R
↳Removing Redundant Rules for Innermost Termination
circ(cons(lift, s), circ(cons(lift, t), u)) -> circ(cons(lift, circ(s, t)), u)
R
↳RRRI
→TRS2
↳Dependency Pair Analysis
CIRC(cons(a, s), t) -> MSUBST(a, t)
CIRC(cons(a, s), t) -> CIRC(s, t)
CIRC(cons(lift, s), cons(a, t)) -> CIRC(s, t)
CIRC(cons(lift, s), cons(lift, t)) -> CIRC(s, t)
CIRC(circ(s, t), u) -> CIRC(s, circ(t, u))
CIRC(circ(s, t), u) -> CIRC(t, u)
MSUBST(msubst(a, s), t) -> MSUBST(a, circ(s, t))
MSUBST(msubst(a, s), t) -> CIRC(s, t)
R
↳RRRI
→TRS2
↳DPs
→DP Problem 1
↳Size-Change Principle
CIRC(circ(s, t), u) -> CIRC(t, u)
CIRC(circ(s, t), u) -> CIRC(s, circ(t, u))
CIRC(cons(lift, s), cons(lift, t)) -> CIRC(s, t)
CIRC(cons(lift, s), cons(a, t)) -> CIRC(s, t)
CIRC(cons(a, s), t) -> CIRC(s, t)
MSUBST(msubst(a, s), t) -> CIRC(s, t)
MSUBST(msubst(a, s), t) -> MSUBST(a, circ(s, t))
CIRC(cons(a, s), t) -> MSUBST(a, t)
circ(cons(a, s), t) -> cons(msubst(a, t), circ(s, t))
circ(cons(lift, s), cons(a, t)) -> cons(a, circ(s, t))
circ(cons(lift, s), cons(lift, t)) -> cons(lift, circ(s, t))
circ(circ(s, t), u) -> circ(s, circ(t, u))
circ(s, id) -> s
circ(id, s) -> s
msubst(a, id) -> a
msubst(msubst(a, s), t) -> msubst(a, circ(s, t))
subst(a, id) -> a
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trivial
cons(x1, x2) -> cons(x1, x2)
msubst(x1, x2) -> msubst(x1, x2)