The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF).

(0) Obligation:

Runtime Complexity Relative TRS:
The TRS R consists of the following rules:

#equal(@x, @y) → #eq(@x, @y)
#less(@x, @y) → #cklt(#compare(@x, @y))
and(@x, @y) → #and(@x, @y)
insert(@x, @l) → insert#1(@l, @x)
insert#1(::(@y, @ys), @x) → insert#2(leq(@x, @y), @x, @y, @ys)
insert#1(nil, @x) → ::(@x, nil)
insert#2(#false, @x, @y, @ys) → ::(@y, insert(@x, @ys))
insert#2(#true, @x, @y, @ys) → ::(@x, ::(@y, @ys))
isortlist(@l) → isortlist#1(@l)
isortlist#1(::(@x, @xs)) → insert(@x, isortlist(@xs))
isortlist#1(nil) → nil
leq(@l1, @l2) → leq#1(@l1, @l2)
leq#1(::(@x, @xs), @l2) → leq#2(@l2, @x, @xs)
leq#1(nil, @l2) → #true
leq#2(::(@y, @ys), @x, @xs) → or(#less(@x, @y), and(#equal(@x, @y), leq(@xs, @ys)))
leq#2(nil, @x, @xs) → #false
or(@x, @y) → #or(@x, @y)

The (relative) TRS S consists of the following rules:

#and(#false, #false) → #false
#and(#false, #true) → #false
#and(#true, #false) → #false
#and(#true, #true) → #true
#cklt(#EQ) → #false
#cklt(#GT) → #false
#cklt(#LT) → #true
#compare(#0, #0) → #EQ
#compare(#0, #neg(@y)) → #GT
#compare(#0, #pos(@y)) → #LT
#compare(#0, #s(@y)) → #LT
#compare(#neg(@x), #0) → #LT
#compare(#neg(@x), #neg(@y)) → #compare(@y, @x)
#compare(#neg(@x), #pos(@y)) → #LT
#compare(#pos(@x), #0) → #GT
#compare(#pos(@x), #neg(@y)) → #GT
#compare(#pos(@x), #pos(@y)) → #compare(@x, @y)
#compare(#s(@x), #0) → #GT
#compare(#s(@x), #s(@y)) → #compare(@x, @y)
#eq(#0, #0) → #true
#eq(#0, #neg(@y)) → #false
#eq(#0, #pos(@y)) → #false
#eq(#0, #s(@y)) → #false
#eq(#neg(@x), #0) → #false
#eq(#neg(@x), #neg(@y)) → #eq(@x, @y)
#eq(#neg(@x), #pos(@y)) → #false
#eq(#pos(@x), #0) → #false
#eq(#pos(@x), #neg(@y)) → #false
#eq(#pos(@x), #pos(@y)) → #eq(@x, @y)
#eq(#s(@x), #0) → #false
#eq(#s(@x), #s(@y)) → #eq(@x, @y)
#eq(::(@x_1, @x_2), ::(@y_1, @y_2)) → #and(#eq(@x_1, @y_1), #eq(@x_2, @y_2))
#eq(::(@x_1, @x_2), nil) → #false
#eq(nil, ::(@y_1, @y_2)) → #false
#eq(nil, nil) → #true
#or(#false, #false) → #false
#or(#false, #true) → #true
#or(#true, #false) → #true
#or(#true, #true) → #true

Rewrite Strategy: INNERMOST

(1) DecreasingLoopProof (EQUIVALENT transformation)

The following loop(s) give(s) rise to the lower bound Ω(n¹):
The rewrite sequence
insert(::(@x17874_3, @xs17875_3), ::(nil, @ys17560_3)) →⁺ ::(nil, insert(::(@x17874_3, @xs17875_3), @ys17560_3))
gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
The pumping substitution is [@ys17560_3 / ::(nil, @ys17560_3)].
The result substitution is [ ].

(2) BOUNDS(n^1, INF)