Term Rewriting System R:
[x, y, z, x1, x2, x3, x4]
f1 -> g1
f1 -> g2
f2 -> g1
f2 -> g2
g1 -> h1
g1 -> h2
g2 -> h1
g2 -> h2
e1(h1, h2, x, y, z) -> e2(x, x, y, z, z)
e2(f1, x, y, z, f2) -> e3(x, y, x, y, y, z, y, z, x, y, z)
e3(x1, x1, x2, x2, x3, x3, x4, x4, x, y, z) -> e4(x1, x1, x2, x2, x3, x3, x4, x4, x, y, z)
e4(g1, x1, g2, x1, g1, x1, g2, x1, x, y, z) -> e1(x1, x1, x, y, z)

Termination of R to be shown.

`   R`
`     ↳Dependency Pair Analysis`

R contains the following Dependency Pairs:

F1 -> G1
F1 -> G2
F2 -> G1
F2 -> G2
E1(h1, h2, x, y, z) -> E2(x, x, y, z, z)
E2(f1, x, y, z, f2) -> E3(x, y, x, y, y, z, y, z, x, y, z)
E3(x1, x1, x2, x2, x3, x3, x4, x4, x, y, z) -> E4(x1, x1, x2, x2, x3, x3, x4, x4, x, y, z)
E4(g1, x1, g2, x1, g1, x1, g2, x1, x, y, z) -> E1(x1, x1, x, y, z)

Furthermore, R contains one SCC.

`   R`
`     ↳DPs`
`       →DP Problem 1`
`         ↳Remaining Obligation(s)`

The following remains to be proven:
Dependency Pairs:

E4(g1, x1, g2, x1, g1, x1, g2, x1, x, y, z) -> E1(x1, x1, x, y, z)
E3(x1, x1, x2, x2, x3, x3, x4, x4, x, y, z) -> E4(x1, x1, x2, x2, x3, x3, x4, x4, x, y, z)
E2(f1, x, y, z, f2) -> E3(x, y, x, y, y, z, y, z, x, y, z)
E1(h1, h2, x, y, z) -> E2(x, x, y, z, z)

Rules:

f1 -> g1
f1 -> g2
f2 -> g1
f2 -> g2
g1 -> h1
g1 -> h2
g2 -> h1
g2 -> h2
e1(h1, h2, x, y, z) -> e2(x, x, y, z, z)
e2(f1, x, y, z, f2) -> e3(x, y, x, y, y, z, y, z, x, y, z)
e3(x1, x1, x2, x2, x3, x3, x4, x4, x, y, z) -> e4(x1, x1, x2, x2, x3, x3, x4, x4, x, y, z)
e4(g1, x1, g2, x1, g1, x1, g2, x1, x, y, z) -> e1(x1, x1, x, y, z)

Termination of R could not be shown.
Duration:
0:00 minutes