Left Termination of the query pattern p_in_2(g, g) w.r.t. the given Prolog program could not be shown:

(0) Obligation:

Clauses:

p(X, Y) :- ','(less(X, Y), ','(!, p(s(X), Y))).
less(0, s(X1)).
less(s(X), s(Y)) :- less(X, Y).

Queries:

p(g,g).

(1) CutEliminatorProof (SOUND transformation)

Eliminated all cuts by simply ignoring them[PROLOG].

(2) Obligation:

Clauses:

p(X, Y) :- ','(less(X, Y), p(s(X), Y)).
less(0, s(X1)).
less(s(X), s(Y)) :- less(X, Y).

Queries:

p(g,g).

(3) PrologToPiTRSProof (SOUND transformation)

We use the technique of [LOPSTR]. With regard to the inferred argument filtering the predicates were used in the following modes:
p_in: (b,b)
less_in: (b,b)
Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:

p_in_gg(X, Y) → U1_gg(X, Y, less_in_gg(X, Y))
less_in_gg(0, s(X1)) → less_out_gg(0, s(X1))
less_in_gg(s(X), s(Y)) → U3_gg(X, Y, less_in_gg(X, Y))
U3_gg(X, Y, less_out_gg(X, Y)) → less_out_gg(s(X), s(Y))
U1_gg(X, Y, less_out_gg(X, Y)) → U2_gg(X, Y, p_in_gg(s(X), Y))
U2_gg(X, Y, p_out_gg(s(X), Y)) → p_out_gg(X, Y)

Pi is empty.

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(4) Obligation:

Pi-finite rewrite system:
The TRS R consists of the following rules:

p_in_gg(X, Y) → U1_gg(X, Y, less_in_gg(X, Y))
less_in_gg(0, s(X1)) → less_out_gg(0, s(X1))
less_in_gg(s(X), s(Y)) → U3_gg(X, Y, less_in_gg(X, Y))
U3_gg(X, Y, less_out_gg(X, Y)) → less_out_gg(s(X), s(Y))
U1_gg(X, Y, less_out_gg(X, Y)) → U2_gg(X, Y, p_in_gg(s(X), Y))
U2_gg(X, Y, p_out_gg(s(X), Y)) → p_out_gg(X, Y)

Pi is empty.

(5) DependencyPairsProof (EQUIVALENT transformation)

Using Dependency Pairs [AG00,LOPSTR] we result in the following initial DP problem:
Pi DP problem:
The TRS P consists of the following rules:

P_IN_GG(X, Y) → U1_GG(X, Y, less_in_gg(X, Y))
P_IN_GG(X, Y) → LESS_IN_GG(X, Y)
LESS_IN_GG(s(X), s(Y)) → U3_GG(X, Y, less_in_gg(X, Y))
LESS_IN_GG(s(X), s(Y)) → LESS_IN_GG(X, Y)
U1_GG(X, Y, less_out_gg(X, Y)) → U2_GG(X, Y, p_in_gg(s(X), Y))
U1_GG(X, Y, less_out_gg(X, Y)) → P_IN_GG(s(X), Y)

The TRS R consists of the following rules:

p_in_gg(X, Y) → U1_gg(X, Y, less_in_gg(X, Y))
less_in_gg(0, s(X1)) → less_out_gg(0, s(X1))
less_in_gg(s(X), s(Y)) → U3_gg(X, Y, less_in_gg(X, Y))
U3_gg(X, Y, less_out_gg(X, Y)) → less_out_gg(s(X), s(Y))
U1_gg(X, Y, less_out_gg(X, Y)) → U2_gg(X, Y, p_in_gg(s(X), Y))
U2_gg(X, Y, p_out_gg(s(X), Y)) → p_out_gg(X, Y)

Pi is empty.
We have to consider all (P,R,Pi)-chains

(6) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

P_IN_GG(X, Y) → U1_GG(X, Y, less_in_gg(X, Y))
P_IN_GG(X, Y) → LESS_IN_GG(X, Y)
LESS_IN_GG(s(X), s(Y)) → U3_GG(X, Y, less_in_gg(X, Y))
LESS_IN_GG(s(X), s(Y)) → LESS_IN_GG(X, Y)
U1_GG(X, Y, less_out_gg(X, Y)) → U2_GG(X, Y, p_in_gg(s(X), Y))
U1_GG(X, Y, less_out_gg(X, Y)) → P_IN_GG(s(X), Y)

The TRS R consists of the following rules:

p_in_gg(X, Y) → U1_gg(X, Y, less_in_gg(X, Y))
less_in_gg(0, s(X1)) → less_out_gg(0, s(X1))
less_in_gg(s(X), s(Y)) → U3_gg(X, Y, less_in_gg(X, Y))
U3_gg(X, Y, less_out_gg(X, Y)) → less_out_gg(s(X), s(Y))
U1_gg(X, Y, less_out_gg(X, Y)) → U2_gg(X, Y, p_in_gg(s(X), Y))
U2_gg(X, Y, p_out_gg(s(X), Y)) → p_out_gg(X, Y)

Pi is empty.
We have to consider all (P,R,Pi)-chains

(7) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 2 SCCs with 3 less nodes.

(8) Complex Obligation (AND)

(9) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

LESS_IN_GG(s(X), s(Y)) → LESS_IN_GG(X, Y)

The TRS R consists of the following rules:

p_in_gg(X, Y) → U1_gg(X, Y, less_in_gg(X, Y))
less_in_gg(0, s(X1)) → less_out_gg(0, s(X1))
less_in_gg(s(X), s(Y)) → U3_gg(X, Y, less_in_gg(X, Y))
U3_gg(X, Y, less_out_gg(X, Y)) → less_out_gg(s(X), s(Y))
U1_gg(X, Y, less_out_gg(X, Y)) → U2_gg(X, Y, p_in_gg(s(X), Y))
U2_gg(X, Y, p_out_gg(s(X), Y)) → p_out_gg(X, Y)

Pi is empty.
We have to consider all (P,R,Pi)-chains

(10) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(11) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

LESS_IN_GG(s(X), s(Y)) → LESS_IN_GG(X, Y)

R is empty.
Pi is empty.
We have to consider all (P,R,Pi)-chains

(12) PiDPToQDPProof (EQUIVALENT transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(13) Obligation:

Q DP problem:
The TRS P consists of the following rules:

LESS_IN_GG(s(X), s(Y)) → LESS_IN_GG(X, Y)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(14) QDPSizeChangeProof (EQUIVALENT transformation)

By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

• LESS_IN_GG(s(X), s(Y)) → LESS_IN_GG(X, Y)
  The graph contains the following edges 1 > 1, 2 > 2

(15) TRUE

(16) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

U1_GG(X, Y, less_out_gg(X, Y)) → P_IN_GG(s(X), Y)
P_IN_GG(X, Y) → U1_GG(X, Y, less_in_gg(X, Y))

The TRS R consists of the following rules:

p_in_gg(X, Y) → U1_gg(X, Y, less_in_gg(X, Y))
less_in_gg(0, s(X1)) → less_out_gg(0, s(X1))
less_in_gg(s(X), s(Y)) → U3_gg(X, Y, less_in_gg(X, Y))
U3_gg(X, Y, less_out_gg(X, Y)) → less_out_gg(s(X), s(Y))
U1_gg(X, Y, less_out_gg(X, Y)) → U2_gg(X, Y, p_in_gg(s(X), Y))
U2_gg(X, Y, p_out_gg(s(X), Y)) → p_out_gg(X, Y)

Pi is empty.
We have to consider all (P,R,Pi)-chains

(17) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(18) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

U1_GG(X, Y, less_out_gg(X, Y)) → P_IN_GG(s(X), Y)
P_IN_GG(X, Y) → U1_GG(X, Y, less_in_gg(X, Y))

The TRS R consists of the following rules:

less_in_gg(0, s(X1)) → less_out_gg(0, s(X1))
less_in_gg(s(X), s(Y)) → U3_gg(X, Y, less_in_gg(X, Y))
U3_gg(X, Y, less_out_gg(X, Y)) → less_out_gg(s(X), s(Y))

Pi is empty.
We have to consider all (P,R,Pi)-chains

(19) PiDPToQDPProof (EQUIVALENT transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(20) Obligation:

Q DP problem:
The TRS P consists of the following rules:

U1_GG(X, Y, less_out_gg(X, Y)) → P_IN_GG(s(X), Y)
P_IN_GG(X, Y) → U1_GG(X, Y, less_in_gg(X, Y))

The TRS R consists of the following rules:

less_in_gg(0, s(X1)) → less_out_gg(0, s(X1))
less_in_gg(s(X), s(Y)) → U3_gg(X, Y, less_in_gg(X, Y))
U3_gg(X, Y, less_out_gg(X, Y)) → less_out_gg(s(X), s(Y))

The set Q consists of the following terms:

less_in_gg(x0, x1)
U3_gg(x0, x1, x2)

We have to consider all (P,Q,R)-chains.

(21) Instantiation (EQUIVALENT transformation)

By instantiating [LPAR04] the rule P_IN_GG(X, Y) → U1_GG(X, Y, less_in_gg(X, Y)) we obtained the following new rules [LPAR04]:

P_IN_GG(s(z0), z1) → U1_GG(s(z0), z1, less_in_gg(s(z0), z1))

(22) Obligation:

Q DP problem:
The TRS P consists of the following rules:

U1_GG(X, Y, less_out_gg(X, Y)) → P_IN_GG(s(X), Y)
P_IN_GG(s(z0), z1) → U1_GG(s(z0), z1, less_in_gg(s(z0), z1))

The TRS R consists of the following rules:

less_in_gg(0, s(X1)) → less_out_gg(0, s(X1))
less_in_gg(s(X), s(Y)) → U3_gg(X, Y, less_in_gg(X, Y))
U3_gg(X, Y, less_out_gg(X, Y)) → less_out_gg(s(X), s(Y))

The set Q consists of the following terms:

less_in_gg(x0, x1)
U3_gg(x0, x1, x2)

We have to consider all (P,Q,R)-chains.

(23) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule P_IN_GG(X, Y) → U1_GG(X, Y, less_in_gg(X, Y)) at position [2] we obtained the following new rules [LPAR04]:

P_IN_GG(0, s(x0)) → U1_GG(0, s(x0), less_out_gg(0, s(x0)))
P_IN_GG(s(x0), s(x1)) → U1_GG(s(x0), s(x1), U3_gg(x0, x1, less_in_gg(x0, x1)))

(24) Obligation:

Q DP problem:
The TRS P consists of the following rules:

U1_GG(X, Y, less_out_gg(X, Y)) → P_IN_GG(s(X), Y)
P_IN_GG(0, s(x0)) → U1_GG(0, s(x0), less_out_gg(0, s(x0)))
P_IN_GG(s(x0), s(x1)) → U1_GG(s(x0), s(x1), U3_gg(x0, x1, less_in_gg(x0, x1)))

The TRS R consists of the following rules:

less_in_gg(0, s(X1)) → less_out_gg(0, s(X1))
less_in_gg(s(X), s(Y)) → U3_gg(X, Y, less_in_gg(X, Y))
U3_gg(X, Y, less_out_gg(X, Y)) → less_out_gg(s(X), s(Y))

The set Q consists of the following terms:

less_in_gg(x0, x1)
U3_gg(x0, x1, x2)

We have to consider all (P,Q,R)-chains.

(25) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.

(26) Obligation:

Q DP problem:
The TRS P consists of the following rules:

P_IN_GG(s(x0), s(x1)) → U1_GG(s(x0), s(x1), U3_gg(x0, x1, less_in_gg(x0, x1)))
U1_GG(X, Y, less_out_gg(X, Y)) → P_IN_GG(s(X), Y)

The TRS R consists of the following rules:

less_in_gg(0, s(X1)) → less_out_gg(0, s(X1))
less_in_gg(s(X), s(Y)) → U3_gg(X, Y, less_in_gg(X, Y))
U3_gg(X, Y, less_out_gg(X, Y)) → less_out_gg(s(X), s(Y))

The set Q consists of the following terms:

less_in_gg(x0, x1)
U3_gg(x0, x1, x2)

We have to consider all (P,Q,R)-chains.

(27) Instantiation (EQUIVALENT transformation)

By instantiating [LPAR04] the rule U1_GG(X, Y, less_out_gg(X, Y)) → P_IN_GG(s(X), Y) we obtained the following new rules [LPAR04]:

U1_GG(s(z0), s(z1), less_out_gg(s(z0), s(z1))) → P_IN_GG(s(s(z0)), s(z1))

(28) Obligation:

Q DP problem:
The TRS P consists of the following rules:

P_IN_GG(s(x0), s(x1)) → U1_GG(s(x0), s(x1), U3_gg(x0, x1, less_in_gg(x0, x1)))
U1_GG(s(z0), s(z1), less_out_gg(s(z0), s(z1))) → P_IN_GG(s(s(z0)), s(z1))

The TRS R consists of the following rules:

less_in_gg(0, s(X1)) → less_out_gg(0, s(X1))
less_in_gg(s(X), s(Y)) → U3_gg(X, Y, less_in_gg(X, Y))
U3_gg(X, Y, less_out_gg(X, Y)) → less_out_gg(s(X), s(Y))

The set Q consists of the following terms:

less_in_gg(x0, x1)
U3_gg(x0, x1, x2)

We have to consider all (P,Q,R)-chains.

(29) Instantiation (EQUIVALENT transformation)

By instantiating [LPAR04] the rule P_IN_GG(s(x0), s(x1)) → U1_GG(s(x0), s(x1), U3_gg(x0, x1, less_in_gg(x0, x1))) we obtained the following new rules [LPAR04]:

P_IN_GG(s(s(z0)), s(z1)) → U1_GG(s(s(z0)), s(z1), U3_gg(s(z0), z1, less_in_gg(s(z0), z1)))

(30) Obligation:

Q DP problem:
The TRS P consists of the following rules:

U1_GG(s(z0), s(z1), less_out_gg(s(z0), s(z1))) → P_IN_GG(s(s(z0)), s(z1))
P_IN_GG(s(s(z0)), s(z1)) → U1_GG(s(s(z0)), s(z1), U3_gg(s(z0), z1, less_in_gg(s(z0), z1)))

The TRS R consists of the following rules:

less_in_gg(0, s(X1)) → less_out_gg(0, s(X1))
less_in_gg(s(X), s(Y)) → U3_gg(X, Y, less_in_gg(X, Y))
U3_gg(X, Y, less_out_gg(X, Y)) → less_out_gg(s(X), s(Y))

The set Q consists of the following terms:

less_in_gg(x0, x1)
U3_gg(x0, x1, x2)

We have to consider all (P,Q,R)-chains.

(31) Instantiation (EQUIVALENT transformation)

By instantiating [LPAR04] the rule U1_GG(s(z0), s(z1), less_out_gg(s(z0), s(z1))) → P_IN_GG(s(s(z0)), s(z1)) we obtained the following new rules [LPAR04]:

U1_GG(s(s(z0)), s(z1), less_out_gg(s(s(z0)), s(z1))) → P_IN_GG(s(s(s(z0))), s(z1))

(32) Obligation:

Q DP problem:
The TRS P consists of the following rules:

P_IN_GG(s(s(z0)), s(z1)) → U1_GG(s(s(z0)), s(z1), U3_gg(s(z0), z1, less_in_gg(s(z0), z1)))
U1_GG(s(s(z0)), s(z1), less_out_gg(s(s(z0)), s(z1))) → P_IN_GG(s(s(s(z0))), s(z1))

The TRS R consists of the following rules:

less_in_gg(0, s(X1)) → less_out_gg(0, s(X1))
less_in_gg(s(X), s(Y)) → U3_gg(X, Y, less_in_gg(X, Y))
U3_gg(X, Y, less_out_gg(X, Y)) → less_out_gg(s(X), s(Y))

The set Q consists of the following terms:

less_in_gg(x0, x1)
U3_gg(x0, x1, x2)

We have to consider all (P,Q,R)-chains.

(33) Instantiation (EQUIVALENT transformation)

By instantiating [LPAR04] the rule P_IN_GG(s(s(z0)), s(z1)) → U1_GG(s(s(z0)), s(z1), U3_gg(s(z0), z1, less_in_gg(s(z0), z1))) we obtained the following new rules [LPAR04]:

P_IN_GG(s(s(s(z0))), s(z1)) → U1_GG(s(s(s(z0))), s(z1), U3_gg(s(s(z0)), z1, less_in_gg(s(s(z0)), z1)))

(34) Obligation:

Q DP problem:
The TRS P consists of the following rules:

U1_GG(s(s(z0)), s(z1), less_out_gg(s(s(z0)), s(z1))) → P_IN_GG(s(s(s(z0))), s(z1))
P_IN_GG(s(s(s(z0))), s(z1)) → U1_GG(s(s(s(z0))), s(z1), U3_gg(s(s(z0)), z1, less_in_gg(s(s(z0)), z1)))

The TRS R consists of the following rules:

less_in_gg(0, s(X1)) → less_out_gg(0, s(X1))
less_in_gg(s(X), s(Y)) → U3_gg(X, Y, less_in_gg(X, Y))
U3_gg(X, Y, less_out_gg(X, Y)) → less_out_gg(s(X), s(Y))

The set Q consists of the following terms:

less_in_gg(x0, x1)
U3_gg(x0, x1, x2)

We have to consider all (P,Q,R)-chains.

(35) PrologToPiTRSProof (SOUND transformation)

We use the technique of [LOPSTR]. With regard to the inferred argument filtering the predicates were used in the following modes:
p_in: (b,b)
less_in: (b,b)
Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:

p_in_gg(X, Y) → U1_gg(X, Y, less_in_gg(X, Y))
less_in_gg(0, s(X1)) → less_out_gg(0, s(X1))
less_in_gg(s(X), s(Y)) → U3_gg(X, Y, less_in_gg(X, Y))
U3_gg(X, Y, less_out_gg(X, Y)) → less_out_gg(s(X), s(Y))
U1_gg(X, Y, less_out_gg(X, Y)) → U2_gg(X, Y, p_in_gg(s(X), Y))
U2_gg(X, Y, p_out_gg(s(X), Y)) → p_out_gg(X, Y)

The argument filtering Pi contains the following mapping:
p_in_gg(x1, x2)  =  p_in_gg(x1, x2)
U1_gg(x1, x2, x3)  =  U1_gg(x1, x2, x3)
less_in_gg(x1, x2)  =  less_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less_out_gg(x1, x2)  =  less_out_gg
U3_gg(x1, x2, x3)  =  U3_gg(x3)
U2_gg(x1, x2, x3)  =  U2_gg(x3)
p_out_gg(x1, x2)  =  p_out_gg

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(36) Obligation:

Pi-finite rewrite system:
The TRS R consists of the following rules:

p_in_gg(X, Y) → U1_gg(X, Y, less_in_gg(X, Y))
less_in_gg(0, s(X1)) → less_out_gg(0, s(X1))
less_in_gg(s(X), s(Y)) → U3_gg(X, Y, less_in_gg(X, Y))
U3_gg(X, Y, less_out_gg(X, Y)) → less_out_gg(s(X), s(Y))
U1_gg(X, Y, less_out_gg(X, Y)) → U2_gg(X, Y, p_in_gg(s(X), Y))
U2_gg(X, Y, p_out_gg(s(X), Y)) → p_out_gg(X, Y)

The argument filtering Pi contains the following mapping:
p_in_gg(x1, x2)  =  p_in_gg(x1, x2)
U1_gg(x1, x2, x3)  =  U1_gg(x1, x2, x3)
less_in_gg(x1, x2)  =  less_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less_out_gg(x1, x2)  =  less_out_gg
U3_gg(x1, x2, x3)  =  U3_gg(x3)
U2_gg(x1, x2, x3)  =  U2_gg(x3)
p_out_gg(x1, x2)  =  p_out_gg

(37) DependencyPairsProof (EQUIVALENT transformation)

Using Dependency Pairs [AG00,LOPSTR] we result in the following initial DP problem:
Pi DP problem:
The TRS P consists of the following rules:

P_IN_GG(X, Y) → U1_GG(X, Y, less_in_gg(X, Y))
P_IN_GG(X, Y) → LESS_IN_GG(X, Y)
LESS_IN_GG(s(X), s(Y)) → U3_GG(X, Y, less_in_gg(X, Y))
LESS_IN_GG(s(X), s(Y)) → LESS_IN_GG(X, Y)
U1_GG(X, Y, less_out_gg(X, Y)) → U2_GG(X, Y, p_in_gg(s(X), Y))
U1_GG(X, Y, less_out_gg(X, Y)) → P_IN_GG(s(X), Y)

The TRS R consists of the following rules:

p_in_gg(X, Y) → U1_gg(X, Y, less_in_gg(X, Y))
less_in_gg(0, s(X1)) → less_out_gg(0, s(X1))
less_in_gg(s(X), s(Y)) → U3_gg(X, Y, less_in_gg(X, Y))
U3_gg(X, Y, less_out_gg(X, Y)) → less_out_gg(s(X), s(Y))
U1_gg(X, Y, less_out_gg(X, Y)) → U2_gg(X, Y, p_in_gg(s(X), Y))
U2_gg(X, Y, p_out_gg(s(X), Y)) → p_out_gg(X, Y)

The argument filtering Pi contains the following mapping:
p_in_gg(x1, x2)  =  p_in_gg(x1, x2)
U1_gg(x1, x2, x3)  =  U1_gg(x1, x2, x3)
less_in_gg(x1, x2)  =  less_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less_out_gg(x1, x2)  =  less_out_gg
U3_gg(x1, x2, x3)  =  U3_gg(x3)
U2_gg(x1, x2, x3)  =  U2_gg(x3)
p_out_gg(x1, x2)  =  p_out_gg
P_IN_GG(x1, x2)  =  P_IN_GG(x1, x2)
U1_GG(x1, x2, x3)  =  U1_GG(x1, x2, x3)
LESS_IN_GG(x1, x2)  =  LESS_IN_GG(x1, x2)
U3_GG(x1, x2, x3)  =  U3_GG(x3)
U2_GG(x1, x2, x3)  =  U2_GG(x3)

We have to consider all (P,R,Pi)-chains

(38) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

P_IN_GG(X, Y) → U1_GG(X, Y, less_in_gg(X, Y))
P_IN_GG(X, Y) → LESS_IN_GG(X, Y)
LESS_IN_GG(s(X), s(Y)) → U3_GG(X, Y, less_in_gg(X, Y))
LESS_IN_GG(s(X), s(Y)) → LESS_IN_GG(X, Y)
U1_GG(X, Y, less_out_gg(X, Y)) → U2_GG(X, Y, p_in_gg(s(X), Y))
U1_GG(X, Y, less_out_gg(X, Y)) → P_IN_GG(s(X), Y)

The TRS R consists of the following rules:

p_in_gg(X, Y) → U1_gg(X, Y, less_in_gg(X, Y))
less_in_gg(0, s(X1)) → less_out_gg(0, s(X1))
less_in_gg(s(X), s(Y)) → U3_gg(X, Y, less_in_gg(X, Y))
U3_gg(X, Y, less_out_gg(X, Y)) → less_out_gg(s(X), s(Y))
U1_gg(X, Y, less_out_gg(X, Y)) → U2_gg(X, Y, p_in_gg(s(X), Y))
U2_gg(X, Y, p_out_gg(s(X), Y)) → p_out_gg(X, Y)

The argument filtering Pi contains the following mapping:
p_in_gg(x1, x2)  =  p_in_gg(x1, x2)
U1_gg(x1, x2, x3)  =  U1_gg(x1, x2, x3)
less_in_gg(x1, x2)  =  less_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less_out_gg(x1, x2)  =  less_out_gg
U3_gg(x1, x2, x3)  =  U3_gg(x3)
U2_gg(x1, x2, x3)  =  U2_gg(x3)
p_out_gg(x1, x2)  =  p_out_gg
P_IN_GG(x1, x2)  =  P_IN_GG(x1, x2)
U1_GG(x1, x2, x3)  =  U1_GG(x1, x2, x3)
LESS_IN_GG(x1, x2)  =  LESS_IN_GG(x1, x2)
U3_GG(x1, x2, x3)  =  U3_GG(x3)
U2_GG(x1, x2, x3)  =  U2_GG(x3)

We have to consider all (P,R,Pi)-chains

(39) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 2 SCCs with 3 less nodes.

(40) Complex Obligation (AND)

(41) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

LESS_IN_GG(s(X), s(Y)) → LESS_IN_GG(X, Y)

The TRS R consists of the following rules:

p_in_gg(X, Y) → U1_gg(X, Y, less_in_gg(X, Y))
less_in_gg(0, s(X1)) → less_out_gg(0, s(X1))
less_in_gg(s(X), s(Y)) → U3_gg(X, Y, less_in_gg(X, Y))
U3_gg(X, Y, less_out_gg(X, Y)) → less_out_gg(s(X), s(Y))
U1_gg(X, Y, less_out_gg(X, Y)) → U2_gg(X, Y, p_in_gg(s(X), Y))
U2_gg(X, Y, p_out_gg(s(X), Y)) → p_out_gg(X, Y)

The argument filtering Pi contains the following mapping:
p_in_gg(x1, x2)  =  p_in_gg(x1, x2)
U1_gg(x1, x2, x3)  =  U1_gg(x1, x2, x3)
less_in_gg(x1, x2)  =  less_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less_out_gg(x1, x2)  =  less_out_gg
U3_gg(x1, x2, x3)  =  U3_gg(x3)
U2_gg(x1, x2, x3)  =  U2_gg(x3)
p_out_gg(x1, x2)  =  p_out_gg
LESS_IN_GG(x1, x2)  =  LESS_IN_GG(x1, x2)

We have to consider all (P,R,Pi)-chains

(42) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(43) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

LESS_IN_GG(s(X), s(Y)) → LESS_IN_GG(X, Y)

R is empty.
Pi is empty.
We have to consider all (P,R,Pi)-chains

(44) PiDPToQDPProof (EQUIVALENT transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(45) Obligation:

Q DP problem:
The TRS P consists of the following rules:

LESS_IN_GG(s(X), s(Y)) → LESS_IN_GG(X, Y)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(46) QDPSizeChangeProof (EQUIVALENT transformation)

By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

• LESS_IN_GG(s(X), s(Y)) → LESS_IN_GG(X, Y)
  The graph contains the following edges 1 > 1, 2 > 2

(47) TRUE

(48) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

U1_GG(X, Y, less_out_gg(X, Y)) → P_IN_GG(s(X), Y)
P_IN_GG(X, Y) → U1_GG(X, Y, less_in_gg(X, Y))

The TRS R consists of the following rules:

p_in_gg(X, Y) → U1_gg(X, Y, less_in_gg(X, Y))
less_in_gg(0, s(X1)) → less_out_gg(0, s(X1))
less_in_gg(s(X), s(Y)) → U3_gg(X, Y, less_in_gg(X, Y))
U3_gg(X, Y, less_out_gg(X, Y)) → less_out_gg(s(X), s(Y))
U1_gg(X, Y, less_out_gg(X, Y)) → U2_gg(X, Y, p_in_gg(s(X), Y))
U2_gg(X, Y, p_out_gg(s(X), Y)) → p_out_gg(X, Y)

The argument filtering Pi contains the following mapping:
p_in_gg(x1, x2)  =  p_in_gg(x1, x2)
U1_gg(x1, x2, x3)  =  U1_gg(x1, x2, x3)
less_in_gg(x1, x2)  =  less_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less_out_gg(x1, x2)  =  less_out_gg
U3_gg(x1, x2, x3)  =  U3_gg(x3)
U2_gg(x1, x2, x3)  =  U2_gg(x3)
p_out_gg(x1, x2)  =  p_out_gg
P_IN_GG(x1, x2)  =  P_IN_GG(x1, x2)
U1_GG(x1, x2, x3)  =  U1_GG(x1, x2, x3)

We have to consider all (P,R,Pi)-chains

(49) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(50) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

U1_GG(X, Y, less_out_gg(X, Y)) → P_IN_GG(s(X), Y)
P_IN_GG(X, Y) → U1_GG(X, Y, less_in_gg(X, Y))

The TRS R consists of the following rules:

less_in_gg(0, s(X1)) → less_out_gg(0, s(X1))
less_in_gg(s(X), s(Y)) → U3_gg(X, Y, less_in_gg(X, Y))
U3_gg(X, Y, less_out_gg(X, Y)) → less_out_gg(s(X), s(Y))

The argument filtering Pi contains the following mapping:
less_in_gg(x1, x2)  =  less_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less_out_gg(x1, x2)  =  less_out_gg
U3_gg(x1, x2, x3)  =  U3_gg(x3)
P_IN_GG(x1, x2)  =  P_IN_GG(x1, x2)
U1_GG(x1, x2, x3)  =  U1_GG(x1, x2, x3)

We have to consider all (P,R,Pi)-chains

(51) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(52) Obligation:

Q DP problem:
The TRS P consists of the following rules:

U1_GG(X, Y, less_out_gg) → P_IN_GG(s(X), Y)
P_IN_GG(X, Y) → U1_GG(X, Y, less_in_gg(X, Y))

The TRS R consists of the following rules:

less_in_gg(0, s(X1)) → less_out_gg
less_in_gg(s(X), s(Y)) → U3_gg(less_in_gg(X, Y))
U3_gg(less_out_gg) → less_out_gg

The set Q consists of the following terms:

less_in_gg(x0, x1)
U3_gg(x0)

We have to consider all (P,Q,R)-chains.

(53) Instantiation (EQUIVALENT transformation)

By instantiating [LPAR04] the rule P_IN_GG(X, Y) → U1_GG(X, Y, less_in_gg(X, Y)) we obtained the following new rules [LPAR04]:

P_IN_GG(s(z0), z1) → U1_GG(s(z0), z1, less_in_gg(s(z0), z1))

(54) Obligation:

Q DP problem:
The TRS P consists of the following rules:

U1_GG(X, Y, less_out_gg) → P_IN_GG(s(X), Y)
P_IN_GG(s(z0), z1) → U1_GG(s(z0), z1, less_in_gg(s(z0), z1))

The TRS R consists of the following rules:

less_in_gg(0, s(X1)) → less_out_gg
less_in_gg(s(X), s(Y)) → U3_gg(less_in_gg(X, Y))
U3_gg(less_out_gg) → less_out_gg

The set Q consists of the following terms:

less_in_gg(x0, x1)
U3_gg(x0)

We have to consider all (P,Q,R)-chains.

(55) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule P_IN_GG(X, Y) → U1_GG(X, Y, less_in_gg(X, Y)) at position [2] we obtained the following new rules [LPAR04]:

P_IN_GG(0, s(x0)) → U1_GG(0, s(x0), less_out_gg)
P_IN_GG(s(x0), s(x1)) → U1_GG(s(x0), s(x1), U3_gg(less_in_gg(x0, x1)))

(56) Obligation:

Q DP problem:
The TRS P consists of the following rules:

U1_GG(X, Y, less_out_gg) → P_IN_GG(s(X), Y)
P_IN_GG(0, s(x0)) → U1_GG(0, s(x0), less_out_gg)
P_IN_GG(s(x0), s(x1)) → U1_GG(s(x0), s(x1), U3_gg(less_in_gg(x0, x1)))

The TRS R consists of the following rules:

less_in_gg(0, s(X1)) → less_out_gg
less_in_gg(s(X), s(Y)) → U3_gg(less_in_gg(X, Y))
U3_gg(less_out_gg) → less_out_gg

The set Q consists of the following terms:

less_in_gg(x0, x1)
U3_gg(x0)

We have to consider all (P,Q,R)-chains.

(57) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.

(58) Obligation:

Q DP problem:
The TRS P consists of the following rules:

P_IN_GG(s(x0), s(x1)) → U1_GG(s(x0), s(x1), U3_gg(less_in_gg(x0, x1)))
U1_GG(X, Y, less_out_gg) → P_IN_GG(s(X), Y)

The TRS R consists of the following rules:

less_in_gg(0, s(X1)) → less_out_gg
less_in_gg(s(X), s(Y)) → U3_gg(less_in_gg(X, Y))
U3_gg(less_out_gg) → less_out_gg

The set Q consists of the following terms:

less_in_gg(x0, x1)
U3_gg(x0)

We have to consider all (P,Q,R)-chains.

(59) Instantiation (EQUIVALENT transformation)

By instantiating [LPAR04] the rule U1_GG(X, Y, less_out_gg) → P_IN_GG(s(X), Y) we obtained the following new rules [LPAR04]:

U1_GG(s(z0), s(z1), less_out_gg) → P_IN_GG(s(s(z0)), s(z1))

(60) Obligation:

Q DP problem:
The TRS P consists of the following rules:

P_IN_GG(s(x0), s(x1)) → U1_GG(s(x0), s(x1), U3_gg(less_in_gg(x0, x1)))
U1_GG(s(z0), s(z1), less_out_gg) → P_IN_GG(s(s(z0)), s(z1))

The TRS R consists of the following rules:

less_in_gg(0, s(X1)) → less_out_gg
less_in_gg(s(X), s(Y)) → U3_gg(less_in_gg(X, Y))
U3_gg(less_out_gg) → less_out_gg

The set Q consists of the following terms:

less_in_gg(x0, x1)
U3_gg(x0)

We have to consider all (P,Q,R)-chains.

(61) Instantiation (EQUIVALENT transformation)

By instantiating [LPAR04] the rule P_IN_GG(s(x0), s(x1)) → U1_GG(s(x0), s(x1), U3_gg(less_in_gg(x0, x1))) we obtained the following new rules [LPAR04]:

P_IN_GG(s(s(z0)), s(z1)) → U1_GG(s(s(z0)), s(z1), U3_gg(less_in_gg(s(z0), z1)))

(62) Obligation:

Q DP problem:
The TRS P consists of the following rules:

U1_GG(s(z0), s(z1), less_out_gg) → P_IN_GG(s(s(z0)), s(z1))
P_IN_GG(s(s(z0)), s(z1)) → U1_GG(s(s(z0)), s(z1), U3_gg(less_in_gg(s(z0), z1)))

The TRS R consists of the following rules:

less_in_gg(0, s(X1)) → less_out_gg
less_in_gg(s(X), s(Y)) → U3_gg(less_in_gg(X, Y))
U3_gg(less_out_gg) → less_out_gg

The set Q consists of the following terms:

less_in_gg(x0, x1)
U3_gg(x0)

We have to consider all (P,Q,R)-chains.

(63) Instantiation (EQUIVALENT transformation)

By instantiating [LPAR04] the rule U1_GG(s(z0), s(z1), less_out_gg) → P_IN_GG(s(s(z0)), s(z1)) we obtained the following new rules [LPAR04]:

U1_GG(s(s(z0)), s(z1), less_out_gg) → P_IN_GG(s(s(s(z0))), s(z1))

(64) Obligation:

Q DP problem:
The TRS P consists of the following rules:

P_IN_GG(s(s(z0)), s(z1)) → U1_GG(s(s(z0)), s(z1), U3_gg(less_in_gg(s(z0), z1)))
U1_GG(s(s(z0)), s(z1), less_out_gg) → P_IN_GG(s(s(s(z0))), s(z1))

The TRS R consists of the following rules:

less_in_gg(0, s(X1)) → less_out_gg
less_in_gg(s(X), s(Y)) → U3_gg(less_in_gg(X, Y))
U3_gg(less_out_gg) → less_out_gg

The set Q consists of the following terms:

less_in_gg(x0, x1)
U3_gg(x0)

We have to consider all (P,Q,R)-chains.

(65) Instantiation (EQUIVALENT transformation)

By instantiating [LPAR04] the rule P_IN_GG(s(s(z0)), s(z1)) → U1_GG(s(s(z0)), s(z1), U3_gg(less_in_gg(s(z0), z1))) we obtained the following new rules [LPAR04]:

P_IN_GG(s(s(s(z0))), s(z1)) → U1_GG(s(s(s(z0))), s(z1), U3_gg(less_in_gg(s(s(z0)), z1)))

(66) Obligation:

Q DP problem:
The TRS P consists of the following rules:

U1_GG(s(s(z0)), s(z1), less_out_gg) → P_IN_GG(s(s(s(z0))), s(z1))
P_IN_GG(s(s(s(z0))), s(z1)) → U1_GG(s(s(s(z0))), s(z1), U3_gg(less_in_gg(s(s(z0)), z1)))

The TRS R consists of the following rules:

less_in_gg(0, s(X1)) → less_out_gg
less_in_gg(s(X), s(Y)) → U3_gg(less_in_gg(X, Y))
U3_gg(less_out_gg) → less_out_gg

The set Q consists of the following terms:

less_in_gg(x0, x1)
U3_gg(x0)

We have to consider all (P,Q,R)-chains.

(67) RootLabelingFC2Proof (SOUND transformation)

We used root labeling (second transformation) [ROOTLAB] with the following heuristic:
LabelAll: All function symbols get labeled

(68) Obligation:

Q DP problem:
The TRS P consists of the following rules:

U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{less_in_gg_2}(z0)), s_{less_in_gg_2}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{less_in_gg_2}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{less_in_gg_2}(z0)), s_{0}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{0}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{less_in_gg_2}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{s_1}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{less_in_gg_2}(z0)), s_{less_out_gg}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{less_out_gg}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{less_in_gg_2}(z0)), s_{U3_gg_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{U3_gg_1}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{0}(z0)), s_{less_in_gg_2}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{less_in_gg_2}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{0}(z0)), s_{0}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{0}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{0}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{s_1}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{0}(z0)), s_{less_out_gg}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{less_out_gg}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{0}(z0)), s_{U3_gg_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{U3_gg_1}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{s_1}(z0)), s_{less_in_gg_2}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{less_in_gg_2}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{s_1}(z0)), s_{0}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{0}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{s_1}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{s_1}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{s_1}(z0)), s_{less_out_gg}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{less_out_gg}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{s_1}(z0)), s_{U3_gg_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{U3_gg_1}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{less_out_gg}(z0)), s_{less_in_gg_2}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{less_in_gg_2}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{less_out_gg}(z0)), s_{0}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{0}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{less_out_gg}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{s_1}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{less_out_gg}(z0)), s_{less_out_gg}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{less_out_gg}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{less_out_gg}(z0)), s_{U3_gg_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{U3_gg_1}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{U3_gg_1}(z0)), s_{less_in_gg_2}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{less_in_gg_2}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{U3_gg_1}(z0)), s_{0}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{0}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{U3_gg_1}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{s_1}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{U3_gg_1}(z0)), s_{less_out_gg}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{less_out_gg}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{U3_gg_1}(z0)), s_{U3_gg_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{U3_gg_1}(z1))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{less_in_gg_2}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{less_in_gg_2}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(s_{s_1}(s_{less_in_gg_2}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{0}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{0}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(s_{s_1}(s_{less_in_gg_2}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{less_in_gg_2}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{less_out_gg}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{less_out_gg}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(s_{s_1}(s_{less_in_gg_2}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{U3_gg_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{U3_gg_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(s_{s_1}(s_{less_in_gg_2}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{less_in_gg_2}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{less_in_gg_2}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(s_{s_1}(s_{0}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{0}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{0}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(s_{s_1}(s_{0}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{0}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{less_out_gg}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{less_out_gg}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(s_{s_1}(s_{0}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{U3_gg_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{U3_gg_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(s_{s_1}(s_{0}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{less_in_gg_2}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{less_in_gg_2}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(s_{s_1}(s_{s_1}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{0}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{0}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(s_{s_1}(s_{s_1}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{s_1}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{less_out_gg}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{less_out_gg}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(s_{s_1}(s_{s_1}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{U3_gg_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{U3_gg_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(s_{s_1}(s_{s_1}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{less_in_gg_2}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{less_in_gg_2}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(s_{s_1}(s_{less_out_gg}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{0}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{0}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(s_{s_1}(s_{less_out_gg}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{less_out_gg}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{less_out_gg}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{less_out_gg}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(s_{s_1}(s_{less_out_gg}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{U3_gg_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{U3_gg_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(s_{s_1}(s_{less_out_gg}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{less_in_gg_2}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{less_in_gg_2}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(s_{s_1}(s_{U3_gg_1}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{0}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{0}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(s_{s_1}(s_{U3_gg_1}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{U3_gg_1}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{less_out_gg}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{less_out_gg}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(s_{s_1}(s_{U3_gg_1}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{U3_gg_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{U3_gg_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(s_{s_1}(s_{U3_gg_1}(z0)), z1)))
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_in_gg_2,0}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_in_gg_2,s_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,0,less_in_gg_2}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,0,0}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,0,0}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,0,s_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,0,s_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,0,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,0,less_out_gg}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,0,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,0,U3_gg_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,s_1,less_in_gg_2}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,s_1,0}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,s_1,0}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,s_1,s_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,s_1,s_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,s_1,less_out_gg}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,s_1,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,s_1,U3_gg_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,0}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_out_gg,0}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,s_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_out_gg,s_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_out_gg,less_out_gg}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,0}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,U3_gg_1,0}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,s_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,U3_gg_1,s_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_in_gg_2,0}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_in_gg_2,s_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,0,less_in_gg_2}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,0,0}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,0,0}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,0,s_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,0,s_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,0,less_out_gg}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,0,less_out_gg}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,0,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,0,U3_gg_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,s_1,less_in_gg_2}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,s_1,0}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,s_1,0}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,s_1,s_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,s_1,s_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_out_gg}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,s_1,less_out_gg}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,s_1,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,s_1,U3_gg_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,0}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_out_gg,0}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,s_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_out_gg,s_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_out_gg,less_out_gg}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,0}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,U3_gg_1,0}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,s_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,U3_gg_1,s_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_in_gg_2,0}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_in_gg_2,s_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,0,less_in_gg_2}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,0,0}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,0,0}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,0,s_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,0,s_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,0,less_out_gg}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,0,less_out_gg}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,0,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,0,U3_gg_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,s_1,less_in_gg_2}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,s_1,0}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,s_1,0}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,s_1,s_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,s_1,s_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_out_gg}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,s_1,less_out_gg}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,s_1,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,s_1,U3_gg_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,0}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_out_gg,0}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,s_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_out_gg,s_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_out_gg,less_out_gg}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,0}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,U3_gg_1,0}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,s_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,U3_gg_1,s_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_in_gg_2,0}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_in_gg_2,s_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,0,less_in_gg_2}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,0,0}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,0,0}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,0,s_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,0,s_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,0,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,0,less_out_gg}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,0,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,0,U3_gg_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,s_1,less_in_gg_2}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,s_1,0}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,s_1,0}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,s_1,s_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,s_1,s_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,s_1,less_out_gg}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,s_1,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,s_1,U3_gg_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,0}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_out_gg,0}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,s_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_out_gg,s_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_out_gg,less_out_gg}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,0}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,U3_gg_1,0}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,s_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,U3_gg_1,s_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_in_gg_2,0}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_in_gg_2,s_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,0,less_in_gg_2}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,0,0}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,0,0}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,0,s_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,0,s_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,0,less_out_gg}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,0,less_out_gg}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,0,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,0,U3_gg_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,s_1,less_in_gg_2}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,s_1,0}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,s_1,0}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,s_1,s_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,s_1,s_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_out_gg}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,s_1,less_out_gg}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,s_1,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,s_1,U3_gg_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,0}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_out_gg,0}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,s_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_out_gg,s_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_out_gg,less_out_gg}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,0}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,U3_gg_1,0}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,s_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,U3_gg_1,s_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1, flat2) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat2) → U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, less_out_gg, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat2) → U1_GG_{less_in_gg_2,less_out_gg,0}(flat0, less_out_gg, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat2) → U1_GG_{less_in_gg_2,less_out_gg,s_1}(flat0, less_out_gg, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat2) → U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(flat0, less_out_gg, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat2) → U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(flat0, less_out_gg, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat2) → U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, less_out_gg, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat2) → U1_GG_{less_in_gg_2,less_out_gg,0}(flat0, less_out_gg, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat2) → U1_GG_{less_in_gg_2,less_out_gg,s_1}(flat0, less_out_gg, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat2) → U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(flat0, less_out_gg, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat2) → U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(flat0, less_out_gg, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat2) → U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, less_out_gg, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat2) → U1_GG_{less_in_gg_2,less_out_gg,0}(flat0, less_out_gg, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat2) → U1_GG_{less_in_gg_2,less_out_gg,s_1}(flat0, less_out_gg, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat2) → U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(flat0, less_out_gg, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat2) → U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(flat0, less_out_gg, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat2) → U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, less_out_gg, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat2) → U1_GG_{less_in_gg_2,less_out_gg,0}(flat0, less_out_gg, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat2) → U1_GG_{less_in_gg_2,less_out_gg,s_1}(flat0, less_out_gg, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat2) → U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(flat0, less_out_gg, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat2) → U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(flat0, less_out_gg, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat2) → U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, less_out_gg, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat2) → U1_GG_{less_in_gg_2,less_out_gg,0}(flat0, less_out_gg, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat2) → U1_GG_{less_in_gg_2,less_out_gg,s_1}(flat0, less_out_gg, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat2) → U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(flat0, less_out_gg, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat2) → U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(flat0, less_out_gg, flat2)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat2) → U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, less_out_gg, flat2)
U1_GG_{0,less_in_gg_2,0}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat2) → U1_GG_{0,less_out_gg,0}(flat0, less_out_gg, flat2)
U1_GG_{0,less_in_gg_2,s_1}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat2) → U1_GG_{0,less_out_gg,s_1}(flat0, less_out_gg, flat2)
U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat2) → U1_GG_{0,less_out_gg,less_out_gg}(flat0, less_out_gg, flat2)
U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat2) → U1_GG_{0,less_out_gg,U3_gg_1}(flat0, less_out_gg, flat2)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat2) → U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, less_out_gg, flat2)
U1_GG_{0,less_in_gg_2,0}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat2) → U1_GG_{0,less_out_gg,0}(flat0, less_out_gg, flat2)
U1_GG_{0,less_in_gg_2,s_1}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat2) → U1_GG_{0,less_out_gg,s_1}(flat0, less_out_gg, flat2)
U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat2) → U1_GG_{0,less_out_gg,less_out_gg}(flat0, less_out_gg, flat2)
U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat2) → U1_GG_{0,less_out_gg,U3_gg_1}(flat0, less_out_gg, flat2)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat2) → U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, less_out_gg, flat2)
U1_GG_{0,less_in_gg_2,0}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat2) → U1_GG_{0,less_out_gg,0}(flat0, less_out_gg, flat2)
U1_GG_{0,less_in_gg_2,s_1}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat2) → U1_GG_{0,less_out_gg,s_1}(flat0, less_out_gg, flat2)
U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat2) → U1_GG_{0,less_out_gg,less_out_gg}(flat0, less_out_gg, flat2)
U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat2) → U1_GG_{0,less_out_gg,U3_gg_1}(flat0, less_out_gg, flat2)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat2) → U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, less_out_gg, flat2)
U1_GG_{0,less_in_gg_2,0}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat2) → U1_GG_{0,less_out_gg,0}(flat0, less_out_gg, flat2)
U1_GG_{0,less_in_gg_2,s_1}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat2) → U1_GG_{0,less_out_gg,s_1}(flat0, less_out_gg, flat2)
U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat2) → U1_GG_{0,less_out_gg,less_out_gg}(flat0, less_out_gg, flat2)
U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat2) → U1_GG_{0,less_out_gg,U3_gg_1}(flat0, less_out_gg, flat2)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat2) → U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, less_out_gg, flat2)
U1_GG_{0,less_in_gg_2,0}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat2) → U1_GG_{0,less_out_gg,0}(flat0, less_out_gg, flat2)
U1_GG_{0,less_in_gg_2,s_1}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat2) → U1_GG_{0,less_out_gg,s_1}(flat0, less_out_gg, flat2)
U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat2) → U1_GG_{0,less_out_gg,less_out_gg}(flat0, less_out_gg, flat2)
U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat2) → U1_GG_{0,less_out_gg,U3_gg_1}(flat0, less_out_gg, flat2)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat2) → U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, less_out_gg, flat2)
U1_GG_{s_1,less_in_gg_2,0}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat2) → U1_GG_{s_1,less_out_gg,0}(flat0, less_out_gg, flat2)
U1_GG_{s_1,less_in_gg_2,s_1}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat2) → U1_GG_{s_1,less_out_gg,s_1}(flat0, less_out_gg, flat2)
U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat2) → U1_GG_{s_1,less_out_gg,less_out_gg}(flat0, less_out_gg, flat2)
U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat2) → U1_GG_{s_1,less_out_gg,U3_gg_1}(flat0, less_out_gg, flat2)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat2) → U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, less_out_gg, flat2)
U1_GG_{s_1,less_in_gg_2,0}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat2) → U1_GG_{s_1,less_out_gg,0}(flat0, less_out_gg, flat2)
U1_GG_{s_1,less_in_gg_2,s_1}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat2) → U1_GG_{s_1,less_out_gg,s_1}(flat0, less_out_gg, flat2)
U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat2) → U1_GG_{s_1,less_out_gg,less_out_gg}(flat0, less_out_gg, flat2)
U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat2) → U1_GG_{s_1,less_out_gg,U3_gg_1}(flat0, less_out_gg, flat2)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat2) → U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, less_out_gg, flat2)
U1_GG_{s_1,less_in_gg_2,0}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat2) → U1_GG_{s_1,less_out_gg,0}(flat0, less_out_gg, flat2)
U1_GG_{s_1,less_in_gg_2,s_1}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat2) → U1_GG_{s_1,less_out_gg,s_1}(flat0, less_out_gg, flat2)
U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat2) → U1_GG_{s_1,less_out_gg,less_out_gg}(flat0, less_out_gg, flat2)
U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat2) → U1_GG_{s_1,less_out_gg,U3_gg_1}(flat0, less_out_gg, flat2)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat2) → U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, less_out_gg, flat2)
U1_GG_{s_1,less_in_gg_2,0}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat2) → U1_GG_{s_1,less_out_gg,0}(flat0, less_out_gg, flat2)
U1_GG_{s_1,less_in_gg_2,s_1}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat2) → U1_GG_{s_1,less_out_gg,s_1}(flat0, less_out_gg, flat2)
U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat2) → U1_GG_{s_1,less_out_gg,less_out_gg}(flat0, less_out_gg, flat2)
U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat2) → U1_GG_{s_1,less_out_gg,U3_gg_1}(flat0, less_out_gg, flat2)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat2) → U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, less_out_gg, flat2)
U1_GG_{s_1,less_in_gg_2,0}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat2) → U1_GG_{s_1,less_out_gg,0}(flat0, less_out_gg, flat2)
U1_GG_{s_1,less_in_gg_2,s_1}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat2) → U1_GG_{s_1,less_out_gg,s_1}(flat0, less_out_gg, flat2)
U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat2) → U1_GG_{s_1,less_out_gg,less_out_gg}(flat0, less_out_gg, flat2)
U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat2) → U1_GG_{s_1,less_out_gg,U3_gg_1}(flat0, less_out_gg, flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat2) → U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, less_out_gg, flat2)
U1_GG_{less_out_gg,less_in_gg_2,0}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat2) → U1_GG_{less_out_gg,less_out_gg,0}(flat0, less_out_gg, flat2)
U1_GG_{less_out_gg,less_in_gg_2,s_1}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat2) → U1_GG_{less_out_gg,less_out_gg,s_1}(flat0, less_out_gg, flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat2) → U1_GG_{less_out_gg,less_out_gg,less_out_gg}(flat0, less_out_gg, flat2)
U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat2) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(flat0, less_out_gg, flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat2) → U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, less_out_gg, flat2)
U1_GG_{less_out_gg,less_in_gg_2,0}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat2) → U1_GG_{less_out_gg,less_out_gg,0}(flat0, less_out_gg, flat2)
U1_GG_{less_out_gg,less_in_gg_2,s_1}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat2) → U1_GG_{less_out_gg,less_out_gg,s_1}(flat0, less_out_gg, flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat2) → U1_GG_{less_out_gg,less_out_gg,less_out_gg}(flat0, less_out_gg, flat2)
U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat2) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(flat0, less_out_gg, flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat2) → U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, less_out_gg, flat2)
U1_GG_{less_out_gg,less_in_gg_2,0}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat2) → U1_GG_{less_out_gg,less_out_gg,0}(flat0, less_out_gg, flat2)
U1_GG_{less_out_gg,less_in_gg_2,s_1}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat2) → U1_GG_{less_out_gg,less_out_gg,s_1}(flat0, less_out_gg, flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat2) → U1_GG_{less_out_gg,less_out_gg,less_out_gg}(flat0, less_out_gg, flat2)
U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat2) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(flat0, less_out_gg, flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat2) → U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, less_out_gg, flat2)
U1_GG_{less_out_gg,less_in_gg_2,0}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat2) → U1_GG_{less_out_gg,less_out_gg,0}(flat0, less_out_gg, flat2)
U1_GG_{less_out_gg,less_in_gg_2,s_1}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat2) → U1_GG_{less_out_gg,less_out_gg,s_1}(flat0, less_out_gg, flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat2) → U1_GG_{less_out_gg,less_out_gg,less_out_gg}(flat0, less_out_gg, flat2)
U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat2) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(flat0, less_out_gg, flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat2) → U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, less_out_gg, flat2)
U1_GG_{less_out_gg,less_in_gg_2,0}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat2) → U1_GG_{less_out_gg,less_out_gg,0}(flat0, less_out_gg, flat2)
U1_GG_{less_out_gg,less_in_gg_2,s_1}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat2) → U1_GG_{less_out_gg,less_out_gg,s_1}(flat0, less_out_gg, flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat2) → U1_GG_{less_out_gg,less_out_gg,less_out_gg}(flat0, less_out_gg, flat2)
U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat2) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(flat0, less_out_gg, flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat2) → U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, less_out_gg, flat2)
U1_GG_{U3_gg_1,less_in_gg_2,0}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat2) → U1_GG_{U3_gg_1,less_out_gg,0}(flat0, less_out_gg, flat2)
U1_GG_{U3_gg_1,less_in_gg_2,s_1}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat2) → U1_GG_{U3_gg_1,less_out_gg,s_1}(flat0, less_out_gg, flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat2) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(flat0, less_out_gg, flat2)
U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat2) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(flat0, less_out_gg, flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat2) → U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, less_out_gg, flat2)
U1_GG_{U3_gg_1,less_in_gg_2,0}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat2) → U1_GG_{U3_gg_1,less_out_gg,0}(flat0, less_out_gg, flat2)
U1_GG_{U3_gg_1,less_in_gg_2,s_1}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat2) → U1_GG_{U3_gg_1,less_out_gg,s_1}(flat0, less_out_gg, flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat2) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(flat0, less_out_gg, flat2)
U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat2) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(flat0, less_out_gg, flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat2) → U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, less_out_gg, flat2)
U1_GG_{U3_gg_1,less_in_gg_2,0}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat2) → U1_GG_{U3_gg_1,less_out_gg,0}(flat0, less_out_gg, flat2)
U1_GG_{U3_gg_1,less_in_gg_2,s_1}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat2) → U1_GG_{U3_gg_1,less_out_gg,s_1}(flat0, less_out_gg, flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat2) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(flat0, less_out_gg, flat2)
U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat2) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(flat0, less_out_gg, flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat2) → U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, less_out_gg, flat2)
U1_GG_{U3_gg_1,less_in_gg_2,0}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat2) → U1_GG_{U3_gg_1,less_out_gg,0}(flat0, less_out_gg, flat2)
U1_GG_{U3_gg_1,less_in_gg_2,s_1}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat2) → U1_GG_{U3_gg_1,less_out_gg,s_1}(flat0, less_out_gg, flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat2) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(flat0, less_out_gg, flat2)
U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat2) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(flat0, less_out_gg, flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat2) → U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, less_out_gg, flat2)
U1_GG_{U3_gg_1,less_in_gg_2,0}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat2) → U1_GG_{U3_gg_1,less_out_gg,0}(flat0, less_out_gg, flat2)
U1_GG_{U3_gg_1,less_in_gg_2,s_1}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat2) → U1_GG_{U3_gg_1,less_out_gg,s_1}(flat0, less_out_gg, flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat2) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(flat0, less_out_gg, flat2)
U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat2) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(flat0, less_out_gg, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U1_GG_{less_in_gg_2,0,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U1_GG_{less_in_gg_2,0,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U1_GG_{less_in_gg_2,0,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U1_GG_{less_in_gg_2,0,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U1_GG_{less_in_gg_2,0,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U1_GG_{less_in_gg_2,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U1_GG_{less_in_gg_2,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U1_GG_{less_in_gg_2,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U1_GG_{less_in_gg_2,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U1_GG_{less_in_gg_2,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{0,0,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U1_GG_{0,0,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{0,0,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U1_GG_{0,0,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{0,0,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U1_GG_{0,0,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{0,0,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U1_GG_{0,0,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{0,0,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U1_GG_{0,0,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{0,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U1_GG_{0,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{0,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U1_GG_{0,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{0,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U1_GG_{0,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{0,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U1_GG_{0,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{0,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U1_GG_{0,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U1_GG_{0,less_out_gg,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U1_GG_{0,less_out_gg,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U1_GG_{0,less_out_gg,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U1_GG_{0,less_out_gg,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U1_GG_{0,less_out_gg,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U1_GG_{0,U3_gg_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U1_GG_{0,U3_gg_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U1_GG_{0,U3_gg_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U1_GG_{0,U3_gg_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U1_GG_{0,U3_gg_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U1_GG_{s_1,0,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U1_GG_{s_1,0,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U1_GG_{s_1,0,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U1_GG_{s_1,0,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U1_GG_{s_1,0,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U1_GG_{s_1,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U1_GG_{s_1,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U1_GG_{s_1,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U1_GG_{s_1,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U1_GG_{s_1,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U1_GG_{s_1,less_out_gg,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U1_GG_{s_1,less_out_gg,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U1_GG_{s_1,less_out_gg,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U1_GG_{s_1,less_out_gg,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U1_GG_{s_1,less_out_gg,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U1_GG_{s_1,U3_gg_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U1_GG_{s_1,U3_gg_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U1_GG_{s_1,U3_gg_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U1_GG_{s_1,U3_gg_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U1_GG_{s_1,U3_gg_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_out_gg,0,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U1_GG_{less_out_gg,0,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_out_gg,0,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U1_GG_{less_out_gg,0,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_out_gg,0,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U1_GG_{less_out_gg,0,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_out_gg,0,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U1_GG_{less_out_gg,0,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_out_gg,0,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U1_GG_{less_out_gg,0,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_out_gg,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U1_GG_{less_out_gg,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_out_gg,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U1_GG_{less_out_gg,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_out_gg,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U1_GG_{less_out_gg,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_out_gg,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U1_GG_{less_out_gg,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_out_gg,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U1_GG_{less_out_gg,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U1_GG_{less_out_gg,less_out_gg,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U1_GG_{less_out_gg,less_out_gg,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U1_GG_{less_out_gg,less_out_gg,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U1_GG_{less_out_gg,less_out_gg,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U1_GG_{less_out_gg,less_out_gg,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{U3_gg_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U1_GG_{U3_gg_1,0,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{U3_gg_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U1_GG_{U3_gg_1,0,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{U3_gg_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U1_GG_{U3_gg_1,0,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{U3_gg_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U1_GG_{U3_gg_1,0,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{U3_gg_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U1_GG_{U3_gg_1,0,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{U3_gg_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U1_GG_{U3_gg_1,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{U3_gg_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U1_GG_{U3_gg_1,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{U3_gg_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U1_GG_{U3_gg_1,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{U3_gg_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U1_GG_{U3_gg_1,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{U3_gg_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U1_GG_{U3_gg_1,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(flat0, flat1, less_out_gg)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → P_IN_GG_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
P_IN_GG_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → P_IN_GG_{less_out_gg,0}(less_out_gg, flat1)
P_IN_GG_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → P_IN_GG_{less_out_gg,s_1}(less_out_gg, flat1)
P_IN_GG_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → P_IN_GG_{less_out_gg,less_out_gg}(less_out_gg, flat1)
P_IN_GG_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → P_IN_GG_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → P_IN_GG_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
P_IN_GG_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → P_IN_GG_{less_out_gg,0}(less_out_gg, flat1)
P_IN_GG_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → P_IN_GG_{less_out_gg,s_1}(less_out_gg, flat1)
P_IN_GG_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → P_IN_GG_{less_out_gg,less_out_gg}(less_out_gg, flat1)
P_IN_GG_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → P_IN_GG_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → P_IN_GG_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
P_IN_GG_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → P_IN_GG_{less_out_gg,0}(less_out_gg, flat1)
P_IN_GG_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → P_IN_GG_{less_out_gg,s_1}(less_out_gg, flat1)
P_IN_GG_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → P_IN_GG_{less_out_gg,less_out_gg}(less_out_gg, flat1)
P_IN_GG_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → P_IN_GG_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → P_IN_GG_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
P_IN_GG_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → P_IN_GG_{less_out_gg,0}(less_out_gg, flat1)
P_IN_GG_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → P_IN_GG_{less_out_gg,s_1}(less_out_gg, flat1)
P_IN_GG_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → P_IN_GG_{less_out_gg,less_out_gg}(less_out_gg, flat1)
P_IN_GG_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → P_IN_GG_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → P_IN_GG_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
P_IN_GG_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → P_IN_GG_{less_out_gg,0}(less_out_gg, flat1)
P_IN_GG_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → P_IN_GG_{less_out_gg,s_1}(less_out_gg, flat1)
P_IN_GG_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → P_IN_GG_{less_out_gg,less_out_gg}(less_out_gg, flat1)
P_IN_GG_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → P_IN_GG_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → P_IN_GG_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → P_IN_GG_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → P_IN_GG_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → P_IN_GG_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → P_IN_GG_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
P_IN_GG_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → P_IN_GG_{0,less_out_gg}(flat0, less_out_gg)
P_IN_GG_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → P_IN_GG_{0,less_out_gg}(flat0, less_out_gg)
P_IN_GG_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → P_IN_GG_{0,less_out_gg}(flat0, less_out_gg)
P_IN_GG_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → P_IN_GG_{0,less_out_gg}(flat0, less_out_gg)
P_IN_GG_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → P_IN_GG_{0,less_out_gg}(flat0, less_out_gg)
P_IN_GG_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → P_IN_GG_{s_1,less_out_gg}(flat0, less_out_gg)
P_IN_GG_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → P_IN_GG_{s_1,less_out_gg}(flat0, less_out_gg)
P_IN_GG_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → P_IN_GG_{s_1,less_out_gg}(flat0, less_out_gg)
P_IN_GG_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → P_IN_GG_{s_1,less_out_gg}(flat0, less_out_gg)
P_IN_GG_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → P_IN_GG_{s_1,less_out_gg}(flat0, less_out_gg)
P_IN_GG_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → P_IN_GG_{less_out_gg,less_out_gg}(flat0, less_out_gg)
P_IN_GG_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → P_IN_GG_{less_out_gg,less_out_gg}(flat0, less_out_gg)
P_IN_GG_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → P_IN_GG_{less_out_gg,less_out_gg}(flat0, less_out_gg)
P_IN_GG_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → P_IN_GG_{less_out_gg,less_out_gg}(flat0, less_out_gg)
P_IN_GG_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → P_IN_GG_{less_out_gg,less_out_gg}(flat0, less_out_gg)
P_IN_GG_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → P_IN_GG_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
P_IN_GG_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → P_IN_GG_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
P_IN_GG_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → P_IN_GG_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
P_IN_GG_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → P_IN_GG_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
P_IN_GG_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → P_IN_GG_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,0,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,0,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,s_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1, flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{0,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{0,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat2) → U1_GG_{0,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat2) → U1_GG_{0,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat2) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{0,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{0,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{0,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{0,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat2) → U1_GG_{0,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat2) → U1_GG_{0,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat2) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{0,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{0,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{0,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{0,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{0,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{0,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{0,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{0,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{0,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{0,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat2) → U1_GG_{0,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat2) → U1_GG_{0,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat2) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{0,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{0,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{0,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{0,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{0,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{0,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{0,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{0,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,0}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,0}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,s_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,s_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat2) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_in_gg_2,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_in_gg_2,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U1_GG_{less_in_gg_2,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U1_GG_{less_in_gg_2,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U1_GG_{less_in_gg_2,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_in_gg_2,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U1_GG_{less_in_gg_2,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_in_gg_2,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_in_gg_2,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_in_gg_2,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U1_GG_{less_in_gg_2,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U1_GG_{less_in_gg_2,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U1_GG_{less_in_gg_2,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_in_gg_2,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U1_GG_{less_in_gg_2,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_in_gg_2,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_in_gg_2,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_in_gg_2,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U1_GG_{less_in_gg_2,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U1_GG_{less_in_gg_2,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U1_GG_{less_in_gg_2,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_in_gg_2,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U1_GG_{less_in_gg_2,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_in_gg_2,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_in_gg_2,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_in_gg_2,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U1_GG_{less_in_gg_2,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U1_GG_{less_in_gg_2,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U1_GG_{less_in_gg_2,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_in_gg_2,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U1_GG_{less_in_gg_2,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_in_gg_2,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_in_gg_2,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_in_gg_2,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U1_GG_{less_in_gg_2,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U1_GG_{less_in_gg_2,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U1_GG_{less_in_gg_2,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_in_gg_2,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U1_GG_{less_in_gg_2,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_in_gg_2,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_in_gg_2,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U1_GG_{less_in_gg_2,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U1_GG_{less_in_gg_2,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_in_gg_2,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_in_gg_2,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_in_gg_2,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U1_GG_{less_in_gg_2,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U1_GG_{less_in_gg_2,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_in_gg_2,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_in_gg_2,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_in_gg_2,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U1_GG_{less_in_gg_2,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U1_GG_{less_in_gg_2,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_in_gg_2,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_in_gg_2,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_in_gg_2,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U1_GG_{less_in_gg_2,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U1_GG_{less_in_gg_2,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_in_gg_2,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_in_gg_2,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_in_gg_2,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U1_GG_{less_in_gg_2,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U1_GG_{less_in_gg_2,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_in_gg_2,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U1_GG_{less_in_gg_2,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_in_gg_2,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U1_GG_{0,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U1_GG_{0,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{0,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U1_GG_{0,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U1_GG_{0,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U1_GG_{0,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U1_GG_{0,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U1_GG_{0,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{0,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U1_GG_{0,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{0,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U1_GG_{0,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{0,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U1_GG_{0,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U1_GG_{0,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U1_GG_{0,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U1_GG_{0,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U1_GG_{0,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{0,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U1_GG_{0,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{0,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U1_GG_{0,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{0,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{0,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U1_GG_{0,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U1_GG_{0,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U1_GG_{0,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U1_GG_{0,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{0,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U1_GG_{0,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{0,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U1_GG_{0,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{0,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U1_GG_{0,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U1_GG_{0,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U1_GG_{0,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U1_GG_{0,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U1_GG_{0,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{0,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U1_GG_{0,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{0,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U1_GG_{0,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{0,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{0,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U1_GG_{0,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U1_GG_{0,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U1_GG_{0,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U1_GG_{0,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{0,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U1_GG_{0,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{0,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U1_GG_{0,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{0,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U1_GG_{0,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U1_GG_{0,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U1_GG_{0,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U1_GG_{0,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U1_GG_{0,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{0,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U1_GG_{0,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{0,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U1_GG_{0,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{0,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U1_GG_{0,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U1_GG_{0,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U1_GG_{0,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U1_GG_{0,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U1_GG_{0,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{0,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U1_GG_{0,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{0,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U1_GG_{0,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{0,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{0,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U1_GG_{0,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U1_GG_{0,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U1_GG_{0,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U1_GG_{0,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{0,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U1_GG_{0,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{0,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U1_GG_{0,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{0,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U1_GG_{0,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U1_GG_{0,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U1_GG_{0,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U1_GG_{0,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U1_GG_{0,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{0,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U1_GG_{0,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{0,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U1_GG_{0,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{0,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{0,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U1_GG_{0,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U1_GG_{0,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U1_GG_{0,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U1_GG_{0,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{0,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U1_GG_{0,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{0,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{0,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U1_GG_{0,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U1_GG_{0,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{0,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{0,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{0,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U1_GG_{0,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U1_GG_{0,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{0,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{0,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{0,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U1_GG_{0,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U1_GG_{0,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{0,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{0,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{0,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U1_GG_{0,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U1_GG_{0,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{0,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{0,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{0,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U1_GG_{0,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U1_GG_{0,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{0,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{0,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U1_GG_{s_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U1_GG_{s_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{s_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U1_GG_{s_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U1_GG_{s_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U1_GG_{s_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U1_GG_{s_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U1_GG_{s_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{s_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U1_GG_{s_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{s_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U1_GG_{s_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{s_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U1_GG_{s_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U1_GG_{s_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U1_GG_{s_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U1_GG_{s_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U1_GG_{s_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{s_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U1_GG_{s_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{s_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U1_GG_{s_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{s_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{s_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U1_GG_{s_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U1_GG_{s_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U1_GG_{s_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U1_GG_{s_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{s_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U1_GG_{s_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{s_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U1_GG_{s_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{s_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U1_GG_{s_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U1_GG_{s_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U1_GG_{s_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U1_GG_{s_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U1_GG_{s_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{s_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U1_GG_{s_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{s_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U1_GG_{s_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{s_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{s_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U1_GG_{s_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U1_GG_{s_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U1_GG_{s_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U1_GG_{s_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{s_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U1_GG_{s_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{s_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U1_GG_{s_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U1_GG_{s_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U1_GG_{s_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U1_GG_{s_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U1_GG_{s_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U1_GG_{s_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U1_GG_{s_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U1_GG_{s_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U1_GG_{s_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U1_GG_{s_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U1_GG_{s_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{s_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U1_GG_{s_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U1_GG_{s_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U1_GG_{s_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U1_GG_{s_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U1_GG_{s_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U1_GG_{s_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U1_GG_{s_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U1_GG_{s_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U1_GG_{s_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{s_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U1_GG_{s_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U1_GG_{s_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U1_GG_{s_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{s_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U1_GG_{s_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U1_GG_{s_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{s_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{s_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{s_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U1_GG_{s_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U1_GG_{s_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{s_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{s_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{s_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U1_GG_{s_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U1_GG_{s_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{s_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{s_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{s_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U1_GG_{s_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U1_GG_{s_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{s_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{s_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{s_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U1_GG_{s_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U1_GG_{s_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{s_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{s_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U1_GG_{less_out_gg,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_out_gg,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_out_gg,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U1_GG_{less_out_gg,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U1_GG_{less_out_gg,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U1_GG_{less_out_gg,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U1_GG_{less_out_gg,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_out_gg,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U1_GG_{less_out_gg,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_out_gg,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U1_GG_{less_out_gg,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_out_gg,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_out_gg,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U1_GG_{less_out_gg,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U1_GG_{less_out_gg,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U1_GG_{less_out_gg,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U1_GG_{less_out_gg,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_out_gg,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U1_GG_{less_out_gg,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_out_gg,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U1_GG_{less_out_gg,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_out_gg,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_out_gg,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U1_GG_{less_out_gg,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U1_GG_{less_out_gg,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U1_GG_{less_out_gg,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U1_GG_{less_out_gg,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_out_gg,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U1_GG_{less_out_gg,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_out_gg,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U1_GG_{less_out_gg,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_out_gg,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_out_gg,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U1_GG_{less_out_gg,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U1_GG_{less_out_gg,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U1_GG_{less_out_gg,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U1_GG_{less_out_gg,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_out_gg,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U1_GG_{less_out_gg,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_out_gg,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U1_GG_{less_out_gg,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_out_gg,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_out_gg,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U1_GG_{less_out_gg,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U1_GG_{less_out_gg,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U1_GG_{less_out_gg,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U1_GG_{less_out_gg,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_out_gg,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U1_GG_{less_out_gg,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_out_gg,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U1_GG_{less_out_gg,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_out_gg,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_out_gg,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U1_GG_{less_out_gg,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U1_GG_{less_out_gg,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U1_GG_{less_out_gg,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U1_GG_{less_out_gg,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_out_gg,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U1_GG_{less_out_gg,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_out_gg,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U1_GG_{less_out_gg,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_out_gg,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_out_gg,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U1_GG_{less_out_gg,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U1_GG_{less_out_gg,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U1_GG_{less_out_gg,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U1_GG_{less_out_gg,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_out_gg,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U1_GG_{less_out_gg,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_out_gg,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U1_GG_{less_out_gg,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_out_gg,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_out_gg,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U1_GG_{less_out_gg,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U1_GG_{less_out_gg,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U1_GG_{less_out_gg,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U1_GG_{less_out_gg,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_out_gg,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U1_GG_{less_out_gg,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_out_gg,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U1_GG_{less_out_gg,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_out_gg,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_out_gg,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U1_GG_{less_out_gg,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U1_GG_{less_out_gg,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U1_GG_{less_out_gg,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U1_GG_{less_out_gg,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_out_gg,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U1_GG_{less_out_gg,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_out_gg,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U1_GG_{less_out_gg,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_out_gg,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_out_gg,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U1_GG_{less_out_gg,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U1_GG_{less_out_gg,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U1_GG_{less_out_gg,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U1_GG_{less_out_gg,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_out_gg,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U1_GG_{less_out_gg,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_out_gg,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U1_GG_{U3_gg_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{U3_gg_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U1_GG_{U3_gg_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U1_GG_{U3_gg_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U1_GG_{U3_gg_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U1_GG_{U3_gg_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U1_GG_{U3_gg_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{U3_gg_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U1_GG_{U3_gg_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{U3_gg_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U1_GG_{U3_gg_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{U3_gg_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U1_GG_{U3_gg_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U1_GG_{U3_gg_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U1_GG_{U3_gg_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U1_GG_{U3_gg_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U1_GG_{U3_gg_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{U3_gg_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U1_GG_{U3_gg_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{U3_gg_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U1_GG_{U3_gg_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{U3_gg_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{U3_gg_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U1_GG_{U3_gg_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U1_GG_{U3_gg_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U1_GG_{U3_gg_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U1_GG_{U3_gg_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{U3_gg_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U1_GG_{U3_gg_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{U3_gg_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U1_GG_{U3_gg_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{U3_gg_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U1_GG_{U3_gg_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U1_GG_{U3_gg_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U1_GG_{U3_gg_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U1_GG_{U3_gg_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U1_GG_{U3_gg_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{U3_gg_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U1_GG_{U3_gg_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{U3_gg_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U1_GG_{U3_gg_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{U3_gg_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{U3_gg_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U1_GG_{U3_gg_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U1_GG_{U3_gg_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U1_GG_{U3_gg_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U1_GG_{U3_gg_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{U3_gg_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U1_GG_{U3_gg_1,0,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{U3_gg_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U1_GG_{U3_gg_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U1_GG_{U3_gg_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U1_GG_{U3_gg_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U1_GG_{U3_gg_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U1_GG_{U3_gg_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U1_GG_{U3_gg_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U1_GG_{U3_gg_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U1_GG_{U3_gg_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U1_GG_{U3_gg_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U1_GG_{U3_gg_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U1_GG_{U3_gg_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{U3_gg_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U1_GG_{U3_gg_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U1_GG_{U3_gg_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U1_GG_{U3_gg_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U1_GG_{U3_gg_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U1_GG_{U3_gg_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U1_GG_{U3_gg_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U1_GG_{U3_gg_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U1_GG_{U3_gg_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U1_GG_{U3_gg_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{U3_gg_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U1_GG_{U3_gg_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U1_GG_{U3_gg_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U1_GG_{U3_gg_1,s_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{U3_gg_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, flat1, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
P_IN_GG_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → P_IN_GG_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → P_IN_GG_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → P_IN_GG_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → P_IN_GG_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → P_IN_GG_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → P_IN_GG_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → P_IN_GG_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → P_IN_GG_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → P_IN_GG_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → P_IN_GG_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → P_IN_GG_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → P_IN_GG_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → P_IN_GG_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → P_IN_GG_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → P_IN_GG_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → P_IN_GG_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → P_IN_GG_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → P_IN_GG_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → P_IN_GG_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → P_IN_GG_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → P_IN_GG_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → P_IN_GG_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → P_IN_GG_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → P_IN_GG_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → P_IN_GG_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → P_IN_GG_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → P_IN_GG_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → P_IN_GG_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → P_IN_GG_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → P_IN_GG_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → P_IN_GG_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → P_IN_GG_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → P_IN_GG_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → P_IN_GG_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → P_IN_GG_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → P_IN_GG_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → P_IN_GG_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → P_IN_GG_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → P_IN_GG_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → P_IN_GG_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → P_IN_GG_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → P_IN_GG_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → P_IN_GG_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → P_IN_GG_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → P_IN_GG_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → P_IN_GG_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
P_IN_GG_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → P_IN_GG_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
P_IN_GG_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → P_IN_GG_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
P_IN_GG_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → P_IN_GG_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
P_IN_GG_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → P_IN_GG_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
P_IN_GG_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → P_IN_GG_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
P_IN_GG_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → P_IN_GG_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
P_IN_GG_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → P_IN_GG_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
P_IN_GG_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → P_IN_GG_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
P_IN_GG_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → P_IN_GG_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
P_IN_GG_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → P_IN_GG_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
P_IN_GG_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → P_IN_GG_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
P_IN_GG_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → P_IN_GG_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
P_IN_GG_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → P_IN_GG_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
P_IN_GG_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → P_IN_GG_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
P_IN_GG_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → P_IN_GG_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
P_IN_GG_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → P_IN_GG_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
P_IN_GG_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → P_IN_GG_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
P_IN_GG_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → P_IN_GG_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
P_IN_GG_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → P_IN_GG_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
P_IN_GG_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → P_IN_GG_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
P_IN_GG_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → P_IN_GG_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
P_IN_GG_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → P_IN_GG_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
P_IN_GG_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → P_IN_GG_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
P_IN_GG_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → P_IN_GG_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
P_IN_GG_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → P_IN_GG_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
P_IN_GG_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → P_IN_GG_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
P_IN_GG_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → P_IN_GG_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
P_IN_GG_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → P_IN_GG_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
P_IN_GG_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → P_IN_GG_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
P_IN_GG_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → P_IN_GG_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
P_IN_GG_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → P_IN_GG_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
P_IN_GG_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → P_IN_GG_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
P_IN_GG_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → P_IN_GG_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
P_IN_GG_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → P_IN_GG_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
P_IN_GG_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → P_IN_GG_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
P_IN_GG_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → P_IN_GG_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
P_IN_GG_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → P_IN_GG_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
P_IN_GG_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → P_IN_GG_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
P_IN_GG_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → P_IN_GG_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
P_IN_GG_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → P_IN_GG_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
P_IN_GG_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → P_IN_GG_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
P_IN_GG_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → P_IN_GG_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
P_IN_GG_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → P_IN_GG_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
P_IN_GG_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → P_IN_GG_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
P_IN_GG_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → P_IN_GG_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
P_IN_GG_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → P_IN_GG_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
P_IN_GG_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → P_IN_GG_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
P_IN_GG_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → P_IN_GG_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
P_IN_GG_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → P_IN_GG_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
P_IN_GG_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → P_IN_GG_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
P_IN_GG_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → P_IN_GG_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
P_IN_GG_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → P_IN_GG_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
P_IN_GG_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → P_IN_GG_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
P_IN_GG_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → P_IN_GG_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
P_IN_GG_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → P_IN_GG_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
P_IN_GG_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → P_IN_GG_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
P_IN_GG_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → P_IN_GG_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
P_IN_GG_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → P_IN_GG_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
P_IN_GG_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → P_IN_GG_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
P_IN_GG_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → P_IN_GG_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
P_IN_GG_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → P_IN_GG_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
P_IN_GG_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → P_IN_GG_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
P_IN_GG_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → P_IN_GG_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
P_IN_GG_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → P_IN_GG_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
P_IN_GG_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → P_IN_GG_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
P_IN_GG_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → P_IN_GG_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
P_IN_GG_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → P_IN_GG_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
P_IN_GG_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → P_IN_GG_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
P_IN_GG_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → P_IN_GG_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
P_IN_GG_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → P_IN_GG_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
P_IN_GG_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → P_IN_GG_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
P_IN_GG_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → P_IN_GG_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
P_IN_GG_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → P_IN_GG_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
P_IN_GG_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → P_IN_GG_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
P_IN_GG_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → P_IN_GG_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
P_IN_GG_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → P_IN_GG_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
P_IN_GG_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → P_IN_GG_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
P_IN_GG_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → P_IN_GG_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
P_IN_GG_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → P_IN_GG_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
P_IN_GG_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → P_IN_GG_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
P_IN_GG_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → P_IN_GG_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
P_IN_GG_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → P_IN_GG_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
P_IN_GG_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → P_IN_GG_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
P_IN_GG_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → P_IN_GG_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
P_IN_GG_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → P_IN_GG_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
P_IN_GG_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → P_IN_GG_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
P_IN_GG_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → P_IN_GG_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
P_IN_GG_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → P_IN_GG_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
P_IN_GG_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → P_IN_GG_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
P_IN_GG_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → P_IN_GG_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
P_IN_GG_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → P_IN_GG_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
P_IN_GG_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → P_IN_GG_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
P_IN_GG_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → P_IN_GG_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
P_IN_GG_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → P_IN_GG_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
P_IN_GG_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → P_IN_GG_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
P_IN_GG_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → P_IN_GG_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
P_IN_GG_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → P_IN_GG_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
P_IN_GG_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → P_IN_GG_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
P_IN_GG_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → P_IN_GG_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
P_IN_GG_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → P_IN_GG_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
P_IN_GG_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → P_IN_GG_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
P_IN_GG_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → P_IN_GG_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
P_IN_GG_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → P_IN_GG_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
P_IN_GG_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → P_IN_GG_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
P_IN_GG_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → P_IN_GG_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
P_IN_GG_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → P_IN_GG_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
P_IN_GG_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → P_IN_GG_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
P_IN_GG_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → P_IN_GG_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
P_IN_GG_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → P_IN_GG_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
P_IN_GG_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → P_IN_GG_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
P_IN_GG_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → P_IN_GG_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
P_IN_GG_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → P_IN_GG_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
P_IN_GG_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → P_IN_GG_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
P_IN_GG_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → P_IN_GG_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
P_IN_GG_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → P_IN_GG_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
P_IN_GG_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → P_IN_GG_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
P_IN_GG_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → P_IN_GG_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
P_IN_GG_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → P_IN_GG_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
P_IN_GG_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → P_IN_GG_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
P_IN_GG_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → P_IN_GG_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
P_IN_GG_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → P_IN_GG_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
P_IN_GG_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → P_IN_GG_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
P_IN_GG_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → P_IN_GG_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
P_IN_GG_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → P_IN_GG_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
P_IN_GG_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → P_IN_GG_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U1_GG_{U3_gg_1,less_in_gg_2,less_in_gg_2}(U3_gg_{less_out_gg}(less_out_gg), flat1, flat2) → U1_GG_{less_out_gg,less_in_gg_2,less_in_gg_2}(less_out_gg, flat1, flat2)
U1_GG_{U3_gg_1,less_in_gg_2,0}(U3_gg_{less_out_gg}(less_out_gg), flat1, flat2) → U1_GG_{less_out_gg,less_in_gg_2,0}(less_out_gg, flat1, flat2)
U1_GG_{U3_gg_1,less_in_gg_2,s_1}(U3_gg_{less_out_gg}(less_out_gg), flat1, flat2) → U1_GG_{less_out_gg,less_in_gg_2,s_1}(less_out_gg, flat1, flat2)
U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(U3_gg_{less_out_gg}(less_out_gg), flat1, flat2) → U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(less_out_gg, flat1, flat2)
U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg), flat1, flat2) → U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(less_out_gg, flat1, flat2)
U1_GG_{U3_gg_1,0,less_in_gg_2}(U3_gg_{less_out_gg}(less_out_gg), flat1, flat2) → U1_GG_{less_out_gg,0,less_in_gg_2}(less_out_gg, flat1, flat2)
U1_GG_{U3_gg_1,0,0}(U3_gg_{less_out_gg}(less_out_gg), flat1, flat2) → U1_GG_{less_out_gg,0,0}(less_out_gg, flat1, flat2)
U1_GG_{U3_gg_1,0,s_1}(U3_gg_{less_out_gg}(less_out_gg), flat1, flat2) → U1_GG_{less_out_gg,0,s_1}(less_out_gg, flat1, flat2)
U1_GG_{U3_gg_1,0,less_out_gg}(U3_gg_{less_out_gg}(less_out_gg), flat1, flat2) → U1_GG_{less_out_gg,0,less_out_gg}(less_out_gg, flat1, flat2)
U1_GG_{U3_gg_1,0,U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg), flat1, flat2) → U1_GG_{less_out_gg,0,U3_gg_1}(less_out_gg, flat1, flat2)
U1_GG_{U3_gg_1,s_1,less_in_gg_2}(U3_gg_{less_out_gg}(less_out_gg), flat1, flat2) → U1_GG_{less_out_gg,s_1,less_in_gg_2}(less_out_gg, flat1, flat2)
U1_GG_{U3_gg_1,s_1,0}(U3_gg_{less_out_gg}(less_out_gg), flat1, flat2) → U1_GG_{less_out_gg,s_1,0}(less_out_gg, flat1, flat2)
U1_GG_{U3_gg_1,s_1,s_1}(U3_gg_{less_out_gg}(less_out_gg), flat1, flat2) → U1_GG_{less_out_gg,s_1,s_1}(less_out_gg, flat1, flat2)
U1_GG_{U3_gg_1,s_1,less_out_gg}(U3_gg_{less_out_gg}(less_out_gg), flat1, flat2) → U1_GG_{less_out_gg,s_1,less_out_gg}(less_out_gg, flat1, flat2)
U1_GG_{U3_gg_1,s_1,U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg), flat1, flat2) → U1_GG_{less_out_gg,s_1,U3_gg_1}(less_out_gg, flat1, flat2)
U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(U3_gg_{less_out_gg}(less_out_gg), flat1, flat2) → U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(less_out_gg, flat1, flat2)
U1_GG_{U3_gg_1,less_out_gg,0}(U3_gg_{less_out_gg}(less_out_gg), flat1, flat2) → U1_GG_{less_out_gg,less_out_gg,0}(less_out_gg, flat1, flat2)
U1_GG_{U3_gg_1,less_out_gg,s_1}(U3_gg_{less_out_gg}(less_out_gg), flat1, flat2) → U1_GG_{less_out_gg,less_out_gg,s_1}(less_out_gg, flat1, flat2)
U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(U3_gg_{less_out_gg}(less_out_gg), flat1, flat2) → U1_GG_{less_out_gg,less_out_gg,less_out_gg}(less_out_gg, flat1, flat2)
U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg), flat1, flat2) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(less_out_gg, flat1, flat2)
U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(U3_gg_{less_out_gg}(less_out_gg), flat1, flat2) → U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(less_out_gg, flat1, flat2)
U1_GG_{U3_gg_1,U3_gg_1,0}(U3_gg_{less_out_gg}(less_out_gg), flat1, flat2) → U1_GG_{less_out_gg,U3_gg_1,0}(less_out_gg, flat1, flat2)
U1_GG_{U3_gg_1,U3_gg_1,s_1}(U3_gg_{less_out_gg}(less_out_gg), flat1, flat2) → U1_GG_{less_out_gg,U3_gg_1,s_1}(less_out_gg, flat1, flat2)
U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(U3_gg_{less_out_gg}(less_out_gg), flat1, flat2) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(less_out_gg, flat1, flat2)
U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg), flat1, flat2) → U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(less_out_gg, flat1, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_out_gg}(less_out_gg), flat2) → U1_GG_{less_in_gg_2,less_out_gg,less_in_gg_2}(flat0, less_out_gg, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,0}(flat0, U3_gg_{less_out_gg}(less_out_gg), flat2) → U1_GG_{less_in_gg_2,less_out_gg,0}(flat0, less_out_gg, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,s_1}(flat0, U3_gg_{less_out_gg}(less_out_gg), flat2) → U1_GG_{less_in_gg_2,less_out_gg,s_1}(flat0, less_out_gg, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_out_gg}(less_out_gg), flat2) → U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(flat0, less_out_gg, flat2)
U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg), flat2) → U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(flat0, less_out_gg, flat2)
U1_GG_{0,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_out_gg}(less_out_gg), flat2) → U1_GG_{0,less_out_gg,less_in_gg_2}(flat0, less_out_gg, flat2)
U1_GG_{0,U3_gg_1,0}(flat0, U3_gg_{less_out_gg}(less_out_gg), flat2) → U1_GG_{0,less_out_gg,0}(flat0, less_out_gg, flat2)
U1_GG_{0,U3_gg_1,s_1}(flat0, U3_gg_{less_out_gg}(less_out_gg), flat2) → U1_GG_{0,less_out_gg,s_1}(flat0, less_out_gg, flat2)
U1_GG_{0,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_out_gg}(less_out_gg), flat2) → U1_GG_{0,less_out_gg,less_out_gg}(flat0, less_out_gg, flat2)
U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg), flat2) → U1_GG_{0,less_out_gg,U3_gg_1}(flat0, less_out_gg, flat2)
U1_GG_{s_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_out_gg}(less_out_gg), flat2) → U1_GG_{s_1,less_out_gg,less_in_gg_2}(flat0, less_out_gg, flat2)
U1_GG_{s_1,U3_gg_1,0}(flat0, U3_gg_{less_out_gg}(less_out_gg), flat2) → U1_GG_{s_1,less_out_gg,0}(flat0, less_out_gg, flat2)
U1_GG_{s_1,U3_gg_1,s_1}(flat0, U3_gg_{less_out_gg}(less_out_gg), flat2) → U1_GG_{s_1,less_out_gg,s_1}(flat0, less_out_gg, flat2)
U1_GG_{s_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_out_gg}(less_out_gg), flat2) → U1_GG_{s_1,less_out_gg,less_out_gg}(flat0, less_out_gg, flat2)
U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg), flat2) → U1_GG_{s_1,less_out_gg,U3_gg_1}(flat0, less_out_gg, flat2)
U1_GG_{less_out_gg,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_out_gg}(less_out_gg), flat2) → U1_GG_{less_out_gg,less_out_gg,less_in_gg_2}(flat0, less_out_gg, flat2)
U1_GG_{less_out_gg,U3_gg_1,0}(flat0, U3_gg_{less_out_gg}(less_out_gg), flat2) → U1_GG_{less_out_gg,less_out_gg,0}(flat0, less_out_gg, flat2)
U1_GG_{less_out_gg,U3_gg_1,s_1}(flat0, U3_gg_{less_out_gg}(less_out_gg), flat2) → U1_GG_{less_out_gg,less_out_gg,s_1}(flat0, less_out_gg, flat2)
U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_out_gg}(less_out_gg), flat2) → U1_GG_{less_out_gg,less_out_gg,less_out_gg}(flat0, less_out_gg, flat2)
U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg), flat2) → U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(flat0, less_out_gg, flat2)
U1_GG_{U3_gg_1,U3_gg_1,less_in_gg_2}(flat0, U3_gg_{less_out_gg}(less_out_gg), flat2) → U1_GG_{U3_gg_1,less_out_gg,less_in_gg_2}(flat0, less_out_gg, flat2)
U1_GG_{U3_gg_1,U3_gg_1,0}(flat0, U3_gg_{less_out_gg}(less_out_gg), flat2) → U1_GG_{U3_gg_1,less_out_gg,0}(flat0, less_out_gg, flat2)
U1_GG_{U3_gg_1,U3_gg_1,s_1}(flat0, U3_gg_{less_out_gg}(less_out_gg), flat2) → U1_GG_{U3_gg_1,less_out_gg,s_1}(flat0, less_out_gg, flat2)
U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(flat0, U3_gg_{less_out_gg}(less_out_gg), flat2) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(flat0, less_out_gg, flat2)
U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg), flat2) → U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(flat0, less_out_gg, flat2)
U1_GG_{less_in_gg_2,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{less_in_gg_2,less_in_gg_2,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_in_gg_2,0,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{less_in_gg_2,0,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_in_gg_2,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{less_in_gg_2,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_in_gg_2,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{less_in_gg_2,less_out_gg,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_in_gg_2,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{less_in_gg_2,U3_gg_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{0,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{0,less_in_gg_2,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{0,0,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{0,0,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{0,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{0,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{0,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{0,less_out_gg,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{0,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{0,U3_gg_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{s_1,less_in_gg_2,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{s_1,0,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{s_1,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{s_1,less_out_gg,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{s_1,U3_gg_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_out_gg,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{less_out_gg,less_in_gg_2,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_out_gg,0,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{less_out_gg,0,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_out_gg,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{less_out_gg,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_out_gg,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{less_out_gg,less_out_gg,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{less_out_gg,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{less_out_gg,U3_gg_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{U3_gg_1,less_in_gg_2,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{U3_gg_1,less_in_gg_2,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{U3_gg_1,0,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{U3_gg_1,0,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{U3_gg_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{U3_gg_1,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{U3_gg_1,less_out_gg,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{U3_gg_1,less_out_gg,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{U3_gg_1,U3_gg_1,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{U3_gg_1,U3_gg_1,less_out_gg}(flat0, flat1, less_out_gg)
P_IN_GG_{U3_gg_1,less_in_gg_2}(U3_gg_{less_out_gg}(less_out_gg), flat1) → P_IN_GG_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
P_IN_GG_{U3_gg_1,0}(U3_gg_{less_out_gg}(less_out_gg), flat1) → P_IN_GG_{less_out_gg,0}(less_out_gg, flat1)
P_IN_GG_{U3_gg_1,s_1}(U3_gg_{less_out_gg}(less_out_gg), flat1) → P_IN_GG_{less_out_gg,s_1}(less_out_gg, flat1)
P_IN_GG_{U3_gg_1,less_out_gg}(U3_gg_{less_out_gg}(less_out_gg), flat1) → P_IN_GG_{less_out_gg,less_out_gg}(less_out_gg, flat1)
P_IN_GG_{U3_gg_1,U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg), flat1) → P_IN_GG_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
P_IN_GG_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → P_IN_GG_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
P_IN_GG_{0,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → P_IN_GG_{0,less_out_gg}(flat0, less_out_gg)
P_IN_GG_{s_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → P_IN_GG_{s_1,less_out_gg}(flat0, less_out_gg)
P_IN_GG_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → P_IN_GG_{less_out_gg,less_out_gg}(flat0, less_out_gg)
P_IN_GG_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → P_IN_GG_{U3_gg_1,less_out_gg}(flat0, less_out_gg)

The TRS R consists of the following rules:

less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → s_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,0}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
s_{U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg)) → s_{less_out_gg}(less_out_gg)
U3_gg_{U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg)) → U3_gg_{less_out_gg}(less_out_gg)

Q is empty.
We have to consider all (P,Q,R)-chains.

(69) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2654 less nodes.

(70) Obligation:

Q DP problem:
The TRS P consists of the following rules:

P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{less_in_gg_2}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{less_in_gg_2}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(s_{s_1}(s_{less_in_gg_2}(z0)), z1)))
U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{s_1,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{less_in_gg_2}(z0)), s_{less_in_gg_2}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{less_in_gg_2}(z1))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{U3_gg_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{U3_gg_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(s_{s_1}(s_{less_in_gg_2}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{less_in_gg_2}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{less_in_gg_2}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(s_{s_1}(s_{less_out_gg}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{U3_gg_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{U3_gg_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(s_{s_1}(s_{less_out_gg}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{less_in_gg_2}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{less_in_gg_2}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(s_{s_1}(s_{U3_gg_1}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{U3_gg_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{U3_gg_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(s_{s_1}(s_{U3_gg_1}(z0)), z1)))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{less_in_gg_2}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{s_1}(z1))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{less_in_gg_2}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{less_out_gg}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{U3_gg_1}(z0)), z1)))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{less_in_gg_2}(z0)), s_{U3_gg_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{U3_gg_1}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{0}(z0)), s_{less_in_gg_2}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{less_in_gg_2}(z1))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{less_in_gg_2}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{less_in_gg_2}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(s_{s_1}(s_{0}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{U3_gg_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{U3_gg_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(s_{s_1}(s_{0}(z0)), z1)))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{0}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{s_1}(z1))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{0}(z0)), z1)))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{0}(z0)), s_{U3_gg_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{U3_gg_1}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{s_1}(z0)), s_{less_in_gg_2}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{less_in_gg_2}(z1))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{less_in_gg_2}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{less_in_gg_2}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(s_{s_1}(s_{s_1}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{U3_gg_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{U3_gg_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(s_{s_1}(s_{s_1}(z0)), z1)))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{s_1}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{s_1}(z1))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{s_1}(z0)), z1)))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{s_1}(z0)), s_{U3_gg_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{U3_gg_1}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{less_out_gg}(z0)), s_{less_in_gg_2}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{less_in_gg_2}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{less_out_gg}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{s_1}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{less_out_gg}(z0)), s_{U3_gg_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{U3_gg_1}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{U3_gg_1}(z0)), s_{less_in_gg_2}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{less_in_gg_2}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{U3_gg_1}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{s_1}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{U3_gg_1}(z0)), s_{U3_gg_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{U3_gg_1}(z1))

The TRS R consists of the following rules:

less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → s_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,0}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
s_{U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg)) → s_{less_out_gg}(less_out_gg)
U3_gg_{U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg)) → U3_gg_{less_out_gg}(less_out_gg)

Q is empty.
We have to consider all (P,Q,R)-chains.

(71) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{less_in_gg_2}(z0)), s_{less_in_gg_2}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{less_in_gg_2}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{less_in_gg_2}(z0)), s_{U3_gg_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{U3_gg_1}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{0}(z0)), s_{less_in_gg_2}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{less_in_gg_2}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{0}(z0)), s_{U3_gg_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{U3_gg_1}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{s_1}(z0)), s_{less_in_gg_2}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{less_in_gg_2}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{s_1}(z0)), s_{U3_gg_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{U3_gg_1}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{less_out_gg}(z0)), s_{less_in_gg_2}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{less_in_gg_2}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{less_out_gg}(z0)), s_{U3_gg_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{U3_gg_1}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{U3_gg_1}(z0)), s_{less_in_gg_2}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{less_in_gg_2}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{U3_gg_1}(z0)), s_{U3_gg_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{U3_gg_1}(z1))

The remaining pairs can at least be oriented weakly.
Used ordering: Polynomial interpretation [POLO]:

POL(0) = 0   
POL(P_IN_GG_{s_1,s_1}(x₁, x₂)) = x₂   
POL(U1_GG_{s_1,s_1,U3_gg_1}(x₁, x₂, x₃)) = x₃   
POL(U1_GG_{s_1,s_1,less_out_gg}(x₁, x₂, x₃)) = 1   
POL(U3_gg_{U3_gg_1}(x₁)) = x₁   
POL(U3_gg_{less_in_gg_2}(x₁)) = x₁   
POL(U3_gg_{less_out_gg}(x₁)) = 1   
POL(less_in_gg_{0,0}(x₁, x₂)) = 0   
POL(less_in_gg_{0,U3_gg_1}(x₁, x₂)) = 0   
POL(less_in_gg_{0,less_in_gg_2}(x₁, x₂)) = 1   
POL(less_in_gg_{0,less_out_gg}(x₁, x₂)) = 0   
POL(less_in_gg_{0,s_1}(x₁, x₂)) = 1   
POL(less_in_gg_{U3_gg_1,0}(x₁, x₂)) = 0   
POL(less_in_gg_{U3_gg_1,U3_gg_1}(x₁, x₂)) = 0   
POL(less_in_gg_{U3_gg_1,less_in_gg_2}(x₁, x₂)) = 0   
POL(less_in_gg_{U3_gg_1,less_out_gg}(x₁, x₂)) = 0   
POL(less_in_gg_{U3_gg_1,s_1}(x₁, x₂)) = 1   
POL(less_in_gg_{less_in_gg_2,0}(x₁, x₂)) = 1   
POL(less_in_gg_{less_in_gg_2,U3_gg_1}(x₁, x₂)) = 0   
POL(less_in_gg_{less_in_gg_2,less_in_gg_2}(x₁, x₂)) = 0   
POL(less_in_gg_{less_in_gg_2,less_out_gg}(x₁, x₂)) = 0   
POL(less_in_gg_{less_in_gg_2,s_1}(x₁, x₂)) = 1   
POL(less_in_gg_{less_out_gg,0}(x₁, x₂)) = 0   
POL(less_in_gg_{less_out_gg,U3_gg_1}(x₁, x₂)) = 0   
POL(less_in_gg_{less_out_gg,less_in_gg_2}(x₁, x₂)) = 0   
POL(less_in_gg_{less_out_gg,less_out_gg}(x₁, x₂)) = 0   
POL(less_in_gg_{less_out_gg,s_1}(x₁, x₂)) = 0   
POL(less_in_gg_{s_1,0}(x₁, x₂)) = 1   
POL(less_in_gg_{s_1,U3_gg_1}(x₁, x₂)) = 0   
POL(less_in_gg_{s_1,less_in_gg_2}(x₁, x₂)) = 0   
POL(less_in_gg_{s_1,less_out_gg}(x₁, x₂)) = 0   
POL(less_in_gg_{s_1,s_1}(x₁, x₂)) = 1   
POL(less_out_gg) = 0   
POL(s_{0}(x₁)) = 0   
POL(s_{U3_gg_1}(x₁)) = 0   
POL(s_{less_in_gg_2}(x₁)) = 0   
POL(s_{less_out_gg}(x₁)) = 0   
POL(s_{s_1}(x₁)) = 1   

The following usable rules [FROCOS05] were oriented:

less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → s_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,0}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
s_{U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg)) → s_{less_out_gg}(less_out_gg)
U3_gg_{U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg)) → U3_gg_{less_out_gg}(less_out_gg)

(72) Obligation:

Q DP problem:
The TRS P consists of the following rules:

P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{less_in_gg_2}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{less_in_gg_2}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(s_{s_1}(s_{less_in_gg_2}(z0)), z1)))
U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{s_1,s_1,less_out_gg}(flat0, flat1, less_out_gg)
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{U3_gg_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{U3_gg_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(s_{s_1}(s_{less_in_gg_2}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{less_in_gg_2}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{less_in_gg_2}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(s_{s_1}(s_{less_out_gg}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{U3_gg_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{U3_gg_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(s_{s_1}(s_{less_out_gg}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{less_in_gg_2}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{less_in_gg_2}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(s_{s_1}(s_{U3_gg_1}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{U3_gg_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{U3_gg_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(s_{s_1}(s_{U3_gg_1}(z0)), z1)))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{less_in_gg_2}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{s_1}(z1))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{less_in_gg_2}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{less_out_gg}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{U3_gg_1}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{less_in_gg_2}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{less_in_gg_2}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(s_{s_1}(s_{0}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{U3_gg_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{U3_gg_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(s_{s_1}(s_{0}(z0)), z1)))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{0}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{s_1}(z1))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{0}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{less_in_gg_2}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{less_in_gg_2}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(s_{s_1}(s_{s_1}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{U3_gg_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{U3_gg_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(s_{s_1}(s_{s_1}(z0)), z1)))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{s_1}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{s_1}(z1))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{s_1}(z0)), z1)))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{less_out_gg}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{s_1}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{U3_gg_1}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{s_1}(z1))

The TRS R consists of the following rules:

less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → s_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,0}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
s_{U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg)) → s_{less_out_gg}(less_out_gg)
U3_gg_{U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg)) → U3_gg_{less_out_gg}(less_out_gg)

Q is empty.
We have to consider all (P,Q,R)-chains.

(73) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 10 less nodes.

(74) Obligation:

Q DP problem:
The TRS P consists of the following rules:

U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{less_in_gg_2}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{s_1}(z1))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{less_in_gg_2}(z0)), z1)))
U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{s_1,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{0}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{s_1}(z1))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{0}(z0)), z1)))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{s_1}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{s_1}(z1))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{s_1}(z0)), z1)))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{less_out_gg}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{s_1}(z1))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{less_out_gg}(z0)), z1)))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{U3_gg_1}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{s_1}(z1))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{U3_gg_1}(z0)), z1)))

The TRS R consists of the following rules:

less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → s_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,0}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
s_{U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg)) → s_{less_out_gg}(less_out_gg)
U3_gg_{U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg)) → U3_gg_{less_out_gg}(less_out_gg)

Q is empty.
We have to consider all (P,Q,R)-chains.

(75) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{0}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{s_1}(z1))

The remaining pairs can at least be oriented weakly.
Used ordering: Matrix interpretation [MATRO]:

POL(U1_GG_{s_1,s_1,less_out_gg}(x1, x2, x3)) =

0

+

[ 0, 1 ]

·

x1

+

[ 0, 0 ]

·

x2

+

[ 0, 0 ]

·

x3

POL(s_{s_1}(x1)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 1 0 /

·

x1

POL(s_{less_in_gg_2}(x1)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 1 /

·

x1

POL(less_out_gg) =

/ 0 \ \ 0 /

POL(P_IN_GG_{s_1,s_1}(x1, x2)) =

0

+

[ 0, 0 ]

·

x1

+

[ 0, 0 ]

·

x2

POL(U1_GG_{s_1,s_1,U3_gg_1}(x1, x2, x3)) =

0

+

[ 0, 1 ]

·

x1

+

[ 0, 0 ]

·

x2

+

[ 0, 0 ]

·

x3

POL(U3_gg_{less_in_gg_2}(x1)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

POL(less_in_gg_{s_1,s_1}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(U3_gg_{less_out_gg}(x1)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

POL(s_{0}(x1)) =

/ 1 \ \ 0 /

+

/ 1 0 \ \ 0 0 /

·

x1

POL(s_{less_out_gg}(x1)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

POL(s_{U3_gg_1}(x1)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

POL(less_in_gg_{less_in_gg_2,less_in_gg_2}(x1, x2)) =

/ 1 \ \ 1 /

+

/ 0 1 \ \ 0 1 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{0,s_1}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 1 0 /

·

x2

POL(0) =

/ 0 \ \ 0 /

POL(less_in_gg_{less_out_gg,less_in_gg_2}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 1 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{less_in_gg_2,0}(x1, x2)) =

/ 1 \ \ 1 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 1 1 \ \ 1 1 /

·

x2

POL(less_in_gg_{less_out_gg,0}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{less_in_gg_2,s_1}(x1, x2)) =

/ 0 \ \ 1 /

+

/ 0 0 \ \ 0 1 /

·

x1

+

/ 0 1 \ \ 1 0 /

·

x2

POL(less_in_gg_{less_out_gg,s_1}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 1 0 /

·

x2

POL(less_in_gg_{less_in_gg_2,less_out_gg}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 1 1 \ \ 1 1 /

·

x2

POL(less_in_gg_{less_out_gg,less_out_gg}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{less_in_gg_2,U3_gg_1}(x1, x2)) =

/ 0 \ \ 1 /

+

/ 0 1 \ \ 0 0 /

·

x1

+

/ 1 0 \ \ 1 1 /

·

x2

POL(less_in_gg_{less_out_gg,U3_gg_1}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{0,less_in_gg_2}(x1, x2)) =

/ 1 \ \ 0 /

+

/ 1 1 \ \ 1 1 /

·

x1

+

/ 0 1 \ \ 0 0 /

·

x2

POL(less_in_gg_{0,less_out_gg}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{s_1,less_in_gg_2}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 1 1 \ \ 1 1 /

·

x1

+

/ 0 1 \ \ 0 1 /

·

x2

POL(less_in_gg_{s_1,less_out_gg}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 1 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{U3_gg_1,less_in_gg_2}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 1 1 \ \ 0 1 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{U3_gg_1,less_out_gg}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 1 \ \ 1 1 /

·

x2

POL(less_in_gg_{U3_gg_1,0}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 1 1 \ \ 0 1 /

·

x2

POL(less_in_gg_{U3_gg_1,s_1}(x1, x2)) =

/ 0 \ \ 1 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 1 \ \ 1 0 /

·

x2

POL(less_in_gg_{U3_gg_1,U3_gg_1}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 1 /

·

x1

+

/ 1 0 \ \ 1 0 /

·

x2

POL(less_in_gg_{0,0}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{0,U3_gg_1}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 1 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{s_1,0}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{s_1,U3_gg_1}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 1 0 \ \ 0 1 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(U3_gg_{U3_gg_1}(x1)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

The following usable rules [FROCOS05] were oriented:

less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → s_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,0}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
s_{U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg)) → s_{less_out_gg}(less_out_gg)
U3_gg_{U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg)) → U3_gg_{less_out_gg}(less_out_gg)

(76) Obligation:

Q DP problem:
The TRS P consists of the following rules:

U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{less_in_gg_2}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{s_1}(z1))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{less_in_gg_2}(z0)), z1)))
U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{s_1,s_1,less_out_gg}(flat0, flat1, less_out_gg)
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{0}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{0}(z0)), z1)))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{s_1}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{s_1}(z1))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{s_1}(z0)), z1)))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{less_out_gg}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{s_1}(z1))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{less_out_gg}(z0)), z1)))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{U3_gg_1}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{s_1}(z1))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{U3_gg_1}(z0)), z1)))

The TRS R consists of the following rules:

less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → s_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,0}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
s_{U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg)) → s_{less_out_gg}(less_out_gg)
U3_gg_{U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg)) → U3_gg_{less_out_gg}(less_out_gg)

Q is empty.
We have to consider all (P,Q,R)-chains.

(77) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.

(78) Obligation:

Q DP problem:
The TRS P consists of the following rules:

P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{less_in_gg_2}(z0)), z1)))
U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{s_1,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{less_in_gg_2}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{s_1}(z1))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{less_out_gg}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{U3_gg_1}(z0)), z1)))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{s_1}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{s_1}(z1))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{s_1}(z0)), z1)))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{less_out_gg}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{s_1}(z1))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{U3_gg_1}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{s_1}(z1))

The TRS R consists of the following rules:

less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → s_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,0}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
s_{U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg)) → s_{less_out_gg}(less_out_gg)
U3_gg_{U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg)) → U3_gg_{less_out_gg}(less_out_gg)

Q is empty.
We have to consider all (P,Q,R)-chains.

(79) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{less_out_gg}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{s_1}(z1))

The remaining pairs can at least be oriented weakly.
Used ordering: Matrix interpretation [MATRO]:

POL(P_IN_GG_{s_1,s_1}(x1, x2)) =

0

+

[ 0, 0 ]

·

x1

+

[ 0, 0 ]

·

x2

POL(s_{s_1}(x1)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 1 0 /

·

x1

POL(s_{less_in_gg_2}(x1)) =

/ 0 \ \ 0 /

+

/ 0 1 \ \ 0 0 /

·

x1

POL(U1_GG_{s_1,s_1,U3_gg_1}(x1, x2, x3)) =

0

+

[ 0, 1 ]

·

x1

+

[ 0, 0 ]

·

x2

+

[ 0, 0 ]

·

x3

POL(U3_gg_{less_in_gg_2}(x1)) =

/ 1 \ \ 0 /

+

/ 0 0 \ \ 1 0 /

·

x1

POL(less_in_gg_{s_1,s_1}(x1, x2)) =

/ 0 \ \ 1 /

+

/ 1 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 1 1 /

·

x2

POL(U3_gg_{less_out_gg}(x1)) =

/ 1 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

POL(less_out_gg) =

/ 0 \ \ 0 /

POL(U1_GG_{s_1,s_1,less_out_gg}(x1, x2, x3)) =

0

+

[ 0, 1 ]

·

x1

+

[ 0, 0 ]

·

x2

+

[ 0, 0 ]

·

x3

POL(s_{less_out_gg}(x1)) =

/ 1 \ \ 0 /

+

/ 1 0 \ \ 1 0 /

·

x1

POL(s_{U3_gg_1}(x1)) =

/ 0 \ \ 0 /

+

/ 1 0 \ \ 0 0 /

·

x1

POL(less_in_gg_{less_in_gg_2,less_in_gg_2}(x1, x2)) =

/ 0 \ \ 1 /

+

/ 0 1 \ \ 0 0 /

·

x1

+

/ 1 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{0,s_1}(x1, x2)) =

/ 0 \ \ 1 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(0) =

/ 0 \ \ 0 /

POL(less_in_gg_{less_out_gg,less_in_gg_2}(x1, x2)) =

/ 0 \ \ 1 /

+

/ 0 0 \ \ 1 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{less_in_gg_2,0}(x1, x2)) =

/ 0 \ \ 1 /

+

/ 0 1 \ \ 1 0 /

·

x1

+

/ 0 0 \ \ 1 1 /

·

x2

POL(less_in_gg_{less_out_gg,0}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{less_in_gg_2,s_1}(x1, x2)) =

/ 0 \ \ 1 /

+

/ 0 0 \ \ 1 0 /

·

x1

+

/ 0 0 \ \ 1 1 /

·

x2

POL(less_in_gg_{less_out_gg,s_1}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{less_in_gg_2,less_out_gg}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 1 1 /

·

x2

POL(less_in_gg_{less_out_gg,less_out_gg}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{less_in_gg_2,U3_gg_1}(x1, x2)) =

/ 0 \ \ 1 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{less_out_gg,U3_gg_1}(x1, x2)) =

/ 0 \ \ 1 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(s_{0}(x1)) =

/ 0 \ \ 1 /

+

/ 0 1 \ \ 0 0 /

·

x1

POL(less_in_gg_{0,less_in_gg_2}(x1, x2)) =

/ 0 \ \ 1 /

+

/ 0 0 \ \ 1 1 /

·

x1

+

/ 1 0 \ \ 1 0 /

·

x2

POL(less_in_gg_{0,less_out_gg}(x1, x2)) =

/ 0 \ \ 1 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{s_1,less_in_gg_2}(x1, x2)) =

/ 0 \ \ 1 /

+

/ 0 0 \ \ 1 1 /

·

x1

+

/ 0 1 \ \ 0 0 /

·

x2

POL(less_in_gg_{s_1,less_out_gg}(x1, x2)) =

/ 0 \ \ 1 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{U3_gg_1,less_in_gg_2}(x1, x2)) =

/ 0 \ \ 1 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{U3_gg_1,less_out_gg}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 1 1 /

·

x2

POL(less_in_gg_{U3_gg_1,0}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 1 0 /

·

x2

POL(less_in_gg_{U3_gg_1,s_1}(x1, x2)) =

/ 0 \ \ 1 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 1 1 /

·

x2

POL(less_in_gg_{U3_gg_1,U3_gg_1}(x1, x2)) =

/ 0 \ \ 1 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{0,0}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{0,U3_gg_1}(x1, x2)) =

/ 0 \ \ 1 /

+

/ 0 0 \ \ 0 1 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{s_1,0}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{s_1,U3_gg_1}(x1, x2)) =

/ 0 \ \ 1 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(U3_gg_{U3_gg_1}(x1)) =

/ 1 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

The following usable rules [FROCOS05] were oriented:

less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → s_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,0}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
s_{U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg)) → s_{less_out_gg}(less_out_gg)
U3_gg_{U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg)) → U3_gg_{less_out_gg}(less_out_gg)

(80) Obligation:

Q DP problem:
The TRS P consists of the following rules:

P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{less_in_gg_2}(z0)), z1)))
U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{s_1,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{less_in_gg_2}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{s_1}(z1))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{less_out_gg}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{U3_gg_1}(z0)), z1)))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{s_1}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{s_1}(z1))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{s_1}(z0)), z1)))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{U3_gg_1}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{s_1}(z1))

The TRS R consists of the following rules:

less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → s_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,0}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
s_{U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg)) → s_{less_out_gg}(less_out_gg)
U3_gg_{U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg)) → U3_gg_{less_out_gg}(less_out_gg)

Q is empty.
We have to consider all (P,Q,R)-chains.

(81) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{U3_gg_1}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{s_1}(z1))

The remaining pairs can at least be oriented weakly.
Used ordering: Matrix interpretation [MATRO]:

POL(P_IN_GG_{s_1,s_1}(x1, x2)) =

0

+

[ 0, 0 ]

·

x1

+

[ 0, 0 ]

·

x2

POL(s_{s_1}(x1)) =

/ 0 \ \ 0 /

+

/ 0 1 \ \ 0 0 /

·

x1

POL(s_{less_in_gg_2}(x1)) =

/ 0 \ \ 0 /

+

/ 0 1 \ \ 1 1 /

·

x1

POL(U1_GG_{s_1,s_1,U3_gg_1}(x1, x2, x3)) =

0

+

[ 1, 0 ]

·

x1

+

[ 0, 0 ]

·

x2

+

[ 0, 0 ]

·

x3

POL(U3_gg_{less_in_gg_2}(x1)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 1 /

·

x1

POL(less_in_gg_{s_1,s_1}(x1, x2)) =

/ 1 \ \ 0 /

+

/ 0 0 \ \ 0 1 /

·

x1

+

/ 0 0 \ \ 1 0 /

·

x2

POL(U3_gg_{less_out_gg}(x1)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

POL(less_out_gg) =

/ 0 \ \ 0 /

POL(U1_GG_{s_1,s_1,less_out_gg}(x1, x2, x3)) =

0

+

[ 1, 0 ]

·

x1

+

[ 0, 0 ]

·

x2

+

[ 0, 0 ]

·

x3

POL(s_{less_out_gg}(x1)) =

/ 0 \ \ 0 /

+

/ 1 0 \ \ 0 0 /

·

x1

POL(s_{U3_gg_1}(x1)) =

/ 0 \ \ 1 /

+

/ 0 0 \ \ 1 0 /

·

x1

POL(less_in_gg_{less_in_gg_2,less_in_gg_2}(x1, x2)) =

/ 0 \ \ 1 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{0,s_1}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(0) =

/ 0 \ \ 0 /

POL(less_in_gg_{less_out_gg,less_in_gg_2}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 1 1 \ \ 0 1 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{less_in_gg_2,0}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 1 1 \ \ 0 1 /

·

x2

POL(less_in_gg_{less_out_gg,0}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{less_in_gg_2,s_1}(x1, x2)) =

/ 1 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 1 1 \ \ 1 1 /

·

x2

POL(less_in_gg_{less_out_gg,s_1}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 1 \ \ 0 0 /

·

x2

POL(less_in_gg_{less_in_gg_2,less_out_gg}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 1 1 \ \ 1 0 /

·

x2

POL(less_in_gg_{less_out_gg,less_out_gg}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{less_in_gg_2,U3_gg_1}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 1 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{less_out_gg,U3_gg_1}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(s_{0}(x1)) =

/ 0 \ \ 1 /

+

/ 0 0 \ \ 1 0 /

·

x1

POL(less_in_gg_{0,less_in_gg_2}(x1, x2)) =

/ 0 \ \ 1 /

+

/ 1 1 \ \ 1 1 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{0,less_out_gg}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{s_1,less_in_gg_2}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 1 1 \ \ 0 1 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{s_1,less_out_gg}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{U3_gg_1,less_in_gg_2}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 1 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{U3_gg_1,less_out_gg}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 1 0 /

·

x2

POL(less_in_gg_{U3_gg_1,0}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 1 \ \ 0 0 /

·

x2

POL(less_in_gg_{U3_gg_1,s_1}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 1 1 \ \ 0 0 /

·

x2

POL(less_in_gg_{U3_gg_1,U3_gg_1}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 1 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{0,0}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{0,U3_gg_1}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{s_1,0}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{s_1,U3_gg_1}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(U3_gg_{U3_gg_1}(x1)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

The following usable rules [FROCOS05] were oriented:

less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → s_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,0}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
s_{U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg)) → s_{less_out_gg}(less_out_gg)
U3_gg_{U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg)) → U3_gg_{less_out_gg}(less_out_gg)

(82) Obligation:

Q DP problem:
The TRS P consists of the following rules:

P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{less_in_gg_2}(z0)), z1)))
U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{s_1,s_1,less_out_gg}(flat0, flat1, less_out_gg)
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{less_in_gg_2}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{s_1}(z1))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{less_out_gg}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{U3_gg_1}(z0)), z1)))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{s_1}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{s_1}(z1))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{s_1}(z0)), z1)))

The TRS R consists of the following rules:

less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → s_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,0}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
s_{U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg)) → s_{less_out_gg}(less_out_gg)
U3_gg_{U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg)) → U3_gg_{less_out_gg}(less_out_gg)

Q is empty.
We have to consider all (P,Q,R)-chains.

(83) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{less_in_gg_2}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{s_1}(z1))

The remaining pairs can at least be oriented weakly.
Used ordering: Matrix interpretation [MATRO]:

POL(P_IN_GG_{s_1,s_1}(x1, x2)) =

0

+

[ 0, 0 ]

·

x1

+

[ 0, 0 ]

·

x2

POL(s_{s_1}(x1)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 1 0 /

·

x1

POL(s_{less_in_gg_2}(x1)) =

/ 1 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

POL(U1_GG_{s_1,s_1,U3_gg_1}(x1, x2, x3)) =

0

+

[ 0, 1 ]

·

x1

+

[ 0, 0 ]

·

x2

+

[ 0, 0 ]

·

x3

POL(U3_gg_{less_in_gg_2}(x1)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

POL(less_in_gg_{s_1,s_1}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(U3_gg_{less_out_gg}(x1)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

POL(less_out_gg) =

/ 1 \ \ 0 /

POL(U1_GG_{s_1,s_1,less_out_gg}(x1, x2, x3)) =

0

+

[ 0, 1 ]

·

x1

+

[ 0, 0 ]

·

x2

+

[ 0, 0 ]

·

x3

POL(s_{less_out_gg}(x1)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

POL(s_{U3_gg_1}(x1)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

POL(less_in_gg_{less_in_gg_2,less_in_gg_2}(x1, x2)) =

/ 1 \ \ 1 /

+

/ 1 0 \ \ 1 1 /

·

x1

+

/ 0 0 \ \ 1 0 /

·

x2

POL(less_in_gg_{0,s_1}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(0) =

/ 0 \ \ 0 /

POL(less_in_gg_{less_out_gg,less_in_gg_2}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 1 \ \ 0 1 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{less_in_gg_2,0}(x1, x2)) =

/ 0 \ \ 1 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 1 1 \ \ 1 0 /

·

x2

POL(less_in_gg_{less_out_gg,0}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 1 \ \ 0 0 /

·

x2

POL(less_in_gg_{less_in_gg_2,s_1}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 1 1 \ \ 1 1 /

·

x2

POL(less_in_gg_{less_out_gg,s_1}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{less_in_gg_2,less_out_gg}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 1 1 \ \ 0 1 /

·

x2

POL(less_in_gg_{less_out_gg,less_out_gg}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{less_in_gg_2,U3_gg_1}(x1, x2)) =

/ 1 \ \ 0 /

+

/ 0 0 \ \ 0 1 /

·

x1

+

/ 1 0 \ \ 1 1 /

·

x2

POL(less_in_gg_{less_out_gg,U3_gg_1}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 1 0 \ \ 0 1 /

·

x2

POL(s_{0}(x1)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

POL(less_in_gg_{0,less_in_gg_2}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 1 \ \ 1 1 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{0,less_out_gg}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 1 \ \ 0 1 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{s_1,less_in_gg_2}(x1, x2)) =

/ 1 \ \ 0 /

+

/ 1 1 \ \ 1 1 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{s_1,less_out_gg}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 1 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{U3_gg_1,less_in_gg_2}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 1 \ \ 0 1 /

·

x1

+

/ 0 0 \ \ 1 0 /

·

x2

POL(less_in_gg_{U3_gg_1,less_out_gg}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 1 \ \ 0 0 /

·

x2

POL(less_in_gg_{U3_gg_1,0}(x1, x2)) =

/ 0 \ \ 1 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 1 \ \ 1 0 /

·

x2

POL(less_in_gg_{U3_gg_1,s_1}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 1 /

·

x2

POL(less_in_gg_{U3_gg_1,U3_gg_1}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 1 0 \ \ 1 1 /

·

x2

POL(less_in_gg_{0,0}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{0,U3_gg_1}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 1 \ \ 0 1 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{s_1,0}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(less_in_gg_{s_1,U3_gg_1}(x1, x2)) =

/ 0 \ \ 0 /

+

/ 1 0 \ \ 0 0 /

·

x1

+

/ 0 0 \ \ 0 0 /

·

x2

POL(U3_gg_{U3_gg_1}(x1)) =

/ 0 \ \ 0 /

+

/ 0 0 \ \ 0 0 /

·

x1

The following usable rules [FROCOS05] were oriented:

less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → s_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,0}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
s_{U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg)) → s_{less_out_gg}(less_out_gg)
U3_gg_{U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg)) → U3_gg_{less_out_gg}(less_out_gg)

(84) Obligation:

Q DP problem:
The TRS P consists of the following rules:

P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_in_gg_2}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{less_in_gg_2}(z0)), z1)))
U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{s_1,s_1,less_out_gg}(flat0, flat1, less_out_gg)
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{less_out_gg}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{less_out_gg}(z0)), z1)))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{U3_gg_1}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{U3_gg_1}(z0)), z1)))
U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{s_1}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{s_1}(z1))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{s_1}(z0)), z1)))

The TRS R consists of the following rules:

less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → s_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,0}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
s_{U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg)) → s_{less_out_gg}(less_out_gg)
U3_gg_{U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg)) → U3_gg_{less_out_gg}(less_out_gg)

Q is empty.
We have to consider all (P,Q,R)-chains.

(85) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes.

(86) Obligation:

Q DP problem:
The TRS P consists of the following rules:

U1_GG_{s_1,s_1,less_out_gg}(s_{s_1}(s_{s_1}(z0)), s_{s_1}(z1), less_out_gg) → P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{s_1}(z1))
P_IN_GG_{s_1,s_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{s_1}(z1)) → U1_GG_{s_1,s_1,U3_gg_1}(s_{s_1}(s_{s_1}(s_{s_1}(z0))), s_{s_1}(z1), U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(s_{s_1}(z0)), z1)))
U1_GG_{s_1,s_1,U3_gg_1}(flat0, flat1, U3_gg_{less_out_gg}(less_out_gg)) → U1_GG_{s_1,s_1,less_out_gg}(flat0, flat1, less_out_gg)

The TRS R consists of the following rules:

less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{0}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0)), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{0}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → s_{less_out_gg}(less_out_gg)
s_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → s_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_in_gg_2}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{0}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{s_1}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{less_out_gg}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(0, s_{U3_gg_1}(_x0))) → U3_gg_{less_out_gg}(less_out_gg)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,0}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,0}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,s_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_out_gg}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1)), flat1) → less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)), flat1)
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_in_gg_2,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{0,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{s_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{less_out_gg,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(flat0, less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
s_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → s_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_in_gg_2}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_in_gg_2,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{0}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{0,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{s_1}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{s_1,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{less_out_gg}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{less_out_gg,U3_gg_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_in_gg_2}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_in_gg_2}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{0}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,0}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{s_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,s_1}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{less_out_gg}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,less_out_gg}(_x0, _x1)))
U3_gg_{less_in_gg_2}(less_in_gg_{s_1,s_1}(s_{U3_gg_1}(_x0), s_{U3_gg_1}(_x1))) → U3_gg_{U3_gg_1}(U3_gg_{less_in_gg_2}(less_in_gg_{U3_gg_1,U3_gg_1}(_x0, _x1)))
less_in_gg_{U3_gg_1,less_in_gg_2}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,less_in_gg_2}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,0}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,0}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,s_1}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,s_1}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,less_out_gg}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,less_out_gg}(less_out_gg, flat1)
less_in_gg_{U3_gg_1,U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg), flat1) → less_in_gg_{less_out_gg,U3_gg_1}(less_out_gg, flat1)
less_in_gg_{less_in_gg_2,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{less_in_gg_2,less_out_gg}(flat0, less_out_gg)
less_in_gg_{0,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{0,less_out_gg}(flat0, less_out_gg)
less_in_gg_{s_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{s_1,less_out_gg}(flat0, less_out_gg)
less_in_gg_{less_out_gg,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{less_out_gg,less_out_gg}(flat0, less_out_gg)
less_in_gg_{U3_gg_1,U3_gg_1}(flat0, U3_gg_{less_out_gg}(less_out_gg)) → less_in_gg_{U3_gg_1,less_out_gg}(flat0, less_out_gg)
s_{U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg)) → s_{less_out_gg}(less_out_gg)
U3_gg_{U3_gg_1}(U3_gg_{less_out_gg}(less_out_gg)) → U3_gg_{less_out_gg}(less_out_gg)

Q is empty.
We have to consider all (P,Q,R)-chains.