MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(C(x0)) → Wait(Right1(x0))
Begin(c(c(c(x0)))) → Wait(Right2(x0))
Begin(c(c(x0))) → Wait(Right3(x0))
Begin(c(x0)) → Wait(Right4(x0))
Begin(b(b(b(x0)))) → Wait(Right5(x0))
Begin(b(b(x0))) → Wait(Right6(x0))
Begin(b(x0)) → Wait(Right7(x0))
Begin(B(B(B(x0)))) → Wait(Right8(x0))
Begin(B(B(x0))) → Wait(Right9(x0))
Begin(B(x0)) → Wait(Right10(x0))
Begin(c(B(B(c(c(b(b(c(c(x0)))))))))) → Wait(Right11(x0))
Begin(B(B(c(c(b(b(c(c(x0))))))))) → Wait(Right12(x0))
Begin(B(c(c(b(b(c(c(x0)))))))) → Wait(Right13(x0))
Begin(c(c(b(b(c(c(x0))))))) → Wait(Right14(x0))
Begin(c(b(b(c(c(x0)))))) → Wait(Right15(x0))
Begin(b(b(c(c(x0))))) → Wait(Right16(x0))
Begin(b(c(c(x0)))) → Wait(Right17(x0))
Begin(c(c(x0))) → Wait(Right18(x0))
Begin(c(x0)) → Wait(Right19(x0))
Begin(b(B(B(x0)))) → Wait(Right20(x0))
Begin(B(B(x0))) → Wait(Right21(x0))
Begin(B(x0)) → Wait(Right22(x0))
Begin(B(b(b(x0)))) → Wait(Right23(x0))
Begin(b(b(x0))) → Wait(Right24(x0))
Begin(b(x0)) → Wait(Right25(x0))
Begin(c(C(C(x0)))) → Wait(Right26(x0))
Begin(C(C(x0))) → Wait(Right27(x0))
Begin(C(x0)) → Wait(Right28(x0))
Begin(C(c(c(x0)))) → Wait(Right29(x0))
Begin(c(c(x0))) → Wait(Right30(x0))
Begin(c(x0)) → Wait(Right31(x0))
Right1(C(End(x0))) → Left(c(c(End(x0))))
Right2(c(End(x0))) → Left(End(x0))
Right3(c(c(End(x0)))) → Left(End(x0))
Right4(c(c(c(End(x0))))) → Left(End(x0))
Right5(b(End(x0))) → Left(B(B(End(x0))))
Right6(b(b(End(x0)))) → Left(B(B(End(x0))))
Right7(b(b(b(End(x0))))) → Left(B(B(End(x0))))
Right8(B(End(x0))) → Left(b(b(End(x0))))
Right9(B(B(End(x0)))) → Left(b(b(End(x0))))
Right10(B(B(B(End(x0))))) → Left(b(b(End(x0))))
Right11(c(End(x0))) → Left(B(B(c(c(b(b(c(c(B(B(c(c(b(b(End(x0))))))))))))))))
Right12(c(c(End(x0)))) → Left(B(B(c(c(b(b(c(c(B(B(c(c(b(b(End(x0))))))))))))))))
Right13(c(c(B(End(x0))))) → Left(B(B(c(c(b(b(c(c(B(B(c(c(b(b(End(x0))))))))))))))))
Right14(c(c(B(B(End(x0)))))) → Left(B(B(c(c(b(b(c(c(B(B(c(c(b(b(End(x0))))))))))))))))
Right15(c(c(B(B(c(End(x0))))))) → Left(B(B(c(c(b(b(c(c(B(B(c(c(b(b(End(x0))))))))))))))))
Right16(c(c(B(B(c(c(End(x0)))))))) → Left(B(B(c(c(b(b(c(c(B(B(c(c(b(b(End(x0))))))))))))))))
Right17(c(c(B(B(c(c(b(End(x0))))))))) → Left(B(B(c(c(b(b(c(c(B(B(c(c(b(b(End(x0))))))))))))))))
Right18(c(c(B(B(c(c(b(b(End(x0)))))))))) → Left(B(B(c(c(b(b(c(c(B(B(c(c(b(b(End(x0))))))))))))))))
Right19(c(c(B(B(c(c(b(b(c(End(x0))))))))))) → Left(B(B(c(c(b(b(c(c(B(B(c(c(b(b(End(x0))))))))))))))))
Right20(b(End(x0))) → Left(End(x0))
Right21(b(b(End(x0)))) → Left(End(x0))
Right22(b(b(B(End(x0))))) → Left(End(x0))
Right23(B(End(x0))) → Left(End(x0))
Right24(B(B(End(x0)))) → Left(End(x0))
Right25(B(B(b(End(x0))))) → Left(End(x0))
Right26(c(End(x0))) → Left(End(x0))
Right27(c(c(End(x0)))) → Left(End(x0))
Right28(c(c(C(End(x0))))) → Left(End(x0))
Right29(C(End(x0))) → Left(End(x0))
Right30(C(C(End(x0)))) → Left(End(x0))
Right31(C(C(c(End(x0))))) → Left(End(x0))
Right1(C(x0)) → AC(Right1(x0))
Right2(C(x0)) → AC(Right2(x0))
Right3(C(x0)) → AC(Right3(x0))
Right4(C(x0)) → AC(Right4(x0))
Right5(C(x0)) → AC(Right5(x0))
Right6(C(x0)) → AC(Right6(x0))
Right7(C(x0)) → AC(Right7(x0))
Right8(C(x0)) → AC(Right8(x0))
Right9(C(x0)) → AC(Right9(x0))
Right10(C(x0)) → AC(Right10(x0))
Right11(C(x0)) → AC(Right11(x0))
Right12(C(x0)) → AC(Right12(x0))
Right13(C(x0)) → AC(Right13(x0))
Right14(C(x0)) → AC(Right14(x0))
Right15(C(x0)) → AC(Right15(x0))
Right16(C(x0)) → AC(Right16(x0))
Right17(C(x0)) → AC(Right17(x0))
Right18(C(x0)) → AC(Right18(x0))
Right19(C(x0)) → AC(Right19(x0))
Right20(C(x0)) → AC(Right20(x0))
Right21(C(x0)) → AC(Right21(x0))
Right22(C(x0)) → AC(Right22(x0))
Right23(C(x0)) → AC(Right23(x0))
Right24(C(x0)) → AC(Right24(x0))
Right25(C(x0)) → AC(Right25(x0))
Right26(C(x0)) → AC(Right26(x0))
Right27(C(x0)) → AC(Right27(x0))
Right28(C(x0)) → AC(Right28(x0))
Right29(C(x0)) → AC(Right29(x0))
Right30(C(x0)) → AC(Right30(x0))
Right31(C(x0)) → AC(Right31(x0))
Right1(c(x0)) → Ac(Right1(x0))
Right2(c(x0)) → Ac(Right2(x0))
Right3(c(x0)) → Ac(Right3(x0))
Right4(c(x0)) → Ac(Right4(x0))
Right5(c(x0)) → Ac(Right5(x0))
Right6(c(x0)) → Ac(Right6(x0))
Right7(c(x0)) → Ac(Right7(x0))
Right8(c(x0)) → Ac(Right8(x0))
Right9(c(x0)) → Ac(Right9(x0))
Right10(c(x0)) → Ac(Right10(x0))
Right11(c(x0)) → Ac(Right11(x0))
Right12(c(x0)) → Ac(Right12(x0))
Right13(c(x0)) → Ac(Right13(x0))
Right14(c(x0)) → Ac(Right14(x0))
Right15(c(x0)) → Ac(Right15(x0))
Right16(c(x0)) → Ac(Right16(x0))
Right17(c(x0)) → Ac(Right17(x0))
Right18(c(x0)) → Ac(Right18(x0))
Right19(c(x0)) → Ac(Right19(x0))
Right20(c(x0)) → Ac(Right20(x0))
Right21(c(x0)) → Ac(Right21(x0))
Right22(c(x0)) → Ac(Right22(x0))
Right23(c(x0)) → Ac(Right23(x0))
Right24(c(x0)) → Ac(Right24(x0))
Right25(c(x0)) → Ac(Right25(x0))
Right26(c(x0)) → Ac(Right26(x0))
Right27(c(x0)) → Ac(Right27(x0))
Right28(c(x0)) → Ac(Right28(x0))
Right29(c(x0)) → Ac(Right29(x0))
Right30(c(x0)) → Ac(Right30(x0))
Right31(c(x0)) → Ac(Right31(x0))
Right1(b(x0)) → Ab(Right1(x0))
Right2(b(x0)) → Ab(Right2(x0))
Right3(b(x0)) → Ab(Right3(x0))
Right4(b(x0)) → Ab(Right4(x0))
Right5(b(x0)) → Ab(Right5(x0))
Right6(b(x0)) → Ab(Right6(x0))
Right7(b(x0)) → Ab(Right7(x0))
Right8(b(x0)) → Ab(Right8(x0))
Right9(b(x0)) → Ab(Right9(x0))
Right10(b(x0)) → Ab(Right10(x0))
Right11(b(x0)) → Ab(Right11(x0))
Right12(b(x0)) → Ab(Right12(x0))
Right13(b(x0)) → Ab(Right13(x0))
Right14(b(x0)) → Ab(Right14(x0))
Right15(b(x0)) → Ab(Right15(x0))
Right16(b(x0)) → Ab(Right16(x0))
Right17(b(x0)) → Ab(Right17(x0))
Right18(b(x0)) → Ab(Right18(x0))
Right19(b(x0)) → Ab(Right19(x0))
Right20(b(x0)) → Ab(Right20(x0))
Right21(b(x0)) → Ab(Right21(x0))
Right22(b(x0)) → Ab(Right22(x0))
Right23(b(x0)) → Ab(Right23(x0))
Right24(b(x0)) → Ab(Right24(x0))
Right25(b(x0)) → Ab(Right25(x0))
Right26(b(x0)) → Ab(Right26(x0))
Right27(b(x0)) → Ab(Right27(x0))
Right28(b(x0)) → Ab(Right28(x0))
Right29(b(x0)) → Ab(Right29(x0))
Right30(b(x0)) → Ab(Right30(x0))
Right31(b(x0)) → Ab(Right31(x0))
Right1(B(x0)) → AB(Right1(x0))
Right2(B(x0)) → AB(Right2(x0))
Right3(B(x0)) → AB(Right3(x0))
Right4(B(x0)) → AB(Right4(x0))
Right5(B(x0)) → AB(Right5(x0))
Right6(B(x0)) → AB(Right6(x0))
Right7(B(x0)) → AB(Right7(x0))
Right8(B(x0)) → AB(Right8(x0))
Right9(B(x0)) → AB(Right9(x0))
Right10(B(x0)) → AB(Right10(x0))
Right11(B(x0)) → AB(Right11(x0))
Right12(B(x0)) → AB(Right12(x0))
Right13(B(x0)) → AB(Right13(x0))
Right14(B(x0)) → AB(Right14(x0))
Right15(B(x0)) → AB(Right15(x0))
Right16(B(x0)) → AB(Right16(x0))
Right17(B(x0)) → AB(Right17(x0))
Right18(B(x0)) → AB(Right18(x0))
Right19(B(x0)) → AB(Right19(x0))
Right20(B(x0)) → AB(Right20(x0))
Right21(B(x0)) → AB(Right21(x0))
Right22(B(x0)) → AB(Right22(x0))
Right23(B(x0)) → AB(Right23(x0))
Right24(B(x0)) → AB(Right24(x0))
Right25(B(x0)) → AB(Right25(x0))
Right26(B(x0)) → AB(Right26(x0))
Right27(B(x0)) → AB(Right27(x0))
Right28(B(x0)) → AB(Right28(x0))
Right29(B(x0)) → AB(Right29(x0))
Right30(B(x0)) → AB(Right30(x0))
Right31(B(x0)) → AB(Right31(x0))
AC(Left(x0)) → Left(C(x0))
Ac(Left(x0)) → Left(c(x0))
Ab(Left(x0)) → Left(b(x0))
AB(Left(x0)) → Left(B(x0))
Wait(Left(x0)) → Begin(x0)
C(C(x0)) → c(c(x0))
c(c(c(c(x0)))) → x0
b(b(b(b(x0)))) → B(B(x0))
B(B(B(B(x0)))) → b(b(x0))
c(c(B(B(c(c(b(b(c(c(x0)))))))))) → B(B(c(c(b(b(c(c(B(B(c(c(b(b(x0))))))))))))))
b(b(B(B(x0)))) → x0
B(B(b(b(x0)))) → x0
c(c(C(C(x0)))) → x0
C(C(c(c(x0)))) → x0

Proof

1 Termination Assumption

We assume termination of the following TRS
Begin(C(x0)) → Wait(Right1(x0))
Begin(c(c(c(x0)))) → Wait(Right2(x0))
Begin(c(c(x0))) → Wait(Right3(x0))
Begin(c(x0)) → Wait(Right4(x0))
Begin(b(b(b(x0)))) → Wait(Right5(x0))
Begin(b(b(x0))) → Wait(Right6(x0))
Begin(b(x0)) → Wait(Right7(x0))
Begin(B(B(B(x0)))) → Wait(Right8(x0))
Begin(B(B(x0))) → Wait(Right9(x0))
Begin(B(x0)) → Wait(Right10(x0))
Begin(c(B(B(c(c(b(b(c(c(x0)))))))))) → Wait(Right11(x0))
Begin(B(B(c(c(b(b(c(c(x0))))))))) → Wait(Right12(x0))
Begin(B(c(c(b(b(c(c(x0)))))))) → Wait(Right13(x0))
Begin(c(c(b(b(c(c(x0))))))) → Wait(Right14(x0))
Begin(c(b(b(c(c(x0)))))) → Wait(Right15(x0))
Begin(b(b(c(c(x0))))) → Wait(Right16(x0))
Begin(b(c(c(x0)))) → Wait(Right17(x0))
Begin(c(c(x0))) → Wait(Right18(x0))
Begin(c(x0)) → Wait(Right19(x0))
Begin(b(B(B(x0)))) → Wait(Right20(x0))
Begin(B(B(x0))) → Wait(Right21(x0))
Begin(B(x0)) → Wait(Right22(x0))
Begin(B(b(b(x0)))) → Wait(Right23(x0))
Begin(b(b(x0))) → Wait(Right24(x0))
Begin(b(x0)) → Wait(Right25(x0))
Begin(c(C(C(x0)))) → Wait(Right26(x0))
Begin(C(C(x0))) → Wait(Right27(x0))
Begin(C(x0)) → Wait(Right28(x0))
Begin(C(c(c(x0)))) → Wait(Right29(x0))
Begin(c(c(x0))) → Wait(Right30(x0))
Begin(c(x0)) → Wait(Right31(x0))
Right1(C(End(x0))) → Left(c(c(End(x0))))
Right2(c(End(x0))) → Left(End(x0))
Right3(c(c(End(x0)))) → Left(End(x0))
Right4(c(c(c(End(x0))))) → Left(End(x0))
Right5(b(End(x0))) → Left(B(B(End(x0))))
Right6(b(b(End(x0)))) → Left(B(B(End(x0))))
Right7(b(b(b(End(x0))))) → Left(B(B(End(x0))))
Right8(B(End(x0))) → Left(b(b(End(x0))))
Right9(B(B(End(x0)))) → Left(b(b(End(x0))))
Right10(B(B(B(End(x0))))) → Left(b(b(End(x0))))
Right11(c(End(x0))) → Left(B(B(c(c(b(b(c(c(B(B(c(c(b(b(End(x0))))))))))))))))
Right12(c(c(End(x0)))) → Left(B(B(c(c(b(b(c(c(B(B(c(c(b(b(End(x0))))))))))))))))
Right13(c(c(B(End(x0))))) → Left(B(B(c(c(b(b(c(c(B(B(c(c(b(b(End(x0))))))))))))))))
Right14(c(c(B(B(End(x0)))))) → Left(B(B(c(c(b(b(c(c(B(B(c(c(b(b(End(x0))))))))))))))))
Right15(c(c(B(B(c(End(x0))))))) → Left(B(B(c(c(b(b(c(c(B(B(c(c(b(b(End(x0))))))))))))))))
Right16(c(c(B(B(c(c(End(x0)))))))) → Left(B(B(c(c(b(b(c(c(B(B(c(c(b(b(End(x0))))))))))))))))
Right17(c(c(B(B(c(c(b(End(x0))))))))) → Left(B(B(c(c(b(b(c(c(B(B(c(c(b(b(End(x0))))))))))))))))
Right18(c(c(B(B(c(c(b(b(End(x0)))))))))) → Left(B(B(c(c(b(b(c(c(B(B(c(c(b(b(End(x0))))))))))))))))
Right19(c(c(B(B(c(c(b(b(c(End(x0))))))))))) → Left(B(B(c(c(b(b(c(c(B(B(c(c(b(b(End(x0))))))))))))))))
Right20(b(End(x0))) → Left(End(x0))
Right21(b(b(End(x0)))) → Left(End(x0))
Right22(b(b(B(End(x0))))) → Left(End(x0))
Right23(B(End(x0))) → Left(End(x0))
Right24(B(B(End(x0)))) → Left(End(x0))
Right25(B(B(b(End(x0))))) → Left(End(x0))
Right26(c(End(x0))) → Left(End(x0))
Right27(c(c(End(x0)))) → Left(End(x0))
Right28(c(c(C(End(x0))))) → Left(End(x0))
Right29(C(End(x0))) → Left(End(x0))
Right30(C(C(End(x0)))) → Left(End(x0))
Right31(C(C(c(End(x0))))) → Left(End(x0))
Right1(C(x0)) → AC(Right1(x0))
Right2(C(x0)) → AC(Right2(x0))
Right3(C(x0)) → AC(Right3(x0))
Right4(C(x0)) → AC(Right4(x0))
Right5(C(x0)) → AC(Right5(x0))
Right6(C(x0)) → AC(Right6(x0))
Right7(C(x0)) → AC(Right7(x0))
Right8(C(x0)) → AC(Right8(x0))
Right9(C(x0)) → AC(Right9(x0))
Right10(C(x0)) → AC(Right10(x0))
Right11(C(x0)) → AC(Right11(x0))
Right12(C(x0)) → AC(Right12(x0))
Right13(C(x0)) → AC(Right13(x0))
Right14(C(x0)) → AC(Right14(x0))
Right15(C(x0)) → AC(Right15(x0))
Right16(C(x0)) → AC(Right16(x0))
Right17(C(x0)) → AC(Right17(x0))
Right18(C(x0)) → AC(Right18(x0))
Right19(C(x0)) → AC(Right19(x0))
Right20(C(x0)) → AC(Right20(x0))
Right21(C(x0)) → AC(Right21(x0))
Right22(C(x0)) → AC(Right22(x0))
Right23(C(x0)) → AC(Right23(x0))
Right24(C(x0)) → AC(Right24(x0))
Right25(C(x0)) → AC(Right25(x0))
Right26(C(x0)) → AC(Right26(x0))
Right27(C(x0)) → AC(Right27(x0))
Right28(C(x0)) → AC(Right28(x0))
Right29(C(x0)) → AC(Right29(x0))
Right30(C(x0)) → AC(Right30(x0))
Right31(C(x0)) → AC(Right31(x0))
Right1(c(x0)) → Ac(Right1(x0))
Right2(c(x0)) → Ac(Right2(x0))
Right3(c(x0)) → Ac(Right3(x0))
Right4(c(x0)) → Ac(Right4(x0))
Right5(c(x0)) → Ac(Right5(x0))
Right6(c(x0)) → Ac(Right6(x0))
Right7(c(x0)) → Ac(Right7(x0))
Right8(c(x0)) → Ac(Right8(x0))
Right9(c(x0)) → Ac(Right9(x0))
Right10(c(x0)) → Ac(Right10(x0))
Right11(c(x0)) → Ac(Right11(x0))
Right12(c(x0)) → Ac(Right12(x0))
Right13(c(x0)) → Ac(Right13(x0))
Right14(c(x0)) → Ac(Right14(x0))
Right15(c(x0)) → Ac(Right15(x0))
Right16(c(x0)) → Ac(Right16(x0))
Right17(c(x0)) → Ac(Right17(x0))
Right18(c(x0)) → Ac(Right18(x0))
Right19(c(x0)) → Ac(Right19(x0))
Right20(c(x0)) → Ac(Right20(x0))
Right21(c(x0)) → Ac(Right21(x0))
Right22(c(x0)) → Ac(Right22(x0))
Right23(c(x0)) → Ac(Right23(x0))
Right24(c(x0)) → Ac(Right24(x0))
Right25(c(x0)) → Ac(Right25(x0))
Right26(c(x0)) → Ac(Right26(x0))
Right27(c(x0)) → Ac(Right27(x0))
Right28(c(x0)) → Ac(Right28(x0))
Right29(c(x0)) → Ac(Right29(x0))
Right30(c(x0)) → Ac(Right30(x0))
Right31(c(x0)) → Ac(Right31(x0))
Right1(b(x0)) → Ab(Right1(x0))
Right2(b(x0)) → Ab(Right2(x0))
Right3(b(x0)) → Ab(Right3(x0))
Right4(b(x0)) → Ab(Right4(x0))
Right5(b(x0)) → Ab(Right5(x0))
Right6(b(x0)) → Ab(Right6(x0))
Right7(b(x0)) → Ab(Right7(x0))
Right8(b(x0)) → Ab(Right8(x0))
Right9(b(x0)) → Ab(Right9(x0))
Right10(b(x0)) → Ab(Right10(x0))
Right11(b(x0)) → Ab(Right11(x0))
Right12(b(x0)) → Ab(Right12(x0))
Right13(b(x0)) → Ab(Right13(x0))
Right14(b(x0)) → Ab(Right14(x0))
Right15(b(x0)) → Ab(Right15(x0))
Right16(b(x0)) → Ab(Right16(x0))
Right17(b(x0)) → Ab(Right17(x0))
Right18(b(x0)) → Ab(Right18(x0))
Right19(b(x0)) → Ab(Right19(x0))
Right20(b(x0)) → Ab(Right20(x0))
Right21(b(x0)) → Ab(Right21(x0))
Right22(b(x0)) → Ab(Right22(x0))
Right23(b(x0)) → Ab(Right23(x0))
Right24(b(x0)) → Ab(Right24(x0))
Right25(b(x0)) → Ab(Right25(x0))
Right26(b(x0)) → Ab(Right26(x0))
Right27(b(x0)) → Ab(Right27(x0))
Right28(b(x0)) → Ab(Right28(x0))
Right29(b(x0)) → Ab(Right29(x0))
Right30(b(x0)) → Ab(Right30(x0))
Right31(b(x0)) → Ab(Right31(x0))
Right1(B(x0)) → AB(Right1(x0))
Right2(B(x0)) → AB(Right2(x0))
Right3(B(x0)) → AB(Right3(x0))
Right4(B(x0)) → AB(Right4(x0))
Right5(B(x0)) → AB(Right5(x0))
Right6(B(x0)) → AB(Right6(x0))
Right7(B(x0)) → AB(Right7(x0))
Right8(B(x0)) → AB(Right8(x0))
Right9(B(x0)) → AB(Right9(x0))
Right10(B(x0)) → AB(Right10(x0))
Right11(B(x0)) → AB(Right11(x0))
Right12(B(x0)) → AB(Right12(x0))
Right13(B(x0)) → AB(Right13(x0))
Right14(B(x0)) → AB(Right14(x0))
Right15(B(x0)) → AB(Right15(x0))
Right16(B(x0)) → AB(Right16(x0))
Right17(B(x0)) → AB(Right17(x0))
Right18(B(x0)) → AB(Right18(x0))
Right19(B(x0)) → AB(Right19(x0))
Right20(B(x0)) → AB(Right20(x0))
Right21(B(x0)) → AB(Right21(x0))
Right22(B(x0)) → AB(Right22(x0))
Right23(B(x0)) → AB(Right23(x0))
Right24(B(x0)) → AB(Right24(x0))
Right25(B(x0)) → AB(Right25(x0))
Right26(B(x0)) → AB(Right26(x0))
Right27(B(x0)) → AB(Right27(x0))
Right28(B(x0)) → AB(Right28(x0))
Right29(B(x0)) → AB(Right29(x0))
Right30(B(x0)) → AB(Right30(x0))
Right31(B(x0)) → AB(Right31(x0))
AC(Left(x0)) → Left(C(x0))
Ac(Left(x0)) → Left(c(x0))
Ab(Left(x0)) → Left(b(x0))
AB(Left(x0)) → Left(B(x0))
Wait(Left(x0)) → Begin(x0)
C(C(x0)) → c(c(x0))
c(c(c(c(x0)))) → x0
b(b(b(b(x0)))) → B(B(x0))
B(B(B(B(x0)))) → b(b(x0))
c(c(B(B(c(c(b(b(c(c(x0)))))))))) → B(B(c(c(b(b(c(c(B(B(c(c(b(b(x0))))))))))))))
b(b(B(B(x0)))) → x0
B(B(b(b(x0)))) → x0
c(c(C(C(x0)))) → x0
C(C(c(c(x0)))) → x0