MAYBE Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalEx2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalEx2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb3in(Ar_1, Ar_0, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 1 /\ Ar_0 >= 1 ] (Comp: ?, Cost: 1) evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ] (Comp: ?, Cost: 1) evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalEx2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb2in(Ar_0, Ar_1, Ar_0 - 1, Ar_1 - 1)) (Comp: ?, Cost: 1) evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= E + 1 ] (Comp: ?, Cost: 1) evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= 1 ] (Comp: ?, Cost: 1) evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb3in(Ar_2, Ar_3, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 - 1)) (Comp: ?, Cost: 1) evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (Comp: 1, Cost: 1) evalEx2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalEx2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb3in(Ar_1, Ar_0, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 1 /\ Ar_0 >= 1 ] (Comp: ?, Cost: 1) evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ] (Comp: ?, Cost: 1) evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalEx2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb2in(Ar_0, Ar_1, Ar_0 - 1, Ar_1 - 1)) (Comp: ?, Cost: 1) evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= E + 1 ] (Comp: ?, Cost: 1) evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= 1 ] (Comp: ?, Cost: 1) evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb3in(Ar_2, Ar_3, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 - 1)) (Comp: ?, Cost: 1) evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalEx2start) = 2 Pol(evalEx2entryin) = 2 Pol(evalEx2bb3in) = 2 Pol(evalEx2bbin) = 2 Pol(evalEx2returnin) = 1 Pol(evalEx2bb2in) = 2 Pol(evalEx2bb1in) = 2 Pol(evalEx2stop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2stop(Ar_0, Ar_1, Ar_2, Ar_3)) evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ] evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalEx2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalEx2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb3in(Ar_1, Ar_0, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 1 /\ Ar_0 >= 1 ] (Comp: 2, Cost: 1) evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ] (Comp: 2, Cost: 1) evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalEx2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb2in(Ar_0, Ar_1, Ar_0 - 1, Ar_1 - 1)) (Comp: ?, Cost: 1) evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= E + 1 ] (Comp: ?, Cost: 1) evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= 1 ] (Comp: ?, Cost: 1) evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb3in(Ar_2, Ar_3, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 - 1)) (Comp: 2, Cost: 1) evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalEx2start) = 3*V_1 Pol(evalEx2entryin) = 3*V_1 Pol(evalEx2bb3in) = 3*V_2 Pol(evalEx2bbin) = 3*V_2 - 1 Pol(evalEx2returnin) = 3*V_2 Pol(evalEx2bb2in) = 3*V_4 + 1 Pol(evalEx2bb1in) = 3*V_4 Pol(evalEx2stop) = 3*V_2 Pol(koat_start) = 3*V_1 orients all transitions weakly and the transition evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 1 /\ Ar_0 >= 1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalEx2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalEx2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb3in(Ar_1, Ar_0, Ar_2, Ar_3)) (Comp: 3*Ar_0, Cost: 1) evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 1 /\ Ar_0 >= 1 ] (Comp: 2, Cost: 1) evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ] (Comp: 2, Cost: 1) evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalEx2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb2in(Ar_0, Ar_1, Ar_0 - 1, Ar_1 - 1)) (Comp: ?, Cost: 1) evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= E + 1 ] (Comp: ?, Cost: 1) evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= 1 ] (Comp: ?, Cost: 1) evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb3in(Ar_2, Ar_3, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 - 1)) (Comp: 2, Cost: 1) evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 4 produces the following problem: 5: T: (Comp: 1, Cost: 1) evalEx2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalEx2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb3in(Ar_1, Ar_0, Ar_2, Ar_3)) (Comp: 3*Ar_0, Cost: 1) evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 1 /\ Ar_0 >= 1 ] (Comp: 2, Cost: 1) evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ] (Comp: 2, Cost: 1) evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] (Comp: 3*Ar_0, Cost: 1) evalEx2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb2in(Ar_0, Ar_1, Ar_0 - 1, Ar_1 - 1)) (Comp: ?, Cost: 1) evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= E + 1 ] (Comp: ?, Cost: 1) evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= 1 ] (Comp: ?, Cost: 1) evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb3in(Ar_2, Ar_3, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 - 1)) (Comp: 2, Cost: 1) evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalEx2bb2in) = 1 Pol(evalEx2bb3in) = 0 Pol(evalEx2bb1in) = 1 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2start(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(evalEx2start(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(evalEx2start(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(evalEx2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 S("evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = ? S("evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 - 1))", 0-0) = ? S("evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 - 1))", 0-1) = ? S("evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 - 1))", 0-2) = ? S("evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 - 1))", 0-3) = ? S("evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb3in(Ar_2, Ar_3, Ar_2, Ar_3))", 0-0) = ? S("evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb3in(Ar_2, Ar_3, Ar_2, Ar_3))", 0-1) = ? S("evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb3in(Ar_2, Ar_3, Ar_2, Ar_3))", 0-2) = ? S("evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb3in(Ar_2, Ar_3, Ar_2, Ar_3))", 0-3) = ? S("evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= 1 ]", 0-0) = ? S("evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= 1 ]", 0-1) = ? S("evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= 1 ]", 0-2) = ? S("evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= 1 ]", 0-3) = ? S("evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= E + 1 ]", 0-0) = ? S("evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= E + 1 ]", 0-1) = ? S("evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= E + 1 ]", 0-2) = ? S("evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= E + 1 ]", 0-3) = ? S("evalEx2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb2in(Ar_0, Ar_1, Ar_0 - 1, Ar_1 - 1))", 0-0) = ? S("evalEx2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb2in(Ar_0, Ar_1, Ar_0 - 1, Ar_1 - 1))", 0-1) = ? S("evalEx2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb2in(Ar_0, Ar_1, Ar_0 - 1, Ar_1 - 1))", 0-2) = ? S("evalEx2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb2in(Ar_0, Ar_1, Ar_0 - 1, Ar_1 - 1))", 0-3) = ? S("evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]", 0-0) = ? S("evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]", 0-1) = ? S("evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]", 0-2) = ? S("evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]", 0-3) = ? S("evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ]", 0-0) = ? S("evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ]", 0-1) = ? S("evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ]", 0-2) = ? S("evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ]", 0-3) = ? S("evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 1 /\\ Ar_0 >= 1 ]", 0-0) = ? S("evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 1 /\\ Ar_0 >= 1 ]", 0-1) = ? S("evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 1 /\\ Ar_0 >= 1 ]", 0-2) = ? S("evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 1 /\\ Ar_0 >= 1 ]", 0-3) = ? S("evalEx2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb3in(Ar_1, Ar_0, Ar_2, Ar_3))", 0-0) = Ar_1 S("evalEx2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb3in(Ar_1, Ar_0, Ar_2, Ar_3))", 0-1) = Ar_0 S("evalEx2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb3in(Ar_1, Ar_0, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalEx2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb3in(Ar_1, Ar_0, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalEx2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalEx2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalEx2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalEx2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 orients the transitions evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb3in(Ar_2, Ar_3, Ar_2, Ar_3)) evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= 1 ] evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= E + 1 ] evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 - 1)) weakly and the transition evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb3in(Ar_2, Ar_3, Ar_2, Ar_3)) strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) evalEx2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalEx2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb3in(Ar_1, Ar_0, Ar_2, Ar_3)) (Comp: 3*Ar_0, Cost: 1) evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 1 /\ Ar_0 >= 1 ] (Comp: 2, Cost: 1) evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ] (Comp: 2, Cost: 1) evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] (Comp: 3*Ar_0, Cost: 1) evalEx2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb2in(Ar_0, Ar_1, Ar_0 - 1, Ar_1 - 1)) (Comp: ?, Cost: 1) evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= E + 1 ] (Comp: ?, Cost: 1) evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= 1 ] (Comp: 3*Ar_0, Cost: 1) evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb3in(Ar_2, Ar_3, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 - 1)) (Comp: 2, Cost: 1) evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 6 to obtain the following invariants: For symbol evalEx2bb1in: X_2 - X_4 - 1 >= 0 /\ X_3 + X_4 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 + 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0 For symbol evalEx2bb2in: X_2 - X_4 - 1 >= 0 /\ X_3 + X_4 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 + 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0 For symbol evalEx2bbin: X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0 This yielded the following problem: 7: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 - 1)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 3*Ar_0, Cost: 1) evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb3in(Ar_2, Ar_3, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ E >= 1 ] (Comp: ?, Cost: 1) evalEx2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= E + 1 ] (Comp: 3*Ar_0, Cost: 1) evalEx2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb2in(Ar_0, Ar_1, Ar_0 - 1, Ar_1 - 1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 2, Cost: 1) evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] (Comp: 2, Cost: 1) evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ] (Comp: 3*Ar_0, Cost: 1) evalEx2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 1 /\ Ar_0 >= 1 ] (Comp: 1, Cost: 1) evalEx2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2bb3in(Ar_1, Ar_0, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalEx2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalEx2entryin(Ar_0, Ar_1, Ar_2, Ar_3)) start location: koat_start leaf cost: 0 Complexity upper bound ? Time: 2.705 sec (SMT: 2.605 sec)