NO Nontermination Proof

Nontermination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

Begin(0(((x0))))	→	Wait(Right1(x0))
Begin(((x0)))	→	Wait(Right2(x0))
Begin(*(x0))	→	Wait(Right3(x0))
Begin(1(((x0))))	→	Wait(Right4(x0))
Begin(((x0)))	→	Wait(Right5(x0))
Begin(*(x0))	→	Wait(Right6(x0))
Begin(#(0(0(x0))))	→	Wait(Right7(x0))
Begin(0(0(x0)))	→	Wait(Right8(x0))
Begin(0(x0))	→	Wait(Right9(x0))
Begin(#(1(1(x0))))	→	Wait(Right10(x0))
Begin(1(1(x0)))	→	Wait(Right11(x0))
Begin(1(x0))	→	Wait(Right12(x0))
Begin(#($($(x0))))	→	Wait(Right13(x0))
Begin($($(x0)))	→	Wait(Right14(x0))
Begin($(x0))	→	Wait(Right15(x0))
Begin(#(#(#(x0))))	→	Wait(Right16(x0))
Begin(#(#(x0)))	→	Wait(Right17(x0))
Begin(#(x0))	→	Wait(Right18(x0))
Begin(#(((x0))))	→	Wait(Right19(x0))
Begin(((x0)))	→	Wait(Right20(x0))
Begin(*(x0))	→	Wait(Right21(x0))
Right1(0(End(x0)))	→	Left(((1(1(End(x0))))))
Right2(0(0(End(x0))))	→	Left(((1(1(End(x0))))))
Right3(0(0(*(End(x0)))))	→	Left(((1(1(End(x0))))))
Right4(1(End(x0)))	→	Left(0(0(#(#(End(x0))))))
Right5(1(1(End(x0))))	→	Left(0(0(#(#(End(x0))))))
Right6(1(1(*(End(x0)))))	→	Left(0(0(#(#(End(x0))))))
Right7(#(End(x0)))	→	Left(0(0(#(#(End(x0))))))
Right8(#(#(End(x0))))	→	Left(0(0(#(#(End(x0))))))
Right9(#(#(0(End(x0)))))	→	Left(0(0(#(#(End(x0))))))
Right10(#(End(x0)))	→	Left(1(1(#(#(End(x0))))))
Right11(#(#(End(x0))))	→	Left(1(1(#(#(End(x0))))))
Right12(#(#(1(End(x0)))))	→	Left(1(1(#(#(End(x0))))))
Right13(#(End(x0)))	→	Left((($($(End(x0))))))
Right14(#(#(End(x0))))	→	Left((($($(End(x0))))))
Right15(#(#($(End(x0)))))	→	Left((($($(End(x0))))))
Right16(#(End(x0)))	→	Left(#(#(End(x0))))
Right17(#(#(End(x0))))	→	Left(#(#(End(x0))))
Right18(#(#(#(End(x0)))))	→	Left(#(#(End(x0))))
Right19(#(End(x0)))	→	Left(((End(x0))))
Right20(#(#(End(x0))))	→	Left(((End(x0))))
Right21(#(#(*(End(x0)))))	→	Left(((End(x0))))
Right1(0(x0))	→	A0(Right1(x0))
Right2(0(x0))	→	A0(Right2(x0))
Right3(0(x0))	→	A0(Right3(x0))
Right4(0(x0))	→	A0(Right4(x0))
Right5(0(x0))	→	A0(Right5(x0))
Right6(0(x0))	→	A0(Right6(x0))
Right7(0(x0))	→	A0(Right7(x0))
Right8(0(x0))	→	A0(Right8(x0))
Right9(0(x0))	→	A0(Right9(x0))
Right10(0(x0))	→	A0(Right10(x0))
Right11(0(x0))	→	A0(Right11(x0))
Right12(0(x0))	→	A0(Right12(x0))
Right13(0(x0))	→	A0(Right13(x0))
Right14(0(x0))	→	A0(Right14(x0))
Right15(0(x0))	→	A0(Right15(x0))
Right16(0(x0))	→	A0(Right16(x0))
Right17(0(x0))	→	A0(Right17(x0))
Right18(0(x0))	→	A0(Right18(x0))
Right19(0(x0))	→	A0(Right19(x0))
Right20(0(x0))	→	A0(Right20(x0))
Right21(0(x0))	→	A0(Right21(x0))
Right1(*(x0))	→	A*(Right1(x0))
Right2(*(x0))	→	A*(Right2(x0))
Right3(*(x0))	→	A*(Right3(x0))
Right4(*(x0))	→	A*(Right4(x0))
Right5(*(x0))	→	A*(Right5(x0))
Right6(*(x0))	→	A*(Right6(x0))
Right7(*(x0))	→	A*(Right7(x0))
Right8(*(x0))	→	A*(Right8(x0))
Right9(*(x0))	→	A*(Right9(x0))
Right10(*(x0))	→	A*(Right10(x0))
Right11(*(x0))	→	A*(Right11(x0))
Right12(*(x0))	→	A*(Right12(x0))
Right13(*(x0))	→	A*(Right13(x0))
Right14(*(x0))	→	A*(Right14(x0))
Right15(*(x0))	→	A*(Right15(x0))
Right16(*(x0))	→	A*(Right16(x0))
Right17(*(x0))	→	A*(Right17(x0))
Right18(*(x0))	→	A*(Right18(x0))
Right19(*(x0))	→	A*(Right19(x0))
Right20(*(x0))	→	A*(Right20(x0))
Right21(*(x0))	→	A*(Right21(x0))
Right1(1(x0))	→	A1(Right1(x0))
Right2(1(x0))	→	A1(Right2(x0))
Right3(1(x0))	→	A1(Right3(x0))
Right4(1(x0))	→	A1(Right4(x0))
Right5(1(x0))	→	A1(Right5(x0))
Right6(1(x0))	→	A1(Right6(x0))
Right7(1(x0))	→	A1(Right7(x0))
Right8(1(x0))	→	A1(Right8(x0))
Right9(1(x0))	→	A1(Right9(x0))
Right10(1(x0))	→	A1(Right10(x0))
Right11(1(x0))	→	A1(Right11(x0))
Right12(1(x0))	→	A1(Right12(x0))
Right13(1(x0))	→	A1(Right13(x0))
Right14(1(x0))	→	A1(Right14(x0))
Right15(1(x0))	→	A1(Right15(x0))
Right16(1(x0))	→	A1(Right16(x0))
Right17(1(x0))	→	A1(Right17(x0))
Right18(1(x0))	→	A1(Right18(x0))
Right19(1(x0))	→	A1(Right19(x0))
Right20(1(x0))	→	A1(Right20(x0))
Right21(1(x0))	→	A1(Right21(x0))
Right1(#(x0))	→	A#(Right1(x0))
Right2(#(x0))	→	A#(Right2(x0))
Right3(#(x0))	→	A#(Right3(x0))
Right4(#(x0))	→	A#(Right4(x0))
Right5(#(x0))	→	A#(Right5(x0))
Right6(#(x0))	→	A#(Right6(x0))
Right7(#(x0))	→	A#(Right7(x0))
Right8(#(x0))	→	A#(Right8(x0))
Right9(#(x0))	→	A#(Right9(x0))
Right10(#(x0))	→	A#(Right10(x0))
Right11(#(x0))	→	A#(Right11(x0))
Right12(#(x0))	→	A#(Right12(x0))
Right13(#(x0))	→	A#(Right13(x0))
Right14(#(x0))	→	A#(Right14(x0))
Right15(#(x0))	→	A#(Right15(x0))
Right16(#(x0))	→	A#(Right16(x0))
Right17(#(x0))	→	A#(Right17(x0))
Right18(#(x0))	→	A#(Right18(x0))
Right19(#(x0))	→	A#(Right19(x0))
Right20(#(x0))	→	A#(Right20(x0))
Right21(#(x0))	→	A#(Right21(x0))
Right1($(x0))	→	A$(Right1(x0))
Right2($(x0))	→	A$(Right2(x0))
Right3($(x0))	→	A$(Right3(x0))
Right4($(x0))	→	A$(Right4(x0))
Right5($(x0))	→	A$(Right5(x0))
Right6($(x0))	→	A$(Right6(x0))
Right7($(x0))	→	A$(Right7(x0))
Right8($(x0))	→	A$(Right8(x0))
Right9($(x0))	→	A$(Right9(x0))
Right10($(x0))	→	A$(Right10(x0))
Right11($(x0))	→	A$(Right11(x0))
Right12($(x0))	→	A$(Right12(x0))
Right13($(x0))	→	A$(Right13(x0))
Right14($(x0))	→	A$(Right14(x0))
Right15($(x0))	→	A$(Right15(x0))
Right16($(x0))	→	A$(Right16(x0))
Right17($(x0))	→	A$(Right17(x0))
Right18($(x0))	→	A$(Right18(x0))
Right19($(x0))	→	A$(Right19(x0))
Right20($(x0))	→	A$(Right20(x0))
Right21($(x0))	→	A$(Right21(x0))
A0(Left(x0))	→	Left(0(x0))
A*(Left(x0))	→	Left(*(x0))
A1(Left(x0))	→	Left(1(x0))
A#(Left(x0))	→	Left(#(x0))
A$(Left(x0))	→	Left($(x0))
Wait(Left(x0))	→	Begin(x0)
0(0(((x0))))	→	((1(1(x0))))
1(1(((x0))))	→	0(0(#(#(x0))))
#(#(0(0(x0))))	→	0(0(#(#(x0))))
#(#(1(1(x0))))	→	1(1(#(#(x0))))
#(#($($(x0))))	→	(($($(x0))))
#(#(#(#(x0))))	→	#(#(x0))
#(#(((x0))))	→	((x0))

Proof

1 Loop

The following loop proves nontermination.

t₀ = Begin(0(0(#(#(End(x91229))))))

→_ε Wait(Right8(#(#(End(x91229)))))

→₁ Wait(Left(0(0(#(#(End(x91229)))))))

→_ε Begin(0(0(#(#(End(x91229))))))

= t₃

where t₃ = t₀σ and σ = {x91229/x91229}

t₀	=	Begin(0(0(#(#(End(x91229))))))
	→_ε	Wait(Right8(#(#(End(x91229)))))
	→₁	Wait(Left(0(0(#(#(End(x91229)))))))
	→_ε	Begin(0(0(#(#(End(x91229))))))
	=	t₃