R
↳Removing Redundant Rules for Innermost Termination
e2(f1, x, y, z, f2) -> e3(x, y, x, y, y, z, y, z, x, y, z)
e4(g1, x1, g2, x1, g1, x1, g2, x1, x, y, z) -> e1(x1, x1, x, y, z)
R
↳RRRI
→TRS2
↳Removing Redundant Rules
f1 -> g1
f1 -> g2
was used.
POL(f2) = 0 POL(h1) = 0 POL(e1(x1, x2, x3, x4, x5)) = x1 + x2 + 2·x3 + x4 + 2·x5 POL(e3(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)) = x1 + x10 + x11 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 POL(e4(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)) = x1 + x10 + x11 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 POL(g2) = 0 POL(f1) = 1 POL(h2) = 0 POL(g1) = 0 POL(e2(x1, x2, x3, x4, x5)) = x1 + x2 + x3 + x4 + x5
R
↳RRRI
→TRS2
↳RRRPolo
→TRS3
↳Removing Redundant Rules
f2 -> g1
f2 -> g2
was used.
POL(f2) = 1 POL(h1) = 0 POL(e1(x1, x2, x3, x4, x5)) = x1 + x2 + 2·x3 + x4 + 2·x5 POL(e3(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)) = x1 + x10 + x11 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 POL(e4(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)) = x1 + x10 + x11 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 POL(g2) = 0 POL(h2) = 0 POL(g1) = 0 POL(e2(x1, x2, x3, x4, x5)) = x1 + x2 + x3 + x4 + x5
R
↳RRRI
→TRS2
↳RRRPolo
→TRS3
↳RRRPolo
...
→TRS4
↳Removing Redundant Rules
e3(x1, x1, x2, x2, x3, x3, x4, x4, x, y, z) -> e4(x1, x1, x2, x2, x3, x3, x4, x4, x, y, z)
was used.
POL(e1(x1, x2, x3, x4, x5)) = x1 + x2 + 2·x3 + x4 + 2·x5 POL(h1) = 0 POL(e3(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)) = 1 + x1 + x10 + x11 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 POL(e4(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)) = x1 + x10 + x11 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 POL(g2) = 0 POL(h2) = 0 POL(g1) = 0 POL(e2(x1, x2, x3, x4, x5)) = x1 + x2 + x3 + x4 + x5
R
↳RRRI
→TRS2
↳RRRPolo
→TRS3
↳RRRPolo
...
→TRS5
↳Removing Redundant Rules
e1(h1, h2, x, y, z) -> e2(x, x, y, z, z)
was used.
POL(h1) = 0 POL(e1(x1, x2, x3, x4, x5)) = 1 + x1 + x2 + 2·x3 + x4 + 2·x5 POL(g2) = 0 POL(h2) = 0 POL(g1) = 0 POL(e2(x1, x2, x3, x4, x5)) = x1 + x2 + x3 + x4 + x5
R
↳RRRI
→TRS2
↳RRRPolo
→TRS3
↳RRRPolo
...
→TRS6
↳Removing Redundant Rules
g2 -> h2
g2 -> h1
was used.
POL(h1) = 0 POL(g2) = 1 POL(h2) = 0 POL(g1) = 0
R
↳RRRI
→TRS2
↳RRRPolo
→TRS3
↳RRRPolo
...
→TRS7
↳Removing Redundant Rules
g1 -> h1
g1 -> h2
was used.
POL(h1) = 0 POL(h2) = 0 POL(g1) = 1
R
↳RRRI
→TRS2
↳RRRPolo
→TRS3
↳RRRPolo
...
→TRS8
↳Dependency Pair Analysis