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($(x0)) Wait(Right15(x0))
Right1(0(End(x0))) Left(*(*(1(1(End(x0))))))
Right2(0(0(End(x0)))) Left(*(*(1(1(End(x0))))))
Right3(0(0(*(End(x0))))) Left(*(*(1(1(End(x0))))))
Right4(1(End(x0))) Left(0(0(#(#(End(x0))))))
Right5(1(1(End(x0)))) Left(0(0(#(#(End(x0))))))
Right6(1(1(*(End(x0))))) Left(0(0(#(#(End(x0))))))
Right7(#(End(x0))) Left(0(0(#(#(End(x0))))))
Right8(#(#(End(x0)))) Left(0(0(#(#(End(x0))))))
Right9(#(#(0(End(x0))))) Left(0(0(#(#(End(x0))))))
Right10(#(End(x0))) Left(1(1(#(#(End(x0))))))
Right11(#(#(End(x0)))) Left(1(1(#(#(End(x0))))))
Right12(#(#(1(End(x0))))) Left(1(1(#(#(End(x0))))))
Right13(#(End(x0))) Left(*(*($($(End(x0))))))
Right14(#(#(End(x0)))) Left(*(*($($(End(x0))))))
Right15(#(#($(End(x0))))) Left(*(*($($(End(x0))))))
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))
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))
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))
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))
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))
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))))

Proof

1 Loop

The following loop proves nontermination.

t0 = Begin(0(0(#(#(End(x54543))))))
ε Wait(Right8(#(#(End(x54543)))))
1 Wait(Left(0(0(#(#(End(x54543)))))))
ε Begin(0(0(#(#(End(x54543))))))
= t3
where t3 = t0σ and σ = {x54543/x54543}