MAYBE Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f14(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f400(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Fresh_24, Fresh_25, Fresh_26, Fresh_27, 1, Ar_5)) [ Fresh_24 >= 1 /\ Fresh_26 >= 1 /\ 0 >= Fresh_25 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Fresh_20, Fresh_21, Fresh_22, Fresh_23, 1, 0)) [ Fresh_20 >= 1 /\ Fresh_22 >= 1 /\ Fresh_21 >= 1 ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, 1)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_0 - 1, Ar_1, Fresh_18, Fresh_19, Ar_2, Ar_5)) [ Fresh_18 >= Ar_2 /\ 0 >= Ar_1 /\ Ar_0 >= 1 ] (Comp: ?, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_0 - 1, Ar_1, Fresh_16, Fresh_17, Ar_2, 0)) [ Fresh_16 >= Ar_2 /\ Ar_1 >= 1 /\ Ar_0 >= 1 ] (Comp: ?, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, 1)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f43(Ar_0, Ar_1, Fresh_14, Fresh_15, Ar_2, Ar_5)) [ Fresh_14 >= Ar_2 /\ 0 >= Ar_2 /\ 0 >= Ar_1 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f43(Ar_0, Ar_1, Fresh_12, Fresh_13, Ar_2, 0)) [ Fresh_12 >= Ar_2 /\ 0 >= Ar_2 /\ Ar_1 >= 1 ] (Comp: ?, Cost: 1) f43(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_5)) [ Ar_2 = Ar_4 ] (Comp: ?, Cost: 1) f43(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, 1)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f53(Ar_0, Ar_1, Fresh_10, Fresh_11, Ar_2 - 1, Ar_5)) [ Fresh_10 + 1 >= Ar_2 /\ Ar_2 >= 1 /\ 0 >= Ar_1 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f53(Ar_0, Ar_1, Fresh_8, Fresh_9, Ar_2 - 1, 0)) [ Fresh_8 + 1 >= Ar_2 /\ Ar_2 >= 1 /\ Ar_1 >= 1 ] (Comp: ?, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f61(Ar_0, Ar_0, Ar_2, Ar_3, Ar_2, Ar_5)) [ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f61(Ar_0, Ar_0, Ar_2, Ar_3, Ar_2, 1)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f63(Ar_0, Ar_1, Fresh_6, Fresh_7, Ar_4, Ar_5)) [ 0 >= Ar_1 /\ Fresh_6 >= Ar_4 ] (Comp: ?, Cost: 1) f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f63(Ar_0, Ar_1, Fresh_4, Fresh_5, Ar_4, 0)) [ Ar_1 >= 1 /\ Fresh_4 >= Ar_4 ] (Comp: ?, Cost: 1) f63(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f71(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_2, Ar_5)) [ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) f63(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f71(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_2, 1)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f73(Ar_0, Ar_1, Fresh_2, Fresh_3, Ar_4, Ar_5)) [ 0 >= Ar_1 /\ Fresh_2 >= Ar_4 ] (Comp: ?, Cost: 1) f71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f73(Ar_0, Ar_1, Fresh_0, Fresh_1, Ar_4, 0)) [ Ar_1 >= 1 /\ Fresh_0 >= Ar_4 ] (Comp: ?, Cost: 1) f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, 1)) [ Ar_2 >= Ar_4 + 1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [Ar_0, Ar_1, Ar_2, Ar_4]. We thus obtain the following problem: 2: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f2(Ar_0, Ar_1, Ar_2, Ar_4)) [ 0 <= 0 ] (Comp: ?, Cost: 1) f73(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f73(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) f71(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f73(Ar_0, Ar_1, Fresh_0, Ar_4)) [ Ar_1 >= 1 /\ Fresh_0 >= Ar_4 ] (Comp: ?, Cost: 1) f71(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f73(Ar_0, Ar_1, Fresh_2, Ar_4)) [ 0 >= Ar_1 /\ Fresh_2 >= Ar_4 ] (Comp: ?, Cost: 1) f63(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f71(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f63(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f71(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) f61(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f63(Ar_0, Ar_1, Fresh_4, Ar_4)) [ Ar_1 >= 1 /\ Fresh_4 >= Ar_4 ] (Comp: ?, Cost: 1) f61(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f63(Ar_0, Ar_1, Fresh_6, Ar_4)) [ 0 >= Ar_1 /\ Fresh_6 >= Ar_4 ] (Comp: ?, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f61(Ar_0, Ar_0, Ar_2, Ar_2)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f61(Ar_0, Ar_0, Ar_2, Ar_2)) [ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f53(Ar_0, Ar_1, Fresh_8, Ar_2 - 1)) [ Fresh_8 + 1 >= Ar_2 /\ Ar_2 >= 1 /\ Ar_1 >= 1 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f53(Ar_0, Ar_1, Fresh_10, Ar_2 - 1)) [ Fresh_10 + 1 >= Ar_2 /\ Ar_2 >= 1 /\ 0 >= Ar_1 ] (Comp: ?, Cost: 1) f43(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f43(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_2 = Ar_4 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f43(Ar_0, Ar_1, Fresh_12, Ar_2)) [ Fresh_12 >= Ar_2 /\ 0 >= Ar_2 /\ Ar_1 >= 1 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f43(Ar_0, Ar_1, Fresh_14, Ar_2)) [ Fresh_14 >= Ar_2 /\ 0 >= Ar_2 /\ 0 >= Ar_1 ] (Comp: ?, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f33(Ar_0 - 1, Ar_1, Fresh_16, Ar_2)) [ Fresh_16 >= Ar_2 /\ Ar_1 >= 1 /\ Ar_0 >= 1 ] (Comp: ?, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f33(Ar_0 - 1, Ar_1, Fresh_18, Ar_2)) [ Fresh_18 >= Ar_2 /\ 0 >= Ar_1 /\ Ar_0 >= 1 ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f23(Fresh_20, Fresh_21, Fresh_22, 1)) [ Fresh_20 >= 1 /\ Fresh_22 >= 1 /\ Fresh_21 >= 1 ] (Comp: ?, Cost: 1) f2(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f23(Fresh_24, Fresh_25, Fresh_26, 1)) [ Fresh_24 >= 1 /\ Fresh_26 >= 1 /\ 0 >= Fresh_25 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f400(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_4)) (Comp: ?, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f14(Ar_0, Ar_1, Ar_2, Ar_4)) [ 0 >= Ar_0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f2(Ar_0, Ar_1, Ar_2, Ar_4)) [ 0 <= 0 ] (Comp: ?, Cost: 1) f73(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f73(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) f71(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f73(Ar_0, Ar_1, Fresh_0, Ar_4)) [ Ar_1 >= 1 /\ Fresh_0 >= Ar_4 ] (Comp: ?, Cost: 1) f71(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f73(Ar_0, Ar_1, Fresh_2, Ar_4)) [ 0 >= Ar_1 /\ Fresh_2 >= Ar_4 ] (Comp: ?, Cost: 1) f63(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f71(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f63(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f71(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) f61(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f63(Ar_0, Ar_1, Fresh_4, Ar_4)) [ Ar_1 >= 1 /\ Fresh_4 >= Ar_4 ] (Comp: ?, Cost: 1) f61(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f63(Ar_0, Ar_1, Fresh_6, Ar_4)) [ 0 >= Ar_1 /\ Fresh_6 >= Ar_4 ] (Comp: ?, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f61(Ar_0, Ar_0, Ar_2, Ar_2)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f61(Ar_0, Ar_0, Ar_2, Ar_2)) [ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f53(Ar_0, Ar_1, Fresh_8, Ar_2 - 1)) [ Fresh_8 + 1 >= Ar_2 /\ Ar_2 >= 1 /\ Ar_1 >= 1 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f53(Ar_0, Ar_1, Fresh_10, Ar_2 - 1)) [ Fresh_10 + 1 >= Ar_2 /\ Ar_2 >= 1 /\ 0 >= Ar_1 ] (Comp: ?, Cost: 1) f43(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f43(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_2 = Ar_4 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f43(Ar_0, Ar_1, Fresh_12, Ar_2)) [ Fresh_12 >= Ar_2 /\ 0 >= Ar_2 /\ Ar_1 >= 1 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f43(Ar_0, Ar_1, Fresh_14, Ar_2)) [ Fresh_14 >= Ar_2 /\ 0 >= Ar_2 /\ 0 >= Ar_1 ] (Comp: ?, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f33(Ar_0 - 1, Ar_1, Fresh_16, Ar_2)) [ Fresh_16 >= Ar_2 /\ Ar_1 >= 1 /\ Ar_0 >= 1 ] (Comp: ?, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f33(Ar_0 - 1, Ar_1, Fresh_18, Ar_2)) [ Fresh_18 >= Ar_2 /\ 0 >= Ar_1 /\ Ar_0 >= 1 ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_2 >= Ar_4 + 1 ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_4 >= Ar_2 ] (Comp: 1, Cost: 1) f2(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f23(Fresh_20, Fresh_21, Fresh_22, 1)) [ Fresh_20 >= 1 /\ Fresh_22 >= 1 /\ Fresh_21 >= 1 ] (Comp: 1, Cost: 1) f2(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f23(Fresh_24, Fresh_25, Fresh_26, 1)) [ Fresh_24 >= 1 /\ Fresh_26 >= 1 /\ 0 >= Fresh_25 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f400(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_4)) (Comp: ?, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f14(Ar_0, Ar_1, Ar_2, Ar_4)) [ 0 >= Ar_0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 1 Pol(f2) = 1 Pol(f73) = 1 Pol(f13) = 1 Pol(f71) = 1 Pol(f63) = 1 Pol(f61) = 1 Pol(f53) = 1 Pol(f6) = 1 Pol(f43) = 1 Pol(f33) = 1 Pol(f4) = 1 Pol(f23) = 1 Pol(f400) = 0 Pol(f14) = 0 orients all transitions weakly and the transitions f4(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f14(Ar_0, Ar_1, Ar_2, Ar_4)) [ 0 >= Ar_0 ] f13(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f400(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f2(Ar_0, Ar_1, Ar_2, Ar_4)) [ 0 <= 0 ] (Comp: ?, Cost: 1) f73(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f73(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) f71(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f73(Ar_0, Ar_1, Fresh_0, Ar_4)) [ Ar_1 >= 1 /\ Fresh_0 >= Ar_4 ] (Comp: ?, Cost: 1) f71(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f73(Ar_0, Ar_1, Fresh_2, Ar_4)) [ 0 >= Ar_1 /\ Fresh_2 >= Ar_4 ] (Comp: ?, Cost: 1) f63(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f71(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f63(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f71(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) f61(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f63(Ar_0, Ar_1, Fresh_4, Ar_4)) [ Ar_1 >= 1 /\ Fresh_4 >= Ar_4 ] (Comp: ?, Cost: 1) f61(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f63(Ar_0, Ar_1, Fresh_6, Ar_4)) [ 0 >= Ar_1 /\ Fresh_6 >= Ar_4 ] (Comp: ?, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f61(Ar_0, Ar_0, Ar_2, Ar_2)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f61(Ar_0, Ar_0, Ar_2, Ar_2)) [ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f53(Ar_0, Ar_1, Fresh_8, Ar_2 - 1)) [ Fresh_8 + 1 >= Ar_2 /\ Ar_2 >= 1 /\ Ar_1 >= 1 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f53(Ar_0, Ar_1, Fresh_10, Ar_2 - 1)) [ Fresh_10 + 1 >= Ar_2 /\ Ar_2 >= 1 /\ 0 >= Ar_1 ] (Comp: ?, Cost: 1) f43(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f43(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_2 = Ar_4 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f43(Ar_0, Ar_1, Fresh_12, Ar_2)) [ Fresh_12 >= Ar_2 /\ 0 >= Ar_2 /\ Ar_1 >= 1 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f43(Ar_0, Ar_1, Fresh_14, Ar_2)) [ Fresh_14 >= Ar_2 /\ 0 >= Ar_2 /\ 0 >= Ar_1 ] (Comp: ?, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f33(Ar_0 - 1, Ar_1, Fresh_16, Ar_2)) [ Fresh_16 >= Ar_2 /\ Ar_1 >= 1 /\ Ar_0 >= 1 ] (Comp: ?, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f33(Ar_0 - 1, Ar_1, Fresh_18, Ar_2)) [ Fresh_18 >= Ar_2 /\ 0 >= Ar_1 /\ Ar_0 >= 1 ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_2 >= Ar_4 + 1 ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_4 >= Ar_2 ] (Comp: 1, Cost: 1) f2(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f23(Fresh_20, Fresh_21, Fresh_22, 1)) [ Fresh_20 >= 1 /\ Fresh_22 >= 1 /\ Fresh_21 >= 1 ] (Comp: 1, Cost: 1) f2(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f23(Fresh_24, Fresh_25, Fresh_26, 1)) [ Fresh_24 >= 1 /\ Fresh_26 >= 1 /\ 0 >= Fresh_25 ] (Comp: 1, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f400(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_4)) (Comp: 1, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f14(Ar_0, Ar_1, Ar_2, Ar_4)) [ 0 >= Ar_0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 4 to obtain the following invariants: For symbol f13: X_3 - X_4 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 >= 0 /\ X_2 + X_4 >= 0 /\ X_1 + X_4 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 >= 0 /\ X_1 - X_2 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0 For symbol f23: -X_4 + 1 >= 0 /\ X_3 - X_4 >= 0 /\ X_1 - X_4 >= 0 /\ X_4 - 1 >= 0 /\ X_3 + X_4 - 2 >= 0 /\ X_1 + X_4 - 2 >= 0 /\ X_3 - 1 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_1 - 1 >= 0 For symbol f33: X_3 - X_4 >= 0 /\ X_1 >= 0 For symbol f4: X_3 - X_4 >= 0 For symbol f43: -X_4 >= 0 /\ X_3 - X_4 >= 0 /\ X_1 - X_4 >= 0 /\ X_1 >= 0 For symbol f53: X_3 - X_4 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 >= 0 /\ X_1 + X_4 >= 0 /\ X_3 >= 0 /\ X_1 + X_3 >= 0 /\ X_1 >= 0 For symbol f6: X_3 - X_4 >= 0 /\ X_1 >= 0 For symbol f61: X_3 - X_4 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 >= 0 /\ -X_3 + X_4 >= 0 /\ X_2 + X_4 >= 0 /\ X_1 + X_4 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 >= 0 /\ X_1 - X_2 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0 For symbol f63: X_3 - X_4 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 >= 0 /\ X_2 + X_4 >= 0 /\ X_1 + X_4 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 >= 0 /\ X_1 - X_2 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0 For symbol f71: X_3 - X_4 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 >= 0 /\ -X_3 + X_4 >= 0 /\ X_2 + X_4 >= 0 /\ X_1 + X_4 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 >= 0 /\ X_1 - X_2 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0 For symbol f73: X_3 - X_4 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 >= 0 /\ X_2 + X_4 >= 0 /\ X_1 + X_4 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 >= 0 /\ X_1 - X_2 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0 This yielded the following problem: 5: T: (Comp: 1, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f14(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ 0 >= Ar_0 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 1, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f400(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) f2(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f23(Fresh_24, Fresh_25, Fresh_26, 1)) [ Fresh_24 >= 1 /\ Fresh_26 >= 1 /\ 0 >= Fresh_25 ] (Comp: 1, Cost: 1) f2(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f23(Fresh_20, Fresh_21, Fresh_22, 1)) [ Fresh_20 >= 1 /\ Fresh_22 >= 1 /\ Fresh_21 >= 1 ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_4)) [ -Ar_4 + 1 >= 0 /\ Ar_2 - Ar_4 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ Ar_4 - 1 >= 0 /\ Ar_2 + Ar_4 - 2 >= 0 /\ Ar_0 + Ar_4 - 2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_4 >= Ar_2 ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_4)) [ -Ar_4 + 1 >= 0 /\ Ar_2 - Ar_4 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ Ar_4 - 1 >= 0 /\ Ar_2 + Ar_4 - 2 >= 0 /\ Ar_0 + Ar_4 - 2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f33(Ar_0 - 1, Ar_1, Fresh_18, Ar_2)) [ Ar_2 - Ar_4 >= 0 /\ Fresh_18 >= Ar_2 /\ 0 >= Ar_1 /\ Ar_0 >= 1 ] (Comp: ?, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f33(Ar_0 - 1, Ar_1, Fresh_16, Ar_2)) [ Ar_2 - Ar_4 >= 0 /\ Fresh_16 >= Ar_2 /\ Ar_1 >= 1 /\ Ar_0 >= 1 ] (Comp: ?, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_0 >= 0 /\ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f43(Ar_0, Ar_1, Fresh_14, Ar_2)) [ Ar_2 - Ar_4 >= 0 /\ Ar_0 >= 0 /\ Fresh_14 >= Ar_2 /\ 0 >= Ar_2 /\ 0 >= Ar_1 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f43(Ar_0, Ar_1, Fresh_12, Ar_2)) [ Ar_2 - Ar_4 >= 0 /\ Ar_0 >= 0 /\ Fresh_12 >= Ar_2 /\ 0 >= Ar_2 /\ Ar_1 >= 1 ] (Comp: ?, Cost: 1) f43(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_2)) [ -Ar_4 >= 0 /\ Ar_2 - Ar_4 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ Ar_0 >= 0 /\ Ar_2 = Ar_4 ] (Comp: ?, Cost: 1) f43(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 - Ar_4 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f53(Ar_0, Ar_1, Fresh_10, Ar_2 - 1)) [ Ar_2 - Ar_4 >= 0 /\ Ar_0 >= 0 /\ Fresh_10 + 1 >= Ar_2 /\ Ar_2 >= 1 /\ 0 >= Ar_1 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f53(Ar_0, Ar_1, Fresh_8, Ar_2 - 1)) [ Ar_2 - Ar_4 >= 0 /\ Ar_0 >= 0 /\ Fresh_8 + 1 >= Ar_2 /\ Ar_2 >= 1 /\ Ar_1 >= 1 ] (Comp: ?, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f61(Ar_0, Ar_0, Ar_2, Ar_2)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 >= 0 /\ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f61(Ar_0, Ar_0, Ar_2, Ar_2)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f61(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f63(Ar_0, Ar_1, Fresh_6, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ -Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ Fresh_6 >= Ar_4 ] (Comp: ?, Cost: 1) f61(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f63(Ar_0, Ar_1, Fresh_4, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ -Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= 1 /\ Fresh_4 >= Ar_4 ] (Comp: ?, Cost: 1) f63(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f71(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) f63(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f71(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f71(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f73(Ar_0, Ar_1, Fresh_2, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ -Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ Fresh_2 >= Ar_4 ] (Comp: ?, Cost: 1) f71(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f73(Ar_0, Ar_1, Fresh_0, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ -Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= 1 /\ Fresh_0 >= Ar_4 ] (Comp: ?, Cost: 1) f73(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) f73(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_4 + 1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f2(Ar_0, Ar_1, Ar_2, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for unsatisfiable constraints removes the following transition from problem 5: f13(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f400(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ] We thus obtain the following problem: 6: T: (Comp: 1, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f14(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ 0 >= Ar_0 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 1, Cost: 1) f2(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f23(Fresh_24, Fresh_25, Fresh_26, 1)) [ Fresh_24 >= 1 /\ Fresh_26 >= 1 /\ 0 >= Fresh_25 ] (Comp: 1, Cost: 1) f2(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f23(Fresh_20, Fresh_21, Fresh_22, 1)) [ Fresh_20 >= 1 /\ Fresh_22 >= 1 /\ Fresh_21 >= 1 ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_4)) [ -Ar_4 + 1 >= 0 /\ Ar_2 - Ar_4 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ Ar_4 - 1 >= 0 /\ Ar_2 + Ar_4 - 2 >= 0 /\ Ar_0 + Ar_4 - 2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_4 >= Ar_2 ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_4)) [ -Ar_4 + 1 >= 0 /\ Ar_2 - Ar_4 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ Ar_4 - 1 >= 0 /\ Ar_2 + Ar_4 - 2 >= 0 /\ Ar_0 + Ar_4 - 2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f33(Ar_0 - 1, Ar_1, Fresh_18, Ar_2)) [ Ar_2 - Ar_4 >= 0 /\ Fresh_18 >= Ar_2 /\ 0 >= Ar_1 /\ Ar_0 >= 1 ] (Comp: ?, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f33(Ar_0 - 1, Ar_1, Fresh_16, Ar_2)) [ Ar_2 - Ar_4 >= 0 /\ Fresh_16 >= Ar_2 /\ Ar_1 >= 1 /\ Ar_0 >= 1 ] (Comp: ?, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_0 >= 0 /\ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f43(Ar_0, Ar_1, Fresh_14, Ar_2)) [ Ar_2 - Ar_4 >= 0 /\ Ar_0 >= 0 /\ Fresh_14 >= Ar_2 /\ 0 >= Ar_2 /\ 0 >= Ar_1 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f43(Ar_0, Ar_1, Fresh_12, Ar_2)) [ Ar_2 - Ar_4 >= 0 /\ Ar_0 >= 0 /\ Fresh_12 >= Ar_2 /\ 0 >= Ar_2 /\ Ar_1 >= 1 ] (Comp: ?, Cost: 1) f43(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_2)) [ -Ar_4 >= 0 /\ Ar_2 - Ar_4 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ Ar_0 >= 0 /\ Ar_2 = Ar_4 ] (Comp: ?, Cost: 1) f43(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 - Ar_4 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f53(Ar_0, Ar_1, Fresh_10, Ar_2 - 1)) [ Ar_2 - Ar_4 >= 0 /\ Ar_0 >= 0 /\ Fresh_10 + 1 >= Ar_2 /\ Ar_2 >= 1 /\ 0 >= Ar_1 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f53(Ar_0, Ar_1, Fresh_8, Ar_2 - 1)) [ Ar_2 - Ar_4 >= 0 /\ Ar_0 >= 0 /\ Fresh_8 + 1 >= Ar_2 /\ Ar_2 >= 1 /\ Ar_1 >= 1 ] (Comp: ?, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f61(Ar_0, Ar_0, Ar_2, Ar_2)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 >= 0 /\ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f61(Ar_0, Ar_0, Ar_2, Ar_2)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f61(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f63(Ar_0, Ar_1, Fresh_6, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ -Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ Fresh_6 >= Ar_4 ] (Comp: ?, Cost: 1) f61(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f63(Ar_0, Ar_1, Fresh_4, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ -Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= 1 /\ Fresh_4 >= Ar_4 ] (Comp: ?, Cost: 1) f63(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f71(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) f63(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f71(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f71(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f73(Ar_0, Ar_1, Fresh_2, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ -Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ Fresh_2 >= Ar_4 ] (Comp: ?, Cost: 1) f71(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f73(Ar_0, Ar_1, Fresh_0, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ -Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= 1 /\ Fresh_0 >= Ar_4 ] (Comp: ?, Cost: 1) f73(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) f73(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_4 + 1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f2(Ar_0, Ar_1, Ar_2, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 6 produces the following problem: 7: T: (Comp: 1, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f14(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ 0 >= Ar_0 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 1, Cost: 1) f2(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f23(Fresh_24, Fresh_25, Fresh_26, 1)) [ Fresh_24 >= 1 /\ Fresh_26 >= 1 /\ 0 >= Fresh_25 ] (Comp: 1, Cost: 1) f2(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f23(Fresh_20, Fresh_21, Fresh_22, 1)) [ Fresh_20 >= 1 /\ Fresh_22 >= 1 /\ Fresh_21 >= 1 ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_4)) [ -Ar_4 + 1 >= 0 /\ Ar_2 - Ar_4 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ Ar_4 - 1 >= 0 /\ Ar_2 + Ar_4 - 2 >= 0 /\ Ar_0 + Ar_4 - 2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_4 >= Ar_2 ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_4)) [ -Ar_4 + 1 >= 0 /\ Ar_2 - Ar_4 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ Ar_4 - 1 >= 0 /\ Ar_2 + Ar_4 - 2 >= 0 /\ Ar_0 + Ar_4 - 2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 >= Ar_4 + 1 ] (Comp: 4, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f33(Ar_0 - 1, Ar_1, Fresh_18, Ar_2)) [ Ar_2 - Ar_4 >= 0 /\ Fresh_18 >= Ar_2 /\ 0 >= Ar_1 /\ Ar_0 >= 1 ] (Comp: ?, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f33(Ar_0 - 1, Ar_1, Fresh_16, Ar_2)) [ Ar_2 - Ar_4 >= 0 /\ Fresh_16 >= Ar_2 /\ Ar_1 >= 1 /\ Ar_0 >= 1 ] (Comp: ?, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_0 >= 0 /\ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f43(Ar_0, Ar_1, Fresh_14, Ar_2)) [ Ar_2 - Ar_4 >= 0 /\ Ar_0 >= 0 /\ Fresh_14 >= Ar_2 /\ 0 >= Ar_2 /\ 0 >= Ar_1 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f43(Ar_0, Ar_1, Fresh_12, Ar_2)) [ Ar_2 - Ar_4 >= 0 /\ Ar_0 >= 0 /\ Fresh_12 >= Ar_2 /\ 0 >= Ar_2 /\ Ar_1 >= 1 ] (Comp: ?, Cost: 1) f43(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_2)) [ -Ar_4 >= 0 /\ Ar_2 - Ar_4 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ Ar_0 >= 0 /\ Ar_2 = Ar_4 ] (Comp: ?, Cost: 1) f43(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 - Ar_4 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f53(Ar_0, Ar_1, Fresh_10, Ar_2 - 1)) [ Ar_2 - Ar_4 >= 0 /\ Ar_0 >= 0 /\ Fresh_10 + 1 >= Ar_2 /\ Ar_2 >= 1 /\ 0 >= Ar_1 ] (Comp: ?, Cost: 1) f6(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f53(Ar_0, Ar_1, Fresh_8, Ar_2 - 1)) [ Ar_2 - Ar_4 >= 0 /\ Ar_0 >= 0 /\ Fresh_8 + 1 >= Ar_2 /\ Ar_2 >= 1 /\ Ar_1 >= 1 ] (Comp: ?, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f61(Ar_0, Ar_0, Ar_2, Ar_2)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 >= 0 /\ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f61(Ar_0, Ar_0, Ar_2, Ar_2)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f61(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f63(Ar_0, Ar_1, Fresh_6, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ -Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ Fresh_6 >= Ar_4 ] (Comp: ?, Cost: 1) f61(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f63(Ar_0, Ar_1, Fresh_4, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ -Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= 1 /\ Fresh_4 >= Ar_4 ] (Comp: ?, Cost: 1) f63(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f71(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) f63(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f71(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f71(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f73(Ar_0, Ar_1, Fresh_2, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ -Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ Fresh_2 >= Ar_4 ] (Comp: ?, Cost: 1) f71(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f73(Ar_0, Ar_1, Fresh_0, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ -Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= 1 /\ Fresh_0 >= Ar_4 ] (Comp: ?, Cost: 1) f73(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) f73(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Ar_4)) [ Ar_2 - Ar_4 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 >= 0 /\ Ar_0 + Ar_4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_4 + 1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_4) -> Com_1(f2(Ar_0, Ar_1, Ar_2, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound ? Time: 10.282 sec (SMT: 9.865 sec)