/home/nowonder/forschung/aprove/TPDB05/TRS/various/08.trs

The program

(VAR x y z x1 x2 x3 x4 w)
(RULES
f1(a(),x) -> g1(x,x)
f1(x,a()) -> g2(x,x)
f2(a(),x) -> g1(x,x)
f2(x,a()) -> g2(x,x)
g1(a(),x) -> h1(x)
g1(x,a()) -> h2(x)
g2(a(),x) -> h1(x)
g2(x,a()) -> h2(x)
h1(a()) -> i()
h2(a()) -> i()
e1(h1(w),h2(w),x,y,z,w) -> e2(x,x,y,z,z,w)
e1(x1,x1,x,y,z,a()) -> e5(x1,x,y,z)
e2(f1(w,w),x,y,z,f2(w,w),w) -> e3(x,y,x,y,y,z,y,z,x,y,z,w)
e2(x,x,y,z,z,a()) -> e6(x,y,z)
e2(i(),x,y,z,i(),a()) -> e6(x,y,z)
e3(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) ->
  e4(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w)
e3(x,y,x,y,y,z,y,z,x,y,z,a()) -> e6(x,y,z)
e4(g1(w,w),x1,g2(w,w),x1,g1(w,w),x1,g2(w,w),x1,x,y,z,w) ->
  e1(x1,x1,x,y,z,w)
e4(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> e5(x1,x,y,z)
e4(x,x,x,x,x,x,x,x,x,x,x,a()) -> e6(x,x,x)
e5(i(),x,y,z) -> e6(x,y,z)
)
(COMMENT Example 7 (TRS $\RR_1$) in \cite{O95})

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