NO
by ttt2 (version ttt2 1.15)
The rewrite relation of the following TRS is considered.
| Begin(b(b(x0))) | → | Wait(Right1(x0)) | 
| Begin(b(x0)) | → | Wait(Right2(x0)) | 
| Begin(P(x0)) | → | Wait(Right3(x0)) | 
| Begin(x(x0)) | → | Wait(Right4(x0)) | 
| Begin(P(x0)) | → | Wait(Right5(x0)) | 
| Begin(x(x0)) | → | Wait(Right6(x0)) | 
| Begin(a(x0)) | → | Wait(Right7(x0)) | 
| Right1(a(End(x0))) | → | Left(P(a(b(End(x0))))) | 
| Right2(a(b(End(x0)))) | → | Left(P(a(b(End(x0))))) | 
| Right3(a(End(x0))) | → | Left(P(a(x(End(x0))))) | 
| Right4(a(End(x0))) | → | Left(x(a(End(x0)))) | 
| Right5(b(End(x0))) | → | Left(b(Q(End(x0)))) | 
| Right6(Q(End(x0))) | → | Left(a(Q(End(x0)))) | 
| Right7(Q(End(x0))) | → | Left(b(b(a(End(x0))))) | 
| Right1(a(x0)) | → | Aa(Right1(x0)) | 
| Right2(a(x0)) | → | Aa(Right2(x0)) | 
| Right3(a(x0)) | → | Aa(Right3(x0)) | 
| Right4(a(x0)) | → | Aa(Right4(x0)) | 
| Right5(a(x0)) | → | Aa(Right5(x0)) | 
| Right6(a(x0)) | → | Aa(Right6(x0)) | 
| Right7(a(x0)) | → | Aa(Right7(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)) | 
| Right1(P(x0)) | → | AP(Right1(x0)) | 
| Right2(P(x0)) | → | AP(Right2(x0)) | 
| Right3(P(x0)) | → | AP(Right3(x0)) | 
| Right4(P(x0)) | → | AP(Right4(x0)) | 
| Right5(P(x0)) | → | AP(Right5(x0)) | 
| Right6(P(x0)) | → | AP(Right6(x0)) | 
| Right7(P(x0)) | → | AP(Right7(x0)) | 
| Right1(x(x0)) | → | Ax(Right1(x0)) | 
| Right2(x(x0)) | → | Ax(Right2(x0)) | 
| Right3(x(x0)) | → | Ax(Right3(x0)) | 
| Right4(x(x0)) | → | Ax(Right4(x0)) | 
| Right5(x(x0)) | → | Ax(Right5(x0)) | 
| Right6(x(x0)) | → | Ax(Right6(x0)) | 
| Right7(x(x0)) | → | Ax(Right7(x0)) | 
| Right1(Q(x0)) | → | AQ(Right1(x0)) | 
| Right2(Q(x0)) | → | AQ(Right2(x0)) | 
| Right3(Q(x0)) | → | AQ(Right3(x0)) | 
| Right4(Q(x0)) | → | AQ(Right4(x0)) | 
| Right5(Q(x0)) | → | AQ(Right5(x0)) | 
| Right6(Q(x0)) | → | AQ(Right6(x0)) | 
| Right7(Q(x0)) | → | AQ(Right7(x0)) | 
| Aa(Left(x0)) | → | Left(a(x0)) | 
| Ab(Left(x0)) | → | Left(b(x0)) | 
| AP(Left(x0)) | → | Left(P(x0)) | 
| Ax(Left(x0)) | → | Left(x(x0)) | 
| AQ(Left(x0)) | → | Left(Q(x0)) | 
| Wait(Left(x0)) | → | Begin(x0) | 
| a(b(b(x0))) | → | P(a(b(x0))) | 
| a(P(x0)) | → | P(a(x(x0))) | 
| a(x(x0)) | → | x(a(x0)) | 
| b(P(x0)) | → | b(Q(x0)) | 
| Q(x(x0)) | → | a(Q(x0)) | 
| Q(a(x0)) | → | b(b(a(x0))) | 
| t0 | = | Begin(x(a(End(x12943)))) | 
| →ε | Wait(Right4(a(End(x12943)))) | |
| →1 | Wait(Left(x(a(End(x12943))))) | |
| →ε | Begin(x(a(End(x12943)))) | |
| = | t3 |