar_0 = 2*Ar_2 + Ar_1 + 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ] (Comp: Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) [ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 4 >= 0 /\ Ar_0 - Ar_1 - 4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 4 >= 0 /\ Ar_0 - 4 >= 0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 4 >= 0 /\ Ar_0 - Ar_1 - 4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 4 >= 0 /\ Ar_0 - 4 >= 0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) [ Ar_0 - Ar_2 - 4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 4 >= 0 /\ Ar_0 - Ar_1 - 4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 4 >= 0 /\ Ar_0 - 4 >= 0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 4 >= 0 /\ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 4 >= 0 /\ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 4 >= 0 /\ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalrealheapsortstep2bb9in) = 6*V_1 - 6*V_3 + 4 Pol(evalrealheapsortstep2bb2in) = 6*V_1 - 6*V_3 + 3 Pol(evalrealheapsortstep2bb7in) = 6*V_1 - 6*V_3 - 1 Pol(evalrealheapsortstep2bb6in) = 6*V_1 - 6*V_3 Pol(evalrealheapsortstep2bb5in) = 6*V_1 - 6*V_3 + 1 Pol(evalrealheapsortstep2bb4in) = 6*V_1 - 6*V_3 + 1 Pol(evalrealheapsortstep2bb3in) = 6*V_1 - 6*V_3 + 2 and size complexities S("evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 4 >= 0 /\\ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 4 >= 0 /\\ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-1) = Ar_0 + 2 S("evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 4 >= 0 /\\ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-2) = ? S("evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 4 >= 0 /\\ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-3) = ? S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) [ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 4 >= 0 /\\ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) [ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 4 >= 0 /\\ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-1) = Ar_0 + 2 S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) [ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 4 >= 0 /\\ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-2) = Ar_0 S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) [ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 4 >= 0 /\\ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-3) = ? S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 4 >= 0 /\\ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 4 >= 0 /\\ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-1) = Ar_0 + 2 S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 4 >= 0 /\\ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-2) = ? S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 4 >= 0 /\\ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-3) = ? S("evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) [ Ar_0 - Ar_2 - 4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 4 >= 0 /\\ Ar_0 - Ar_1 - 4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 4 >= 0 /\\ Ar_0 - 4 >= 0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) [ Ar_0 - Ar_2 - 4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 4 >= 0 /\\ Ar_0 - Ar_1 - 4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 4 >= 0 /\\ Ar_0 - 4 >= 0 ]", 0-1) = Ar_0 + 2 S("evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) [ Ar_0 - Ar_2 - 4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 4 >= 0 /\\ Ar_0 - Ar_1 - 4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 4 >= 0 /\\ Ar_0 - 4 >= 0 ]", 0-2) = ? S("evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) [ Ar_0 - Ar_2 - 4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 4 >= 0 /\\ Ar_0 - Ar_1 - 4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 4 >= 0 /\\ Ar_0 - 4 >= 0 ]", 0-3) = ? S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 4 >= 0 /\\ Ar_0 - Ar_1 - 4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 4 >= 0 /\\ Ar_0 - 4 >= 0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 4 >= 0 /\\ Ar_0 - Ar_1 - 4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 4 >= 0 /\\ Ar_0 - 4 >= 0 ]", 0-1) = Ar_0 + 2 S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 4 >= 0 /\\ Ar_0 - Ar_1 - 4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 4 >= 0 /\\ Ar_0 - 4 >= 0 ]", 0-2) = ? S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 4 >= 0 /\\ Ar_0 - Ar_1 - 4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 4 >= 0 /\\ Ar_0 - 4 >= 0 ]", 0-3) = ? S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 4 >= 0 /\\ Ar_0 - Ar_1 - 4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 4 >= 0 /\\ Ar_0 - 4 >= 0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 4 >= 0 /\\ Ar_0 - Ar_1 - 4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 4 >= 0 /\\ Ar_0 - 4 >= 0 ]", 0-1) = Ar_0 + 2 S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 4 >= 0 /\\ Ar_0 - Ar_1 - 4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 4 >= 0 /\\ Ar_0 - 4 >= 0 ]", 0-2) = ? S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 4 >= 0 /\\ Ar_0 - Ar_1 - 4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 4 >= 0 /\\ Ar_0 - 4 >= 0 ]", 0-3) = ? S("evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) [ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) [ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-1) = Ar_0 + 2 S("evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) [ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-2) = ? S("evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) [ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-3) = ? S("evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-1) = Ar_0 + 2 S("evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-2) = ? S("evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-3) = ? S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ]", 0-1) = Ar_0 + 2 S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ]", 0-2) = ? S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ]", 0-3) = ? S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_0 = 2*Ar_2 + Ar_1 + 3 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_0 = 2*Ar_2 + Ar_1 + 3 ]", 0-1) = Ar_0 + 2 S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_0 = 2*Ar_2 + Ar_1 + 3 ]", 0-2) = ? S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_0 = 2*Ar_2 + Ar_1 + 3 ]", 0-3) = ? S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ]", 0-1) = Ar_0 + 2 S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ]", 0-2) = ? S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ]", 0-3) = ? S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ]", 0-1) = Ar_0 + 2 S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ]", 0-2) = ? S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ]", 0-3) = ? S("evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 - Ar_1 - 2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 - Ar_1 - 2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-1) = Ar_0 + 2 S("evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 - Ar_1 - 2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-2) = 0 S("evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 - Ar_1 - 2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-3) = ? S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_1 + 1 >= Ar_0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_1 + 1 >= Ar_0 ]", 0-1) = Ar_0 + 2 S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_1 + 1 >= Ar_0 ]", 0-2) = ? S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_1 + 1 >= Ar_0 ]", 0-3) = ? S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_0 >= Ar_1 + 2 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_0 >= Ar_1 + 2 ]", 0-1) = Ar_0 + 2 S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_0 >= Ar_1 + 2 ]", 0-2) = ? S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_0 >= Ar_1 + 2 ]", 0-3) = ? S("evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_0 + Ar_1 + 2 S("evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3)) [ Ar_0 - 3 >= 0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3)) [ Ar_0 - 3 >= 0 ]", 0-1) = 0 S("evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3)) [ Ar_0 - 3 >= 0 ]", 0-2) = Ar_2 S("evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3)) [ Ar_0 - 3 >= 0 ]", 0-3) = Ar_3 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ]", 0-1) = Ar_1 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ]", 0-2) = Ar_2 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ]", 0-3) = Ar_3 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ]", 0-0) = Ar_0 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ]", 0-1) = Ar_1 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ]", 0-2) = Ar_2 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ]", 0-3) = Ar_3 S("evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 orients the transitions evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ] evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 4 >= 0 /\ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 4 >= 0 /\ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 4 >= 0 /\ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) [ Ar_0 - Ar_2 - 4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 4 >= 0 /\ Ar_0 - Ar_1 - 4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 4 >= 0 /\ Ar_0 - 4 >= 0 ] evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) [ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 4 >= 0 /\ Ar_0 - Ar_1 - 4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 4 >= 0 /\ Ar_0 - 4 >= 0 ] evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 4 >= 0 /\ Ar_0 - Ar_1 - 4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 4 >= 0 /\ Ar_0 - 4 >= 0 ] evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ Ar_0 = 2*Ar_2 + Ar_1 + 3 ] evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ] weakly and the transitions evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ] evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 4 >= 0 /\ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 4 >= 0 /\ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 4 >= 0 /\ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) [ Ar_0 - Ar_2 - 4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 4 >= 0 /\ Ar_0 - Ar_1 - 4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 4 >= 0 /\ Ar_0 - 4 >= 0 ] evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) [ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 4 >= 0 /\ Ar_0 - Ar_1 - 4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 4 >= 0 /\ Ar_0 - 4 >= 0 ] evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 4 >= 0 /\ Ar_0 - Ar_1 - 4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 4 >= 0 /\ Ar_0 - 4 >= 0 ] evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ Ar_0 = 2*Ar_2 + Ar_1 + 3 ] evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ] strictly and produces the following problem: 10: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 1, Cost: 1) evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ] (Comp: 1, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ] (Comp: 1, Cost: 1) evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3)) [ Ar_0 - 3 >= 0 ] (Comp: 2, Cost: 1) evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ Ar_0 >= Ar_1 + 2 ] (Comp: 2, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ Ar_1 + 1 >= Ar_0 ] (Comp: Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 - Ar_1 - 2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] (Comp: 6*Ar_0^2 + 16*Ar_0 + 8, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ] (Comp: Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ] (Comp: 6*Ar_0^2 + 16*Ar_0 + 8, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ Ar_0 = 2*Ar_2 + Ar_1 + 3 ] (Comp: 6*Ar_0^2 + 16*Ar_0 + 8, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ] (Comp: Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] (Comp: 6*Ar_0^2 + 16*Ar_0 + 8, Cost: 1) evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) [ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] (Comp: 6*Ar_0^2 + 16*Ar_0 + 8, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 4 >= 0 /\ Ar_0 - Ar_1 - 4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 4 >= 0 /\ Ar_0 - 4 >= 0 ] (Comp: 6*Ar_0^2 + 16*Ar_0 + 8, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 4 >= 0 /\ Ar_0 - Ar_1 - 4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 4 >= 0 /\ Ar_0 - 4 >= 0 ] (Comp: 6*Ar_0^2 + 16*Ar_0 + 8, Cost: 1) evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) [ Ar_0 - Ar_2 - 4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 4 >= 0 /\ Ar_0 - Ar_1 - 4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 4 >= 0 /\ Ar_0 - 4 >= 0 ] (Comp: 6*Ar_0^2 + 16*Ar_0 + 8, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 4 >= 0 /\ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] (Comp: 6*Ar_0^2 + 16*Ar_0 + 8, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 4 >= 0 /\ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] (Comp: 6*Ar_0^2 + 16*Ar_0 + 8, Cost: 1) evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 4 >= 0 /\ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 164*Ar_0 + 60*Ar_0^2 + 96 Time: 4.777 sec (SMT: 4.569 sec)