/export/starexec/sandbox/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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WORST_CASE(Omega(n^1), O(n^2))
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2).

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 312 ms]
(4) CpxRelTRS
(5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CpxWeightedTrs
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CpxTypedWeightedTrs
    (9) CompletionProof [UPPER BOUND(ID), 0 ms]
    (10) CpxTypedWeightedCompleteTrs
    (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 17 ms]
    (12) CpxRNTS
    (13) CompleteCoflocoProof [FINISHED, 53.0 s]
    (14) BOUNDS(1, n^2)
(15) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(16) CpxRelTRS
    (17) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (18) typed CpxTrs
    (19) OrderProof [LOWER BOUND(ID), 7 ms]
    (20) typed CpxTrs
    (21) RewriteLemmaProof [LOWER BOUND(ID), 511 ms]
    (22) BEST
        (23) proven lower bound
            (24) LowerBoundPropagationProof [FINISHED, 0 ms]
            (25) BOUNDS(n^1, INF)
        (26) typed CpxTrs
            (27) RewriteLemmaProof [LOWER BOUND(ID), 162 ms]
            (28) typed CpxTrs
            (29) RewriteLemmaProof [LOWER BOUND(ID), 128 ms]
            (30) typed CpxTrs
            (31) RewriteLemmaProof [LOWER BOUND(ID), 360 ms]
            (32) BOUNDS(1, INF)


----------------------------------------

(0)
Obligation:
The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2).


The TRS R consists of the following rules:

   cond1(true, x, y) -> cond2(gr(y, 0), x, y)
   cond2(true, x, y) -> cond2(gr(y, 0), p(x), p(y))
   cond2(false, x, y) -> cond1(and(eq(x, y), gr(x, 0)), x, y)
   gr(0, x) -> false
   gr(s(x), 0) -> true
   gr(s(x), s(y)) -> gr(x, y)
   p(0) -> 0
   p(s(x)) -> x
   eq(0, 0) -> true
   eq(s(x), 0) -> false
   eq(0, s(x)) -> false
   eq(s(x), s(y)) -> eq(x, y)
   and(true, true) -> true
   and(false, x) -> false
   and(x, false) -> false

S is empty.
Rewrite Strategy: INNERMOST
----------------------------------------

(1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID))
The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem:

   encArg(true) -> true
   encArg(0) -> 0
   encArg(false) -> false
   encArg(s(x_1)) -> s(encArg(x_1))
   encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2))
   encArg(cons_p(x_1)) -> p(encArg(x_1))
   encArg(cons_eq(x_1, x_2)) -> eq(encArg(x_1), encArg(x_2))
   encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2))
   encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_true -> true
   encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2))
   encode_0 -> 0
   encode_p(x_1) -> p(encArg(x_1))
   encode_false -> false
   encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2))
   encode_eq(x_1, x_2) -> eq(encArg(x_1), encArg(x_2))
   encode_s(x_1) -> s(encArg(x_1))


----------------------------------------

(2)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2).


The TRS R consists of the following rules:

   cond1(true, x, y) -> cond2(gr(y, 0), x, y)
   cond2(true, x, y) -> cond2(gr(y, 0), p(x), p(y))
   cond2(false, x, y) -> cond1(and(eq(x, y), gr(x, 0)), x, y)
   gr(0, x) -> false
   gr(s(x), 0) -> true
   gr(s(x), s(y)) -> gr(x, y)
   p(0) -> 0
   p(s(x)) -> x
   eq(0, 0) -> true
   eq(s(x), 0) -> false
   eq(0, s(x)) -> false
   eq(s(x), s(y)) -> eq(x, y)
   and(true, true) -> true
   and(false, x) -> false
   and(x, false) -> false

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

   encArg(true) -> true
   encArg(0) -> 0
   encArg(false) -> false
   encArg(s(x_1)) -> s(encArg(x_1))
   encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2))
   encArg(cons_p(x_1)) -> p(encArg(x_1))
   encArg(cons_eq(x_1, x_2)) -> eq(encArg(x_1), encArg(x_2))
   encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2))
   encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_true -> true
   encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2))
   encode_0 -> 0
   encode_p(x_1) -> p(encArg(x_1))
   encode_false -> false
   encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2))
   encode_eq(x_1, x_2) -> eq(encArg(x_1), encArg(x_2))
   encode_s(x_1) -> s(encArg(x_1))

Rewrite Strategy: INNERMOST
----------------------------------------

(3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID))
proved innermost termination of relative rules
----------------------------------------

(4)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2).


The TRS R consists of the following rules:

   cond1(true, x, y) -> cond2(gr(y, 0), x, y)
   cond2(true, x, y) -> cond2(gr(y, 0), p(x), p(y))
   cond2(false, x, y) -> cond1(and(eq(x, y), gr(x, 0)), x, y)
   gr(0, x) -> false
   gr(s(x), 0) -> true
   gr(s(x), s(y)) -> gr(x, y)
   p(0) -> 0
   p(s(x)) -> x
   eq(0, 0) -> true
   eq(s(x), 0) -> false
   eq(0, s(x)) -> false
   eq(s(x), s(y)) -> eq(x, y)
   and(true, true) -> true
   and(false, x) -> false
   and(x, false) -> false

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

   encArg(true) -> true
   encArg(0) -> 0
   encArg(false) -> false
   encArg(s(x_1)) -> s(encArg(x_1))
   encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2))
   encArg(cons_p(x_1)) -> p(encArg(x_1))
   encArg(cons_eq(x_1, x_2)) -> eq(encArg(x_1), encArg(x_2))
   encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2))
   encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_true -> true
   encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2))
   encode_0 -> 0
   encode_p(x_1) -> p(encArg(x_1))
   encode_false -> false
   encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2))
   encode_eq(x_1, x_2) -> eq(encArg(x_1), encArg(x_2))
   encode_s(x_1) -> s(encArg(x_1))

Rewrite Strategy: INNERMOST
----------------------------------------

(5) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
Transformed relative TRS to weighted TRS
----------------------------------------

(6)
Obligation:
The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2).


The TRS R consists of the following rules:

   cond1(true, x, y) -> cond2(gr(y, 0), x, y) [1]
   cond2(true, x, y) -> cond2(gr(y, 0), p(x), p(y)) [1]
   cond2(false, x, y) -> cond1(and(eq(x, y), gr(x, 0)), x, y) [1]
   gr(0, x) -> false [1]
   gr(s(x), 0) -> true [1]
   gr(s(x), s(y)) -> gr(x, y) [1]
   p(0) -> 0 [1]
   p(s(x)) -> x [1]
   eq(0, 0) -> true [1]
   eq(s(x), 0) -> false [1]
   eq(0, s(x)) -> false [1]
   eq(s(x), s(y)) -> eq(x, y) [1]
   and(true, true) -> true [1]
   and(false, x) -> false [1]
   and(x, false) -> false [1]
   encArg(true) -> true [0]
   encArg(0) -> 0 [0]
   encArg(false) -> false [0]
   encArg(s(x_1)) -> s(encArg(x_1)) [0]
   encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_p(x_1)) -> p(encArg(x_1)) [0]
   encArg(cons_eq(x_1, x_2)) -> eq(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) [0]
   encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_true -> true [0]
   encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) [0]
   encode_0 -> 0 [0]
   encode_p(x_1) -> p(encArg(x_1)) [0]
   encode_false -> false [0]
   encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) [0]
   encode_eq(x_1, x_2) -> eq(encArg(x_1), encArg(x_2)) [0]
   encode_s(x_1) -> s(encArg(x_1)) [0]

Rewrite Strategy: INNERMOST
----------------------------------------

(7) TypeInferenceProof (BOTH BOUNDS(ID, ID))
Infered types.
----------------------------------------

(8)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   cond1(true, x, y) -> cond2(gr(y, 0), x, y) [1]
   cond2(true, x, y) -> cond2(gr(y, 0), p(x), p(y)) [1]
   cond2(false, x, y) -> cond1(and(eq(x, y), gr(x, 0)), x, y) [1]
   gr(0, x) -> false [1]
   gr(s(x), 0) -> true [1]
   gr(s(x), s(y)) -> gr(x, y) [1]
   p(0) -> 0 [1]
   p(s(x)) -> x [1]
   eq(0, 0) -> true [1]
   eq(s(x), 0) -> false [1]
   eq(0, s(x)) -> false [1]
   eq(s(x), s(y)) -> eq(x, y) [1]
   and(true, true) -> true [1]
   and(false, x) -> false [1]
   and(x, false) -> false [1]
   encArg(true) -> true [0]
   encArg(0) -> 0 [0]
   encArg(false) -> false [0]
   encArg(s(x_1)) -> s(encArg(x_1)) [0]
   encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_p(x_1)) -> p(encArg(x_1)) [0]
   encArg(cons_eq(x_1, x_2)) -> eq(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) [0]
   encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_true -> true [0]
   encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) [0]
   encode_0 -> 0 [0]
   encode_p(x_1) -> p(encArg(x_1)) [0]
   encode_false -> false [0]
   encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) [0]
   encode_eq(x_1, x_2) -> eq(encArg(x_1), encArg(x_2)) [0]
   encode_s(x_1) -> s(encArg(x_1)) [0]

The TRS has the following type information:
cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
true :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
0 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
false :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
and :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
eq :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
s :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encArg :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_eq :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_and :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_true :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_0 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_false :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_and :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_eq :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_s :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and

Rewrite Strategy: INNERMOST
----------------------------------------

(9) CompletionProof (UPPER BOUND(ID))
The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added:

   encArg(v0) -> null_encArg [0]
   encode_cond1(v0, v1, v2) -> null_encode_cond1 [0]
   encode_true -> null_encode_true [0]
   encode_cond2(v0, v1, v2) -> null_encode_cond2 [0]
   encode_gr(v0, v1) -> null_encode_gr [0]
   encode_0 -> null_encode_0 [0]
   encode_p(v0) -> null_encode_p [0]
   encode_false -> null_encode_false [0]
   encode_and(v0, v1) -> null_encode_and [0]
   encode_eq(v0, v1) -> null_encode_eq [0]
   encode_s(v0) -> null_encode_s [0]
   cond1(v0, v1, v2) -> null_cond1 [0]
   cond2(v0, v1, v2) -> null_cond2 [0]
   gr(v0, v1) -> null_gr [0]
   p(v0) -> null_p [0]
   eq(v0, v1) -> null_eq [0]
   and(v0, v1) -> null_and [0]

And the following fresh constants:    null_encArg, null_encode_cond1, null_encode_true, null_encode_cond2, null_encode_gr, null_encode_0, null_encode_p, null_encode_false, null_encode_and, null_encode_eq, null_encode_s, null_cond1, null_cond2, null_gr, null_p, null_eq, null_and

----------------------------------------

(10)
Obligation:
Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is:

Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   cond1(true, x, y) -> cond2(gr(y, 0), x, y) [1]
   cond2(true, x, y) -> cond2(gr(y, 0), p(x), p(y)) [1]
   cond2(false, x, y) -> cond1(and(eq(x, y), gr(x, 0)), x, y) [1]
   gr(0, x) -> false [1]
   gr(s(x), 0) -> true [1]
   gr(s(x), s(y)) -> gr(x, y) [1]
   p(0) -> 0 [1]
   p(s(x)) -> x [1]
   eq(0, 0) -> true [1]
   eq(s(x), 0) -> false [1]
   eq(0, s(x)) -> false [1]
   eq(s(x), s(y)) -> eq(x, y) [1]
   and(true, true) -> true [1]
   and(false, x) -> false [1]
   and(x, false) -> false [1]
   encArg(true) -> true [0]
   encArg(0) -> 0 [0]
   encArg(false) -> false [0]
   encArg(s(x_1)) -> s(encArg(x_1)) [0]
   encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_p(x_1)) -> p(encArg(x_1)) [0]
   encArg(cons_eq(x_1, x_2)) -> eq(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) [0]
   encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_true -> true [0]
   encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) [0]
   encode_0 -> 0 [0]
   encode_p(x_1) -> p(encArg(x_1)) [0]
   encode_false -> false [0]
   encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) [0]
   encode_eq(x_1, x_2) -> eq(encArg(x_1), encArg(x_2)) [0]
   encode_s(x_1) -> s(encArg(x_1)) [0]
   encArg(v0) -> null_encArg [0]
   encode_cond1(v0, v1, v2) -> null_encode_cond1 [0]
   encode_true -> null_encode_true [0]
   encode_cond2(v0, v1, v2) -> null_encode_cond2 [0]
   encode_gr(v0, v1) -> null_encode_gr [0]
   encode_0 -> null_encode_0 [0]
   encode_p(v0) -> null_encode_p [0]
   encode_false -> null_encode_false [0]
   encode_and(v0, v1) -> null_encode_and [0]
   encode_eq(v0, v1) -> null_encode_eq [0]
   encode_s(v0) -> null_encode_s [0]
   cond1(v0, v1, v2) -> null_cond1 [0]
   cond2(v0, v1, v2) -> null_cond2 [0]
   gr(v0, v1) -> null_gr [0]
   p(v0) -> null_p [0]
   eq(v0, v1) -> null_eq [0]
   and(v0, v1) -> null_and [0]

The TRS has the following type information:
cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
true :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
0 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
false :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
and :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
eq :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
s :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
encArg :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
cons_cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
cons_cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
cons_gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
cons_p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
cons_eq :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
cons_and :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
encode_cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
encode_true :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
encode_cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
encode_gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
encode_0 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
encode_p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
encode_false :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
encode_and :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
encode_eq :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
encode_s :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
null_encArg :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
null_encode_cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
null_encode_true :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
null_encode_cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
null_encode_gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
null_encode_0 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
null_encode_p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
null_encode_false :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
null_encode_and :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
null_encode_eq :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
null_encode_s :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
null_cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
null_cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
null_gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
null_p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
null_eq :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and
null_and :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_p:null_encode_false:null_encode_and:null_encode_eq:null_encode_s:null_cond1:null_cond2:null_gr:null_p:null_eq:null_and

Rewrite Strategy: INNERMOST
----------------------------------------

(11) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID))
Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction.
The constant constructors are abstracted as follows:

   true => 2
   0 => 0
   false => 1
   null_encArg => 0
   null_encode_cond1 => 0
   null_encode_true => 0
   null_encode_cond2 => 0
   null_encode_gr => 0
   null_encode_0 => 0
   null_encode_p => 0
   null_encode_false => 0
   null_encode_and => 0
   null_encode_eq => 0
   null_encode_s => 0
   null_cond1 => 0
   null_cond2 => 0
   null_gr => 0
   null_p => 0
   null_eq => 0
   null_and => 0

----------------------------------------

(12)
Obligation:
Complexity RNTS consisting of the following rules:

   and(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 1 }-> 1 :|: z' = x, z = 1, x >= 0
   and(z, z') -{ 1 }-> 1 :|: x >= 0, z' = 1, z = x
   and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   cond1(z, z', z'') -{ 1 }-> cond2(gr(y, 0), x, y) :|: z = 2, z' = x, z'' = y, x >= 0, y >= 0
   cond1(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   cond2(z, z', z'') -{ 1 }-> cond2(gr(y, 0), p(x), p(y)) :|: z = 2, z' = x, z'' = y, x >= 0, y >= 0
   cond2(z, z', z'') -{ 1 }-> cond1(and(eq(x, y), gr(x, 0)), x, y) :|: z' = x, z'' = y, z = 1, x >= 0, y >= 0
   cond2(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   encArg(z) -{ 0 }-> p(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> eq(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> and(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encArg(z) -{ 0 }-> 1 + encArg(x_1) :|: z = 1 + x_1, x_1 >= 0
   encode_0 -{ 0 }-> 0 :|: 
   encode_and(z, z') -{ 0 }-> and(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   encode_cond1(z, z', z'') -{ 0 }-> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, x_3 >= 0, x_2 >= 0, z = x_1, z' = x_2, z'' = x_3
   encode_cond1(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   encode_cond2(z, z', z'') -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, x_3 >= 0, x_2 >= 0, z = x_1, z' = x_2, z'' = x_3
   encode_cond2(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   encode_eq(z, z') -{ 0 }-> eq(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_eq(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   encode_false -{ 0 }-> 1 :|: 
   encode_false -{ 0 }-> 0 :|: 
   encode_gr(z, z') -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_gr(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   encode_p(z) -{ 0 }-> p(encArg(x_1)) :|: x_1 >= 0, z = x_1
   encode_p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_s(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1
   encode_true -{ 0 }-> 2 :|: 
   encode_true -{ 0 }-> 0 :|: 
   eq(z, z') -{ 1 }-> eq(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x
   eq(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0
   eq(z, z') -{ 1 }-> 1 :|: x >= 0, z = 1 + x, z' = 0
   eq(z, z') -{ 1 }-> 1 :|: z' = 1 + x, x >= 0, z = 0
   eq(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   gr(z, z') -{ 1 }-> gr(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x
   gr(z, z') -{ 1 }-> 2 :|: x >= 0, z = 1 + x, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' = x, x >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   p(z) -{ 1 }-> x :|: x >= 0, z = 1 + x
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0

Only complete derivations are relevant for the runtime complexity.

----------------------------------------

(13) CompleteCoflocoProof (FINISHED)
Transformed the RNTS (where only complete derivations are relevant) into cost relations for CoFloCo:

eq(start(V1, V, V2),0,[cond1(V1, V, V2, Out)],[V1 >= 0,V >= 0,V2 >= 0]).
eq(start(V1, V, V2),0,[cond2(V1, V, V2, Out)],[V1 >= 0,V >= 0,V2 >= 0]).
eq(start(V1, V, V2),0,[gr(V1, V, Out)],[V1 >= 0,V >= 0]).
eq(start(V1, V, V2),0,[p(V1, Out)],[V1 >= 0]).
eq(start(V1, V, V2),0,[eq(V1, V, Out)],[V1 >= 0,V >= 0]).
eq(start(V1, V, V2),0,[and(V1, V, Out)],[V1 >= 0,V >= 0]).
eq(start(V1, V, V2),0,[encArg(V1, Out)],[V1 >= 0]).
eq(start(V1, V, V2),0,[fun(V1, V, V2, Out)],[V1 >= 0,V >= 0,V2 >= 0]).
eq(start(V1, V, V2),0,[fun1(Out)],[]).
eq(start(V1, V, V2),0,[fun2(V1, V, V2, Out)],[V1 >= 0,V >= 0,V2 >= 0]).
eq(start(V1, V, V2),0,[fun3(V1, V, Out)],[V1 >= 0,V >= 0]).
eq(start(V1, V, V2),0,[fun4(Out)],[]).
eq(start(V1, V, V2),0,[fun5(V1, Out)],[V1 >= 0]).
eq(start(V1, V, V2),0,[fun6(Out)],[]).
eq(start(V1, V, V2),0,[fun7(V1, V, Out)],[V1 >= 0,V >= 0]).
eq(start(V1, V, V2),0,[fun8(V1, V, Out)],[V1 >= 0,V >= 0]).
eq(start(V1, V, V2),0,[fun9(V1, Out)],[V1 >= 0]).
eq(cond1(V1, V, V2, Out),1,[gr(V3, 0, Ret0),cond2(Ret0, V4, V3, Ret)],[Out = Ret,V1 = 2,V = V4,V2 = V3,V4 >= 0,V3 >= 0]).
eq(cond2(V1, V, V2, Out),1,[gr(V6, 0, Ret01),p(V5, Ret1),p(V6, Ret2),cond2(Ret01, Ret1, Ret2, Ret3)],[Out = Ret3,V1 = 2,V = V5,V2 = V6,V5 >= 0,V6 >= 0]).
eq(cond2(V1, V, V2, Out),1,[eq(V8, V7, Ret00),gr(V8, 0, Ret011),and(Ret00, Ret011, Ret02),cond1(Ret02, V8, V7, Ret4)],[Out = Ret4,V = V8,V2 = V7,V1 = 1,V8 >= 0,V7 >= 0]).
eq(gr(V1, V, Out),1,[],[Out = 1,V = V9,V9 >= 0,V1 = 0]).
eq(gr(V1, V, Out),1,[],[Out = 2,V10 >= 0,V1 = 1 + V10,V = 0]).
eq(gr(V1, V, Out),1,[gr(V12, V11, Ret5)],[Out = Ret5,V = 1 + V11,V12 >= 0,V11 >= 0,V1 = 1 + V12]).
eq(p(V1, Out),1,[],[Out = 0,V1 = 0]).
eq(p(V1, Out),1,[],[Out = V13,V13 >= 0,V1 = 1 + V13]).
eq(eq(V1, V, Out),1,[],[Out = 2,V1 = 0,V = 0]).
eq(eq(V1, V, Out),1,[],[Out = 1,V14 >= 0,V1 = 1 + V14,V = 0]).
eq(eq(V1, V, Out),1,[],[Out = 1,V = 1 + V15,V15 >= 0,V1 = 0]).
eq(eq(V1, V, Out),1,[eq(V17, V16, Ret6)],[Out = Ret6,V = 1 + V16,V17 >= 0,V16 >= 0,V1 = 1 + V17]).
eq(and(V1, V, Out),1,[],[Out = 2,V1 = 2,V = 2]).
eq(and(V1, V, Out),1,[],[Out = 1,V = V18,V1 = 1,V18 >= 0]).
eq(and(V1, V, Out),1,[],[Out = 1,V19 >= 0,V = 1,V1 = V19]).
eq(encArg(V1, Out),0,[],[Out = 2,V1 = 2]).
eq(encArg(V1, Out),0,[],[Out = 0,V1 = 0]).
eq(encArg(V1, Out),0,[],[Out = 1,V1 = 1]).
eq(encArg(V1, Out),0,[encArg(V20, Ret11)],[Out = 1 + Ret11,V1 = 1 + V20,V20 >= 0]).
eq(encArg(V1, Out),0,[encArg(V22, Ret03),encArg(V23, Ret12),encArg(V21, Ret21),cond1(Ret03, Ret12, Ret21, Ret7)],[Out = Ret7,V22 >= 0,V1 = 1 + V21 + V22 + V23,V21 >= 0,V23 >= 0]).
eq(encArg(V1, Out),0,[encArg(V24, Ret04),encArg(V26, Ret13),encArg(V25, Ret22),cond2(Ret04, Ret13, Ret22, Ret8)],[Out = Ret8,V24 >= 0,V1 = 1 + V24 + V25 + V26,V25 >= 0,V26 >= 0]).
eq(encArg(V1, Out),0,[encArg(V28, Ret05),encArg(V27, Ret14),gr(Ret05, Ret14, Ret9)],[Out = Ret9,V28 >= 0,V1 = 1 + V27 + V28,V27 >= 0]).
eq(encArg(V1, Out),0,[encArg(V29, Ret06),p(Ret06, Ret10)],[Out = Ret10,V1 = 1 + V29,V29 >= 0]).
eq(encArg(V1, Out),0,[encArg(V31, Ret07),encArg(V30, Ret15),eq(Ret07, Ret15, Ret16)],[Out = Ret16,V31 >= 0,V1 = 1 + V30 + V31,V30 >= 0]).
eq(encArg(V1, Out),0,[encArg(V32, Ret08),encArg(V33, Ret17),and(Ret08, Ret17, Ret18)],[Out = Ret18,V32 >= 0,V1 = 1 + V32 + V33,V33 >= 0]).
eq(fun(V1, V, V2, Out),0,[encArg(V36, Ret09),encArg(V35, Ret19),encArg(V34, Ret23),cond1(Ret09, Ret19, Ret23, Ret20)],[Out = Ret20,V36 >= 0,V34 >= 0,V35 >= 0,V1 = V36,V = V35,V2 = V34]).
eq(fun1(Out),0,[],[Out = 2]).
eq(fun2(V1, V, V2, Out),0,[encArg(V39, Ret010),encArg(V38, Ret110),encArg(V37, Ret24),cond2(Ret010, Ret110, Ret24, Ret25)],[Out = Ret25,V39 >= 0,V37 >= 0,V38 >= 0,V1 = V39,V = V38,V2 = V37]).
eq(fun3(V1, V, Out),0,[encArg(V40, Ret012),encArg(V41, Ret111),gr(Ret012, Ret111, Ret26)],[Out = Ret26,V40 >= 0,V41 >= 0,V1 = V40,V = V41]).
eq(fun4(Out),0,[],[Out = 0]).
eq(fun5(V1, Out),0,[encArg(V42, Ret013),p(Ret013, Ret27)],[Out = Ret27,V42 >= 0,V1 = V42]).
eq(fun6(Out),0,[],[Out = 1]).
eq(fun7(V1, V, Out),0,[encArg(V43, Ret014),encArg(V44, Ret112),and(Ret014, Ret112, Ret28)],[Out = Ret28,V43 >= 0,V44 >= 0,V1 = V43,V = V44]).
eq(fun8(V1, V, Out),0,[encArg(V46, Ret015),encArg(V45, Ret113),eq(Ret015, Ret113, Ret29)],[Out = Ret29,V46 >= 0,V45 >= 0,V1 = V46,V = V45]).
eq(fun9(V1, Out),0,[encArg(V47, Ret114)],[Out = 1 + Ret114,V47 >= 0,V1 = V47]).
eq(encArg(V1, Out),0,[],[Out = 0,V48 >= 0,V1 = V48]).
eq(fun(V1, V, V2, Out),0,[],[Out = 0,V50 >= 0,V2 = V51,V49 >= 0,V1 = V50,V = V49,V51 >= 0]).
eq(fun1(Out),0,[],[Out = 0]).
eq(fun2(V1, V, V2, Out),0,[],[Out = 0,V54 >= 0,V2 = V52,V53 >= 0,V1 = V54,V = V53,V52 >= 0]).
eq(fun3(V1, V, Out),0,[],[Out = 0,V55 >= 0,V56 >= 0,V1 = V55,V = V56]).
eq(fun5(V1, Out),0,[],[Out = 0,V57 >= 0,V1 = V57]).
eq(fun6(Out),0,[],[Out = 0]).
eq(fun7(V1, V, Out),0,[],[Out = 0,V58 >= 0,V59 >= 0,V1 = V58,V = V59]).
eq(fun8(V1, V, Out),0,[],[Out = 0,V61 >= 0,V60 >= 0,V1 = V61,V = V60]).
eq(fun9(V1, Out),0,[],[Out = 0,V62 >= 0,V1 = V62]).
eq(cond1(V1, V, V2, Out),0,[],[Out = 0,V63 >= 0,V2 = V65,V64 >= 0,V1 = V63,V = V64,V65 >= 0]).
eq(cond2(V1, V, V2, Out),0,[],[Out = 0,V67 >= 0,V2 = V68,V66 >= 0,V1 = V67,V = V66,V68 >= 0]).
eq(gr(V1, V, Out),0,[],[Out = 0,V70 >= 0,V69 >= 0,V1 = V70,V = V69]).
eq(p(V1, Out),0,[],[Out = 0,V71 >= 0,V1 = V71]).
eq(eq(V1, V, Out),0,[],[Out = 0,V73 >= 0,V72 >= 0,V1 = V73,V = V72]).
eq(and(V1, V, Out),0,[],[Out = 0,V75 >= 0,V74 >= 0,V1 = V75,V = V74]).
input_output_vars(cond1(V1,V,V2,Out),[V1,V,V2],[Out]).
input_output_vars(cond2(V1,V,V2,Out),[V1,V,V2],[Out]).
input_output_vars(gr(V1,V,Out),[V1,V],[Out]).
input_output_vars(p(V1,Out),[V1],[Out]).
input_output_vars(eq(V1,V,Out),[V1,V],[Out]).
input_output_vars(and(V1,V,Out),[V1,V],[Out]).
input_output_vars(encArg(V1,Out),[V1],[Out]).
input_output_vars(fun(V1,V,V2,Out),[V1,V,V2],[Out]).
input_output_vars(fun1(Out),[],[Out]).
input_output_vars(fun2(V1,V,V2,Out),[V1,V,V2],[Out]).
input_output_vars(fun3(V1,V,Out),[V1,V],[Out]).
input_output_vars(fun4(Out),[],[Out]).
input_output_vars(fun5(V1,Out),[V1],[Out]).
input_output_vars(fun6(Out),[],[Out]).
input_output_vars(fun7(V1,V,Out),[V1,V],[Out]).
input_output_vars(fun8(V1,V,Out),[V1,V],[Out]).
input_output_vars(fun9(V1,Out),[V1],[Out]).


CoFloCo proof output:
Preprocessing Cost Relations
=====================================

#### Computed strongly connected components 
0. non_recursive  : [and/3]
1. recursive  : [eq/3]
2. recursive  : [gr/3]
3. non_recursive  : [p/2]
4. recursive  : [cond1/4,cond2/4]
5. recursive [non_tail,multiple] : [encArg/2]
6. non_recursive  : [fun/4]
7. non_recursive  : [fun1/1]
8. non_recursive  : [fun2/4]
9. non_recursive  : [fun3/3]
10. non_recursive  : [fun4/1]
11. non_recursive  : [fun5/2]
12. non_recursive  : [fun6/1]
13. non_recursive  : [fun7/3]
14. non_recursive  : [fun8/3]
15. non_recursive  : [fun9/2]
16. non_recursive  : [start/3]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into and/3
1. SCC is partially evaluated into eq/3
2. SCC is partially evaluated into gr/3
3. SCC is partially evaluated into p/2
4. SCC is partially evaluated into cond2/4
5. SCC is partially evaluated into encArg/2
6. SCC is partially evaluated into fun/4
7. SCC is partially evaluated into fun1/1
8. SCC is partially evaluated into fun2/4
9. SCC is partially evaluated into fun3/3
10. SCC is completely evaluated into other SCCs
11. SCC is partially evaluated into fun5/2
12. SCC is partially evaluated into fun6/1
13. SCC is partially evaluated into fun7/3
14. SCC is partially evaluated into fun8/3
15. SCC is partially evaluated into fun9/2
16. SCC is partially evaluated into start/3

Control-Flow Refinement of Cost Relations
=====================================

### Specialization of cost equations and/3 
* CE 37 is refined into CE [68] 
* CE 36 is refined into CE [69] 
* CE 34 is refined into CE [70] 
* CE 35 is refined into CE [71] 


### Cost equations --> "Loop" of and/3 
* CEs [68] --> Loop 38 
* CEs [69] --> Loop 39 
* CEs [70] --> Loop 40 
* CEs [71] --> Loop 41 

### Ranking functions of CR and(V1,V,Out) 

#### Partial ranking functions of CR and(V1,V,Out) 


### Specialization of cost equations eq/3 
* CE 33 is refined into CE [72] 
* CE 30 is refined into CE [73] 
* CE 31 is refined into CE [74] 
* CE 29 is refined into CE [75] 
* CE 32 is refined into CE [76] 


### Cost equations --> "Loop" of eq/3 
* CEs [76] --> Loop 42 
* CEs [72] --> Loop 43 
* CEs [73] --> Loop 44 
* CEs [74] --> Loop 45 
* CEs [75] --> Loop 46 

### Ranking functions of CR eq(V1,V,Out) 
* RF of phase [42]: [V,V1]

#### Partial ranking functions of CR eq(V1,V,Out) 
* Partial RF of phase [42]:
  - RF of loop [42:1]:
    V
    V1


### Specialization of cost equations gr/3 
* CE 21 is refined into CE [77] 
* CE 19 is refined into CE [78] 
* CE 18 is refined into CE [79] 
* CE 20 is refined into CE [80] 


### Cost equations --> "Loop" of gr/3 
* CEs [80] --> Loop 47 
* CEs [77] --> Loop 48 
* CEs [78] --> Loop 49 
* CEs [79] --> Loop 50 

### Ranking functions of CR gr(V1,V,Out) 
* RF of phase [47]: [V,V1]

#### Partial ranking functions of CR gr(V1,V,Out) 
* Partial RF of phase [47]:
  - RF of loop [47:1]:
    V
    V1


### Specialization of cost equations p/2 
* CE 27 is refined into CE [81] 
* CE 26 is refined into CE [82] 
* CE 28 is refined into CE [83] 


### Cost equations --> "Loop" of p/2 
* CEs [81] --> Loop 51 
* CEs [82,83] --> Loop 52 

### Ranking functions of CR p(V1,Out) 

#### Partial ranking functions of CR p(V1,Out) 


### Specialization of cost equations cond2/4 
* CE 22 is refined into CE [84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110] 
* CE 25 is refined into CE [111] 
* CE 24 is refined into CE [112,113,114,115,116,117,118,119,120,121] 
* CE 23 is refined into CE [122,123] 


### Cost equations --> "Loop" of cond2/4 
* CEs [117] --> Loop 53 
* CEs [116] --> Loop 54 
* CEs [115] --> Loop 55 
* CEs [114] --> Loop 56 
* CEs [121] --> Loop 57 
* CEs [120] --> Loop 58 
* CEs [119] --> Loop 59 
* CEs [118] --> Loop 60 
* CEs [113] --> Loop 61 
* CEs [112] --> Loop 62 
* CEs [122] --> Loop 63 
* CEs [123] --> Loop 64 
* CEs [108,109,110] --> Loop 65 
* CEs [92,93,94,95] --> Loop 66 
* CEs [84,85,86,87,88,89,90,91,96,97,98,99,100,101,102,103,104,105,106,107,111] --> Loop 67 

### Ranking functions of CR cond2(V1,V,V2,Out) 
* RF of phase [53]: [V,V2]
* RF of phase [55]: [V2]

#### Partial ranking functions of CR cond2(V1,V,V2,Out) 
* Partial RF of phase [53]:
  - RF of loop [53:1]:
    V
    V2
* Partial RF of phase [55]:
  - RF of loop [55:1]:
    V2


### Specialization of cost equations encArg/2 
* CE 41 is refined into CE [124] 
* CE 40 is refined into CE [125] 
* CE 42 is refined into CE [126] 
* CE 45 is refined into CE [127,128,129,130,131] 
* CE 47 is refined into CE [132,133,134,135,136,137,138] 
* CE 48 is refined into CE [139,140,141,142] 
* CE 43 is refined into CE [143] 
* CE 46 is refined into CE [144,145] 
* CE 39 is refined into CE [146,147,148,149] 
* CE 38 is refined into CE [150] 
* CE 44 is refined into CE [151,152,153] 


### Cost equations --> "Loop" of encArg/2 
* CEs [146,147,148,149,153] --> Loop 68 
* CEs [150,151,152] --> Loop 69 
* CEs [143] --> Loop 70 
* CEs [145] --> Loop 71 
* CEs [144] --> Loop 72 
* CEs [131] --> Loop 73 
* CEs [128] --> Loop 74 
* CEs [138,140] --> Loop 75 
* CEs [132] --> Loop 76 
* CEs [137] --> Loop 77 
* CEs [130,136] --> Loop 78 
* CEs [141] --> Loop 79 
* CEs [134] --> Loop 80 
* CEs [139] --> Loop 81 
* CEs [127,133] --> Loop 82 
* CEs [129,135,142] --> Loop 83 
* CEs [124] --> Loop 84 
* CEs [125] --> Loop 85 
* CEs [126] --> Loop 86 

### Ranking functions of CR encArg(V1,Out) 
* RF of phase [68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83]: [V1]

#### Partial ranking functions of CR encArg(V1,Out) 
* Partial RF of phase [68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83]:
  - RF of loop [68:1,68:2,68:3,69:1,69:2,69:3,70:1,71:1,72:1,73:1,73:2,74:1,74:2,75:1,75:2,76:1,76:2,77:1,77:2,78:1,78:2,79:1,79:2,80:1,80:2,81:1,81:2,82:1,82:2,83:1,83:2]:
    V1


### Specialization of cost equations fun/4 
* CE 49 is refined into CE [154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180] 
* CE 50 is refined into CE [181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234] 
* CE 51 is refined into CE [235] 


### Cost equations --> "Loop" of fun/4 
* CEs [157,158,159,175,176,177,190,191,192,193,194,195,196,197,198] --> Loop 87 
* CEs [155,161,164,170,173,179,185,186,187,203,204,205,212,213,214,230,231,232] --> Loop 88 
* CEs [154,156,160,162,163,165,166,167,168,169,171,172,174,178,180,181,182,183,184,188,189,199,200,201,202,206,207,208,209,210,211,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,233,234,235] --> Loop 89 

### Ranking functions of CR fun(V1,V,V2,Out) 

#### Partial ranking functions of CR fun(V1,V,V2,Out) 


### Specialization of cost equations fun1/1 
* CE 52 is refined into CE [236] 
* CE 53 is refined into CE [237] 


### Cost equations --> "Loop" of fun1/1 
* CEs [236] --> Loop 90 
* CEs [237] --> Loop 91 

### Ranking functions of CR fun1(Out) 

#### Partial ranking functions of CR fun1(Out) 


### Specialization of cost equations fun2/4 
* CE 54 is refined into CE [238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286] 
* CE 55 is refined into CE [287] 


### Cost equations --> "Loop" of fun2/4 
* CEs [246,247,248,249,250,251,252,253,281,282,283] --> Loop 92 
* CEs [241,242,243,256,257,262,263,274,275,279,285] --> Loop 93 
* CEs [238,239,240,244,245,254,255,258,259,260,261,264,265,266,267,268,269,270,271,272,273,276,277,278,280,284,286,287] --> Loop 94 

### Ranking functions of CR fun2(V1,V,V2,Out) 

#### Partial ranking functions of CR fun2(V1,V,V2,Out) 


### Specialization of cost equations fun3/3 
* CE 56 is refined into CE [288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313] 
* CE 57 is refined into CE [314] 


### Cost equations --> "Loop" of fun3/3 
* CEs [296] --> Loop 95 
* CEs [293,295,310] --> Loop 96 
* CEs [294,311] --> Loop 97 
* CEs [289,292,298,300,303,306] --> Loop 98 
* CEs [288,291,297,302,305,308,312] --> Loop 99 
* CEs [290,299,301,304,307,309,313,314] --> Loop 100 

### Ranking functions of CR fun3(V1,V,Out) 

#### Partial ranking functions of CR fun3(V1,V,Out) 


### Specialization of cost equations fun5/2 
* CE 58 is refined into CE [315,316,317,318,319] 
* CE 59 is refined into CE [320] 


### Cost equations --> "Loop" of fun5/2 
* CEs [316,318] --> Loop 101 
* CEs [315,317,319,320] --> Loop 102 

### Ranking functions of CR fun5(V1,Out) 

#### Partial ranking functions of CR fun5(V1,Out) 


### Specialization of cost equations fun6/1 
* CE 60 is refined into CE [321] 
* CE 61 is refined into CE [322] 


### Cost equations --> "Loop" of fun6/1 
* CEs [321] --> Loop 103 
* CEs [322] --> Loop 104 

### Ranking functions of CR fun6(Out) 

#### Partial ranking functions of CR fun6(Out) 


### Specialization of cost equations fun7/3 
* CE 62 is refined into CE [323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341] 
* CE 63 is refined into CE [342] 


### Cost equations --> "Loop" of fun7/3 
* CEs [328] --> Loop 105 
* CEs [327,330] --> Loop 106 
* CEs [329,340] --> Loop 107 
* CEs [323,325,333,338] --> Loop 108 
* CEs [324,332,335] --> Loop 109 
* CEs [326,331,334,336,337,339,341,342] --> Loop 110 

### Ranking functions of CR fun7(V1,V,Out) 

#### Partial ranking functions of CR fun7(V1,V,Out) 


### Specialization of cost equations fun8/3 
* CE 64 is refined into CE [343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373] 
* CE 65 is refined into CE [374] 


### Cost equations --> "Loop" of fun8/3 
* CEs [354] --> Loop 111 
* CEs [350,352,353,368,370] --> Loop 112 
* CEs [351,371] --> Loop 113 
* CEs [344,345,347,348,356,358,360,361,365] --> Loop 114 
* CEs [343,349,355,362,364,367,372] --> Loop 115 
* CEs [346,357,359,363,366,369,373,374] --> Loop 116 

### Ranking functions of CR fun8(V1,V,Out) 

#### Partial ranking functions of CR fun8(V1,V,Out) 


### Specialization of cost equations fun9/2 
* CE 66 is refined into CE [375,376,377] 
* CE 67 is refined into CE [378] 


### Cost equations --> "Loop" of fun9/2 
* CEs [377] --> Loop 117 
* CEs [378] --> Loop 118 
* CEs [375,376] --> Loop 119 

### Ranking functions of CR fun9(V1,Out) 

#### Partial ranking functions of CR fun9(V1,Out) 


### Specialization of cost equations start/3 
* CE 1 is refined into CE [379] 
* CE 2 is refined into CE [380,381,382,383] 
* CE 3 is refined into CE [384,385,386] 
* CE 4 is refined into CE [387,388,389,390,391] 
* CE 5 is refined into CE [392,393] 
* CE 6 is refined into CE [394,395,396,397,398,399,400] 
* CE 7 is refined into CE [401,402,403,404] 
* CE 8 is refined into CE [405,406,407] 
* CE 9 is refined into CE [408,409] 
* CE 10 is refined into CE [410,411] 
* CE 11 is refined into CE [412,413] 
* CE 12 is refined into CE [414,415,416] 
* CE 13 is refined into CE [417,418] 
* CE 14 is refined into CE [419,420] 
* CE 15 is refined into CE [421,422,423,424] 
* CE 16 is refined into CE [425,426,427,428] 
* CE 17 is refined into CE [429,430,431] 


### Cost equations --> "Loop" of start/3 
* CEs [379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431] --> Loop 120 

### Ranking functions of CR start(V1,V,V2) 

#### Partial ranking functions of CR start(V1,V,V2) 


Computing Bounds
=====================================

#### Cost of chains of and(V1,V,Out):
* Chain [41]: 1
  with precondition: [V1=1,Out=1,V>=0] 

* Chain [40]: 1
  with precondition: [V1=2,V=2,Out=2] 

* Chain [39]: 1
  with precondition: [V=1,Out=1,V1>=0] 

* Chain [38]: 0
  with precondition: [Out=0,V1>=0,V>=0] 


#### Cost of chains of eq(V1,V,Out):
* Chain [[42],46]: 1*it(42)+1
  Such that:it(42) =< V1

  with precondition: [Out=2,V1=V,V1>=1] 

* Chain [[42],45]: 1*it(42)+1
  Such that:it(42) =< V1

  with precondition: [Out=1,V1>=1,V>=V1+1] 

* Chain [[42],44]: 1*it(42)+1
  Such that:it(42) =< V

  with precondition: [Out=1,V>=1,V1>=V+1] 

* Chain [[42],43]: 1*it(42)+0
  Such that:it(42) =< V

  with precondition: [Out=0,V1>=1,V>=1] 

* Chain [46]: 1
  with precondition: [V1=0,V=0,Out=2] 

* Chain [45]: 1
  with precondition: [V1=0,Out=1,V>=1] 

* Chain [44]: 1
  with precondition: [V=0,Out=1,V1>=1] 

* Chain [43]: 0
  with precondition: [Out=0,V1>=0,V>=0] 


#### Cost of chains of gr(V1,V,Out):
* Chain [[47],50]: 1*it(47)+1
  Such that:it(47) =< V1

  with precondition: [Out=1,V1>=1,V>=V1] 

* Chain [[47],49]: 1*it(47)+1
  Such that:it(47) =< V

  with precondition: [Out=2,V>=1,V1>=V+1] 

* Chain [[47],48]: 1*it(47)+0
  Such that:it(47) =< V

  with precondition: [Out=0,V1>=1,V>=1] 

* Chain [50]: 1
  with precondition: [V1=0,Out=1,V>=0] 

* Chain [49]: 1
  with precondition: [V=0,Out=2,V1>=1] 

* Chain [48]: 0
  with precondition: [Out=0,V1>=0,V>=0] 


#### Cost of chains of p(V1,Out):
* Chain [52]: 1
  with precondition: [Out=0,V1>=0] 

* Chain [51]: 1
  with precondition: [V1=Out+1,V1>=1] 


#### Cost of chains of cond2(V1,V,V2,Out):
* Chain [[55],67]: 12*it(55)+4
  Such that:aux(3) =< V2
it(55) =< aux(3)

  with precondition: [V1=2,Out=0,V>=0,V2>=1] 

* Chain [[55],62,67]: 4*it(55)+8
  Such that:it(55) =< V2

  with precondition: [V1=2,Out=0,V>=0,V2>=1] 

* Chain [[55],60,67]: 4*it(55)+7
  Such that:it(55) =< V2

  with precondition: [V1=2,Out=0,V>=0,V2>=1] 

* Chain [[55],59,67]: 12*it(55)+7
  Such that:aux(6) =< V2
it(55) =< aux(6)

  with precondition: [V1=2,Out=0,V>=0,V2>=2] 

* Chain [[55],56,67]: 4*it(55)+8
  Such that:it(55) =< V2

  with precondition: [V1=2,Out=0,V>=0,V2>=2] 

* Chain [[55],56,62,67]: 4*it(55)+12
  Such that:it(55) =< V2

  with precondition: [V1=2,Out=0,V>=0,V2>=2] 

* Chain [[55],56,60,67]: 4*it(55)+11
  Such that:it(55) =< V2

  with precondition: [V1=2,Out=0,V>=0,V2>=2] 

* Chain [[53],[55],67]: 16*it(53)+4
  Such that:aux(8) =< V2
it(53) =< aux(8)

  with precondition: [V1=2,Out=0,V>=1,V2>=2] 

* Chain [[53],[55],62,67]: 8*it(53)+8
  Such that:aux(9) =< V2
it(53) =< aux(9)

  with precondition: [V1=2,Out=0,V>=1,V2>=2] 

* Chain [[53],[55],60,67]: 8*it(53)+7
  Such that:aux(10) =< V2
it(53) =< aux(10)

  with precondition: [V1=2,Out=0,V>=1,V2>=2] 

* Chain [[53],[55],59,67]: 16*it(53)+7
  Such that:aux(11) =< V2
it(53) =< aux(11)

  with precondition: [V1=2,Out=0,V>=1,V2>=3] 

* Chain [[53],[55],56,67]: 8*it(53)+8
  Such that:aux(12) =< V2
it(53) =< aux(12)

  with precondition: [V1=2,Out=0,V>=1,V2>=3] 

* Chain [[53],[55],56,62,67]: 8*it(53)+12
  Such that:aux(13) =< V2
it(53) =< aux(13)

  with precondition: [V1=2,Out=0,V>=1,V2>=3] 

* Chain [[53],[55],56,60,67]: 8*it(53)+11
  Such that:aux(14) =< V2
it(53) =< aux(14)

  with precondition: [V1=2,Out=0,V>=1,V2>=3] 

* Chain [[53],67]: 12*it(53)+4*s(11)+4
  Such that:aux(1) =< V
aux(15) =< V2
it(53) =< aux(15)
s(11) =< aux(1)

  with precondition: [V1=2,Out=0,V>=1,V2>=1] 

* Chain [[53],62,67]: 4*it(53)+8
  Such that:it(53) =< V2

  with precondition: [V1=2,Out=0,V2>=1,V>=V2] 

* Chain [[53],61,67]: 4*it(53)+4*s(11)+8
  Such that:aux(1) =< V-V2
it(53) =< V2
s(11) =< aux(1)

  with precondition: [V1=2,Out=0,V2>=1,V>=V2+1] 

* Chain [[53],61,66]: 4*it(53)+8
  Such that:it(53) =< V2

  with precondition: [V1=2,Out=0,V2>=1,V>=V2+2] 

* Chain [[53],60,67]: 4*it(53)+7
  Such that:it(53) =< V2

  with precondition: [V1=2,Out=0,V>=1,V2>=1] 

* Chain [[53],59,67]: 12*it(53)+7
  Such that:aux(16) =< V2
it(53) =< aux(16)

  with precondition: [V1=2,Out=0,V>=1,V2>=2] 

* Chain [[53],58,67]: 8*it(53)+7
  Such that:aux(17) =< V
it(53) =< aux(17)

  with precondition: [V1=2,Out=0,V>=2,V2>=1] 

* Chain [[53],57,67]: 12*it(53)+4*s(11)+7
  Such that:aux(1) =< V
aux(18) =< V2
it(53) =< aux(18)
s(11) =< aux(1)

  with precondition: [V1=2,Out=0,V>=2,V2>=2] 

* Chain [[53],56,67]: 4*it(53)+8
  Such that:it(53) =< V2

  with precondition: [V1=2,Out=0,V>=1,V2>=2] 

* Chain [[53],56,62,67]: 4*it(53)+12
  Such that:it(53) =< V2

  with precondition: [V1=2,Out=0,V>=1,V2>=2] 

* Chain [[53],56,60,67]: 4*it(53)+11
  Such that:it(53) =< V2

  with precondition: [V1=2,Out=0,V>=1,V2>=2] 

* Chain [[53],54,67]: 8*it(53)+8
  Such that:aux(19) =< V
it(53) =< aux(19)

  with precondition: [V1=2,Out=0,V>=2,V2>=2] 

* Chain [[53],54,62,67]: 4*it(53)+12
  Such that:it(53) =< V2

  with precondition: [V1=2,Out=0,V>=2,V2>=2] 

* Chain [[53],54,61,67]: 8*it(53)+12
  Such that:aux(20) =< V
it(53) =< aux(20)

  with precondition: [V1=2,Out=0,V>=3,V2>=2] 

* Chain [[53],54,61,66]: 4*it(53)+12
  Such that:it(53) =< V2

  with precondition: [V1=2,Out=0,V>=4,V2>=2] 

* Chain [[53],54,60,67]: 4*it(53)+11
  Such that:it(53) =< V2

  with precondition: [V1=2,Out=0,V>=2,V2>=2] 

* Chain [[53],54,58,67]: 8*it(53)+11
  Such that:aux(21) =< V
it(53) =< aux(21)

  with precondition: [V1=2,Out=0,V>=3,V2>=2] 

* Chain [67]: 8*s(6)+4*s(11)+4
  Such that:aux(1) =< V
aux(2) =< V2
s(11) =< aux(1)
s(6) =< aux(2)

  with precondition: [Out=0,V1>=0,V>=0,V2>=0] 

* Chain [66]: 4
  with precondition: [V1=1,V2=0,Out=0,V>=1] 

* Chain [65]: 3*s(29)+4
  Such that:aux(22) =< V2
s(29) =< aux(22)

  with precondition: [V1=1,Out=0,V=V2,V>=1] 

* Chain [64,67]: 13*s(6)+9
  Such that:aux(23) =< V2
s(6) =< aux(23)

  with precondition: [V1=1,Out=0,V=V2,V>=1] 

* Chain [63,[55],67]: 13*it(55)+10
  Such that:aux(24) =< V2
it(55) =< aux(24)

  with precondition: [V1=1,Out=0,V=V2,V>=1] 

* Chain [63,[55],62,67]: 5*it(55)+14
  Such that:aux(25) =< V2
it(55) =< aux(25)

  with precondition: [V1=1,Out=0,V=V2,V>=1] 

* Chain [63,[55],60,67]: 5*it(55)+13
  Such that:aux(26) =< V2
it(55) =< aux(26)

  with precondition: [V1=1,Out=0,V=V2,V>=1] 

* Chain [63,[55],59,67]: 13*it(55)+13
  Such that:aux(27) =< V2
it(55) =< aux(27)

  with precondition: [V1=1,Out=0,V=V2,V>=2] 

* Chain [63,[55],56,67]: 5*it(55)+14
  Such that:aux(28) =< V2
it(55) =< aux(28)

  with precondition: [V1=1,Out=0,V=V2,V>=2] 

* Chain [63,[55],56,62,67]: 5*it(55)+18
  Such that:aux(29) =< V2
it(55) =< aux(29)

  with precondition: [V1=1,Out=0,V=V2,V>=2] 

* Chain [63,[55],56,60,67]: 5*it(55)+17
  Such that:aux(30) =< V2
it(55) =< aux(30)

  with precondition: [V1=1,Out=0,V=V2,V>=2] 

* Chain [63,[53],[55],67]: 17*it(53)+10
  Such that:aux(31) =< V2
it(53) =< aux(31)

  with precondition: [V1=1,Out=0,V=V2,V>=2] 

* Chain [63,[53],[55],62,67]: 9*it(53)+14
  Such that:aux(32) =< V2
it(53) =< aux(32)

  with precondition: [V1=1,Out=0,V=V2,V>=2] 

* Chain [63,[53],[55],60,67]: 9*it(53)+13
  Such that:aux(33) =< V2
it(53) =< aux(33)

  with precondition: [V1=1,Out=0,V=V2,V>=2] 

* Chain [63,[53],[55],59,67]: 17*it(53)+13
  Such that:aux(34) =< V2
it(53) =< aux(34)

  with precondition: [V1=1,Out=0,V=V2,V>=3] 

* Chain [63,[53],[55],56,67]: 9*it(53)+14
  Such that:aux(35) =< V2
it(53) =< aux(35)

  with precondition: [V1=1,Out=0,V=V2,V>=3] 

* Chain [63,[53],[55],56,62,67]: 9*it(53)+18
  Such that:aux(36) =< V2
it(53) =< aux(36)

  with precondition: [V1=1,Out=0,V=V2,V>=3] 

* Chain [63,[53],[55],56,60,67]: 9*it(53)+17
  Such that:aux(37) =< V2
it(53) =< aux(37)

  with precondition: [V1=1,Out=0,V=V2,V>=3] 

* Chain [63,[53],67]: 17*it(53)+10
  Such that:aux(38) =< V2
it(53) =< aux(38)

  with precondition: [V1=1,Out=0,V=V2,V>=1] 

* Chain [63,[53],62,67]: 5*it(53)+14
  Such that:aux(39) =< V2
it(53) =< aux(39)

  with precondition: [V1=1,Out=0,V=V2,V>=1] 

* Chain [63,[53],60,67]: 5*it(53)+13
  Such that:aux(40) =< V2
it(53) =< aux(40)

  with precondition: [V1=1,Out=0,V=V2,V>=1] 

* Chain [63,[53],59,67]: 13*it(53)+13
  Such that:aux(41) =< V2
it(53) =< aux(41)

  with precondition: [V1=1,Out=0,V=V2,V>=2] 

* Chain [63,[53],58,67]: 9*it(53)+13
  Such that:aux(42) =< V2
it(53) =< aux(42)

  with precondition: [V1=1,Out=0,V=V2,V>=2] 

* Chain [63,[53],57,67]: 17*it(53)+13
  Such that:aux(43) =< V2
it(53) =< aux(43)

  with precondition: [V1=1,Out=0,V=V2,V>=2] 

* Chain [63,[53],56,67]: 5*it(53)+14
  Such that:aux(44) =< V2
it(53) =< aux(44)

  with precondition: [V1=1,Out=0,V=V2,V>=2] 

* Chain [63,[53],56,62,67]: 5*it(53)+18
  Such that:aux(45) =< V2
it(53) =< aux(45)

  with precondition: [V1=1,Out=0,V=V2,V>=2] 

* Chain [63,[53],56,60,67]: 5*it(53)+17
  Such that:aux(46) =< V2
it(53) =< aux(46)

  with precondition: [V1=1,Out=0,V=V2,V>=2] 

* Chain [63,[53],54,67]: 9*it(53)+14
  Such that:aux(47) =< V2
it(53) =< aux(47)

  with precondition: [V1=1,Out=0,V=V2,V>=2] 

* Chain [63,[53],54,62,67]: 5*it(53)+18
  Such that:aux(48) =< V2
it(53) =< aux(48)

  with precondition: [V1=1,Out=0,V=V2,V>=2] 

* Chain [63,[53],54,61,67]: 9*it(53)+18
  Such that:aux(49) =< V2
it(53) =< aux(49)

  with precondition: [V1=1,Out=0,V=V2,V>=3] 

* Chain [63,[53],54,61,66]: 5*it(53)+18
  Such that:aux(50) =< V2
it(53) =< aux(50)

  with precondition: [V1=1,Out=0,V=V2,V>=4] 

* Chain [63,[53],54,60,67]: 5*it(53)+17
  Such that:aux(51) =< V2
it(53) =< aux(51)

  with precondition: [V1=1,Out=0,V=V2,V>=2] 

* Chain [63,[53],54,58,67]: 9*it(53)+17
  Such that:aux(52) =< V2
it(53) =< aux(52)

  with precondition: [V1=1,Out=0,V=V2,V>=3] 

* Chain [63,67]: 13*s(6)+10
  Such that:aux(53) =< V2
s(6) =< aux(53)

  with precondition: [V1=1,Out=0,V=V2,V>=1] 

* Chain [63,60,67]: 1*s(35)+13
  Such that:s(35) =< V

  with precondition: [V1=1,Out=0,V=V2,V>=1] 

* Chain [63,59,67]: 9*s(6)+13
  Such that:aux(54) =< V2
s(6) =< aux(54)

  with precondition: [V1=1,Out=0,V=V2,V>=1] 

* Chain [63,58,67]: 5*s(11)+13
  Such that:aux(55) =< V2
s(11) =< aux(55)

  with precondition: [V1=1,Out=0,V=V2,V>=1] 

* Chain [63,57,67]: 13*s(6)+13
  Such that:aux(56) =< V2
s(6) =< aux(56)

  with precondition: [V1=1,Out=0,V=V2,V>=1] 

* Chain [63,56,67]: 1*s(35)+14
  Such that:s(35) =< V

  with precondition: [V1=1,Out=0,V=V2,V>=1] 

* Chain [63,56,62,67]: 1*s(35)+18
  Such that:s(35) =< V

  with precondition: [V1=1,Out=0,V=V2,V>=1] 

* Chain [63,56,60,67]: 1*s(35)+17
  Such that:s(35) =< V

  with precondition: [V1=1,Out=0,V=V2,V>=1] 

* Chain [63,54,67]: 5*s(11)+14
  Such that:aux(57) =< V2
s(11) =< aux(57)

  with precondition: [V1=1,Out=0,V=V2,V>=1] 

* Chain [63,54,62,67]: 1*s(35)+18
  Such that:s(35) =< V

  with precondition: [V1=1,Out=0,V=V2,V>=1] 

* Chain [63,54,61,67]: 5*s(11)+18
  Such that:aux(58) =< V2
s(11) =< aux(58)

  with precondition: [V1=1,Out=0,V=V2,V>=2] 

* Chain [63,54,61,66]: 1*s(35)+18
  Such that:s(35) =< V

  with precondition: [V1=1,Out=0,V=V2,V>=3] 

* Chain [63,54,60,67]: 1*s(35)+17
  Such that:s(35) =< V

  with precondition: [V1=1,Out=0,V=V2,V>=1] 

* Chain [63,54,58,67]: 5*s(11)+17
  Such that:aux(59) =< V2
s(11) =< aux(59)

  with precondition: [V1=1,Out=0,V=V2,V>=2] 

* Chain [62,67]: 8
  with precondition: [V1=2,V2=0,Out=0,V>=0] 

* Chain [61,67]: 4*s(11)+8
  Such that:aux(1) =< V
s(11) =< aux(1)

  with precondition: [V1=2,V2=0,Out=0,V>=1] 

* Chain [61,66]: 8
  with precondition: [V1=2,V2=0,Out=0,V>=2] 

* Chain [60,67]: 7
  with precondition: [V1=2,Out=0,V>=0,V2>=0] 

* Chain [59,67]: 8*s(6)+7
  Such that:aux(2) =< V2
s(6) =< aux(2)

  with precondition: [V1=2,Out=0,V>=0,V2>=1] 

* Chain [58,67]: 4*s(11)+7
  Such that:aux(1) =< V
s(11) =< aux(1)

  with precondition: [V1=2,Out=0,V>=1,V2>=0] 

* Chain [57,67]: 8*s(6)+4*s(11)+7
  Such that:aux(1) =< V
aux(2) =< V2
s(11) =< aux(1)
s(6) =< aux(2)

  with precondition: [V1=2,Out=0,V>=1,V2>=1] 

* Chain [56,67]: 8
  with precondition: [V1=2,Out=0,V>=0,V2>=1] 

* Chain [56,62,67]: 12
  with precondition: [V1=2,Out=0,V>=0,V2>=1] 

* Chain [56,60,67]: 11
  with precondition: [V1=2,Out=0,V>=0,V2>=1] 

* Chain [54,67]: 4*s(11)+8
  Such that:aux(1) =< V
s(11) =< aux(1)

  with precondition: [V1=2,Out=0,V>=1,V2>=1] 

* Chain [54,62,67]: 12
  with precondition: [V1=2,Out=0,V>=1,V2>=1] 

* Chain [54,61,67]: 4*s(11)+12
  Such that:aux(1) =< V
s(11) =< aux(1)

  with precondition: [V1=2,Out=0,V>=2,V2>=1] 

* Chain [54,61,66]: 12
  with precondition: [V1=2,Out=0,V>=3,V2>=1] 

* Chain [54,60,67]: 11
  with precondition: [V1=2,Out=0,V>=1,V2>=1] 

* Chain [54,58,67]: 4*s(11)+11
  Such that:aux(1) =< V
s(11) =< aux(1)

  with precondition: [V1=2,Out=0,V>=2,V2>=1] 


#### Cost of chains of encArg(V1,Out):
* Chain [86]: 0
  with precondition: [V1=1,Out=1] 

* Chain [85]: 0
  with precondition: [V1=2,Out=2] 

* Chain [84]: 0
  with precondition: [Out=0,V1>=0] 

* Chain [multiple([68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83],[[86],[85],[84]])]: 14*it(68)+18*it(69)+2*it(71)+1*it(73)+1*it(74)+2*it(75)+2*it(76)+1*it(77)+3*it(79)+448*s(249)+132*s(251)+4*s(255)+339*s(256)+1*s(259)+1*s(260)+1*s(261)+2*s(262)+2*s(264)+0
  Such that:aux(72) =< 2*V1
aux(90) =< V1
aux(91) =< 2*V1+1
aux(92) =< 2/3*V1
aux(93) =< 3/5*V1
aux(94) =< 4/5*V1
aux(95) =< 4/7*V1
it(69) =< aux(90)
it(71) =< aux(90)
it(73) =< aux(90)
it(74) =< aux(90)
it(75) =< aux(90)
it(76) =< aux(90)
it(77) =< aux(90)
it(79) =< aux(90)
it(83) =< aux(90)
it([84]) =< aux(91)
it(75) =< aux(92)
it(77) =< aux(92)
it(68) =< aux(93)
it(74) =< aux(94)
it(75) =< aux(94)
it(77) =< aux(94)
it(79) =< aux(94)
it(73) =< aux(95)
it(77) =< aux(95)
aux(76) =< aux(72)
aux(81) =< aux(72)-1
aux(73) =< aux(72)-2
aux(75) =< aux(72)+2
it(74) =< it([84])*(1/5)+aux(94)
it(75) =< it([84])*(1/5)+aux(94)
it(76) =< it([84])*(1/5)+aux(94)
it(77) =< it([84])*(1/5)+aux(94)
it(79) =< it([84])*(1/5)+aux(94)
it(83) =< it([84])*(1/5)+aux(94)
it(75) =< it([84])*(1/3)+aux(92)
it(76) =< it([84])*(1/3)+aux(92)
it(77) =< it([84])*(1/3)+aux(92)
it(79) =< it([84])*(1/3)+aux(92)
it(83) =< it([84])*(1/3)+aux(92)
it(73) =< it([84])*(3/7)+aux(95)
it(74) =< it([84])*(3/7)+aux(95)
it(75) =< it([84])*(3/7)+aux(95)
it(76) =< it([84])*(3/7)+aux(95)
it(77) =< it([84])*(3/7)+aux(95)
it(79) =< it([84])*(3/7)+aux(95)
it(83) =< it([84])*(3/7)+aux(95)
it(68) =< it([84])*(1/5)+aux(93)
it(69) =< it([84])*(1/5)+aux(93)
s(265) =< it(83)*aux(76)
s(263) =< it(75)*aux(81)
s(261) =< it(77)*aux(73)
s(260) =< it(75)*aux(81)
s(259) =< it(73)*aux(73)
s(257) =< it(69)*aux(76)
s(258) =< it(69)*aux(75)
s(252) =< it(68)*aux(73)
s(253) =< it(68)*aux(72)
s(264) =< s(265)
s(262) =< s(263)
s(255) =< s(258)
s(256) =< s(257)
s(249) =< s(252)
s(251) =< s(253)

  with precondition: [V1>=1,Out>=0,2*V1>=Out] 


#### Cost of chains of fun(V1,V,V2,Out):
* Chain [89]: 288*s(310)+32*s(311)+16*s(312)+16*s(313)+32*s(314)+32*s(315)+16*s(316)+48*s(317)+224*s(319)+16*s(326)+16*s(327)+16*s(328)+32*s(333)+32*s(334)+64*s(335)+5424*s(336)+7168*s(337)+2112*s(338)+324*s(346)+36*s(347)+18*s(348)+18*s(349)+36*s(350)+36*s(351)+18*s(352)+54*s(353)+252*s(355)+18*s(362)+18*s(363)+18*s(364)+36*s(369)+36*s(370)+72*s(371)+6102*s(372)+8064*s(373)+2376*s(374)+486*s(382)+54*s(383)+27*s(384)+27*s(385)+54*s(386)+54*s(387)+27*s(388)+81*s(389)+378*s(391)+27*s(398)+27*s(399)+27*s(400)+54*s(405)+54*s(406)+108*s(407)+9153*s(408)+12096*s(409)+3564*s(410)+176*s(1025)+1120*s(1138)+380*s(2333)+4*s(2416)+14
  Such that:s(2411) =< 1
aux(139) =< 2
aux(140) =< V1
aux(141) =< 2*V1
aux(142) =< 2*V1+1
aux(143) =< 2/3*V1
aux(144) =< 3/5*V1
aux(145) =< 4/5*V1
aux(146) =< 4/7*V1
aux(147) =< V
aux(148) =< 2*V
aux(149) =< 2*V+1
aux(150) =< 2/3*V
aux(151) =< 3/5*V
aux(152) =< 4/5*V
aux(153) =< 4/7*V
aux(154) =< V2
aux(155) =< 2*V2
aux(156) =< 2*V2+1
aux(157) =< 2/3*V2
aux(158) =< 3/5*V2
aux(159) =< 4/5*V2
aux(160) =< 4/7*V2
s(1138) =< aux(155)
s(2333) =< aux(139)
s(2416) =< s(2411)
s(382) =< aux(154)
s(383) =< aux(154)
s(384) =< aux(154)
s(385) =< aux(154)
s(386) =< aux(154)
s(387) =< aux(154)
s(388) =< aux(154)
s(389) =< aux(154)
s(390) =< aux(154)
s(386) =< aux(157)
s(388) =< aux(157)
s(391) =< aux(158)
s(385) =< aux(159)
s(386) =< aux(159)
s(388) =< aux(159)
s(389) =< aux(159)
s(384) =< aux(160)
s(388) =< aux(160)
s(392) =< aux(155)
s(393) =< aux(155)-1
s(394) =< aux(155)-2
s(395) =< aux(155)+2
s(385) =< aux(156)*(1/5)+aux(159)
s(386) =< aux(156)*(1/5)+aux(159)
s(387) =< aux(156)*(1/5)+aux(159)
s(388) =< aux(156)*(1/5)+aux(159)
s(389) =< aux(156)*(1/5)+aux(159)
s(390) =< aux(156)*(1/5)+aux(159)
s(386) =< aux(156)*(1/3)+aux(157)
s(387) =< aux(156)*(1/3)+aux(157)
s(388) =< aux(156)*(1/3)+aux(157)
s(389) =< aux(156)*(1/3)+aux(157)
s(390) =< aux(156)*(1/3)+aux(157)
s(384) =< aux(156)*(3/7)+aux(160)
s(385) =< aux(156)*(3/7)+aux(160)
s(386) =< aux(156)*(3/7)+aux(160)
s(387) =< aux(156)*(3/7)+aux(160)
s(388) =< aux(156)*(3/7)+aux(160)
s(389) =< aux(156)*(3/7)+aux(160)
s(390) =< aux(156)*(3/7)+aux(160)
s(391) =< aux(156)*(1/5)+aux(158)
s(382) =< aux(156)*(1/5)+aux(158)
s(396) =< s(390)*s(392)
s(397) =< s(386)*s(393)
s(398) =< s(388)*s(394)
s(399) =< s(386)*s(393)
s(400) =< s(384)*s(394)
s(401) =< s(382)*s(392)
s(402) =< s(382)*s(395)
s(403) =< s(391)*s(394)
s(404) =< s(391)*aux(155)
s(405) =< s(396)
s(406) =< s(397)
s(407) =< s(402)
s(408) =< s(401)
s(409) =< s(403)
s(410) =< s(404)
s(346) =< aux(147)
s(347) =< aux(147)
s(348) =< aux(147)
s(349) =< aux(147)
s(350) =< aux(147)
s(351) =< aux(147)
s(352) =< aux(147)
s(353) =< aux(147)
s(354) =< aux(147)
s(350) =< aux(150)
s(352) =< aux(150)
s(355) =< aux(151)
s(349) =< aux(152)
s(350) =< aux(152)
s(352) =< aux(152)
s(353) =< aux(152)
s(348) =< aux(153)
s(352) =< aux(153)
s(356) =< aux(148)
s(357) =< aux(148)-1
s(358) =< aux(148)-2
s(359) =< aux(148)+2
s(349) =< aux(149)*(1/5)+aux(152)
s(350) =< aux(149)*(1/5)+aux(152)
s(351) =< aux(149)*(1/5)+aux(152)
s(352) =< aux(149)*(1/5)+aux(152)
s(353) =< aux(149)*(1/5)+aux(152)
s(354) =< aux(149)*(1/5)+aux(152)
s(350) =< aux(149)*(1/3)+aux(150)
s(351) =< aux(149)*(1/3)+aux(150)
s(352) =< aux(149)*(1/3)+aux(150)
s(353) =< aux(149)*(1/3)+aux(150)
s(354) =< aux(149)*(1/3)+aux(150)
s(348) =< aux(149)*(3/7)+aux(153)
s(349) =< aux(149)*(3/7)+aux(153)
s(350) =< aux(149)*(3/7)+aux(153)
s(351) =< aux(149)*(3/7)+aux(153)
s(352) =< aux(149)*(3/7)+aux(153)
s(353) =< aux(149)*(3/7)+aux(153)
s(354) =< aux(149)*(3/7)+aux(153)
s(355) =< aux(149)*(1/5)+aux(151)
s(346) =< aux(149)*(1/5)+aux(151)
s(360) =< s(354)*s(356)
s(361) =< s(350)*s(357)
s(362) =< s(352)*s(358)
s(363) =< s(350)*s(357)
s(364) =< s(348)*s(358)
s(365) =< s(346)*s(356)
s(366) =< s(346)*s(359)
s(367) =< s(355)*s(358)
s(368) =< s(355)*aux(148)
s(369) =< s(360)
s(370) =< s(361)
s(371) =< s(366)
s(372) =< s(365)
s(373) =< s(367)
s(374) =< s(368)
s(310) =< aux(140)
s(311) =< aux(140)
s(312) =< aux(140)
s(313) =< aux(140)
s(314) =< aux(140)
s(315) =< aux(140)
s(316) =< aux(140)
s(317) =< aux(140)
s(318) =< aux(140)
s(314) =< aux(143)
s(316) =< aux(143)
s(319) =< aux(144)
s(313) =< aux(145)
s(314) =< aux(145)
s(316) =< aux(145)
s(317) =< aux(145)
s(312) =< aux(146)
s(316) =< aux(146)
s(320) =< aux(141)
s(321) =< aux(141)-1
s(322) =< aux(141)-2
s(323) =< aux(141)+2
s(313) =< aux(142)*(1/5)+aux(145)
s(314) =< aux(142)*(1/5)+aux(145)
s(315) =< aux(142)*(1/5)+aux(145)
s(316) =< aux(142)*(1/5)+aux(145)
s(317) =< aux(142)*(1/5)+aux(145)
s(318) =< aux(142)*(1/5)+aux(145)
s(314) =< aux(142)*(1/3)+aux(143)
s(315) =< aux(142)*(1/3)+aux(143)
s(316) =< aux(142)*(1/3)+aux(143)
s(317) =< aux(142)*(1/3)+aux(143)
s(318) =< aux(142)*(1/3)+aux(143)
s(312) =< aux(142)*(3/7)+aux(146)
s(313) =< aux(142)*(3/7)+aux(146)
s(314) =< aux(142)*(3/7)+aux(146)
s(315) =< aux(142)*(3/7)+aux(146)
s(316) =< aux(142)*(3/7)+aux(146)
s(317) =< aux(142)*(3/7)+aux(146)
s(318) =< aux(142)*(3/7)+aux(146)
s(319) =< aux(142)*(1/5)+aux(144)
s(310) =< aux(142)*(1/5)+aux(144)
s(324) =< s(318)*s(320)
s(325) =< s(314)*s(321)
s(326) =< s(316)*s(322)
s(327) =< s(314)*s(321)
s(328) =< s(312)*s(322)
s(329) =< s(310)*s(320)
s(330) =< s(310)*s(323)
s(331) =< s(319)*s(322)
s(332) =< s(319)*aux(141)
s(333) =< s(324)
s(334) =< s(325)
s(335) =< s(330)
s(336) =< s(329)
s(337) =< s(331)
s(338) =< s(332)
s(1025) =< aux(148)

  with precondition: [Out=0,V1>=0,V>=0,V2>=0] 

* Chain [88]: 144*s(2661)+16*s(2662)+8*s(2663)+8*s(2664)+16*s(2665)+16*s(2666)+8*s(2667)+24*s(2668)+112*s(2670)+8*s(2677)+8*s(2678)+8*s(2679)+16*s(2684)+16*s(2685)+32*s(2686)+2712*s(2687)+3584*s(2688)+1056*s(2689)+162*s(2697)+18*s(2698)+9*s(2699)+9*s(2700)+18*s(2701)+18*s(2702)+9*s(2703)+27*s(2704)+126*s(2706)+9*s(2713)+9*s(2714)+9*s(2715)+18*s(2720)+18*s(2721)+36*s(2722)+3051*s(2723)+4032*s(2724)+1188*s(2725)+152*s(2908)+896*s(2909)+14
  Such that:aux(171) =< 2
aux(172) =< V1
aux(173) =< 2*V1
aux(174) =< 2*V1+1
aux(175) =< 2/3*V1
aux(176) =< 3/5*V1
aux(177) =< 4/5*V1
aux(178) =< 4/7*V1
aux(179) =< V
aux(180) =< 2*V
aux(181) =< 2*V+1
aux(182) =< 2/3*V
aux(183) =< 3/5*V
aux(184) =< 4/5*V
aux(185) =< 4/7*V
s(2908) =< aux(180)
s(2909) =< aux(171)
s(2697) =< aux(179)
s(2698) =< aux(179)
s(2699) =< aux(179)
s(2700) =< aux(179)
s(2701) =< aux(179)
s(2702) =< aux(179)
s(2703) =< aux(179)
s(2704) =< aux(179)
s(2705) =< aux(179)
s(2701) =< aux(182)
s(2703) =< aux(182)
s(2706) =< aux(183)
s(2700) =< aux(184)
s(2701) =< aux(184)
s(2703) =< aux(184)
s(2704) =< aux(184)
s(2699) =< aux(185)
s(2703) =< aux(185)
s(2707) =< aux(180)
s(2708) =< aux(180)-1
s(2709) =< aux(180)-2
s(2710) =< aux(180)+2
s(2700) =< aux(181)*(1/5)+aux(184)
s(2701) =< aux(181)*(1/5)+aux(184)
s(2702) =< aux(181)*(1/5)+aux(184)
s(2703) =< aux(181)*(1/5)+aux(184)
s(2704) =< aux(181)*(1/5)+aux(184)
s(2705) =< aux(181)*(1/5)+aux(184)
s(2701) =< aux(181)*(1/3)+aux(182)
s(2702) =< aux(181)*(1/3)+aux(182)
s(2703) =< aux(181)*(1/3)+aux(182)
s(2704) =< aux(181)*(1/3)+aux(182)
s(2705) =< aux(181)*(1/3)+aux(182)
s(2699) =< aux(181)*(3/7)+aux(185)
s(2700) =< aux(181)*(3/7)+aux(185)
s(2701) =< aux(181)*(3/7)+aux(185)
s(2702) =< aux(181)*(3/7)+aux(185)
s(2703) =< aux(181)*(3/7)+aux(185)
s(2704) =< aux(181)*(3/7)+aux(185)
s(2705) =< aux(181)*(3/7)+aux(185)
s(2706) =< aux(181)*(1/5)+aux(183)
s(2697) =< aux(181)*(1/5)+aux(183)
s(2711) =< s(2705)*s(2707)
s(2712) =< s(2701)*s(2708)
s(2713) =< s(2703)*s(2709)
s(2714) =< s(2701)*s(2708)
s(2715) =< s(2699)*s(2709)
s(2716) =< s(2697)*s(2707)
s(2717) =< s(2697)*s(2710)
s(2718) =< s(2706)*s(2709)
s(2719) =< s(2706)*aux(180)
s(2720) =< s(2711)
s(2721) =< s(2712)
s(2722) =< s(2717)
s(2723) =< s(2716)
s(2724) =< s(2718)
s(2725) =< s(2719)
s(2661) =< aux(172)
s(2662) =< aux(172)
s(2663) =< aux(172)
s(2664) =< aux(172)
s(2665) =< aux(172)
s(2666) =< aux(172)
s(2667) =< aux(172)
s(2668) =< aux(172)
s(2669) =< aux(172)
s(2665) =< aux(175)
s(2667) =< aux(175)
s(2670) =< aux(176)
s(2664) =< aux(177)
s(2665) =< aux(177)
s(2667) =< aux(177)
s(2668) =< aux(177)
s(2663) =< aux(178)
s(2667) =< aux(178)
s(2671) =< aux(173)
s(2672) =< aux(173)-1
s(2673) =< aux(173)-2
s(2674) =< aux(173)+2
s(2664) =< aux(174)*(1/5)+aux(177)
s(2665) =< aux(174)*(1/5)+aux(177)
s(2666) =< aux(174)*(1/5)+aux(177)
s(2667) =< aux(174)*(1/5)+aux(177)
s(2668) =< aux(174)*(1/5)+aux(177)
s(2669) =< aux(174)*(1/5)+aux(177)
s(2665) =< aux(174)*(1/3)+aux(175)
s(2666) =< aux(174)*(1/3)+aux(175)
s(2667) =< aux(174)*(1/3)+aux(175)
s(2668) =< aux(174)*(1/3)+aux(175)
s(2669) =< aux(174)*(1/3)+aux(175)
s(2663) =< aux(174)*(3/7)+aux(178)
s(2664) =< aux(174)*(3/7)+aux(178)
s(2665) =< aux(174)*(3/7)+aux(178)
s(2666) =< aux(174)*(3/7)+aux(178)
s(2667) =< aux(174)*(3/7)+aux(178)
s(2668) =< aux(174)*(3/7)+aux(178)
s(2669) =< aux(174)*(3/7)+aux(178)
s(2670) =< aux(174)*(1/5)+aux(176)
s(2661) =< aux(174)*(1/5)+aux(176)
s(2675) =< s(2669)*s(2671)
s(2676) =< s(2665)*s(2672)
s(2677) =< s(2667)*s(2673)
s(2678) =< s(2665)*s(2672)
s(2679) =< s(2663)*s(2673)
s(2680) =< s(2661)*s(2671)
s(2681) =< s(2661)*s(2674)
s(2682) =< s(2670)*s(2673)
s(2683) =< s(2670)*aux(173)
s(2684) =< s(2675)
s(2685) =< s(2676)
s(2686) =< s(2681)
s(2687) =< s(2680)
s(2688) =< s(2682)
s(2689) =< s(2683)

  with precondition: [V2=2,Out=0,V1>=0,V>=0] 

* Chain [87]: 216*s(3333)+24*s(3334)+12*s(3335)+12*s(3336)+24*s(3337)+24*s(3338)+12*s(3339)+36*s(3340)+168*s(3342)+12*s(3349)+12*s(3350)+12*s(3351)+24*s(3356)+24*s(3357)+48*s(3358)+4068*s(3359)+5376*s(3360)+1584*s(3361)+108*s(3369)+12*s(3370)+6*s(3371)+6*s(3372)+12*s(3373)+12*s(3374)+6*s(3375)+18*s(3376)+84*s(3378)+6*s(3385)+6*s(3386)+6*s(3387)+12*s(3392)+12*s(3393)+24*s(3394)+2034*s(3395)+2688*s(3396)+792*s(3397)+380*s(3580)+224*s(3657)+4*s(3735)+14
  Such that:s(3730) =< 1
aux(193) =< 2
aux(194) =< V1
aux(195) =< 2*V1
aux(196) =< 2*V1+1
aux(197) =< 2/3*V1
aux(198) =< 3/5*V1
aux(199) =< 4/5*V1
aux(200) =< 4/7*V1
aux(201) =< V2
aux(202) =< 2*V2
aux(203) =< 2*V2+1
aux(204) =< 2/3*V2
aux(205) =< 3/5*V2
aux(206) =< 4/5*V2
aux(207) =< 4/7*V2
s(3657) =< aux(202)
s(3580) =< aux(193)
s(3735) =< s(3730)
s(3369) =< aux(201)
s(3370) =< aux(201)
s(3371) =< aux(201)
s(3372) =< aux(201)
s(3373) =< aux(201)
s(3374) =< aux(201)
s(3375) =< aux(201)
s(3376) =< aux(201)
s(3377) =< aux(201)
s(3373) =< aux(204)
s(3375) =< aux(204)
s(3378) =< aux(205)
s(3372) =< aux(206)
s(3373) =< aux(206)
s(3375) =< aux(206)
s(3376) =< aux(206)
s(3371) =< aux(207)
s(3375) =< aux(207)
s(3379) =< aux(202)
s(3380) =< aux(202)-1
s(3381) =< aux(202)-2
s(3382) =< aux(202)+2
s(3372) =< aux(203)*(1/5)+aux(206)
s(3373) =< aux(203)*(1/5)+aux(206)
s(3374) =< aux(203)*(1/5)+aux(206)
s(3375) =< aux(203)*(1/5)+aux(206)
s(3376) =< aux(203)*(1/5)+aux(206)
s(3377) =< aux(203)*(1/5)+aux(206)
s(3373) =< aux(203)*(1/3)+aux(204)
s(3374) =< aux(203)*(1/3)+aux(204)
s(3375) =< aux(203)*(1/3)+aux(204)
s(3376) =< aux(203)*(1/3)+aux(204)
s(3377) =< aux(203)*(1/3)+aux(204)
s(3371) =< aux(203)*(3/7)+aux(207)
s(3372) =< aux(203)*(3/7)+aux(207)
s(3373) =< aux(203)*(3/7)+aux(207)
s(3374) =< aux(203)*(3/7)+aux(207)
s(3375) =< aux(203)*(3/7)+aux(207)
s(3376) =< aux(203)*(3/7)+aux(207)
s(3377) =< aux(203)*(3/7)+aux(207)
s(3378) =< aux(203)*(1/5)+aux(205)
s(3369) =< aux(203)*(1/5)+aux(205)
s(3383) =< s(3377)*s(3379)
s(3384) =< s(3373)*s(3380)
s(3385) =< s(3375)*s(3381)
s(3386) =< s(3373)*s(3380)
s(3387) =< s(3371)*s(3381)
s(3388) =< s(3369)*s(3379)
s(3389) =< s(3369)*s(3382)
s(3390) =< s(3378)*s(3381)
s(3391) =< s(3378)*aux(202)
s(3392) =< s(3383)
s(3393) =< s(3384)
s(3394) =< s(3389)
s(3395) =< s(3388)
s(3396) =< s(3390)
s(3397) =< s(3391)
s(3333) =< aux(194)
s(3334) =< aux(194)
s(3335) =< aux(194)
s(3336) =< aux(194)
s(3337) =< aux(194)
s(3338) =< aux(194)
s(3339) =< aux(194)
s(3340) =< aux(194)
s(3341) =< aux(194)
s(3337) =< aux(197)
s(3339) =< aux(197)
s(3342) =< aux(198)
s(3336) =< aux(199)
s(3337) =< aux(199)
s(3339) =< aux(199)
s(3340) =< aux(199)
s(3335) =< aux(200)
s(3339) =< aux(200)
s(3343) =< aux(195)
s(3344) =< aux(195)-1
s(3345) =< aux(195)-2
s(3346) =< aux(195)+2
s(3336) =< aux(196)*(1/5)+aux(199)
s(3337) =< aux(196)*(1/5)+aux(199)
s(3338) =< aux(196)*(1/5)+aux(199)
s(3339) =< aux(196)*(1/5)+aux(199)
s(3340) =< aux(196)*(1/5)+aux(199)
s(3341) =< aux(196)*(1/5)+aux(199)
s(3337) =< aux(196)*(1/3)+aux(197)
s(3338) =< aux(196)*(1/3)+aux(197)
s(3339) =< aux(196)*(1/3)+aux(197)
s(3340) =< aux(196)*(1/3)+aux(197)
s(3341) =< aux(196)*(1/3)+aux(197)
s(3335) =< aux(196)*(3/7)+aux(200)
s(3336) =< aux(196)*(3/7)+aux(200)
s(3337) =< aux(196)*(3/7)+aux(200)
s(3338) =< aux(196)*(3/7)+aux(200)
s(3339) =< aux(196)*(3/7)+aux(200)
s(3340) =< aux(196)*(3/7)+aux(200)
s(3341) =< aux(196)*(3/7)+aux(200)
s(3342) =< aux(196)*(1/5)+aux(198)
s(3333) =< aux(196)*(1/5)+aux(198)
s(3347) =< s(3341)*s(3343)
s(3348) =< s(3337)*s(3344)
s(3349) =< s(3339)*s(3345)
s(3350) =< s(3337)*s(3344)
s(3351) =< s(3335)*s(3345)
s(3352) =< s(3333)*s(3343)
s(3353) =< s(3333)*s(3346)
s(3354) =< s(3342)*s(3345)
s(3355) =< s(3342)*aux(195)
s(3356) =< s(3347)
s(3357) =< s(3348)
s(3358) =< s(3353)
s(3359) =< s(3352)
s(3360) =< s(3354)
s(3361) =< s(3355)

  with precondition: [V=2,Out=0,V1>=0,V2>=0] 


#### Cost of chains of fun1(Out):
* Chain [91]: 0
  with precondition: [Out=0] 

* Chain [90]: 0
  with precondition: [Out=2] 


#### Cost of chains of fun2(V1,V,V2,Out):
* Chain [94]: 162*s(4215)+18*s(4216)+9*s(4217)+9*s(4218)+18*s(4219)+18*s(4220)+9*s(4221)+27*s(4222)+126*s(4224)+9*s(4231)+9*s(4232)+9*s(4233)+18*s(4238)+18*s(4239)+36*s(4240)+3051*s(4241)+4032*s(4242)+1188*s(4243)+198*s(4251)+22*s(4252)+11*s(4253)+11*s(4254)+22*s(4255)+22*s(4256)+11*s(4257)+33*s(4258)+154*s(4260)+11*s(4267)+11*s(4268)+11*s(4269)+22*s(4274)+22*s(4275)+44*s(4276)+3729*s(4277)+4928*s(4278)+1452*s(4279)+234*s(4287)+26*s(4288)+13*s(4289)+13*s(4290)+26*s(4291)+26*s(4292)+13*s(4293)+39*s(4294)+182*s(4296)+13*s(4303)+13*s(4304)+13*s(4305)+26*s(4310)+26*s(4311)+52*s(4312)+4407*s(4313)+5824*s(4314)+1716*s(4315)+620*s(4318)+1103*s(4319)+428*s(5210)+18
  Such that:aux(259) =< 2
aux(260) =< V1
aux(261) =< 2*V1
aux(262) =< 2*V1+1
aux(263) =< 2/3*V1
aux(264) =< 3/5*V1
aux(265) =< 4/5*V1
aux(266) =< 4/7*V1
aux(267) =< V
aux(268) =< 2*V
aux(269) =< 2*V+1
aux(270) =< 2/3*V
aux(271) =< 3/5*V
aux(272) =< 4/5*V
aux(273) =< 4/7*V
aux(274) =< V2
aux(275) =< 2*V2
aux(276) =< 2*V2+1
aux(277) =< 2/3*V2
aux(278) =< 3/5*V2
aux(279) =< 4/5*V2
aux(280) =< 4/7*V2
s(5210) =< aux(259)
s(4319) =< aux(275)
s(4287) =< aux(274)
s(4288) =< aux(274)
s(4289) =< aux(274)
s(4290) =< aux(274)
s(4291) =< aux(274)
s(4292) =< aux(274)
s(4293) =< aux(274)
s(4294) =< aux(274)
s(4295) =< aux(274)
s(4291) =< aux(277)
s(4293) =< aux(277)
s(4296) =< aux(278)
s(4290) =< aux(279)
s(4291) =< aux(279)
s(4293) =< aux(279)
s(4294) =< aux(279)
s(4289) =< aux(280)
s(4293) =< aux(280)
s(4297) =< aux(275)
s(4298) =< aux(275)-1
s(4299) =< aux(275)-2
s(4300) =< aux(275)+2
s(4290) =< aux(276)*(1/5)+aux(279)
s(4291) =< aux(276)*(1/5)+aux(279)
s(4292) =< aux(276)*(1/5)+aux(279)
s(4293) =< aux(276)*(1/5)+aux(279)
s(4294) =< aux(276)*(1/5)+aux(279)
s(4295) =< aux(276)*(1/5)+aux(279)
s(4291) =< aux(276)*(1/3)+aux(277)
s(4292) =< aux(276)*(1/3)+aux(277)
s(4293) =< aux(276)*(1/3)+aux(277)
s(4294) =< aux(276)*(1/3)+aux(277)
s(4295) =< aux(276)*(1/3)+aux(277)
s(4289) =< aux(276)*(3/7)+aux(280)
s(4290) =< aux(276)*(3/7)+aux(280)
s(4291) =< aux(276)*(3/7)+aux(280)
s(4292) =< aux(276)*(3/7)+aux(280)
s(4293) =< aux(276)*(3/7)+aux(280)
s(4294) =< aux(276)*(3/7)+aux(280)
s(4295) =< aux(276)*(3/7)+aux(280)
s(4296) =< aux(276)*(1/5)+aux(278)
s(4287) =< aux(276)*(1/5)+aux(278)
s(4301) =< s(4295)*s(4297)
s(4302) =< s(4291)*s(4298)
s(4303) =< s(4293)*s(4299)
s(4304) =< s(4291)*s(4298)
s(4305) =< s(4289)*s(4299)
s(4306) =< s(4287)*s(4297)
s(4307) =< s(4287)*s(4300)
s(4308) =< s(4296)*s(4299)
s(4309) =< s(4296)*aux(275)
s(4310) =< s(4301)
s(4311) =< s(4302)
s(4312) =< s(4307)
s(4313) =< s(4306)
s(4314) =< s(4308)
s(4315) =< s(4309)
s(4318) =< aux(268)
s(4251) =< aux(267)
s(4252) =< aux(267)
s(4253) =< aux(267)
s(4254) =< aux(267)
s(4255) =< aux(267)
s(4256) =< aux(267)
s(4257) =< aux(267)
s(4258) =< aux(267)
s(4259) =< aux(267)
s(4255) =< aux(270)
s(4257) =< aux(270)
s(4260) =< aux(271)
s(4254) =< aux(272)
s(4255) =< aux(272)
s(4257) =< aux(272)
s(4258) =< aux(272)
s(4253) =< aux(273)
s(4257) =< aux(273)
s(4261) =< aux(268)
s(4262) =< aux(268)-1
s(4263) =< aux(268)-2
s(4264) =< aux(268)+2
s(4254) =< aux(269)*(1/5)+aux(272)
s(4255) =< aux(269)*(1/5)+aux(272)
s(4256) =< aux(269)*(1/5)+aux(272)
s(4257) =< aux(269)*(1/5)+aux(272)
s(4258) =< aux(269)*(1/5)+aux(272)
s(4259) =< aux(269)*(1/5)+aux(272)
s(4255) =< aux(269)*(1/3)+aux(270)
s(4256) =< aux(269)*(1/3)+aux(270)
s(4257) =< aux(269)*(1/3)+aux(270)
s(4258) =< aux(269)*(1/3)+aux(270)
s(4259) =< aux(269)*(1/3)+aux(270)
s(4253) =< aux(269)*(3/7)+aux(273)
s(4254) =< aux(269)*(3/7)+aux(273)
s(4255) =< aux(269)*(3/7)+aux(273)
s(4256) =< aux(269)*(3/7)+aux(273)
s(4257) =< aux(269)*(3/7)+aux(273)
s(4258) =< aux(269)*(3/7)+aux(273)
s(4259) =< aux(269)*(3/7)+aux(273)
s(4260) =< aux(269)*(1/5)+aux(271)
s(4251) =< aux(269)*(1/5)+aux(271)
s(4265) =< s(4259)*s(4261)
s(4266) =< s(4255)*s(4262)
s(4267) =< s(4257)*s(4263)
s(4268) =< s(4255)*s(4262)
s(4269) =< s(4253)*s(4263)
s(4270) =< s(4251)*s(4261)
s(4271) =< s(4251)*s(4264)
s(4272) =< s(4260)*s(4263)
s(4273) =< s(4260)*aux(268)
s(4274) =< s(4265)
s(4275) =< s(4266)
s(4276) =< s(4271)
s(4277) =< s(4270)
s(4278) =< s(4272)
s(4279) =< s(4273)
s(4215) =< aux(260)
s(4216) =< aux(260)
s(4217) =< aux(260)
s(4218) =< aux(260)
s(4219) =< aux(260)
s(4220) =< aux(260)
s(4221) =< aux(260)
s(4222) =< aux(260)
s(4223) =< aux(260)
s(4219) =< aux(263)
s(4221) =< aux(263)
s(4224) =< aux(264)
s(4218) =< aux(265)
s(4219) =< aux(265)
s(4221) =< aux(265)
s(4222) =< aux(265)
s(4217) =< aux(266)
s(4221) =< aux(266)
s(4225) =< aux(261)
s(4226) =< aux(261)-1
s(4227) =< aux(261)-2
s(4228) =< aux(261)+2
s(4218) =< aux(262)*(1/5)+aux(265)
s(4219) =< aux(262)*(1/5)+aux(265)
s(4220) =< aux(262)*(1/5)+aux(265)
s(4221) =< aux(262)*(1/5)+aux(265)
s(4222) =< aux(262)*(1/5)+aux(265)
s(4223) =< aux(262)*(1/5)+aux(265)
s(4219) =< aux(262)*(1/3)+aux(263)
s(4220) =< aux(262)*(1/3)+aux(263)
s(4221) =< aux(262)*(1/3)+aux(263)
s(4222) =< aux(262)*(1/3)+aux(263)
s(4223) =< aux(262)*(1/3)+aux(263)
s(4217) =< aux(262)*(3/7)+aux(266)
s(4218) =< aux(262)*(3/7)+aux(266)
s(4219) =< aux(262)*(3/7)+aux(266)
s(4220) =< aux(262)*(3/7)+aux(266)
s(4221) =< aux(262)*(3/7)+aux(266)
s(4222) =< aux(262)*(3/7)+aux(266)
s(4223) =< aux(262)*(3/7)+aux(266)
s(4224) =< aux(262)*(1/5)+aux(264)
s(4215) =< aux(262)*(1/5)+aux(264)
s(4229) =< s(4223)*s(4225)
s(4230) =< s(4219)*s(4226)
s(4231) =< s(4221)*s(4227)
s(4232) =< s(4219)*s(4226)
s(4233) =< s(4217)*s(4227)
s(4234) =< s(4215)*s(4225)
s(4235) =< s(4215)*s(4228)
s(4236) =< s(4224)*s(4227)
s(4237) =< s(4224)*aux(261)
s(4238) =< s(4229)
s(4239) =< s(4230)
s(4240) =< s(4235)
s(4241) =< s(4234)
s(4242) =< s(4236)
s(4243) =< s(4237)

  with precondition: [Out=0,V1>=0,V>=0,V2>=0] 

* Chain [93]: 90*s(5533)+10*s(5534)+5*s(5535)+5*s(5536)+10*s(5537)+10*s(5538)+5*s(5539)+15*s(5540)+70*s(5542)+5*s(5549)+5*s(5550)+5*s(5551)+10*s(5556)+10*s(5557)+20*s(5558)+1695*s(5559)+2240*s(5560)+660*s(5561)+108*s(5569)+12*s(5570)+6*s(5571)+6*s(5572)+12*s(5573)+12*s(5574)+6*s(5575)+18*s(5576)+84*s(5578)+6*s(5585)+6*s(5586)+6*s(5587)+12*s(5592)+12*s(5593)+24*s(5594)+2034*s(5595)+2688*s(5596)+792*s(5597)+148*s(5600)+1211*s(5601)+18
  Such that:aux(289) =< 2
aux(290) =< V1
aux(291) =< 2*V1
aux(292) =< 2*V1+1
aux(293) =< 2/3*V1
aux(294) =< 3/5*V1
aux(295) =< 4/5*V1
aux(296) =< 4/7*V1
aux(297) =< V
aux(298) =< 2*V
aux(299) =< 2*V+1
aux(300) =< 2/3*V
aux(301) =< 3/5*V
aux(302) =< 4/5*V
aux(303) =< 4/7*V
s(5600) =< aux(298)
s(5601) =< aux(289)
s(5569) =< aux(297)
s(5570) =< aux(297)
s(5571) =< aux(297)
s(5572) =< aux(297)
s(5573) =< aux(297)
s(5574) =< aux(297)
s(5575) =< aux(297)
s(5576) =< aux(297)
s(5577) =< aux(297)
s(5573) =< aux(300)
s(5575) =< aux(300)
s(5578) =< aux(301)
s(5572) =< aux(302)
s(5573) =< aux(302)
s(5575) =< aux(302)
s(5576) =< aux(302)
s(5571) =< aux(303)
s(5575) =< aux(303)
s(5579) =< aux(298)
s(5580) =< aux(298)-1
s(5581) =< aux(298)-2
s(5582) =< aux(298)+2
s(5572) =< aux(299)*(1/5)+aux(302)
s(5573) =< aux(299)*(1/5)+aux(302)
s(5574) =< aux(299)*(1/5)+aux(302)
s(5575) =< aux(299)*(1/5)+aux(302)
s(5576) =< aux(299)*(1/5)+aux(302)
s(5577) =< aux(299)*(1/5)+aux(302)
s(5573) =< aux(299)*(1/3)+aux(300)
s(5574) =< aux(299)*(1/3)+aux(300)
s(5575) =< aux(299)*(1/3)+aux(300)
s(5576) =< aux(299)*(1/3)+aux(300)
s(5577) =< aux(299)*(1/3)+aux(300)
s(5571) =< aux(299)*(3/7)+aux(303)
s(5572) =< aux(299)*(3/7)+aux(303)
s(5573) =< aux(299)*(3/7)+aux(303)
s(5574) =< aux(299)*(3/7)+aux(303)
s(5575) =< aux(299)*(3/7)+aux(303)
s(5576) =< aux(299)*(3/7)+aux(303)
s(5577) =< aux(299)*(3/7)+aux(303)
s(5578) =< aux(299)*(1/5)+aux(301)
s(5569) =< aux(299)*(1/5)+aux(301)
s(5583) =< s(5577)*s(5579)
s(5584) =< s(5573)*s(5580)
s(5585) =< s(5575)*s(5581)
s(5586) =< s(5573)*s(5580)
s(5587) =< s(5571)*s(5581)
s(5588) =< s(5569)*s(5579)
s(5589) =< s(5569)*s(5582)
s(5590) =< s(5578)*s(5581)
s(5591) =< s(5578)*aux(298)
s(5592) =< s(5583)
s(5593) =< s(5584)
s(5594) =< s(5589)
s(5595) =< s(5588)
s(5596) =< s(5590)
s(5597) =< s(5591)
s(5533) =< aux(290)
s(5534) =< aux(290)
s(5535) =< aux(290)
s(5536) =< aux(290)
s(5537) =< aux(290)
s(5538) =< aux(290)
s(5539) =< aux(290)
s(5540) =< aux(290)
s(5541) =< aux(290)
s(5537) =< aux(293)
s(5539) =< aux(293)
s(5542) =< aux(294)
s(5536) =< aux(295)
s(5537) =< aux(295)
s(5539) =< aux(295)
s(5540) =< aux(295)
s(5535) =< aux(296)
s(5539) =< aux(296)
s(5543) =< aux(291)
s(5544) =< aux(291)-1
s(5545) =< aux(291)-2
s(5546) =< aux(291)+2
s(5536) =< aux(292)*(1/5)+aux(295)
s(5537) =< aux(292)*(1/5)+aux(295)
s(5538) =< aux(292)*(1/5)+aux(295)
s(5539) =< aux(292)*(1/5)+aux(295)
s(5540) =< aux(292)*(1/5)+aux(295)
s(5541) =< aux(292)*(1/5)+aux(295)
s(5537) =< aux(292)*(1/3)+aux(293)
s(5538) =< aux(292)*(1/3)+aux(293)
s(5539) =< aux(292)*(1/3)+aux(293)
s(5540) =< aux(292)*(1/3)+aux(293)
s(5541) =< aux(292)*(1/3)+aux(293)
s(5535) =< aux(292)*(3/7)+aux(296)
s(5536) =< aux(292)*(3/7)+aux(296)
s(5537) =< aux(292)*(3/7)+aux(296)
s(5538) =< aux(292)*(3/7)+aux(296)
s(5539) =< aux(292)*(3/7)+aux(296)
s(5540) =< aux(292)*(3/7)+aux(296)
s(5541) =< aux(292)*(3/7)+aux(296)
s(5542) =< aux(292)*(1/5)+aux(294)
s(5533) =< aux(292)*(1/5)+aux(294)
s(5547) =< s(5541)*s(5543)
s(5548) =< s(5537)*s(5544)
s(5549) =< s(5539)*s(5545)
s(5550) =< s(5537)*s(5544)
s(5551) =< s(5535)*s(5545)
s(5552) =< s(5533)*s(5543)
s(5553) =< s(5533)*s(5546)
s(5554) =< s(5542)*s(5545)
s(5555) =< s(5542)*aux(291)
s(5556) =< s(5547)
s(5557) =< s(5548)
s(5558) =< s(5553)
s(5559) =< s(5552)
s(5560) =< s(5554)
s(5561) =< s(5555)

  with precondition: [V2=2,Out=0,V1>=0,V>=0] 

* Chain [92]: 144*s(5981)+16*s(5982)+8*s(5983)+8*s(5984)+16*s(5985)+16*s(5986)+8*s(5987)+24*s(5988)+112*s(5990)+8*s(5997)+8*s(5998)+8*s(5999)+16*s(6004)+16*s(6005)+32*s(6006)+2712*s(6007)+3584*s(6008)+1056*s(6009)+72*s(6017)+8*s(6018)+4*s(6019)+4*s(6020)+8*s(6021)+8*s(6022)+4*s(6023)+12*s(6024)+56*s(6026)+4*s(6033)+4*s(6034)+4*s(6035)+8*s(6040)+8*s(6041)+16*s(6042)+1356*s(6043)+1792*s(6044)+528*s(6045)+1110*s(6048)+224*s(6049)+18
  Such that:aux(314) =< 2
aux(315) =< V1
aux(316) =< 2*V1
aux(317) =< 2*V1+1
aux(318) =< 2/3*V1
aux(319) =< 3/5*V1
aux(320) =< 4/5*V1
aux(321) =< 4/7*V1
aux(322) =< V2
aux(323) =< 2*V2
aux(324) =< 2*V2+1
aux(325) =< 2/3*V2
aux(326) =< 3/5*V2
aux(327) =< 4/5*V2
aux(328) =< 4/7*V2
s(6048) =< aux(314)
s(6049) =< aux(323)
s(6017) =< aux(322)
s(6018) =< aux(322)
s(6019) =< aux(322)
s(6020) =< aux(322)
s(6021) =< aux(322)
s(6022) =< aux(322)
s(6023) =< aux(322)
s(6024) =< aux(322)
s(6025) =< aux(322)
s(6021) =< aux(325)
s(6023) =< aux(325)
s(6026) =< aux(326)
s(6020) =< aux(327)
s(6021) =< aux(327)
s(6023) =< aux(327)
s(6024) =< aux(327)
s(6019) =< aux(328)
s(6023) =< aux(328)
s(6027) =< aux(323)
s(6028) =< aux(323)-1
s(6029) =< aux(323)-2
s(6030) =< aux(323)+2
s(6020) =< aux(324)*(1/5)+aux(327)
s(6021) =< aux(324)*(1/5)+aux(327)
s(6022) =< aux(324)*(1/5)+aux(327)
s(6023) =< aux(324)*(1/5)+aux(327)
s(6024) =< aux(324)*(1/5)+aux(327)
s(6025) =< aux(324)*(1/5)+aux(327)
s(6021) =< aux(324)*(1/3)+aux(325)
s(6022) =< aux(324)*(1/3)+aux(325)
s(6023) =< aux(324)*(1/3)+aux(325)
s(6024) =< aux(324)*(1/3)+aux(325)
s(6025) =< aux(324)*(1/3)+aux(325)
s(6019) =< aux(324)*(3/7)+aux(328)
s(6020) =< aux(324)*(3/7)+aux(328)
s(6021) =< aux(324)*(3/7)+aux(328)
s(6022) =< aux(324)*(3/7)+aux(328)
s(6023) =< aux(324)*(3/7)+aux(328)
s(6024) =< aux(324)*(3/7)+aux(328)
s(6025) =< aux(324)*(3/7)+aux(328)
s(6026) =< aux(324)*(1/5)+aux(326)
s(6017) =< aux(324)*(1/5)+aux(326)
s(6031) =< s(6025)*s(6027)
s(6032) =< s(6021)*s(6028)
s(6033) =< s(6023)*s(6029)
s(6034) =< s(6021)*s(6028)
s(6035) =< s(6019)*s(6029)
s(6036) =< s(6017)*s(6027)
s(6037) =< s(6017)*s(6030)
s(6038) =< s(6026)*s(6029)
s(6039) =< s(6026)*aux(323)
s(6040) =< s(6031)
s(6041) =< s(6032)
s(6042) =< s(6037)
s(6043) =< s(6036)
s(6044) =< s(6038)
s(6045) =< s(6039)
s(5981) =< aux(315)
s(5982) =< aux(315)
s(5983) =< aux(315)
s(5984) =< aux(315)
s(5985) =< aux(315)
s(5986) =< aux(315)
s(5987) =< aux(315)
s(5988) =< aux(315)
s(5989) =< aux(315)
s(5985) =< aux(318)
s(5987) =< aux(318)
s(5990) =< aux(319)
s(5984) =< aux(320)
s(5985) =< aux(320)
s(5987) =< aux(320)
s(5988) =< aux(320)
s(5983) =< aux(321)
s(5987) =< aux(321)
s(5991) =< aux(316)
s(5992) =< aux(316)-1
s(5993) =< aux(316)-2
s(5994) =< aux(316)+2
s(5984) =< aux(317)*(1/5)+aux(320)
s(5985) =< aux(317)*(1/5)+aux(320)
s(5986) =< aux(317)*(1/5)+aux(320)
s(5987) =< aux(317)*(1/5)+aux(320)
s(5988) =< aux(317)*(1/5)+aux(320)
s(5989) =< aux(317)*(1/5)+aux(320)
s(5985) =< aux(317)*(1/3)+aux(318)
s(5986) =< aux(317)*(1/3)+aux(318)
s(5987) =< aux(317)*(1/3)+aux(318)
s(5988) =< aux(317)*(1/3)+aux(318)
s(5989) =< aux(317)*(1/3)+aux(318)
s(5983) =< aux(317)*(3/7)+aux(321)
s(5984) =< aux(317)*(3/7)+aux(321)
s(5985) =< aux(317)*(3/7)+aux(321)
s(5986) =< aux(317)*(3/7)+aux(321)
s(5987) =< aux(317)*(3/7)+aux(321)
s(5988) =< aux(317)*(3/7)+aux(321)
s(5989) =< aux(317)*(3/7)+aux(321)
s(5990) =< aux(317)*(1/5)+aux(319)
s(5981) =< aux(317)*(1/5)+aux(319)
s(5995) =< s(5989)*s(5991)
s(5996) =< s(5985)*s(5992)
s(5997) =< s(5987)*s(5993)
s(5998) =< s(5985)*s(5992)
s(5999) =< s(5983)*s(5993)
s(6000) =< s(5981)*s(5991)
s(6001) =< s(5981)*s(5994)
s(6002) =< s(5990)*s(5993)
s(6003) =< s(5990)*aux(316)
s(6004) =< s(5995)
s(6005) =< s(5996)
s(6006) =< s(6001)
s(6007) =< s(6000)
s(6008) =< s(6002)
s(6009) =< s(6003)

  with precondition: [V=2,Out=0,V1>=0,V2>=0] 


#### Cost of chains of fun3(V1,V,Out):
* Chain [100]: 36*s(6650)+4*s(6651)+2*s(6652)+2*s(6653)+4*s(6654)+4*s(6655)+2*s(6656)+6*s(6657)+28*s(6659)+2*s(6666)+2*s(6667)+2*s(6668)+4*s(6673)+4*s(6674)+8*s(6675)+678*s(6676)+896*s(6677)+264*s(6678)+54*s(6686)+6*s(6687)+3*s(6688)+3*s(6689)+6*s(6690)+6*s(6691)+3*s(6692)+9*s(6693)+42*s(6695)+3*s(6702)+3*s(6703)+3*s(6704)+6*s(6709)+6*s(6710)+12*s(6711)+1017*s(6712)+1344*s(6713)+396*s(6714)+3*s(6715)+1*s(6790)+0
  Such that:s(6790) =< 2
aux(347) =< V1
aux(348) =< 2*V1
aux(349) =< 2*V1+1
aux(350) =< 2/3*V1
aux(351) =< 3/5*V1
aux(352) =< 4/5*V1
aux(353) =< 4/7*V1
aux(354) =< V
aux(355) =< 2*V
aux(356) =< 2*V+1
aux(357) =< 2/3*V
aux(358) =< 3/5*V
aux(359) =< 4/5*V
aux(360) =< 4/7*V
s(6715) =< aux(355)
s(6686) =< aux(354)
s(6687) =< aux(354)
s(6688) =< aux(354)
s(6689) =< aux(354)
s(6690) =< aux(354)
s(6691) =< aux(354)
s(6692) =< aux(354)
s(6693) =< aux(354)
s(6694) =< aux(354)
s(6690) =< aux(357)
s(6692) =< aux(357)
s(6695) =< aux(358)
s(6689) =< aux(359)
s(6690) =< aux(359)
s(6692) =< aux(359)
s(6693) =< aux(359)
s(6688) =< aux(360)
s(6692) =< aux(360)
s(6696) =< aux(355)
s(6697) =< aux(355)-1
s(6698) =< aux(355)-2
s(6699) =< aux(355)+2
s(6689) =< aux(356)*(1/5)+aux(359)
s(6690) =< aux(356)*(1/5)+aux(359)
s(6691) =< aux(356)*(1/5)+aux(359)
s(6692) =< aux(356)*(1/5)+aux(359)
s(6693) =< aux(356)*(1/5)+aux(359)
s(6694) =< aux(356)*(1/5)+aux(359)
s(6690) =< aux(356)*(1/3)+aux(357)
s(6691) =< aux(356)*(1/3)+aux(357)
s(6692) =< aux(356)*(1/3)+aux(357)
s(6693) =< aux(356)*(1/3)+aux(357)
s(6694) =< aux(356)*(1/3)+aux(357)
s(6688) =< aux(356)*(3/7)+aux(360)
s(6689) =< aux(356)*(3/7)+aux(360)
s(6690) =< aux(356)*(3/7)+aux(360)
s(6691) =< aux(356)*(3/7)+aux(360)
s(6692) =< aux(356)*(3/7)+aux(360)
s(6693) =< aux(356)*(3/7)+aux(360)
s(6694) =< aux(356)*(3/7)+aux(360)
s(6695) =< aux(356)*(1/5)+aux(358)
s(6686) =< aux(356)*(1/5)+aux(358)
s(6700) =< s(6694)*s(6696)
s(6701) =< s(6690)*s(6697)
s(6702) =< s(6692)*s(6698)
s(6703) =< s(6690)*s(6697)
s(6704) =< s(6688)*s(6698)
s(6705) =< s(6686)*s(6696)
s(6706) =< s(6686)*s(6699)
s(6707) =< s(6695)*s(6698)
s(6708) =< s(6695)*aux(355)
s(6709) =< s(6700)
s(6710) =< s(6701)
s(6711) =< s(6706)
s(6712) =< s(6705)
s(6713) =< s(6707)
s(6714) =< s(6708)
s(6650) =< aux(347)
s(6651) =< aux(347)
s(6652) =< aux(347)
s(6653) =< aux(347)
s(6654) =< aux(347)
s(6655) =< aux(347)
s(6656) =< aux(347)
s(6657) =< aux(347)
s(6658) =< aux(347)
s(6654) =< aux(350)
s(6656) =< aux(350)
s(6659) =< aux(351)
s(6653) =< aux(352)
s(6654) =< aux(352)
s(6656) =< aux(352)
s(6657) =< aux(352)
s(6652) =< aux(353)
s(6656) =< aux(353)
s(6660) =< aux(348)
s(6661) =< aux(348)-1
s(6662) =< aux(348)-2
s(6663) =< aux(348)+2
s(6653) =< aux(349)*(1/5)+aux(352)
s(6654) =< aux(349)*(1/5)+aux(352)
s(6655) =< aux(349)*(1/5)+aux(352)
s(6656) =< aux(349)*(1/5)+aux(352)
s(6657) =< aux(349)*(1/5)+aux(352)
s(6658) =< aux(349)*(1/5)+aux(352)
s(6654) =< aux(349)*(1/3)+aux(350)
s(6655) =< aux(349)*(1/3)+aux(350)
s(6656) =< aux(349)*(1/3)+aux(350)
s(6657) =< aux(349)*(1/3)+aux(350)
s(6658) =< aux(349)*(1/3)+aux(350)
s(6652) =< aux(349)*(3/7)+aux(353)
s(6653) =< aux(349)*(3/7)+aux(353)
s(6654) =< aux(349)*(3/7)+aux(353)
s(6655) =< aux(349)*(3/7)+aux(353)
s(6656) =< aux(349)*(3/7)+aux(353)
s(6657) =< aux(349)*(3/7)+aux(353)
s(6658) =< aux(349)*(3/7)+aux(353)
s(6659) =< aux(349)*(1/5)+aux(351)
s(6650) =< aux(349)*(1/5)+aux(351)
s(6664) =< s(6658)*s(6660)
s(6665) =< s(6654)*s(6661)
s(6666) =< s(6656)*s(6662)
s(6667) =< s(6654)*s(6661)
s(6668) =< s(6652)*s(6662)
s(6669) =< s(6650)*s(6660)
s(6670) =< s(6650)*s(6663)
s(6671) =< s(6659)*s(6662)
s(6672) =< s(6659)*aux(348)
s(6673) =< s(6664)
s(6674) =< s(6665)
s(6675) =< s(6670)
s(6676) =< s(6669)
s(6677) =< s(6671)
s(6678) =< s(6672)

  with precondition: [Out=0,V1>=0,V>=0] 

* Chain [99]: 54*s(6837)+6*s(6838)+3*s(6839)+3*s(6840)+6*s(6841)+6*s(6842)+3*s(6843)+9*s(6844)+42*s(6846)+3*s(6853)+3*s(6854)+3*s(6855)+6*s(6860)+6*s(6861)+12*s(6862)+1017*s(6863)+1344*s(6864)+396*s(6865)+72*s(6873)+8*s(6874)+4*s(6875)+4*s(6876)+8*s(6877)+8*s(6878)+4*s(6879)+12*s(6880)+56*s(6882)+4*s(6889)+4*s(6890)+4*s(6891)+8*s(6896)+8*s(6897)+16*s(6898)+1356*s(6899)+1792*s(6900)+528*s(6901)+1*s(6974)+2*s(7047)+1
  Such that:aux(362) =< 2
aux(363) =< V1
aux(364) =< 2*V1
aux(365) =< 2*V1+1
aux(366) =< 2/3*V1
aux(367) =< 3/5*V1
aux(368) =< 4/5*V1
aux(369) =< 4/7*V1
aux(370) =< V
aux(371) =< 2*V
aux(372) =< 2*V+1
aux(373) =< 2/3*V
aux(374) =< 3/5*V
aux(375) =< 4/5*V
aux(376) =< 4/7*V
s(7047) =< aux(362)
s(6873) =< aux(370)
s(6874) =< aux(370)
s(6875) =< aux(370)
s(6876) =< aux(370)
s(6877) =< aux(370)
s(6878) =< aux(370)
s(6879) =< aux(370)
s(6880) =< aux(370)
s(6881) =< aux(370)
s(6877) =< aux(373)
s(6879) =< aux(373)
s(6882) =< aux(374)
s(6876) =< aux(375)
s(6877) =< aux(375)
s(6879) =< aux(375)
s(6880) =< aux(375)
s(6875) =< aux(376)
s(6879) =< aux(376)
s(6883) =< aux(371)
s(6884) =< aux(371)-1
s(6885) =< aux(371)-2
s(6886) =< aux(371)+2
s(6876) =< aux(372)*(1/5)+aux(375)
s(6877) =< aux(372)*(1/5)+aux(375)
s(6878) =< aux(372)*(1/5)+aux(375)
s(6879) =< aux(372)*(1/5)+aux(375)
s(6880) =< aux(372)*(1/5)+aux(375)
s(6881) =< aux(372)*(1/5)+aux(375)
s(6877) =< aux(372)*(1/3)+aux(373)
s(6878) =< aux(372)*(1/3)+aux(373)
s(6879) =< aux(372)*(1/3)+aux(373)
s(6880) =< aux(372)*(1/3)+aux(373)
s(6881) =< aux(372)*(1/3)+aux(373)
s(6875) =< aux(372)*(3/7)+aux(376)
s(6876) =< aux(372)*(3/7)+aux(376)
s(6877) =< aux(372)*(3/7)+aux(376)
s(6878) =< aux(372)*(3/7)+aux(376)
s(6879) =< aux(372)*(3/7)+aux(376)
s(6880) =< aux(372)*(3/7)+aux(376)
s(6881) =< aux(372)*(3/7)+aux(376)
s(6882) =< aux(372)*(1/5)+aux(374)
s(6873) =< aux(372)*(1/5)+aux(374)
s(6887) =< s(6881)*s(6883)
s(6888) =< s(6877)*s(6884)
s(6889) =< s(6879)*s(6885)
s(6890) =< s(6877)*s(6884)
s(6891) =< s(6875)*s(6885)
s(6892) =< s(6873)*s(6883)
s(6893) =< s(6873)*s(6886)
s(6894) =< s(6882)*s(6885)
s(6895) =< s(6882)*aux(371)
s(6896) =< s(6887)
s(6897) =< s(6888)
s(6898) =< s(6893)
s(6899) =< s(6892)
s(6900) =< s(6894)
s(6901) =< s(6895)
s(6837) =< aux(363)
s(6838) =< aux(363)
s(6839) =< aux(363)
s(6840) =< aux(363)
s(6841) =< aux(363)
s(6842) =< aux(363)
s(6843) =< aux(363)
s(6844) =< aux(363)
s(6845) =< aux(363)
s(6841) =< aux(366)
s(6843) =< aux(366)
s(6846) =< aux(367)
s(6840) =< aux(368)
s(6841) =< aux(368)
s(6843) =< aux(368)
s(6844) =< aux(368)
s(6839) =< aux(369)
s(6843) =< aux(369)
s(6847) =< aux(364)
s(6848) =< aux(364)-1
s(6849) =< aux(364)-2
s(6850) =< aux(364)+2
s(6840) =< aux(365)*(1/5)+aux(368)
s(6841) =< aux(365)*(1/5)+aux(368)
s(6842) =< aux(365)*(1/5)+aux(368)
s(6843) =< aux(365)*(1/5)+aux(368)
s(6844) =< aux(365)*(1/5)+aux(368)
s(6845) =< aux(365)*(1/5)+aux(368)
s(6841) =< aux(365)*(1/3)+aux(366)
s(6842) =< aux(365)*(1/3)+aux(366)
s(6843) =< aux(365)*(1/3)+aux(366)
s(6844) =< aux(365)*(1/3)+aux(366)
s(6845) =< aux(365)*(1/3)+aux(366)
s(6839) =< aux(365)*(3/7)+aux(369)
s(6840) =< aux(365)*(3/7)+aux(369)
s(6841) =< aux(365)*(3/7)+aux(369)
s(6842) =< aux(365)*(3/7)+aux(369)
s(6843) =< aux(365)*(3/7)+aux(369)
s(6844) =< aux(365)*(3/7)+aux(369)
s(6845) =< aux(365)*(3/7)+aux(369)
s(6846) =< aux(365)*(1/5)+aux(367)
s(6837) =< aux(365)*(1/5)+aux(367)
s(6851) =< s(6845)*s(6847)
s(6852) =< s(6841)*s(6848)
s(6853) =< s(6843)*s(6849)
s(6854) =< s(6841)*s(6848)
s(6855) =< s(6839)*s(6849)
s(6856) =< s(6837)*s(6847)
s(6857) =< s(6837)*s(6850)
s(6858) =< s(6846)*s(6849)
s(6859) =< s(6846)*aux(364)
s(6860) =< s(6851)
s(6861) =< s(6852)
s(6862) =< s(6857)
s(6863) =< s(6856)
s(6864) =< s(6858)
s(6865) =< s(6859)
s(6974) =< aux(371)

  with precondition: [Out=1,V1>=0,V>=0] 

* Chain [98]: 54*s(7092)+6*s(7093)+3*s(7094)+3*s(7095)+6*s(7096)+6*s(7097)+3*s(7098)+9*s(7099)+42*s(7101)+3*s(7108)+3*s(7109)+3*s(7110)+6*s(7115)+6*s(7116)+12*s(7117)+1017*s(7118)+1344*s(7119)+396*s(7120)+72*s(7128)+8*s(7129)+4*s(7130)+4*s(7131)+8*s(7132)+8*s(7133)+4*s(7134)+12*s(7135)+56*s(7137)+4*s(7144)+4*s(7145)+4*s(7146)+8*s(7151)+8*s(7152)+16*s(7153)+1356*s(7154)+1792*s(7155)+528*s(7156)+1*s(7229)+1*s(7338)+1
  Such that:s(7338) =< 1
aux(378) =< V1
aux(379) =< 2*V1
aux(380) =< 2*V1+1
aux(381) =< 2/3*V1
aux(382) =< 3/5*V1
aux(383) =< 4/5*V1
aux(384) =< 4/7*V1
aux(385) =< V
aux(386) =< 2*V
aux(387) =< 2*V+1
aux(388) =< 2/3*V
aux(389) =< 3/5*V
aux(390) =< 4/5*V
aux(391) =< 4/7*V
s(7128) =< aux(385)
s(7129) =< aux(385)
s(7130) =< aux(385)
s(7131) =< aux(385)
s(7132) =< aux(385)
s(7133) =< aux(385)
s(7134) =< aux(385)
s(7135) =< aux(385)
s(7136) =< aux(385)
s(7132) =< aux(388)
s(7134) =< aux(388)
s(7137) =< aux(389)
s(7131) =< aux(390)
s(7132) =< aux(390)
s(7134) =< aux(390)
s(7135) =< aux(390)
s(7130) =< aux(391)
s(7134) =< aux(391)
s(7138) =< aux(386)
s(7139) =< aux(386)-1
s(7140) =< aux(386)-2
s(7141) =< aux(386)+2
s(7131) =< aux(387)*(1/5)+aux(390)
s(7132) =< aux(387)*(1/5)+aux(390)
s(7133) =< aux(387)*(1/5)+aux(390)
s(7134) =< aux(387)*(1/5)+aux(390)
s(7135) =< aux(387)*(1/5)+aux(390)
s(7136) =< aux(387)*(1/5)+aux(390)
s(7132) =< aux(387)*(1/3)+aux(388)
s(7133) =< aux(387)*(1/3)+aux(388)
s(7134) =< aux(387)*(1/3)+aux(388)
s(7135) =< aux(387)*(1/3)+aux(388)
s(7136) =< aux(387)*(1/3)+aux(388)
s(7130) =< aux(387)*(3/7)+aux(391)
s(7131) =< aux(387)*(3/7)+aux(391)
s(7132) =< aux(387)*(3/7)+aux(391)
s(7133) =< aux(387)*(3/7)+aux(391)
s(7134) =< aux(387)*(3/7)+aux(391)
s(7135) =< aux(387)*(3/7)+aux(391)
s(7136) =< aux(387)*(3/7)+aux(391)
s(7137) =< aux(387)*(1/5)+aux(389)
s(7128) =< aux(387)*(1/5)+aux(389)
s(7142) =< s(7136)*s(7138)
s(7143) =< s(7132)*s(7139)
s(7144) =< s(7134)*s(7140)
s(7145) =< s(7132)*s(7139)
s(7146) =< s(7130)*s(7140)
s(7147) =< s(7128)*s(7138)
s(7148) =< s(7128)*s(7141)
s(7149) =< s(7137)*s(7140)
s(7150) =< s(7137)*aux(386)
s(7151) =< s(7142)
s(7152) =< s(7143)
s(7153) =< s(7148)
s(7154) =< s(7147)
s(7155) =< s(7149)
s(7156) =< s(7150)
s(7092) =< aux(378)
s(7093) =< aux(378)
s(7094) =< aux(378)
s(7095) =< aux(378)
s(7096) =< aux(378)
s(7097) =< aux(378)
s(7098) =< aux(378)
s(7099) =< aux(378)
s(7100) =< aux(378)
s(7096) =< aux(381)
s(7098) =< aux(381)
s(7101) =< aux(382)
s(7095) =< aux(383)
s(7096) =< aux(383)
s(7098) =< aux(383)
s(7099) =< aux(383)
s(7094) =< aux(384)
s(7098) =< aux(384)
s(7102) =< aux(379)
s(7103) =< aux(379)-1
s(7104) =< aux(379)-2
s(7105) =< aux(379)+2
s(7095) =< aux(380)*(1/5)+aux(383)
s(7096) =< aux(380)*(1/5)+aux(383)
s(7097) =< aux(380)*(1/5)+aux(383)
s(7098) =< aux(380)*(1/5)+aux(383)
s(7099) =< aux(380)*(1/5)+aux(383)
s(7100) =< aux(380)*(1/5)+aux(383)
s(7096) =< aux(380)*(1/3)+aux(381)
s(7097) =< aux(380)*(1/3)+aux(381)
s(7098) =< aux(380)*(1/3)+aux(381)
s(7099) =< aux(380)*(1/3)+aux(381)
s(7100) =< aux(380)*(1/3)+aux(381)
s(7094) =< aux(380)*(3/7)+aux(384)
s(7095) =< aux(380)*(3/7)+aux(384)
s(7096) =< aux(380)*(3/7)+aux(384)
s(7097) =< aux(380)*(3/7)+aux(384)
s(7098) =< aux(380)*(3/7)+aux(384)
s(7099) =< aux(380)*(3/7)+aux(384)
s(7100) =< aux(380)*(3/7)+aux(384)
s(7101) =< aux(380)*(1/5)+aux(382)
s(7092) =< aux(380)*(1/5)+aux(382)
s(7106) =< s(7100)*s(7102)
s(7107) =< s(7096)*s(7103)
s(7108) =< s(7098)*s(7104)
s(7109) =< s(7096)*s(7103)
s(7110) =< s(7094)*s(7104)
s(7111) =< s(7092)*s(7102)
s(7112) =< s(7092)*s(7105)
s(7113) =< s(7101)*s(7104)
s(7114) =< s(7101)*aux(379)
s(7115) =< s(7106)
s(7116) =< s(7107)
s(7117) =< s(7112)
s(7118) =< s(7111)
s(7119) =< s(7113)
s(7120) =< s(7114)
s(7229) =< aux(379)

  with precondition: [Out=2,V1>=1,V>=0] 

* Chain [97]: 18*s(7346)+2*s(7347)+1*s(7348)+1*s(7349)+2*s(7350)+2*s(7351)+1*s(7352)+3*s(7353)+14*s(7355)+1*s(7362)+1*s(7363)+1*s(7364)+2*s(7369)+2*s(7370)+4*s(7371)+339*s(7372)+448*s(7373)+132*s(7374)+2*s(7375)+0
  Such that:s(7339) =< V1
s(7340) =< 2*V1
s(7341) =< 2*V1+1
s(7342) =< 2/3*V1
s(7343) =< 3/5*V1
s(7344) =< 4/5*V1
s(7345) =< 4/7*V1
aux(392) =< 2
s(7375) =< aux(392)
s(7346) =< s(7339)
s(7347) =< s(7339)
s(7348) =< s(7339)
s(7349) =< s(7339)
s(7350) =< s(7339)
s(7351) =< s(7339)
s(7352) =< s(7339)
s(7353) =< s(7339)
s(7354) =< s(7339)
s(7350) =< s(7342)
s(7352) =< s(7342)
s(7355) =< s(7343)
s(7349) =< s(7344)
s(7350) =< s(7344)
s(7352) =< s(7344)
s(7353) =< s(7344)
s(7348) =< s(7345)
s(7352) =< s(7345)
s(7356) =< s(7340)
s(7357) =< s(7340)-1
s(7358) =< s(7340)-2
s(7359) =< s(7340)+2
s(7349) =< s(7341)*(1/5)+s(7344)
s(7350) =< s(7341)*(1/5)+s(7344)
s(7351) =< s(7341)*(1/5)+s(7344)
s(7352) =< s(7341)*(1/5)+s(7344)
s(7353) =< s(7341)*(1/5)+s(7344)
s(7354) =< s(7341)*(1/5)+s(7344)
s(7350) =< s(7341)*(1/3)+s(7342)
s(7351) =< s(7341)*(1/3)+s(7342)
s(7352) =< s(7341)*(1/3)+s(7342)
s(7353) =< s(7341)*(1/3)+s(7342)
s(7354) =< s(7341)*(1/3)+s(7342)
s(7348) =< s(7341)*(3/7)+s(7345)
s(7349) =< s(7341)*(3/7)+s(7345)
s(7350) =< s(7341)*(3/7)+s(7345)
s(7351) =< s(7341)*(3/7)+s(7345)
s(7352) =< s(7341)*(3/7)+s(7345)
s(7353) =< s(7341)*(3/7)+s(7345)
s(7354) =< s(7341)*(3/7)+s(7345)
s(7355) =< s(7341)*(1/5)+s(7343)
s(7346) =< s(7341)*(1/5)+s(7343)
s(7360) =< s(7354)*s(7356)
s(7361) =< s(7350)*s(7357)
s(7362) =< s(7352)*s(7358)
s(7363) =< s(7350)*s(7357)
s(7364) =< s(7348)*s(7358)
s(7365) =< s(7346)*s(7356)
s(7366) =< s(7346)*s(7359)
s(7367) =< s(7355)*s(7358)
s(7368) =< s(7355)*s(7340)
s(7369) =< s(7360)
s(7370) =< s(7361)
s(7371) =< s(7366)
s(7372) =< s(7365)
s(7373) =< s(7367)
s(7374) =< s(7368)

  with precondition: [V=2,Out=0,V1>=0] 

* Chain [96]: 36*s(7384)+4*s(7385)+2*s(7386)+2*s(7387)+4*s(7388)+4*s(7389)+2*s(7390)+6*s(7391)+28*s(7393)+2*s(7400)+2*s(7401)+2*s(7402)+4*s(7407)+4*s(7408)+8*s(7409)+678*s(7410)+896*s(7411)+264*s(7412)+1*s(7449)+1
  Such that:s(7449) =< 2
aux(393) =< V1
aux(394) =< 2*V1
aux(395) =< 2*V1+1
aux(396) =< 2/3*V1
aux(397) =< 3/5*V1
aux(398) =< 4/5*V1
aux(399) =< 4/7*V1
s(7384) =< aux(393)
s(7385) =< aux(393)
s(7386) =< aux(393)
s(7387) =< aux(393)
s(7388) =< aux(393)
s(7389) =< aux(393)
s(7390) =< aux(393)
s(7391) =< aux(393)
s(7392) =< aux(393)
s(7388) =< aux(396)
s(7390) =< aux(396)
s(7393) =< aux(397)
s(7387) =< aux(398)
s(7388) =< aux(398)
s(7390) =< aux(398)
s(7391) =< aux(398)
s(7386) =< aux(399)
s(7390) =< aux(399)
s(7394) =< aux(394)
s(7395) =< aux(394)-1
s(7396) =< aux(394)-2
s(7397) =< aux(394)+2
s(7387) =< aux(395)*(1/5)+aux(398)
s(7388) =< aux(395)*(1/5)+aux(398)
s(7389) =< aux(395)*(1/5)+aux(398)
s(7390) =< aux(395)*(1/5)+aux(398)
s(7391) =< aux(395)*(1/5)+aux(398)
s(7392) =< aux(395)*(1/5)+aux(398)
s(7388) =< aux(395)*(1/3)+aux(396)
s(7389) =< aux(395)*(1/3)+aux(396)
s(7390) =< aux(395)*(1/3)+aux(396)
s(7391) =< aux(395)*(1/3)+aux(396)
s(7392) =< aux(395)*(1/3)+aux(396)
s(7386) =< aux(395)*(3/7)+aux(399)
s(7387) =< aux(395)*(3/7)+aux(399)
s(7388) =< aux(395)*(3/7)+aux(399)
s(7389) =< aux(395)*(3/7)+aux(399)
s(7390) =< aux(395)*(3/7)+aux(399)
s(7391) =< aux(395)*(3/7)+aux(399)
s(7392) =< aux(395)*(3/7)+aux(399)
s(7393) =< aux(395)*(1/5)+aux(397)
s(7384) =< aux(395)*(1/5)+aux(397)
s(7398) =< s(7392)*s(7394)
s(7399) =< s(7388)*s(7395)
s(7400) =< s(7390)*s(7396)
s(7401) =< s(7388)*s(7395)
s(7402) =< s(7386)*s(7396)
s(7403) =< s(7384)*s(7394)
s(7404) =< s(7384)*s(7397)
s(7405) =< s(7393)*s(7396)
s(7406) =< s(7393)*aux(394)
s(7407) =< s(7398)
s(7408) =< s(7399)
s(7409) =< s(7404)
s(7410) =< s(7403)
s(7411) =< s(7405)
s(7412) =< s(7406)

  with precondition: [V=2,Out=1,V1>=0] 

* Chain [95]: 18*s(7457)+2*s(7458)+1*s(7459)+1*s(7460)+2*s(7461)+2*s(7462)+1*s(7463)+3*s(7464)+14*s(7466)+1*s(7473)+1*s(7474)+1*s(7475)+2*s(7480)+2*s(7481)+4*s(7482)+339*s(7483)+448*s(7484)+132*s(7485)+1*s(7486)+1
  Such that:s(7486) =< 2
s(7450) =< V1
s(7451) =< 2*V1
s(7452) =< 2*V1+1
s(7453) =< 2/3*V1
s(7454) =< 3/5*V1
s(7455) =< 4/5*V1
s(7456) =< 4/7*V1
s(7457) =< s(7450)
s(7458) =< s(7450)
s(7459) =< s(7450)
s(7460) =< s(7450)
s(7461) =< s(7450)
s(7462) =< s(7450)
s(7463) =< s(7450)
s(7464) =< s(7450)
s(7465) =< s(7450)
s(7461) =< s(7453)
s(7463) =< s(7453)
s(7466) =< s(7454)
s(7460) =< s(7455)
s(7461) =< s(7455)
s(7463) =< s(7455)
s(7464) =< s(7455)
s(7459) =< s(7456)
s(7463) =< s(7456)
s(7467) =< s(7451)
s(7468) =< s(7451)-1
s(7469) =< s(7451)-2
s(7470) =< s(7451)+2
s(7460) =< s(7452)*(1/5)+s(7455)
s(7461) =< s(7452)*(1/5)+s(7455)
s(7462) =< s(7452)*(1/5)+s(7455)
s(7463) =< s(7452)*(1/5)+s(7455)
s(7464) =< s(7452)*(1/5)+s(7455)
s(7465) =< s(7452)*(1/5)+s(7455)
s(7461) =< s(7452)*(1/3)+s(7453)
s(7462) =< s(7452)*(1/3)+s(7453)
s(7463) =< s(7452)*(1/3)+s(7453)
s(7464) =< s(7452)*(1/3)+s(7453)
s(7465) =< s(7452)*(1/3)+s(7453)
s(7459) =< s(7452)*(3/7)+s(7456)
s(7460) =< s(7452)*(3/7)+s(7456)
s(7461) =< s(7452)*(3/7)+s(7456)
s(7462) =< s(7452)*(3/7)+s(7456)
s(7463) =< s(7452)*(3/7)+s(7456)
s(7464) =< s(7452)*(3/7)+s(7456)
s(7465) =< s(7452)*(3/7)+s(7456)
s(7466) =< s(7452)*(1/5)+s(7454)
s(7457) =< s(7452)*(1/5)+s(7454)
s(7471) =< s(7465)*s(7467)
s(7472) =< s(7461)*s(7468)
s(7473) =< s(7463)*s(7469)
s(7474) =< s(7461)*s(7468)
s(7475) =< s(7459)*s(7469)
s(7476) =< s(7457)*s(7467)
s(7477) =< s(7457)*s(7470)
s(7478) =< s(7466)*s(7469)
s(7479) =< s(7466)*s(7451)
s(7480) =< s(7471)
s(7481) =< s(7472)
s(7482) =< s(7477)
s(7483) =< s(7476)
s(7484) =< s(7478)
s(7485) =< s(7479)

  with precondition: [V=2,Out=2,2*V1>=3] 


#### Cost of chains of fun5(V1,Out):
* Chain [102]: 18*s(7829)+2*s(7830)+1*s(7831)+1*s(7832)+2*s(7833)+2*s(7834)+1*s(7835)+3*s(7836)+14*s(7838)+1*s(7845)+1*s(7846)+1*s(7847)+2*s(7852)+2*s(7853)+4*s(7854)+339*s(7855)+448*s(7856)+132*s(7857)+1
  Such that:s(7822) =< V1
s(7823) =< 2*V1
s(7824) =< 2*V1+1
s(7825) =< 2/3*V1
s(7826) =< 3/5*V1
s(7827) =< 4/5*V1
s(7828) =< 4/7*V1
s(7829) =< s(7822)
s(7830) =< s(7822)
s(7831) =< s(7822)
s(7832) =< s(7822)
s(7833) =< s(7822)
s(7834) =< s(7822)
s(7835) =< s(7822)
s(7836) =< s(7822)
s(7837) =< s(7822)
s(7833) =< s(7825)
s(7835) =< s(7825)
s(7838) =< s(7826)
s(7832) =< s(7827)
s(7833) =< s(7827)
s(7835) =< s(7827)
s(7836) =< s(7827)
s(7831) =< s(7828)
s(7835) =< s(7828)
s(7839) =< s(7823)
s(7840) =< s(7823)-1
s(7841) =< s(7823)-2
s(7842) =< s(7823)+2
s(7832) =< s(7824)*(1/5)+s(7827)
s(7833) =< s(7824)*(1/5)+s(7827)
s(7834) =< s(7824)*(1/5)+s(7827)
s(7835) =< s(7824)*(1/5)+s(7827)
s(7836) =< s(7824)*(1/5)+s(7827)
s(7837) =< s(7824)*(1/5)+s(7827)
s(7833) =< s(7824)*(1/3)+s(7825)
s(7834) =< s(7824)*(1/3)+s(7825)
s(7835) =< s(7824)*(1/3)+s(7825)
s(7836) =< s(7824)*(1/3)+s(7825)
s(7837) =< s(7824)*(1/3)+s(7825)
s(7831) =< s(7824)*(3/7)+s(7828)
s(7832) =< s(7824)*(3/7)+s(7828)
s(7833) =< s(7824)*(3/7)+s(7828)
s(7834) =< s(7824)*(3/7)+s(7828)
s(7835) =< s(7824)*(3/7)+s(7828)
s(7836) =< s(7824)*(3/7)+s(7828)
s(7837) =< s(7824)*(3/7)+s(7828)
s(7838) =< s(7824)*(1/5)+s(7826)
s(7829) =< s(7824)*(1/5)+s(7826)
s(7843) =< s(7837)*s(7839)
s(7844) =< s(7833)*s(7840)
s(7845) =< s(7835)*s(7841)
s(7846) =< s(7833)*s(7840)
s(7847) =< s(7831)*s(7841)
s(7848) =< s(7829)*s(7839)
s(7849) =< s(7829)*s(7842)
s(7850) =< s(7838)*s(7841)
s(7851) =< s(7838)*s(7823)
s(7852) =< s(7843)
s(7853) =< s(7844)
s(7854) =< s(7849)
s(7855) =< s(7848)
s(7856) =< s(7850)
s(7857) =< s(7851)

  with precondition: [Out=0,V1>=0] 

* Chain [101]: 18*s(7865)+2*s(7866)+1*s(7867)+1*s(7868)+2*s(7869)+2*s(7870)+1*s(7871)+3*s(7872)+14*s(7874)+1*s(7881)+1*s(7882)+1*s(7883)+2*s(7888)+2*s(7889)+4*s(7890)+339*s(7891)+448*s(7892)+132*s(7893)+1
  Such that:s(7858) =< V1
s(7859) =< 2*V1
s(7860) =< 2*V1+1
s(7861) =< 2/3*V1
s(7862) =< 3/5*V1
s(7863) =< 4/5*V1
s(7864) =< 4/7*V1
s(7865) =< s(7858)
s(7866) =< s(7858)
s(7867) =< s(7858)
s(7868) =< s(7858)
s(7869) =< s(7858)
s(7870) =< s(7858)
s(7871) =< s(7858)
s(7872) =< s(7858)
s(7873) =< s(7858)
s(7869) =< s(7861)
s(7871) =< s(7861)
s(7874) =< s(7862)
s(7868) =< s(7863)
s(7869) =< s(7863)
s(7871) =< s(7863)
s(7872) =< s(7863)
s(7867) =< s(7864)
s(7871) =< s(7864)
s(7875) =< s(7859)
s(7876) =< s(7859)-1
s(7877) =< s(7859)-2
s(7878) =< s(7859)+2
s(7868) =< s(7860)*(1/5)+s(7863)
s(7869) =< s(7860)*(1/5)+s(7863)
s(7870) =< s(7860)*(1/5)+s(7863)
s(7871) =< s(7860)*(1/5)+s(7863)
s(7872) =< s(7860)*(1/5)+s(7863)
s(7873) =< s(7860)*(1/5)+s(7863)
s(7869) =< s(7860)*(1/3)+s(7861)
s(7870) =< s(7860)*(1/3)+s(7861)
s(7871) =< s(7860)*(1/3)+s(7861)
s(7872) =< s(7860)*(1/3)+s(7861)
s(7873) =< s(7860)*(1/3)+s(7861)
s(7867) =< s(7860)*(3/7)+s(7864)
s(7868) =< s(7860)*(3/7)+s(7864)
s(7869) =< s(7860)*(3/7)+s(7864)
s(7870) =< s(7860)*(3/7)+s(7864)
s(7871) =< s(7860)*(3/7)+s(7864)
s(7872) =< s(7860)*(3/7)+s(7864)
s(7873) =< s(7860)*(3/7)+s(7864)
s(7874) =< s(7860)*(1/5)+s(7862)
s(7865) =< s(7860)*(1/5)+s(7862)
s(7879) =< s(7873)*s(7875)
s(7880) =< s(7869)*s(7876)
s(7881) =< s(7871)*s(7877)
s(7882) =< s(7869)*s(7876)
s(7883) =< s(7867)*s(7877)
s(7884) =< s(7865)*s(7875)
s(7885) =< s(7865)*s(7878)
s(7886) =< s(7874)*s(7877)
s(7887) =< s(7874)*s(7859)
s(7888) =< s(7879)
s(7889) =< s(7880)
s(7890) =< s(7885)
s(7891) =< s(7884)
s(7892) =< s(7886)
s(7893) =< s(7887)

  with precondition: [V1>=1,Out>=0,2*V1>=Out+1] 


#### Cost of chains of fun6(Out):
* Chain [104]: 0
  with precondition: [Out=0] 

* Chain [103]: 0
  with precondition: [Out=1] 


#### Cost of chains of fun7(V1,V,Out):
* Chain [110]: 36*s(7901)+4*s(7902)+2*s(7903)+2*s(7904)+4*s(7905)+4*s(7906)+2*s(7907)+6*s(7908)+28*s(7910)+2*s(7917)+2*s(7918)+2*s(7919)+4*s(7924)+4*s(7925)+8*s(7926)+678*s(7927)+896*s(7928)+264*s(7929)+54*s(7937)+6*s(7938)+3*s(7939)+3*s(7940)+6*s(7941)+6*s(7942)+3*s(7943)+9*s(7944)+42*s(7946)+3*s(7953)+3*s(7954)+3*s(7955)+6*s(7960)+6*s(7961)+12*s(7962)+1017*s(7963)+1344*s(7964)+396*s(7965)+0
  Such that:aux(423) =< V1
aux(424) =< 2*V1
aux(425) =< 2*V1+1
aux(426) =< 2/3*V1
aux(427) =< 3/5*V1
aux(428) =< 4/5*V1
aux(429) =< 4/7*V1
aux(430) =< V
aux(431) =< 2*V
aux(432) =< 2*V+1
aux(433) =< 2/3*V
aux(434) =< 3/5*V
aux(435) =< 4/5*V
aux(436) =< 4/7*V
s(7937) =< aux(430)
s(7938) =< aux(430)
s(7939) =< aux(430)
s(7940) =< aux(430)
s(7941) =< aux(430)
s(7942) =< aux(430)
s(7943) =< aux(430)
s(7944) =< aux(430)
s(7945) =< aux(430)
s(7941) =< aux(433)
s(7943) =< aux(433)
s(7946) =< aux(434)
s(7940) =< aux(435)
s(7941) =< aux(435)
s(7943) =< aux(435)
s(7944) =< aux(435)
s(7939) =< aux(436)
s(7943) =< aux(436)
s(7947) =< aux(431)
s(7948) =< aux(431)-1
s(7949) =< aux(431)-2
s(7950) =< aux(431)+2
s(7940) =< aux(432)*(1/5)+aux(435)
s(7941) =< aux(432)*(1/5)+aux(435)
s(7942) =< aux(432)*(1/5)+aux(435)
s(7943) =< aux(432)*(1/5)+aux(435)
s(7944) =< aux(432)*(1/5)+aux(435)
s(7945) =< aux(432)*(1/5)+aux(435)
s(7941) =< aux(432)*(1/3)+aux(433)
s(7942) =< aux(432)*(1/3)+aux(433)
s(7943) =< aux(432)*(1/3)+aux(433)
s(7944) =< aux(432)*(1/3)+aux(433)
s(7945) =< aux(432)*(1/3)+aux(433)
s(7939) =< aux(432)*(3/7)+aux(436)
s(7940) =< aux(432)*(3/7)+aux(436)
s(7941) =< aux(432)*(3/7)+aux(436)
s(7942) =< aux(432)*(3/7)+aux(436)
s(7943) =< aux(432)*(3/7)+aux(436)
s(7944) =< aux(432)*(3/7)+aux(436)
s(7945) =< aux(432)*(3/7)+aux(436)
s(7946) =< aux(432)*(1/5)+aux(434)
s(7937) =< aux(432)*(1/5)+aux(434)
s(7951) =< s(7945)*s(7947)
s(7952) =< s(7941)*s(7948)
s(7953) =< s(7943)*s(7949)
s(7954) =< s(7941)*s(7948)
s(7955) =< s(7939)*s(7949)
s(7956) =< s(7937)*s(7947)
s(7957) =< s(7937)*s(7950)
s(7958) =< s(7946)*s(7949)
s(7959) =< s(7946)*aux(431)
s(7960) =< s(7951)
s(7961) =< s(7952)
s(7962) =< s(7957)
s(7963) =< s(7956)
s(7964) =< s(7958)
s(7965) =< s(7959)
s(7901) =< aux(423)
s(7902) =< aux(423)
s(7903) =< aux(423)
s(7904) =< aux(423)
s(7905) =< aux(423)
s(7906) =< aux(423)
s(7907) =< aux(423)
s(7908) =< aux(423)
s(7909) =< aux(423)
s(7905) =< aux(426)
s(7907) =< aux(426)
s(7910) =< aux(427)
s(7904) =< aux(428)
s(7905) =< aux(428)
s(7907) =< aux(428)
s(7908) =< aux(428)
s(7903) =< aux(429)
s(7907) =< aux(429)
s(7911) =< aux(424)
s(7912) =< aux(424)-1
s(7913) =< aux(424)-2
s(7914) =< aux(424)+2
s(7904) =< aux(425)*(1/5)+aux(428)
s(7905) =< aux(425)*(1/5)+aux(428)
s(7906) =< aux(425)*(1/5)+aux(428)
s(7907) =< aux(425)*(1/5)+aux(428)
s(7908) =< aux(425)*(1/5)+aux(428)
s(7909) =< aux(425)*(1/5)+aux(428)
s(7905) =< aux(425)*(1/3)+aux(426)
s(7906) =< aux(425)*(1/3)+aux(426)
s(7907) =< aux(425)*(1/3)+aux(426)
s(7908) =< aux(425)*(1/3)+aux(426)
s(7909) =< aux(425)*(1/3)+aux(426)
s(7903) =< aux(425)*(3/7)+aux(429)
s(7904) =< aux(425)*(3/7)+aux(429)
s(7905) =< aux(425)*(3/7)+aux(429)
s(7906) =< aux(425)*(3/7)+aux(429)
s(7907) =< aux(425)*(3/7)+aux(429)
s(7908) =< aux(425)*(3/7)+aux(429)
s(7909) =< aux(425)*(3/7)+aux(429)
s(7910) =< aux(425)*(1/5)+aux(427)
s(7901) =< aux(425)*(1/5)+aux(427)
s(7915) =< s(7909)*s(7911)
s(7916) =< s(7905)*s(7912)
s(7917) =< s(7907)*s(7913)
s(7918) =< s(7905)*s(7912)
s(7919) =< s(7903)*s(7913)
s(7920) =< s(7901)*s(7911)
s(7921) =< s(7901)*s(7914)
s(7922) =< s(7910)*s(7913)
s(7923) =< s(7910)*aux(424)
s(7924) =< s(7915)
s(7925) =< s(7916)
s(7926) =< s(7921)
s(7927) =< s(7920)
s(7928) =< s(7922)
s(7929) =< s(7923)

  with precondition: [Out=0,V1>=0,V>=0] 

* Chain [109]: 18*s(8081)+2*s(8082)+1*s(8083)+1*s(8084)+2*s(8085)+2*s(8086)+1*s(8087)+3*s(8088)+14*s(8090)+1*s(8097)+1*s(8098)+1*s(8099)+2*s(8104)+2*s(8105)+4*s(8106)+339*s(8107)+448*s(8108)+132*s(8109)+36*s(8117)+4*s(8118)+2*s(8119)+2*s(8120)+4*s(8121)+4*s(8122)+2*s(8123)+6*s(8124)+28*s(8126)+2*s(8133)+2*s(8134)+2*s(8135)+4*s(8140)+4*s(8141)+8*s(8142)+678*s(8143)+896*s(8144)+264*s(8145)+1
  Such that:s(8074) =< V1
s(8075) =< 2*V1
s(8076) =< 2*V1+1
s(8077) =< 2/3*V1
s(8078) =< 3/5*V1
s(8079) =< 4/5*V1
s(8080) =< 4/7*V1
aux(437) =< V
aux(438) =< 2*V
aux(439) =< 2*V+1
aux(440) =< 2/3*V
aux(441) =< 3/5*V
aux(442) =< 4/5*V
aux(443) =< 4/7*V
s(8117) =< aux(437)
s(8118) =< aux(437)
s(8119) =< aux(437)
s(8120) =< aux(437)
s(8121) =< aux(437)
s(8122) =< aux(437)
s(8123) =< aux(437)
s(8124) =< aux(437)
s(8125) =< aux(437)
s(8121) =< aux(440)
s(8123) =< aux(440)
s(8126) =< aux(441)
s(8120) =< aux(442)
s(8121) =< aux(442)
s(8123) =< aux(442)
s(8124) =< aux(442)
s(8119) =< aux(443)
s(8123) =< aux(443)
s(8127) =< aux(438)
s(8128) =< aux(438)-1
s(8129) =< aux(438)-2
s(8130) =< aux(438)+2
s(8120) =< aux(439)*(1/5)+aux(442)
s(8121) =< aux(439)*(1/5)+aux(442)
s(8122) =< aux(439)*(1/5)+aux(442)
s(8123) =< aux(439)*(1/5)+aux(442)
s(8124) =< aux(439)*(1/5)+aux(442)
s(8125) =< aux(439)*(1/5)+aux(442)
s(8121) =< aux(439)*(1/3)+aux(440)
s(8122) =< aux(439)*(1/3)+aux(440)
s(8123) =< aux(439)*(1/3)+aux(440)
s(8124) =< aux(439)*(1/3)+aux(440)
s(8125) =< aux(439)*(1/3)+aux(440)
s(8119) =< aux(439)*(3/7)+aux(443)
s(8120) =< aux(439)*(3/7)+aux(443)
s(8121) =< aux(439)*(3/7)+aux(443)
s(8122) =< aux(439)*(3/7)+aux(443)
s(8123) =< aux(439)*(3/7)+aux(443)
s(8124) =< aux(439)*(3/7)+aux(443)
s(8125) =< aux(439)*(3/7)+aux(443)
s(8126) =< aux(439)*(1/5)+aux(441)
s(8117) =< aux(439)*(1/5)+aux(441)
s(8131) =< s(8125)*s(8127)
s(8132) =< s(8121)*s(8128)
s(8133) =< s(8123)*s(8129)
s(8134) =< s(8121)*s(8128)
s(8135) =< s(8119)*s(8129)
s(8136) =< s(8117)*s(8127)
s(8137) =< s(8117)*s(8130)
s(8138) =< s(8126)*s(8129)
s(8139) =< s(8126)*aux(438)
s(8140) =< s(8131)
s(8141) =< s(8132)
s(8142) =< s(8137)
s(8143) =< s(8136)
s(8144) =< s(8138)
s(8145) =< s(8139)
s(8081) =< s(8074)
s(8082) =< s(8074)
s(8083) =< s(8074)
s(8084) =< s(8074)
s(8085) =< s(8074)
s(8086) =< s(8074)
s(8087) =< s(8074)
s(8088) =< s(8074)
s(8089) =< s(8074)
s(8085) =< s(8077)
s(8087) =< s(8077)
s(8090) =< s(8078)
s(8084) =< s(8079)
s(8085) =< s(8079)
s(8087) =< s(8079)
s(8088) =< s(8079)
s(8083) =< s(8080)
s(8087) =< s(8080)
s(8091) =< s(8075)
s(8092) =< s(8075)-1
s(8093) =< s(8075)-2
s(8094) =< s(8075)+2
s(8084) =< s(8076)*(1/5)+s(8079)
s(8085) =< s(8076)*(1/5)+s(8079)
s(8086) =< s(8076)*(1/5)+s(8079)
s(8087) =< s(8076)*(1/5)+s(8079)
s(8088) =< s(8076)*(1/5)+s(8079)
s(8089) =< s(8076)*(1/5)+s(8079)
s(8085) =< s(8076)*(1/3)+s(8077)
s(8086) =< s(8076)*(1/3)+s(8077)
s(8087) =< s(8076)*(1/3)+s(8077)
s(8088) =< s(8076)*(1/3)+s(8077)
s(8089) =< s(8076)*(1/3)+s(8077)
s(8083) =< s(8076)*(3/7)+s(8080)
s(8084) =< s(8076)*(3/7)+s(8080)
s(8085) =< s(8076)*(3/7)+s(8080)
s(8086) =< s(8076)*(3/7)+s(8080)
s(8087) =< s(8076)*(3/7)+s(8080)
s(8088) =< s(8076)*(3/7)+s(8080)
s(8089) =< s(8076)*(3/7)+s(8080)
s(8090) =< s(8076)*(1/5)+s(8078)
s(8081) =< s(8076)*(1/5)+s(8078)
s(8095) =< s(8089)*s(8091)
s(8096) =< s(8085)*s(8092)
s(8097) =< s(8087)*s(8093)
s(8098) =< s(8085)*s(8092)
s(8099) =< s(8083)*s(8093)
s(8100) =< s(8081)*s(8091)
s(8101) =< s(8081)*s(8094)
s(8102) =< s(8090)*s(8093)
s(8103) =< s(8090)*s(8075)
s(8104) =< s(8095)
s(8105) =< s(8096)
s(8106) =< s(8101)
s(8107) =< s(8100)
s(8108) =< s(8102)
s(8109) =< s(8103)

  with precondition: [Out=2,V1>=1,V>=1] 

* Chain [108]: 36*s(8189)+4*s(8190)+2*s(8191)+2*s(8192)+4*s(8193)+4*s(8194)+2*s(8195)+6*s(8196)+28*s(8198)+2*s(8205)+2*s(8206)+2*s(8207)+4*s(8212)+4*s(8213)+8*s(8214)+678*s(8215)+896*s(8216)+264*s(8217)+72*s(8225)+8*s(8226)+4*s(8227)+4*s(8228)+8*s(8229)+8*s(8230)+4*s(8231)+12*s(8232)+56*s(8234)+4*s(8241)+4*s(8242)+4*s(8243)+8*s(8248)+8*s(8249)+16*s(8250)+1356*s(8251)+1792*s(8252)+528*s(8253)+1
  Such that:aux(444) =< V1
aux(445) =< 2*V1
aux(446) =< 2*V1+1
aux(447) =< 2/3*V1
aux(448) =< 3/5*V1
aux(449) =< 4/5*V1
aux(450) =< 4/7*V1
aux(451) =< V
aux(452) =< 2*V
aux(453) =< 2*V+1
aux(454) =< 2/3*V
aux(455) =< 3/5*V
aux(456) =< 4/5*V
aux(457) =< 4/7*V
s(8225) =< aux(451)
s(8226) =< aux(451)
s(8227) =< aux(451)
s(8228) =< aux(451)
s(8229) =< aux(451)
s(8230) =< aux(451)
s(8231) =< aux(451)
s(8232) =< aux(451)
s(8233) =< aux(451)
s(8229) =< aux(454)
s(8231) =< aux(454)
s(8234) =< aux(455)
s(8228) =< aux(456)
s(8229) =< aux(456)
s(8231) =< aux(456)
s(8232) =< aux(456)
s(8227) =< aux(457)
s(8231) =< aux(457)
s(8235) =< aux(452)
s(8236) =< aux(452)-1
s(8237) =< aux(452)-2
s(8238) =< aux(452)+2
s(8228) =< aux(453)*(1/5)+aux(456)
s(8229) =< aux(453)*(1/5)+aux(456)
s(8230) =< aux(453)*(1/5)+aux(456)
s(8231) =< aux(453)*(1/5)+aux(456)
s(8232) =< aux(453)*(1/5)+aux(456)
s(8233) =< aux(453)*(1/5)+aux(456)
s(8229) =< aux(453)*(1/3)+aux(454)
s(8230) =< aux(453)*(1/3)+aux(454)
s(8231) =< aux(453)*(1/3)+aux(454)
s(8232) =< aux(453)*(1/3)+aux(454)
s(8233) =< aux(453)*(1/3)+aux(454)
s(8227) =< aux(453)*(3/7)+aux(457)
s(8228) =< aux(453)*(3/7)+aux(457)
s(8229) =< aux(453)*(3/7)+aux(457)
s(8230) =< aux(453)*(3/7)+aux(457)
s(8231) =< aux(453)*(3/7)+aux(457)
s(8232) =< aux(453)*(3/7)+aux(457)
s(8233) =< aux(453)*(3/7)+aux(457)
s(8234) =< aux(453)*(1/5)+aux(455)
s(8225) =< aux(453)*(1/5)+aux(455)
s(8239) =< s(8233)*s(8235)
s(8240) =< s(8229)*s(8236)
s(8241) =< s(8231)*s(8237)
s(8242) =< s(8229)*s(8236)
s(8243) =< s(8227)*s(8237)
s(8244) =< s(8225)*s(8235)
s(8245) =< s(8225)*s(8238)
s(8246) =< s(8234)*s(8237)
s(8247) =< s(8234)*aux(452)
s(8248) =< s(8239)
s(8249) =< s(8240)
s(8250) =< s(8245)
s(8251) =< s(8244)
s(8252) =< s(8246)
s(8253) =< s(8247)
s(8189) =< aux(444)
s(8190) =< aux(444)
s(8191) =< aux(444)
s(8192) =< aux(444)
s(8193) =< aux(444)
s(8194) =< aux(444)
s(8195) =< aux(444)
s(8196) =< aux(444)
s(8197) =< aux(444)
s(8193) =< aux(447)
s(8195) =< aux(447)
s(8198) =< aux(448)
s(8192) =< aux(449)
s(8193) =< aux(449)
s(8195) =< aux(449)
s(8196) =< aux(449)
s(8191) =< aux(450)
s(8195) =< aux(450)
s(8199) =< aux(445)
s(8200) =< aux(445)-1
s(8201) =< aux(445)-2
s(8202) =< aux(445)+2
s(8192) =< aux(446)*(1/5)+aux(449)
s(8193) =< aux(446)*(1/5)+aux(449)
s(8194) =< aux(446)*(1/5)+aux(449)
s(8195) =< aux(446)*(1/5)+aux(449)
s(8196) =< aux(446)*(1/5)+aux(449)
s(8197) =< aux(446)*(1/5)+aux(449)
s(8193) =< aux(446)*(1/3)+aux(447)
s(8194) =< aux(446)*(1/3)+aux(447)
s(8195) =< aux(446)*(1/3)+aux(447)
s(8196) =< aux(446)*(1/3)+aux(447)
s(8197) =< aux(446)*(1/3)+aux(447)
s(8191) =< aux(446)*(3/7)+aux(450)
s(8192) =< aux(446)*(3/7)+aux(450)
s(8193) =< aux(446)*(3/7)+aux(450)
s(8194) =< aux(446)*(3/7)+aux(450)
s(8195) =< aux(446)*(3/7)+aux(450)
s(8196) =< aux(446)*(3/7)+aux(450)
s(8197) =< aux(446)*(3/7)+aux(450)
s(8198) =< aux(446)*(1/5)+aux(448)
s(8189) =< aux(446)*(1/5)+aux(448)
s(8203) =< s(8197)*s(8199)
s(8204) =< s(8193)*s(8200)
s(8205) =< s(8195)*s(8201)
s(8206) =< s(8193)*s(8200)
s(8207) =< s(8191)*s(8201)
s(8208) =< s(8189)*s(8199)
s(8209) =< s(8189)*s(8202)
s(8210) =< s(8198)*s(8201)
s(8211) =< s(8198)*aux(445)
s(8212) =< s(8203)
s(8213) =< s(8204)
s(8214) =< s(8209)
s(8215) =< s(8208)
s(8216) =< s(8210)
s(8217) =< s(8211)

  with precondition: [Out=1,V1>=0,V>=1] 

* Chain [107]: 18*s(8405)+2*s(8406)+1*s(8407)+1*s(8408)+2*s(8409)+2*s(8410)+1*s(8411)+3*s(8412)+14*s(8414)+1*s(8421)+1*s(8422)+1*s(8423)+2*s(8428)+2*s(8429)+4*s(8430)+339*s(8431)+448*s(8432)+132*s(8433)+0
  Such that:s(8398) =< V1
s(8399) =< 2*V1
s(8400) =< 2*V1+1
s(8401) =< 2/3*V1
s(8402) =< 3/5*V1
s(8403) =< 4/5*V1
s(8404) =< 4/7*V1
s(8405) =< s(8398)
s(8406) =< s(8398)
s(8407) =< s(8398)
s(8408) =< s(8398)
s(8409) =< s(8398)
s(8410) =< s(8398)
s(8411) =< s(8398)
s(8412) =< s(8398)
s(8413) =< s(8398)
s(8409) =< s(8401)
s(8411) =< s(8401)
s(8414) =< s(8402)
s(8408) =< s(8403)
s(8409) =< s(8403)
s(8411) =< s(8403)
s(8412) =< s(8403)
s(8407) =< s(8404)
s(8411) =< s(8404)
s(8415) =< s(8399)
s(8416) =< s(8399)-1
s(8417) =< s(8399)-2
s(8418) =< s(8399)+2
s(8408) =< s(8400)*(1/5)+s(8403)
s(8409) =< s(8400)*(1/5)+s(8403)
s(8410) =< s(8400)*(1/5)+s(8403)
s(8411) =< s(8400)*(1/5)+s(8403)
s(8412) =< s(8400)*(1/5)+s(8403)
s(8413) =< s(8400)*(1/5)+s(8403)
s(8409) =< s(8400)*(1/3)+s(8401)
s(8410) =< s(8400)*(1/3)+s(8401)
s(8411) =< s(8400)*(1/3)+s(8401)
s(8412) =< s(8400)*(1/3)+s(8401)
s(8413) =< s(8400)*(1/3)+s(8401)
s(8407) =< s(8400)*(3/7)+s(8404)
s(8408) =< s(8400)*(3/7)+s(8404)
s(8409) =< s(8400)*(3/7)+s(8404)
s(8410) =< s(8400)*(3/7)+s(8404)
s(8411) =< s(8400)*(3/7)+s(8404)
s(8412) =< s(8400)*(3/7)+s(8404)
s(8413) =< s(8400)*(3/7)+s(8404)
s(8414) =< s(8400)*(1/5)+s(8402)
s(8405) =< s(8400)*(1/5)+s(8402)
s(8419) =< s(8413)*s(8415)
s(8420) =< s(8409)*s(8416)
s(8421) =< s(8411)*s(8417)
s(8422) =< s(8409)*s(8416)
s(8423) =< s(8407)*s(8417)
s(8424) =< s(8405)*s(8415)
s(8425) =< s(8405)*s(8418)
s(8426) =< s(8414)*s(8417)
s(8427) =< s(8414)*s(8399)
s(8428) =< s(8419)
s(8429) =< s(8420)
s(8430) =< s(8425)
s(8431) =< s(8424)
s(8432) =< s(8426)
s(8433) =< s(8427)

  with precondition: [V=2,Out=0,V1>=0] 

* Chain [106]: 36*s(8441)+4*s(8442)+2*s(8443)+2*s(8444)+4*s(8445)+4*s(8446)+2*s(8447)+6*s(8448)+28*s(8450)+2*s(8457)+2*s(8458)+2*s(8459)+4*s(8464)+4*s(8465)+8*s(8466)+678*s(8467)+896*s(8468)+264*s(8469)+1
  Such that:aux(458) =< V1
aux(459) =< 2*V1
aux(460) =< 2*V1+1
aux(461) =< 2/3*V1
aux(462) =< 3/5*V1
aux(463) =< 4/5*V1
aux(464) =< 4/7*V1
s(8441) =< aux(458)
s(8442) =< aux(458)
s(8443) =< aux(458)
s(8444) =< aux(458)
s(8445) =< aux(458)
s(8446) =< aux(458)
s(8447) =< aux(458)
s(8448) =< aux(458)
s(8449) =< aux(458)
s(8445) =< aux(461)
s(8447) =< aux(461)
s(8450) =< aux(462)
s(8444) =< aux(463)
s(8445) =< aux(463)
s(8447) =< aux(463)
s(8448) =< aux(463)
s(8443) =< aux(464)
s(8447) =< aux(464)
s(8451) =< aux(459)
s(8452) =< aux(459)-1
s(8453) =< aux(459)-2
s(8454) =< aux(459)+2
s(8444) =< aux(460)*(1/5)+aux(463)
s(8445) =< aux(460)*(1/5)+aux(463)
s(8446) =< aux(460)*(1/5)+aux(463)
s(8447) =< aux(460)*(1/5)+aux(463)
s(8448) =< aux(460)*(1/5)+aux(463)
s(8449) =< aux(460)*(1/5)+aux(463)
s(8445) =< aux(460)*(1/3)+aux(461)
s(8446) =< aux(460)*(1/3)+aux(461)
s(8447) =< aux(460)*(1/3)+aux(461)
s(8448) =< aux(460)*(1/3)+aux(461)
s(8449) =< aux(460)*(1/3)+aux(461)
s(8443) =< aux(460)*(3/7)+aux(464)
s(8444) =< aux(460)*(3/7)+aux(464)
s(8445) =< aux(460)*(3/7)+aux(464)
s(8446) =< aux(460)*(3/7)+aux(464)
s(8447) =< aux(460)*(3/7)+aux(464)
s(8448) =< aux(460)*(3/7)+aux(464)
s(8449) =< aux(460)*(3/7)+aux(464)
s(8450) =< aux(460)*(1/5)+aux(462)
s(8441) =< aux(460)*(1/5)+aux(462)
s(8455) =< s(8449)*s(8451)
s(8456) =< s(8445)*s(8452)
s(8457) =< s(8447)*s(8453)
s(8458) =< s(8445)*s(8452)
s(8459) =< s(8443)*s(8453)
s(8460) =< s(8441)*s(8451)
s(8461) =< s(8441)*s(8454)
s(8462) =< s(8450)*s(8453)
s(8463) =< s(8450)*aux(459)
s(8464) =< s(8455)
s(8465) =< s(8456)
s(8466) =< s(8461)
s(8467) =< s(8460)
s(8468) =< s(8462)
s(8469) =< s(8463)

  with precondition: [Out=1,V1>=1,V>=0] 

* Chain [105]: 18*s(8513)+2*s(8514)+1*s(8515)+1*s(8516)+2*s(8517)+2*s(8518)+1*s(8519)+3*s(8520)+14*s(8522)+1*s(8529)+1*s(8530)+1*s(8531)+2*s(8536)+2*s(8537)+4*s(8538)+339*s(8539)+448*s(8540)+132*s(8541)+1
  Such that:s(8506) =< V1
s(8507) =< 2*V1
s(8508) =< 2*V1+1
s(8509) =< 2/3*V1
s(8510) =< 3/5*V1
s(8511) =< 4/5*V1
s(8512) =< 4/7*V1
s(8513) =< s(8506)
s(8514) =< s(8506)
s(8515) =< s(8506)
s(8516) =< s(8506)
s(8517) =< s(8506)
s(8518) =< s(8506)
s(8519) =< s(8506)
s(8520) =< s(8506)
s(8521) =< s(8506)
s(8517) =< s(8509)
s(8519) =< s(8509)
s(8522) =< s(8510)
s(8516) =< s(8511)
s(8517) =< s(8511)
s(8519) =< s(8511)
s(8520) =< s(8511)
s(8515) =< s(8512)
s(8519) =< s(8512)
s(8523) =< s(8507)
s(8524) =< s(8507)-1
s(8525) =< s(8507)-2
s(8526) =< s(8507)+2
s(8516) =< s(8508)*(1/5)+s(8511)
s(8517) =< s(8508)*(1/5)+s(8511)
s(8518) =< s(8508)*(1/5)+s(8511)
s(8519) =< s(8508)*(1/5)+s(8511)
s(8520) =< s(8508)*(1/5)+s(8511)
s(8521) =< s(8508)*(1/5)+s(8511)
s(8517) =< s(8508)*(1/3)+s(8509)
s(8518) =< s(8508)*(1/3)+s(8509)
s(8519) =< s(8508)*(1/3)+s(8509)
s(8520) =< s(8508)*(1/3)+s(8509)
s(8521) =< s(8508)*(1/3)+s(8509)
s(8515) =< s(8508)*(3/7)+s(8512)
s(8516) =< s(8508)*(3/7)+s(8512)
s(8517) =< s(8508)*(3/7)+s(8512)
s(8518) =< s(8508)*(3/7)+s(8512)
s(8519) =< s(8508)*(3/7)+s(8512)
s(8520) =< s(8508)*(3/7)+s(8512)
s(8521) =< s(8508)*(3/7)+s(8512)
s(8522) =< s(8508)*(1/5)+s(8510)
s(8513) =< s(8508)*(1/5)+s(8510)
s(8527) =< s(8521)*s(8523)
s(8528) =< s(8517)*s(8524)
s(8529) =< s(8519)*s(8525)
s(8530) =< s(8517)*s(8524)
s(8531) =< s(8515)*s(8525)
s(8532) =< s(8513)*s(8523)
s(8533) =< s(8513)*s(8526)
s(8534) =< s(8522)*s(8525)
s(8535) =< s(8522)*s(8507)
s(8536) =< s(8527)
s(8537) =< s(8528)
s(8538) =< s(8533)
s(8539) =< s(8532)
s(8540) =< s(8534)
s(8541) =< s(8535)

  with precondition: [V=2,Out=2,V1>=1] 


#### Cost of chains of fun8(V1,V,Out):
* Chain [116]: 36*s(8765)+4*s(8766)+2*s(8767)+2*s(8768)+4*s(8769)+4*s(8770)+2*s(8771)+6*s(8772)+28*s(8774)+2*s(8781)+2*s(8782)+2*s(8783)+4*s(8788)+4*s(8789)+8*s(8790)+678*s(8791)+896*s(8792)+264*s(8793)+54*s(8801)+6*s(8802)+3*s(8803)+3*s(8804)+6*s(8805)+6*s(8806)+3*s(8807)+9*s(8808)+42*s(8810)+3*s(8817)+3*s(8818)+3*s(8819)+6*s(8824)+6*s(8825)+12*s(8826)+1017*s(8827)+1344*s(8828)+396*s(8829)+3*s(8830)+1*s(8905)+0
  Such that:s(8905) =< 2
aux(482) =< V1
aux(483) =< 2*V1
aux(484) =< 2*V1+1
aux(485) =< 2/3*V1
aux(486) =< 3/5*V1
aux(487) =< 4/5*V1
aux(488) =< 4/7*V1
aux(489) =< V
aux(490) =< 2*V
aux(491) =< 2*V+1
aux(492) =< 2/3*V
aux(493) =< 3/5*V
aux(494) =< 4/5*V
aux(495) =< 4/7*V
s(8830) =< aux(490)
s(8801) =< aux(489)
s(8802) =< aux(489)
s(8803) =< aux(489)
s(8804) =< aux(489)
s(8805) =< aux(489)
s(8806) =< aux(489)
s(8807) =< aux(489)
s(8808) =< aux(489)
s(8809) =< aux(489)
s(8805) =< aux(492)
s(8807) =< aux(492)
s(8810) =< aux(493)
s(8804) =< aux(494)
s(8805) =< aux(494)
s(8807) =< aux(494)
s(8808) =< aux(494)
s(8803) =< aux(495)
s(8807) =< aux(495)
s(8811) =< aux(490)
s(8812) =< aux(490)-1
s(8813) =< aux(490)-2
s(8814) =< aux(490)+2
s(8804) =< aux(491)*(1/5)+aux(494)
s(8805) =< aux(491)*(1/5)+aux(494)
s(8806) =< aux(491)*(1/5)+aux(494)
s(8807) =< aux(491)*(1/5)+aux(494)
s(8808) =< aux(491)*(1/5)+aux(494)
s(8809) =< aux(491)*(1/5)+aux(494)
s(8805) =< aux(491)*(1/3)+aux(492)
s(8806) =< aux(491)*(1/3)+aux(492)
s(8807) =< aux(491)*(1/3)+aux(492)
s(8808) =< aux(491)*(1/3)+aux(492)
s(8809) =< aux(491)*(1/3)+aux(492)
s(8803) =< aux(491)*(3/7)+aux(495)
s(8804) =< aux(491)*(3/7)+aux(495)
s(8805) =< aux(491)*(3/7)+aux(495)
s(8806) =< aux(491)*(3/7)+aux(495)
s(8807) =< aux(491)*(3/7)+aux(495)
s(8808) =< aux(491)*(3/7)+aux(495)
s(8809) =< aux(491)*(3/7)+aux(495)
s(8810) =< aux(491)*(1/5)+aux(493)
s(8801) =< aux(491)*(1/5)+aux(493)
s(8815) =< s(8809)*s(8811)
s(8816) =< s(8805)*s(8812)
s(8817) =< s(8807)*s(8813)
s(8818) =< s(8805)*s(8812)
s(8819) =< s(8803)*s(8813)
s(8820) =< s(8801)*s(8811)
s(8821) =< s(8801)*s(8814)
s(8822) =< s(8810)*s(8813)
s(8823) =< s(8810)*aux(490)
s(8824) =< s(8815)
s(8825) =< s(8816)
s(8826) =< s(8821)
s(8827) =< s(8820)
s(8828) =< s(8822)
s(8829) =< s(8823)
s(8765) =< aux(482)
s(8766) =< aux(482)
s(8767) =< aux(482)
s(8768) =< aux(482)
s(8769) =< aux(482)
s(8770) =< aux(482)
s(8771) =< aux(482)
s(8772) =< aux(482)
s(8773) =< aux(482)
s(8769) =< aux(485)
s(8771) =< aux(485)
s(8774) =< aux(486)
s(8768) =< aux(487)
s(8769) =< aux(487)
s(8771) =< aux(487)
s(8772) =< aux(487)
s(8767) =< aux(488)
s(8771) =< aux(488)
s(8775) =< aux(483)
s(8776) =< aux(483)-1
s(8777) =< aux(483)-2
s(8778) =< aux(483)+2
s(8768) =< aux(484)*(1/5)+aux(487)
s(8769) =< aux(484)*(1/5)+aux(487)
s(8770) =< aux(484)*(1/5)+aux(487)
s(8771) =< aux(484)*(1/5)+aux(487)
s(8772) =< aux(484)*(1/5)+aux(487)
s(8773) =< aux(484)*(1/5)+aux(487)
s(8769) =< aux(484)*(1/3)+aux(485)
s(8770) =< aux(484)*(1/3)+aux(485)
s(8771) =< aux(484)*(1/3)+aux(485)
s(8772) =< aux(484)*(1/3)+aux(485)
s(8773) =< aux(484)*(1/3)+aux(485)
s(8767) =< aux(484)*(3/7)+aux(488)
s(8768) =< aux(484)*(3/7)+aux(488)
s(8769) =< aux(484)*(3/7)+aux(488)
s(8770) =< aux(484)*(3/7)+aux(488)
s(8771) =< aux(484)*(3/7)+aux(488)
s(8772) =< aux(484)*(3/7)+aux(488)
s(8773) =< aux(484)*(3/7)+aux(488)
s(8774) =< aux(484)*(1/5)+aux(486)
s(8765) =< aux(484)*(1/5)+aux(486)
s(8779) =< s(8773)*s(8775)
s(8780) =< s(8769)*s(8776)
s(8781) =< s(8771)*s(8777)
s(8782) =< s(8769)*s(8776)
s(8783) =< s(8767)*s(8777)
s(8784) =< s(8765)*s(8775)
s(8785) =< s(8765)*s(8778)
s(8786) =< s(8774)*s(8777)
s(8787) =< s(8774)*aux(483)
s(8788) =< s(8779)
s(8789) =< s(8780)
s(8790) =< s(8785)
s(8791) =< s(8784)
s(8792) =< s(8786)
s(8793) =< s(8787)

  with precondition: [Out=0,V1>=0,V>=0] 

* Chain [115]: 54*s(8952)+6*s(8953)+3*s(8954)+3*s(8955)+6*s(8956)+6*s(8957)+3*s(8958)+9*s(8959)+42*s(8961)+3*s(8968)+3*s(8969)+3*s(8970)+6*s(8975)+6*s(8976)+12*s(8977)+1017*s(8978)+1344*s(8979)+396*s(8980)+72*s(8988)+8*s(8989)+4*s(8990)+4*s(8991)+8*s(8992)+8*s(8993)+4*s(8994)+12*s(8995)+56*s(8997)+4*s(9004)+4*s(9005)+4*s(9006)+8*s(9011)+8*s(9012)+16*s(9013)+1356*s(9014)+1792*s(9015)+528*s(9016)+1*s(9089)+2*s(9162)+1
  Such that:aux(497) =< 2
aux(498) =< V1
aux(499) =< 2*V1
aux(500) =< 2*V1+1
aux(501) =< 2/3*V1
aux(502) =< 3/5*V1
aux(503) =< 4/5*V1
aux(504) =< 4/7*V1
aux(505) =< V
aux(506) =< 2*V
aux(507) =< 2*V+1
aux(508) =< 2/3*V
aux(509) =< 3/5*V
aux(510) =< 4/5*V
aux(511) =< 4/7*V
s(9162) =< aux(497)
s(8988) =< aux(505)
s(8989) =< aux(505)
s(8990) =< aux(505)
s(8991) =< aux(505)
s(8992) =< aux(505)
s(8993) =< aux(505)
s(8994) =< aux(505)
s(8995) =< aux(505)
s(8996) =< aux(505)
s(8992) =< aux(508)
s(8994) =< aux(508)
s(8997) =< aux(509)
s(8991) =< aux(510)
s(8992) =< aux(510)
s(8994) =< aux(510)
s(8995) =< aux(510)
s(8990) =< aux(511)
s(8994) =< aux(511)
s(8998) =< aux(506)
s(8999) =< aux(506)-1
s(9000) =< aux(506)-2
s(9001) =< aux(506)+2
s(8991) =< aux(507)*(1/5)+aux(510)
s(8992) =< aux(507)*(1/5)+aux(510)
s(8993) =< aux(507)*(1/5)+aux(510)
s(8994) =< aux(507)*(1/5)+aux(510)
s(8995) =< aux(507)*(1/5)+aux(510)
s(8996) =< aux(507)*(1/5)+aux(510)
s(8992) =< aux(507)*(1/3)+aux(508)
s(8993) =< aux(507)*(1/3)+aux(508)
s(8994) =< aux(507)*(1/3)+aux(508)
s(8995) =< aux(507)*(1/3)+aux(508)
s(8996) =< aux(507)*(1/3)+aux(508)
s(8990) =< aux(507)*(3/7)+aux(511)
s(8991) =< aux(507)*(3/7)+aux(511)
s(8992) =< aux(507)*(3/7)+aux(511)
s(8993) =< aux(507)*(3/7)+aux(511)
s(8994) =< aux(507)*(3/7)+aux(511)
s(8995) =< aux(507)*(3/7)+aux(511)
s(8996) =< aux(507)*(3/7)+aux(511)
s(8997) =< aux(507)*(1/5)+aux(509)
s(8988) =< aux(507)*(1/5)+aux(509)
s(9002) =< s(8996)*s(8998)
s(9003) =< s(8992)*s(8999)
s(9004) =< s(8994)*s(9000)
s(9005) =< s(8992)*s(8999)
s(9006) =< s(8990)*s(9000)
s(9007) =< s(8988)*s(8998)
s(9008) =< s(8988)*s(9001)
s(9009) =< s(8997)*s(9000)
s(9010) =< s(8997)*aux(506)
s(9011) =< s(9002)
s(9012) =< s(9003)
s(9013) =< s(9008)
s(9014) =< s(9007)
s(9015) =< s(9009)
s(9016) =< s(9010)
s(8952) =< aux(498)
s(8953) =< aux(498)
s(8954) =< aux(498)
s(8955) =< aux(498)
s(8956) =< aux(498)
s(8957) =< aux(498)
s(8958) =< aux(498)
s(8959) =< aux(498)
s(8960) =< aux(498)
s(8956) =< aux(501)
s(8958) =< aux(501)
s(8961) =< aux(502)
s(8955) =< aux(503)
s(8956) =< aux(503)
s(8958) =< aux(503)
s(8959) =< aux(503)
s(8954) =< aux(504)
s(8958) =< aux(504)
s(8962) =< aux(499)
s(8963) =< aux(499)-1
s(8964) =< aux(499)-2
s(8965) =< aux(499)+2
s(8955) =< aux(500)*(1/5)+aux(503)
s(8956) =< aux(500)*(1/5)+aux(503)
s(8957) =< aux(500)*(1/5)+aux(503)
s(8958) =< aux(500)*(1/5)+aux(503)
s(8959) =< aux(500)*(1/5)+aux(503)
s(8960) =< aux(500)*(1/5)+aux(503)
s(8956) =< aux(500)*(1/3)+aux(501)
s(8957) =< aux(500)*(1/3)+aux(501)
s(8958) =< aux(500)*(1/3)+aux(501)
s(8959) =< aux(500)*(1/3)+aux(501)
s(8960) =< aux(500)*(1/3)+aux(501)
s(8954) =< aux(500)*(3/7)+aux(504)
s(8955) =< aux(500)*(3/7)+aux(504)
s(8956) =< aux(500)*(3/7)+aux(504)
s(8957) =< aux(500)*(3/7)+aux(504)
s(8958) =< aux(500)*(3/7)+aux(504)
s(8959) =< aux(500)*(3/7)+aux(504)
s(8960) =< aux(500)*(3/7)+aux(504)
s(8961) =< aux(500)*(1/5)+aux(502)
s(8952) =< aux(500)*(1/5)+aux(502)
s(8966) =< s(8960)*s(8962)
s(8967) =< s(8956)*s(8963)
s(8968) =< s(8958)*s(8964)
s(8969) =< s(8956)*s(8963)
s(8970) =< s(8954)*s(8964)
s(8971) =< s(8952)*s(8962)
s(8972) =< s(8952)*s(8965)
s(8973) =< s(8961)*s(8964)
s(8974) =< s(8961)*aux(499)
s(8975) =< s(8966)
s(8976) =< s(8967)
s(8977) =< s(8972)
s(8978) =< s(8971)
s(8979) =< s(8973)
s(8980) =< s(8974)
s(9089) =< aux(506)

  with precondition: [Out=2,V1>=0,V>=0] 

* Chain [114]: 90*s(9207)+10*s(9208)+5*s(9209)+5*s(9210)+10*s(9211)+10*s(9212)+5*s(9213)+15*s(9214)+70*s(9216)+5*s(9223)+5*s(9224)+5*s(9225)+10*s(9230)+10*s(9231)+20*s(9232)+1695*s(9233)+2240*s(9234)+660*s(9235)+126*s(9243)+14*s(9244)+7*s(9245)+7*s(9246)+14*s(9247)+14*s(9248)+7*s(9249)+21*s(9250)+98*s(9252)+7*s(9259)+7*s(9260)+7*s(9261)+14*s(9266)+14*s(9267)+28*s(9268)+2373*s(9269)+3136*s(9270)+924*s(9271)+1*s(9416)+1*s(9489)+1*s(9598)+1*s(9635)+1
  Such that:s(9635) =< 1
s(9598) =< 2
aux(514) =< V1
aux(515) =< 2*V1
aux(516) =< 2*V1+1
aux(517) =< 2/3*V1
aux(518) =< 3/5*V1
aux(519) =< 4/5*V1
aux(520) =< 4/7*V1
aux(521) =< V
aux(522) =< 2*V
aux(523) =< 2*V+1
aux(524) =< 2/3*V
aux(525) =< 3/5*V
aux(526) =< 4/5*V
aux(527) =< 4/7*V
s(9243) =< aux(521)
s(9244) =< aux(521)
s(9245) =< aux(521)
s(9246) =< aux(521)
s(9247) =< aux(521)
s(9248) =< aux(521)
s(9249) =< aux(521)
s(9250) =< aux(521)
s(9251) =< aux(521)
s(9247) =< aux(524)
s(9249) =< aux(524)
s(9252) =< aux(525)
s(9246) =< aux(526)
s(9247) =< aux(526)
s(9249) =< aux(526)
s(9250) =< aux(526)
s(9245) =< aux(527)
s(9249) =< aux(527)
s(9253) =< aux(522)
s(9254) =< aux(522)-1
s(9255) =< aux(522)-2
s(9256) =< aux(522)+2
s(9246) =< aux(523)*(1/5)+aux(526)
s(9247) =< aux(523)*(1/5)+aux(526)
s(9248) =< aux(523)*(1/5)+aux(526)
s(9249) =< aux(523)*(1/5)+aux(526)
s(9250) =< aux(523)*(1/5)+aux(526)
s(9251) =< aux(523)*(1/5)+aux(526)
s(9247) =< aux(523)*(1/3)+aux(524)
s(9248) =< aux(523)*(1/3)+aux(524)
s(9249) =< aux(523)*(1/3)+aux(524)
s(9250) =< aux(523)*(1/3)+aux(524)
s(9251) =< aux(523)*(1/3)+aux(524)
s(9245) =< aux(523)*(3/7)+aux(527)
s(9246) =< aux(523)*(3/7)+aux(527)
s(9247) =< aux(523)*(3/7)+aux(527)
s(9248) =< aux(523)*(3/7)+aux(527)
s(9249) =< aux(523)*(3/7)+aux(527)
s(9250) =< aux(523)*(3/7)+aux(527)
s(9251) =< aux(523)*(3/7)+aux(527)
s(9252) =< aux(523)*(1/5)+aux(525)
s(9243) =< aux(523)*(1/5)+aux(525)
s(9257) =< s(9251)*s(9253)
s(9258) =< s(9247)*s(9254)
s(9259) =< s(9249)*s(9255)
s(9260) =< s(9247)*s(9254)
s(9261) =< s(9245)*s(9255)
s(9262) =< s(9243)*s(9253)
s(9263) =< s(9243)*s(9256)
s(9264) =< s(9252)*s(9255)
s(9265) =< s(9252)*aux(522)
s(9266) =< s(9257)
s(9267) =< s(9258)
s(9268) =< s(9263)
s(9269) =< s(9262)
s(9270) =< s(9264)
s(9271) =< s(9265)
s(9207) =< aux(514)
s(9208) =< aux(514)
s(9209) =< aux(514)
s(9210) =< aux(514)
s(9211) =< aux(514)
s(9212) =< aux(514)
s(9213) =< aux(514)
s(9214) =< aux(514)
s(9215) =< aux(514)
s(9211) =< aux(517)
s(9213) =< aux(517)
s(9216) =< aux(518)
s(9210) =< aux(519)
s(9211) =< aux(519)
s(9213) =< aux(519)
s(9214) =< aux(519)
s(9209) =< aux(520)
s(9213) =< aux(520)
s(9217) =< aux(515)
s(9218) =< aux(515)-1
s(9219) =< aux(515)-2
s(9220) =< aux(515)+2
s(9210) =< aux(516)*(1/5)+aux(519)
s(9211) =< aux(516)*(1/5)+aux(519)
s(9212) =< aux(516)*(1/5)+aux(519)
s(9213) =< aux(516)*(1/5)+aux(519)
s(9214) =< aux(516)*(1/5)+aux(519)
s(9215) =< aux(516)*(1/5)+aux(519)
s(9211) =< aux(516)*(1/3)+aux(517)
s(9212) =< aux(516)*(1/3)+aux(517)
s(9213) =< aux(516)*(1/3)+aux(517)
s(9214) =< aux(516)*(1/3)+aux(517)
s(9215) =< aux(516)*(1/3)+aux(517)
s(9209) =< aux(516)*(3/7)+aux(520)
s(9210) =< aux(516)*(3/7)+aux(520)
s(9211) =< aux(516)*(3/7)+aux(520)
s(9212) =< aux(516)*(3/7)+aux(520)
s(9213) =< aux(516)*(3/7)+aux(520)
s(9214) =< aux(516)*(3/7)+aux(520)
s(9215) =< aux(516)*(3/7)+aux(520)
s(9216) =< aux(516)*(1/5)+aux(518)
s(9207) =< aux(516)*(1/5)+aux(518)
s(9221) =< s(9215)*s(9217)
s(9222) =< s(9211)*s(9218)
s(9223) =< s(9213)*s(9219)
s(9224) =< s(9211)*s(9218)
s(9225) =< s(9209)*s(9219)
s(9226) =< s(9207)*s(9217)
s(9227) =< s(9207)*s(9220)
s(9228) =< s(9216)*s(9219)
s(9229) =< s(9216)*aux(515)
s(9230) =< s(9221)
s(9231) =< s(9222)
s(9232) =< s(9227)
s(9233) =< s(9226)
s(9234) =< s(9228)
s(9235) =< s(9229)
s(9416) =< aux(522)
s(9489) =< aux(515)

  with precondition: [Out=1,V1>=1,V>=0] 

* Chain [113]: 18*s(9643)+2*s(9644)+1*s(9645)+1*s(9646)+2*s(9647)+2*s(9648)+1*s(9649)+3*s(9650)+14*s(9652)+1*s(9659)+1*s(9660)+1*s(9661)+2*s(9666)+2*s(9667)+4*s(9668)+339*s(9669)+448*s(9670)+132*s(9671)+2*s(9672)+0
  Such that:s(9636) =< V1
s(9637) =< 2*V1
s(9638) =< 2*V1+1
s(9639) =< 2/3*V1
s(9640) =< 3/5*V1
s(9641) =< 4/5*V1
s(9642) =< 4/7*V1
aux(528) =< 2
s(9672) =< aux(528)
s(9643) =< s(9636)
s(9644) =< s(9636)
s(9645) =< s(9636)
s(9646) =< s(9636)
s(9647) =< s(9636)
s(9648) =< s(9636)
s(9649) =< s(9636)
s(9650) =< s(9636)
s(9651) =< s(9636)
s(9647) =< s(9639)
s(9649) =< s(9639)
s(9652) =< s(9640)
s(9646) =< s(9641)
s(9647) =< s(9641)
s(9649) =< s(9641)
s(9650) =< s(9641)
s(9645) =< s(9642)
s(9649) =< s(9642)
s(9653) =< s(9637)
s(9654) =< s(9637)-1
s(9655) =< s(9637)-2
s(9656) =< s(9637)+2
s(9646) =< s(9638)*(1/5)+s(9641)
s(9647) =< s(9638)*(1/5)+s(9641)
s(9648) =< s(9638)*(1/5)+s(9641)
s(9649) =< s(9638)*(1/5)+s(9641)
s(9650) =< s(9638)*(1/5)+s(9641)
s(9651) =< s(9638)*(1/5)+s(9641)
s(9647) =< s(9638)*(1/3)+s(9639)
s(9648) =< s(9638)*(1/3)+s(9639)
s(9649) =< s(9638)*(1/3)+s(9639)
s(9650) =< s(9638)*(1/3)+s(9639)
s(9651) =< s(9638)*(1/3)+s(9639)
s(9645) =< s(9638)*(3/7)+s(9642)
s(9646) =< s(9638)*(3/7)+s(9642)
s(9647) =< s(9638)*(3/7)+s(9642)
s(9648) =< s(9638)*(3/7)+s(9642)
s(9649) =< s(9638)*(3/7)+s(9642)
s(9650) =< s(9638)*(3/7)+s(9642)
s(9651) =< s(9638)*(3/7)+s(9642)
s(9652) =< s(9638)*(1/5)+s(9640)
s(9643) =< s(9638)*(1/5)+s(9640)
s(9657) =< s(9651)*s(9653)
s(9658) =< s(9647)*s(9654)
s(9659) =< s(9649)*s(9655)
s(9660) =< s(9647)*s(9654)
s(9661) =< s(9645)*s(9655)
s(9662) =< s(9643)*s(9653)
s(9663) =< s(9643)*s(9656)
s(9664) =< s(9652)*s(9655)
s(9665) =< s(9652)*s(9637)
s(9666) =< s(9657)
s(9667) =< s(9658)
s(9668) =< s(9663)
s(9669) =< s(9662)
s(9670) =< s(9664)
s(9671) =< s(9665)

  with precondition: [V=2,Out=0,V1>=0] 

* Chain [112]: 54*s(9681)+6*s(9682)+3*s(9683)+3*s(9684)+6*s(9685)+6*s(9686)+3*s(9687)+9*s(9688)+42*s(9690)+3*s(9697)+3*s(9698)+3*s(9699)+6*s(9704)+6*s(9705)+12*s(9706)+1017*s(9707)+1344*s(9708)+396*s(9709)+1*s(9746)+1*s(9783)+18*s(9791)+2*s(9792)+1*s(9793)+1*s(9794)+2*s(9795)+2*s(9796)+1*s(9797)+3*s(9798)+14*s(9800)+1*s(9807)+1*s(9808)+1*s(9809)+2*s(9814)+2*s(9815)+4*s(9816)+339*s(9817)+448*s(9818)+132*s(9819)+1
  Such that:s(9746) =< 1
s(9783) =< 2
s(9784) =< V
s(9785) =< 2*V
s(9786) =< 2*V+1
s(9787) =< 2/3*V
s(9788) =< 3/5*V
s(9789) =< 4/5*V
s(9790) =< 4/7*V
aux(529) =< V1
aux(530) =< 2*V1
aux(531) =< 2*V1+1
aux(532) =< 2/3*V1
aux(533) =< 3/5*V1
aux(534) =< 4/5*V1
aux(535) =< 4/7*V1
s(9681) =< aux(529)
s(9682) =< aux(529)
s(9683) =< aux(529)
s(9684) =< aux(529)
s(9685) =< aux(529)
s(9686) =< aux(529)
s(9687) =< aux(529)
s(9688) =< aux(529)
s(9689) =< aux(529)
s(9685) =< aux(532)
s(9687) =< aux(532)
s(9690) =< aux(533)
s(9684) =< aux(534)
s(9685) =< aux(534)
s(9687) =< aux(534)
s(9688) =< aux(534)
s(9683) =< aux(535)
s(9687) =< aux(535)
s(9691) =< aux(530)
s(9692) =< aux(530)-1
s(9693) =< aux(530)-2
s(9694) =< aux(530)+2
s(9684) =< aux(531)*(1/5)+aux(534)
s(9685) =< aux(531)*(1/5)+aux(534)
s(9686) =< aux(531)*(1/5)+aux(534)
s(9687) =< aux(531)*(1/5)+aux(534)
s(9688) =< aux(531)*(1/5)+aux(534)
s(9689) =< aux(531)*(1/5)+aux(534)
s(9685) =< aux(531)*(1/3)+aux(532)
s(9686) =< aux(531)*(1/3)+aux(532)
s(9687) =< aux(531)*(1/3)+aux(532)
s(9688) =< aux(531)*(1/3)+aux(532)
s(9689) =< aux(531)*(1/3)+aux(532)
s(9683) =< aux(531)*(3/7)+aux(535)
s(9684) =< aux(531)*(3/7)+aux(535)
s(9685) =< aux(531)*(3/7)+aux(535)
s(9686) =< aux(531)*(3/7)+aux(535)
s(9687) =< aux(531)*(3/7)+aux(535)
s(9688) =< aux(531)*(3/7)+aux(535)
s(9689) =< aux(531)*(3/7)+aux(535)
s(9690) =< aux(531)*(1/5)+aux(533)
s(9681) =< aux(531)*(1/5)+aux(533)
s(9695) =< s(9689)*s(9691)
s(9696) =< s(9685)*s(9692)
s(9697) =< s(9687)*s(9693)
s(9698) =< s(9685)*s(9692)
s(9699) =< s(9683)*s(9693)
s(9700) =< s(9681)*s(9691)
s(9701) =< s(9681)*s(9694)
s(9702) =< s(9690)*s(9693)
s(9703) =< s(9690)*aux(530)
s(9704) =< s(9695)
s(9705) =< s(9696)
s(9706) =< s(9701)
s(9707) =< s(9700)
s(9708) =< s(9702)
s(9709) =< s(9703)
s(9791) =< s(9784)
s(9792) =< s(9784)
s(9793) =< s(9784)
s(9794) =< s(9784)
s(9795) =< s(9784)
s(9796) =< s(9784)
s(9797) =< s(9784)
s(9798) =< s(9784)
s(9799) =< s(9784)
s(9795) =< s(9787)
s(9797) =< s(9787)
s(9800) =< s(9788)
s(9794) =< s(9789)
s(9795) =< s(9789)
s(9797) =< s(9789)
s(9798) =< s(9789)
s(9793) =< s(9790)
s(9797) =< s(9790)
s(9801) =< s(9785)
s(9802) =< s(9785)-1
s(9803) =< s(9785)-2
s(9804) =< s(9785)+2
s(9794) =< s(9786)*(1/5)+s(9789)
s(9795) =< s(9786)*(1/5)+s(9789)
s(9796) =< s(9786)*(1/5)+s(9789)
s(9797) =< s(9786)*(1/5)+s(9789)
s(9798) =< s(9786)*(1/5)+s(9789)
s(9799) =< s(9786)*(1/5)+s(9789)
s(9795) =< s(9786)*(1/3)+s(9787)
s(9796) =< s(9786)*(1/3)+s(9787)
s(9797) =< s(9786)*(1/3)+s(9787)
s(9798) =< s(9786)*(1/3)+s(9787)
s(9799) =< s(9786)*(1/3)+s(9787)
s(9793) =< s(9786)*(3/7)+s(9790)
s(9794) =< s(9786)*(3/7)+s(9790)
s(9795) =< s(9786)*(3/7)+s(9790)
s(9796) =< s(9786)*(3/7)+s(9790)
s(9797) =< s(9786)*(3/7)+s(9790)
s(9798) =< s(9786)*(3/7)+s(9790)
s(9799) =< s(9786)*(3/7)+s(9790)
s(9800) =< s(9786)*(1/5)+s(9788)
s(9791) =< s(9786)*(1/5)+s(9788)
s(9805) =< s(9799)*s(9801)
s(9806) =< s(9795)*s(9802)
s(9807) =< s(9797)*s(9803)
s(9808) =< s(9795)*s(9802)
s(9809) =< s(9793)*s(9803)
s(9810) =< s(9791)*s(9801)
s(9811) =< s(9791)*s(9804)
s(9812) =< s(9800)*s(9803)
s(9813) =< s(9800)*s(9785)
s(9814) =< s(9805)
s(9815) =< s(9806)
s(9816) =< s(9811)
s(9817) =< s(9810)
s(9818) =< s(9812)
s(9819) =< s(9813)

  with precondition: [Out=1,V1>=0,V>=1] 

* Chain [111]: 18*s(9827)+2*s(9828)+1*s(9829)+1*s(9830)+2*s(9831)+2*s(9832)+1*s(9833)+3*s(9834)+14*s(9836)+1*s(9843)+1*s(9844)+1*s(9845)+2*s(9850)+2*s(9851)+4*s(9852)+339*s(9853)+448*s(9854)+132*s(9855)+1*s(9856)+1
  Such that:s(9856) =< 2
s(9820) =< V1
s(9821) =< 2*V1
s(9822) =< 2*V1+1
s(9823) =< 2/3*V1
s(9824) =< 3/5*V1
s(9825) =< 4/5*V1
s(9826) =< 4/7*V1
s(9827) =< s(9820)
s(9828) =< s(9820)
s(9829) =< s(9820)
s(9830) =< s(9820)
s(9831) =< s(9820)
s(9832) =< s(9820)
s(9833) =< s(9820)
s(9834) =< s(9820)
s(9835) =< s(9820)
s(9831) =< s(9823)
s(9833) =< s(9823)
s(9836) =< s(9824)
s(9830) =< s(9825)
s(9831) =< s(9825)
s(9833) =< s(9825)
s(9834) =< s(9825)
s(9829) =< s(9826)
s(9833) =< s(9826)
s(9837) =< s(9821)
s(9838) =< s(9821)-1
s(9839) =< s(9821)-2
s(9840) =< s(9821)+2
s(9830) =< s(9822)*(1/5)+s(9825)
s(9831) =< s(9822)*(1/5)+s(9825)
s(9832) =< s(9822)*(1/5)+s(9825)
s(9833) =< s(9822)*(1/5)+s(9825)
s(9834) =< s(9822)*(1/5)+s(9825)
s(9835) =< s(9822)*(1/5)+s(9825)
s(9831) =< s(9822)*(1/3)+s(9823)
s(9832) =< s(9822)*(1/3)+s(9823)
s(9833) =< s(9822)*(1/3)+s(9823)
s(9834) =< s(9822)*(1/3)+s(9823)
s(9835) =< s(9822)*(1/3)+s(9823)
s(9829) =< s(9822)*(3/7)+s(9826)
s(9830) =< s(9822)*(3/7)+s(9826)
s(9831) =< s(9822)*(3/7)+s(9826)
s(9832) =< s(9822)*(3/7)+s(9826)
s(9833) =< s(9822)*(3/7)+s(9826)
s(9834) =< s(9822)*(3/7)+s(9826)
s(9835) =< s(9822)*(3/7)+s(9826)
s(9836) =< s(9822)*(1/5)+s(9824)
s(9827) =< s(9822)*(1/5)+s(9824)
s(9841) =< s(9835)*s(9837)
s(9842) =< s(9831)*s(9838)
s(9843) =< s(9833)*s(9839)
s(9844) =< s(9831)*s(9838)
s(9845) =< s(9829)*s(9839)
s(9846) =< s(9827)*s(9837)
s(9847) =< s(9827)*s(9840)
s(9848) =< s(9836)*s(9839)
s(9849) =< s(9836)*s(9821)
s(9850) =< s(9841)
s(9851) =< s(9842)
s(9852) =< s(9847)
s(9853) =< s(9846)
s(9854) =< s(9848)
s(9855) =< s(9849)

  with precondition: [V=2,Out=2,V1>=1] 


#### Cost of chains of fun9(V1,Out):
* Chain [119]: 18*s(10088)+2*s(10089)+1*s(10090)+1*s(10091)+2*s(10092)+2*s(10093)+1*s(10094)+3*s(10095)+14*s(10097)+1*s(10104)+1*s(10105)+1*s(10106)+2*s(10111)+2*s(10112)+4*s(10113)+339*s(10114)+448*s(10115)+132*s(10116)+0
  Such that:s(10081) =< V1
s(10082) =< 2*V1
s(10083) =< 2*V1+1
s(10084) =< 2/3*V1
s(10085) =< 3/5*V1
s(10086) =< 4/5*V1
s(10087) =< 4/7*V1
s(10088) =< s(10081)
s(10089) =< s(10081)
s(10090) =< s(10081)
s(10091) =< s(10081)
s(10092) =< s(10081)
s(10093) =< s(10081)
s(10094) =< s(10081)
s(10095) =< s(10081)
s(10096) =< s(10081)
s(10092) =< s(10084)
s(10094) =< s(10084)
s(10097) =< s(10085)
s(10091) =< s(10086)
s(10092) =< s(10086)
s(10094) =< s(10086)
s(10095) =< s(10086)
s(10090) =< s(10087)
s(10094) =< s(10087)
s(10098) =< s(10082)
s(10099) =< s(10082)-1
s(10100) =< s(10082)-2
s(10101) =< s(10082)+2
s(10091) =< s(10083)*(1/5)+s(10086)
s(10092) =< s(10083)*(1/5)+s(10086)
s(10093) =< s(10083)*(1/5)+s(10086)
s(10094) =< s(10083)*(1/5)+s(10086)
s(10095) =< s(10083)*(1/5)+s(10086)
s(10096) =< s(10083)*(1/5)+s(10086)
s(10092) =< s(10083)*(1/3)+s(10084)
s(10093) =< s(10083)*(1/3)+s(10084)
s(10094) =< s(10083)*(1/3)+s(10084)
s(10095) =< s(10083)*(1/3)+s(10084)
s(10096) =< s(10083)*(1/3)+s(10084)
s(10090) =< s(10083)*(3/7)+s(10087)
s(10091) =< s(10083)*(3/7)+s(10087)
s(10092) =< s(10083)*(3/7)+s(10087)
s(10093) =< s(10083)*(3/7)+s(10087)
s(10094) =< s(10083)*(3/7)+s(10087)
s(10095) =< s(10083)*(3/7)+s(10087)
s(10096) =< s(10083)*(3/7)+s(10087)
s(10097) =< s(10083)*(1/5)+s(10085)
s(10088) =< s(10083)*(1/5)+s(10085)
s(10102) =< s(10096)*s(10098)
s(10103) =< s(10092)*s(10099)
s(10104) =< s(10094)*s(10100)
s(10105) =< s(10092)*s(10099)
s(10106) =< s(10090)*s(10100)
s(10107) =< s(10088)*s(10098)
s(10108) =< s(10088)*s(10101)
s(10109) =< s(10097)*s(10100)
s(10110) =< s(10097)*s(10082)
s(10111) =< s(10102)
s(10112) =< s(10103)
s(10113) =< s(10108)
s(10114) =< s(10107)
s(10115) =< s(10109)
s(10116) =< s(10110)

  with precondition: [V1>=1,Out>=1,2*V1+1>=Out] 

* Chain [118]: 0
  with precondition: [Out=0,V1>=0] 

* Chain [117]: 0
  with precondition: [Out=1,V1>=0] 


#### Cost of chains of start(V1,V,V2):
* Chain [120]: 307*s(10119)+871*s(10124)+8*s(10130)+198*s(10151)+1764*s(10164)+98*s(10166)+98*s(10167)+196*s(10168)+196*s(10169)+98*s(10170)+294*s(10171)+1372*s(10173)+98*s(10180)+98*s(10181)+98*s(10182)+196*s(10187)+196*s(10188)+392*s(10189)+33222*s(10190)+43904*s(10191)+12936*s(10192)+2671*s(10216)+4420*s(10217)+11*s(10218)+900*s(10219)+50*s(10221)+50*s(10222)+100*s(10223)+100*s(10224)+50*s(10225)+150*s(10226)+700*s(10228)+50*s(10235)+50*s(10236)+50*s(10237)+100*s(10242)+100*s(10243)+200*s(10244)+16950*s(10245)+22400*s(10246)+6600*s(10247)+1422*s(10277)+79*s(10279)+79*s(10280)+158*s(10281)+158*s(10282)+79*s(10283)+237*s(10284)+1106*s(10286)+79*s(10293)+79*s(10294)+79*s(10295)+158*s(10300)+158*s(10301)+316*s(10302)+26781*s(10303)+35392*s(10304)+10428*s(10305)+1105*s(10306)+2*s(10793)+18
  Such that:aux(553) =< 1
aux(554) =< 2
aux(555) =< V1
aux(556) =< 2*V1
aux(557) =< 2*V1+1
aux(558) =< 2/3*V1
aux(559) =< 3/5*V1
aux(560) =< 4/5*V1
aux(561) =< 4/7*V1
aux(562) =< V
aux(563) =< V-V2
aux(564) =< 2*V
aux(565) =< 2*V+1
aux(566) =< 2/3*V
aux(567) =< 3/5*V
aux(568) =< 4/5*V
aux(569) =< 4/7*V
aux(570) =< V2
aux(571) =< 2*V2
aux(572) =< 2*V2+1
aux(573) =< 2/3*V2
aux(574) =< 3/5*V2
aux(575) =< 4/5*V2
aux(576) =< 4/7*V2
s(10218) =< aux(553)
s(10217) =< aux(554)
s(10151) =< aux(555)
s(10119) =< aux(562)
s(10216) =< aux(571)
s(10219) =< aux(570)
s(10124) =< aux(570)
s(10221) =< aux(570)
s(10222) =< aux(570)
s(10223) =< aux(570)
s(10224) =< aux(570)
s(10225) =< aux(570)
s(10226) =< aux(570)
s(10227) =< aux(570)
s(10223) =< aux(573)
s(10225) =< aux(573)
s(10228) =< aux(574)
s(10222) =< aux(575)
s(10223) =< aux(575)
s(10225) =< aux(575)
s(10226) =< aux(575)
s(10221) =< aux(576)
s(10225) =< aux(576)
s(10229) =< aux(571)
s(10230) =< aux(571)-1
s(10231) =< aux(571)-2
s(10232) =< aux(571)+2
s(10222) =< aux(572)*(1/5)+aux(575)
s(10223) =< aux(572)*(1/5)+aux(575)
s(10224) =< aux(572)*(1/5)+aux(575)
s(10225) =< aux(572)*(1/5)+aux(575)
s(10226) =< aux(572)*(1/5)+aux(575)
s(10227) =< aux(572)*(1/5)+aux(575)
s(10223) =< aux(572)*(1/3)+aux(573)
s(10224) =< aux(572)*(1/3)+aux(573)
s(10225) =< aux(572)*(1/3)+aux(573)
s(10226) =< aux(572)*(1/3)+aux(573)
s(10227) =< aux(572)*(1/3)+aux(573)
s(10221) =< aux(572)*(3/7)+aux(576)
s(10222) =< aux(572)*(3/7)+aux(576)
s(10223) =< aux(572)*(3/7)+aux(576)
s(10224) =< aux(572)*(3/7)+aux(576)
s(10225) =< aux(572)*(3/7)+aux(576)
s(10226) =< aux(572)*(3/7)+aux(576)
s(10227) =< aux(572)*(3/7)+aux(576)
s(10228) =< aux(572)*(1/5)+aux(574)
s(10219) =< aux(572)*(1/5)+aux(574)
s(10233) =< s(10227)*s(10229)
s(10234) =< s(10223)*s(10230)
s(10235) =< s(10225)*s(10231)
s(10236) =< s(10223)*s(10230)
s(10237) =< s(10221)*s(10231)
s(10238) =< s(10219)*s(10229)
s(10239) =< s(10219)*s(10232)
s(10240) =< s(10228)*s(10231)
s(10241) =< s(10228)*aux(571)
s(10242) =< s(10233)
s(10243) =< s(10234)
s(10244) =< s(10239)
s(10245) =< s(10238)
s(10246) =< s(10240)
s(10247) =< s(10241)
s(10164) =< aux(555)
s(10166) =< aux(555)
s(10167) =< aux(555)
s(10168) =< aux(555)
s(10169) =< aux(555)
s(10170) =< aux(555)
s(10171) =< aux(555)
s(10172) =< aux(555)
s(10168) =< aux(558)
s(10170) =< aux(558)
s(10173) =< aux(559)
s(10167) =< aux(560)
s(10168) =< aux(560)
s(10170) =< aux(560)
s(10171) =< aux(560)
s(10166) =< aux(561)
s(10170) =< aux(561)
s(10174) =< aux(556)
s(10175) =< aux(556)-1
s(10176) =< aux(556)-2
s(10177) =< aux(556)+2
s(10167) =< aux(557)*(1/5)+aux(560)
s(10168) =< aux(557)*(1/5)+aux(560)
s(10169) =< aux(557)*(1/5)+aux(560)
s(10170) =< aux(557)*(1/5)+aux(560)
s(10171) =< aux(557)*(1/5)+aux(560)
s(10172) =< aux(557)*(1/5)+aux(560)
s(10168) =< aux(557)*(1/3)+aux(558)
s(10169) =< aux(557)*(1/3)+aux(558)
s(10170) =< aux(557)*(1/3)+aux(558)
s(10171) =< aux(557)*(1/3)+aux(558)
s(10172) =< aux(557)*(1/3)+aux(558)
s(10166) =< aux(557)*(3/7)+aux(561)
s(10167) =< aux(557)*(3/7)+aux(561)
s(10168) =< aux(557)*(3/7)+aux(561)
s(10169) =< aux(557)*(3/7)+aux(561)
s(10170) =< aux(557)*(3/7)+aux(561)
s(10171) =< aux(557)*(3/7)+aux(561)
s(10172) =< aux(557)*(3/7)+aux(561)
s(10173) =< aux(557)*(1/5)+aux(559)
s(10164) =< aux(557)*(1/5)+aux(559)
s(10178) =< s(10172)*s(10174)
s(10179) =< s(10168)*s(10175)
s(10180) =< s(10170)*s(10176)
s(10181) =< s(10168)*s(10175)
s(10182) =< s(10166)*s(10176)
s(10183) =< s(10164)*s(10174)
s(10184) =< s(10164)*s(10177)
s(10185) =< s(10173)*s(10176)
s(10186) =< s(10173)*aux(556)
s(10187) =< s(10178)
s(10188) =< s(10179)
s(10189) =< s(10184)
s(10190) =< s(10183)
s(10191) =< s(10185)
s(10192) =< s(10186)
s(10277) =< aux(562)
s(10279) =< aux(562)
s(10280) =< aux(562)
s(10281) =< aux(562)
s(10282) =< aux(562)
s(10283) =< aux(562)
s(10284) =< aux(562)
s(10285) =< aux(562)
s(10281) =< aux(566)
s(10283) =< aux(566)
s(10286) =< aux(567)
s(10280) =< aux(568)
s(10281) =< aux(568)
s(10283) =< aux(568)
s(10284) =< aux(568)
s(10279) =< aux(569)
s(10283) =< aux(569)
s(10287) =< aux(564)
s(10288) =< aux(564)-1
s(10289) =< aux(564)-2
s(10290) =< aux(564)+2
s(10280) =< aux(565)*(1/5)+aux(568)
s(10281) =< aux(565)*(1/5)+aux(568)
s(10282) =< aux(565)*(1/5)+aux(568)
s(10283) =< aux(565)*(1/5)+aux(568)
s(10284) =< aux(565)*(1/5)+aux(568)
s(10285) =< aux(565)*(1/5)+aux(568)
s(10281) =< aux(565)*(1/3)+aux(566)
s(10282) =< aux(565)*(1/3)+aux(566)
s(10283) =< aux(565)*(1/3)+aux(566)
s(10284) =< aux(565)*(1/3)+aux(566)
s(10285) =< aux(565)*(1/3)+aux(566)
s(10279) =< aux(565)*(3/7)+aux(569)
s(10280) =< aux(565)*(3/7)+aux(569)
s(10281) =< aux(565)*(3/7)+aux(569)
s(10282) =< aux(565)*(3/7)+aux(569)
s(10283) =< aux(565)*(3/7)+aux(569)
s(10284) =< aux(565)*(3/7)+aux(569)
s(10285) =< aux(565)*(3/7)+aux(569)
s(10286) =< aux(565)*(1/5)+aux(567)
s(10277) =< aux(565)*(1/5)+aux(567)
s(10291) =< s(10285)*s(10287)
s(10292) =< s(10281)*s(10288)
s(10293) =< s(10283)*s(10289)
s(10294) =< s(10281)*s(10288)
s(10295) =< s(10279)*s(10289)
s(10296) =< s(10277)*s(10287)
s(10297) =< s(10277)*s(10290)
s(10298) =< s(10286)*s(10289)
s(10299) =< s(10286)*aux(564)
s(10300) =< s(10291)
s(10301) =< s(10292)
s(10302) =< s(10297)
s(10303) =< s(10296)
s(10304) =< s(10298)
s(10305) =< s(10299)
s(10306) =< aux(564)
s(10793) =< aux(556)
s(10130) =< aux(563)

  with precondition: [] 


Closed-form bounds of start(V1,V,V2): 
-------------------------------------
* Chain [120] with precondition: [] 
    - Upper bound: nat(V1)*3726+8869+nat(V1)*196*nat(nat(2*V1)+ -2)+nat(V1)*294*nat(nat(2*V1)+ -1)+nat(V1)*33810*nat(2*V1)+nat(V)*3151+nat(V)*158*nat(nat(2*V)+ -2)+nat(V)*237*nat(nat(2*V)+ -1)+nat(V)*27255*nat(2*V)+nat(V2)*2671+nat(V2)*100*nat(nat(2*V2)+ -2)+nat(V2)*150*nat(nat(2*V2)+ -1)+nat(V2)*17250*nat(2*V2)+nat(nat(2*V1)+ -2)*43904*nat(3/5*V1)+nat(nat(2*V)+ -2)*35392*nat(3/5*V)+nat(nat(2*V2)+ -2)*22400*nat(3/5*V2)+nat(2*V1)*2+nat(2*V1)*12936*nat(3/5*V1)+nat(2*V)*1105+nat(2*V)*10428*nat(3/5*V)+nat(2*V2)*2671+nat(2*V2)*6600*nat(3/5*V2)+nat(3/5*V1)*1372+nat(3/5*V)*1106+nat(3/5*V2)*700+nat(V-V2)*8 
    - Complexity: n^2 

### Maximum cost of start(V1,V,V2): nat(V1)*3726+8869+nat(V1)*196*nat(nat(2*V1)+ -2)+nat(V1)*294*nat(nat(2*V1)+ -1)+nat(V1)*33810*nat(2*V1)+nat(V)*3151+nat(V)*158*nat(nat(2*V)+ -2)+nat(V)*237*nat(nat(2*V)+ -1)+nat(V)*27255*nat(2*V)+nat(V2)*2671+nat(V2)*100*nat(nat(2*V2)+ -2)+nat(V2)*150*nat(nat(2*V2)+ -1)+nat(V2)*17250*nat(2*V2)+nat(nat(2*V1)+ -2)*43904*nat(3/5*V1)+nat(nat(2*V)+ -2)*35392*nat(3/5*V)+nat(nat(2*V2)+ -2)*22400*nat(3/5*V2)+nat(2*V1)*2+nat(2*V1)*12936*nat(3/5*V1)+nat(2*V)*1105+nat(2*V)*10428*nat(3/5*V)+nat(2*V2)*2671+nat(2*V2)*6600*nat(3/5*V2)+nat(3/5*V1)*1372+nat(3/5*V)*1106+nat(3/5*V2)*700+nat(V-V2)*8 
Asymptotic class: n^2 
* Total analysis performed in 49779 ms.


----------------------------------------

(14)
BOUNDS(1, n^2)

----------------------------------------

(15) RenamingProof (BOTH BOUNDS(ID, ID))
Renamed function symbols to avoid clashes with predefined symbol.
----------------------------------------

(16)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF).


The TRS R consists of the following rules:

   cond1(true, x, y) -> cond2(gr(y, 0'), x, y)
   cond2(true, x, y) -> cond2(gr(y, 0'), p(x), p(y))
   cond2(false, x, y) -> cond1(and(eq(x, y), gr(x, 0')), x, y)
   gr(0', x) -> false
   gr(s(x), 0') -> true
   gr(s(x), s(y)) -> gr(x, y)
   p(0') -> 0'
   p(s(x)) -> x
   eq(0', 0') -> true
   eq(s(x), 0') -> false
   eq(0', s(x)) -> false
   eq(s(x), s(y)) -> eq(x, y)
   and(true, true) -> true
   and(false, x) -> false
   and(x, false) -> false

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

   encArg(true) -> true
   encArg(0') -> 0'
   encArg(false) -> false
   encArg(s(x_1)) -> s(encArg(x_1))
   encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2))
   encArg(cons_p(x_1)) -> p(encArg(x_1))
   encArg(cons_eq(x_1, x_2)) -> eq(encArg(x_1), encArg(x_2))
   encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2))
   encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_true -> true
   encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2))
   encode_0 -> 0'
   encode_p(x_1) -> p(encArg(x_1))
   encode_false -> false
   encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2))
   encode_eq(x_1, x_2) -> eq(encArg(x_1), encArg(x_2))
   encode_s(x_1) -> s(encArg(x_1))

Rewrite Strategy: INNERMOST
----------------------------------------

(17) TypeInferenceProof (BOTH BOUNDS(ID, ID))
Infered types.
----------------------------------------

(18)
Obligation:
Innermost TRS:
Rules:
cond1(true, x, y) -> cond2(gr(y, 0'), x, y)
cond2(true, x, y) -> cond2(gr(y, 0'), p(x), p(y))
cond2(false, x, y) -> cond1(and(eq(x, y), gr(x, 0')), x, y)
gr(0', x) -> false
gr(s(x), 0') -> true
gr(s(x), s(y)) -> gr(x, y)
p(0') -> 0'
p(s(x)) -> x
eq(0', 0') -> true
eq(s(x), 0') -> false
eq(0', s(x)) -> false
eq(s(x), s(y)) -> eq(x, y)
and(true, true) -> true
and(false, x) -> false
and(x, false) -> false
encArg(true) -> true
encArg(0') -> 0'
encArg(false) -> false
encArg(s(x_1)) -> s(encArg(x_1))
encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2))
encArg(cons_p(x_1)) -> p(encArg(x_1))
encArg(cons_eq(x_1, x_2)) -> eq(encArg(x_1), encArg(x_2))
encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2))
encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
encode_true -> true
encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2))
encode_0 -> 0'
encode_p(x_1) -> p(encArg(x_1))
encode_false -> false
encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2))
encode_eq(x_1, x_2) -> eq(encArg(x_1), encArg(x_2))
encode_s(x_1) -> s(encArg(x_1))

Types:
cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
true :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
0' :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
false :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
and :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
eq :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
s :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encArg :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_eq :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_and :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_true :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_0 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_false :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_and :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_eq :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_s :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
hole_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and1_4 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4 :: Nat -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and

----------------------------------------

(19) OrderProof (LOWER BOUND(ID))
Heuristically decided to analyse the following defined symbols:
cond1, cond2, gr, eq, encArg

They will be analysed ascendingly in the following order:
cond1 = cond2
gr < cond1
cond1 < encArg
gr < cond2
eq < cond2
cond2 < encArg
gr < encArg
eq < encArg

----------------------------------------

(20)
Obligation:
Innermost TRS:
Rules:
cond1(true, x, y) -> cond2(gr(y, 0'), x, y)
cond2(true, x, y) -> cond2(gr(y, 0'), p(x), p(y))
cond2(false, x, y) -> cond1(and(eq(x, y), gr(x, 0')), x, y)
gr(0', x) -> false
gr(s(x), 0') -> true
gr(s(x), s(y)) -> gr(x, y)
p(0') -> 0'
p(s(x)) -> x
eq(0', 0') -> true
eq(s(x), 0') -> false
eq(0', s(x)) -> false
eq(s(x), s(y)) -> eq(x, y)
and(true, true) -> true
and(false, x) -> false
and(x, false) -> false
encArg(true) -> true
encArg(0') -> 0'
encArg(false) -> false
encArg(s(x_1)) -> s(encArg(x_1))
encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2))
encArg(cons_p(x_1)) -> p(encArg(x_1))
encArg(cons_eq(x_1, x_2)) -> eq(encArg(x_1), encArg(x_2))
encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2))
encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
encode_true -> true
encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2))
encode_0 -> 0'
encode_p(x_1) -> p(encArg(x_1))
encode_false -> false
encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2))
encode_eq(x_1, x_2) -> eq(encArg(x_1), encArg(x_2))
encode_s(x_1) -> s(encArg(x_1))

Types:
cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
true :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
0' :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
false :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
and :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
eq :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
s :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encArg :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_eq :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_and :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_true :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_0 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_false :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_and :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_eq :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_s :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
hole_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and1_4 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4 :: Nat -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and


Generator Equations:
gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(0) <=> true
gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(x, 1)) <=> s(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(x))


The following defined symbols remain to be analysed:
gr, cond1, cond2, eq, encArg

They will be analysed ascendingly in the following order:
cond1 = cond2
gr < cond1
cond1 < encArg
gr < cond2
eq < cond2
cond2 < encArg
gr < encArg
eq < encArg

----------------------------------------

(21) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
gr(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(1, n4_4)), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(1, n4_4))) -> *3_4, rt in Omega(n4_4)

Induction Base:
gr(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(1, 0)), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(1, 0)))

Induction Step:
gr(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(1, +(n4_4, 1))), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(1, +(n4_4, 1)))) ->_R^Omega(1)
gr(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(1, n4_4)), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(1, n4_4))) ->_IH
*3_4

We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n).
----------------------------------------

(22)
Complex Obligation (BEST)

----------------------------------------

(23)
Obligation:
Proved the lower bound n^1 for the following obligation:

Innermost TRS:
Rules:
cond1(true, x, y) -> cond2(gr(y, 0'), x, y)
cond2(true, x, y) -> cond2(gr(y, 0'), p(x), p(y))
cond2(false, x, y) -> cond1(and(eq(x, y), gr(x, 0')), x, y)
gr(0', x) -> false
gr(s(x), 0') -> true
gr(s(x), s(y)) -> gr(x, y)
p(0') -> 0'
p(s(x)) -> x
eq(0', 0') -> true
eq(s(x), 0') -> false
eq(0', s(x)) -> false
eq(s(x), s(y)) -> eq(x, y)
and(true, true) -> true
and(false, x) -> false
and(x, false) -> false
encArg(true) -> true
encArg(0') -> 0'
encArg(false) -> false
encArg(s(x_1)) -> s(encArg(x_1))
encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2))
encArg(cons_p(x_1)) -> p(encArg(x_1))
encArg(cons_eq(x_1, x_2)) -> eq(encArg(x_1), encArg(x_2))
encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2))
encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
encode_true -> true
encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2))
encode_0 -> 0'
encode_p(x_1) -> p(encArg(x_1))
encode_false -> false
encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2))
encode_eq(x_1, x_2) -> eq(encArg(x_1), encArg(x_2))
encode_s(x_1) -> s(encArg(x_1))

Types:
cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
true :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
0' :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
false :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
and :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
eq :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
s :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encArg :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_eq :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_and :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_true :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_0 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_false :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_and :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_eq :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_s :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
hole_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and1_4 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4 :: Nat -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and


Generator Equations:
gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(0) <=> true
gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(x, 1)) <=> s(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(x))


The following defined symbols remain to be analysed:
gr, cond1, cond2, eq, encArg

They will be analysed ascendingly in the following order:
cond1 = cond2
gr < cond1
cond1 < encArg
gr < cond2
eq < cond2
cond2 < encArg
gr < encArg
eq < encArg

----------------------------------------

(24) LowerBoundPropagationProof (FINISHED)
Propagated lower bound.
----------------------------------------

(25)
BOUNDS(n^1, INF)

----------------------------------------

(26)
Obligation:
Innermost TRS:
Rules:
cond1(true, x, y) -> cond2(gr(y, 0'), x, y)
cond2(true, x, y) -> cond2(gr(y, 0'), p(x), p(y))
cond2(false, x, y) -> cond1(and(eq(x, y), gr(x, 0')), x, y)
gr(0', x) -> false
gr(s(x), 0') -> true
gr(s(x), s(y)) -> gr(x, y)
p(0') -> 0'
p(s(x)) -> x
eq(0', 0') -> true
eq(s(x), 0') -> false
eq(0', s(x)) -> false
eq(s(x), s(y)) -> eq(x, y)
and(true, true) -> true
and(false, x) -> false
and(x, false) -> false
encArg(true) -> true
encArg(0') -> 0'
encArg(false) -> false
encArg(s(x_1)) -> s(encArg(x_1))
encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2))
encArg(cons_p(x_1)) -> p(encArg(x_1))
encArg(cons_eq(x_1, x_2)) -> eq(encArg(x_1), encArg(x_2))
encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2))
encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
encode_true -> true
encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2))
encode_0 -> 0'
encode_p(x_1) -> p(encArg(x_1))
encode_false -> false
encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2))
encode_eq(x_1, x_2) -> eq(encArg(x_1), encArg(x_2))
encode_s(x_1) -> s(encArg(x_1))

Types:
cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
true :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
0' :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
false :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
and :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
eq :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
s :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encArg :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_eq :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_and :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_true :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_0 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_false :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_and :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_eq :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_s :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
hole_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and1_4 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4 :: Nat -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and


Lemmas:
gr(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(1, n4_4)), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(1, n4_4))) -> *3_4, rt in Omega(n4_4)


Generator Equations:
gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(0) <=> true
gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(x, 1)) <=> s(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(x))


The following defined symbols remain to be analysed:
eq, cond1, cond2, encArg

They will be analysed ascendingly in the following order:
cond1 = cond2
cond1 < encArg
eq < cond2
cond2 < encArg
eq < encArg

----------------------------------------

(27) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
eq(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(1, n1350_4)), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(1, n1350_4))) -> *3_4, rt in Omega(n1350_4)

Induction Base:
eq(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(1, 0)), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(1, 0)))

Induction Step:
eq(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(1, +(n1350_4, 1))), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(1, +(n1350_4, 1)))) ->_R^Omega(1)
eq(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(1, n1350_4)), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(1, n1350_4))) ->_IH
*3_4

We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n).
----------------------------------------

(28)
Obligation:
Innermost TRS:
Rules:
cond1(true, x, y) -> cond2(gr(y, 0'), x, y)
cond2(true, x, y) -> cond2(gr(y, 0'), p(x), p(y))
cond2(false, x, y) -> cond1(and(eq(x, y), gr(x, 0')), x, y)
gr(0', x) -> false
gr(s(x), 0') -> true
gr(s(x), s(y)) -> gr(x, y)
p(0') -> 0'
p(s(x)) -> x
eq(0', 0') -> true
eq(s(x), 0') -> false
eq(0', s(x)) -> false
eq(s(x), s(y)) -> eq(x, y)
and(true, true) -> true
and(false, x) -> false
and(x, false) -> false
encArg(true) -> true
encArg(0') -> 0'
encArg(false) -> false
encArg(s(x_1)) -> s(encArg(x_1))
encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2))
encArg(cons_p(x_1)) -> p(encArg(x_1))
encArg(cons_eq(x_1, x_2)) -> eq(encArg(x_1), encArg(x_2))
encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2))
encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
encode_true -> true
encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2))
encode_0 -> 0'
encode_p(x_1) -> p(encArg(x_1))
encode_false -> false
encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2))
encode_eq(x_1, x_2) -> eq(encArg(x_1), encArg(x_2))
encode_s(x_1) -> s(encArg(x_1))

Types:
cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
true :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
0' :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
false :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
and :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
eq :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
s :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encArg :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_eq :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_and :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_true :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_0 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_false :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_and :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_eq :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_s :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
hole_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and1_4 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4 :: Nat -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and


Lemmas:
gr(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(1, n4_4)), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(1, n4_4))) -> *3_4, rt in Omega(n4_4)
eq(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(1, n1350_4)), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(1, n1350_4))) -> *3_4, rt in Omega(n1350_4)


Generator Equations:
gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(0) <=> true
gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(x, 1)) <=> s(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(x))


The following defined symbols remain to be analysed:
cond2, cond1, encArg

They will be analysed ascendingly in the following order:
cond1 = cond2
cond1 < encArg
cond2 < encArg

----------------------------------------

(29) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
cond2(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(0), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(n3931_4), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(n3931_4)) -> *3_4, rt in Omega(n3931_4)

Induction Base:
cond2(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(0), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(0), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(0))

Induction Step:
cond2(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(0), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(n3931_4, 1)), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(n3931_4, 1))) ->_R^Omega(1)
cond2(gr(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(n3931_4, 1)), 0'), p(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(n3931_4, 1))), p(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(n3931_4, 1)))) ->_R^Omega(1)
cond2(true, p(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(1, n3931_4))), p(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(1, n3931_4)))) ->_R^Omega(1)
cond2(true, gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(n3931_4), p(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(1, n3931_4)))) ->_R^Omega(1)
cond2(true, gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(n3931_4), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(n3931_4)) ->_IH
*3_4

We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n).
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(30)
Obligation:
Innermost TRS:
Rules:
cond1(true, x, y) -> cond2(gr(y, 0'), x, y)
cond2(true, x, y) -> cond2(gr(y, 0'), p(x), p(y))
cond2(false, x, y) -> cond1(and(eq(x, y), gr(x, 0')), x, y)
gr(0', x) -> false
gr(s(x), 0') -> true
gr(s(x), s(y)) -> gr(x, y)
p(0') -> 0'
p(s(x)) -> x
eq(0', 0') -> true
eq(s(x), 0') -> false
eq(0', s(x)) -> false
eq(s(x), s(y)) -> eq(x, y)
and(true, true) -> true
and(false, x) -> false
and(x, false) -> false
encArg(true) -> true
encArg(0') -> 0'
encArg(false) -> false
encArg(s(x_1)) -> s(encArg(x_1))
encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2))
encArg(cons_p(x_1)) -> p(encArg(x_1))
encArg(cons_eq(x_1, x_2)) -> eq(encArg(x_1), encArg(x_2))
encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2))
encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3))
encode_true -> true
encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3))
encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2))
encode_0 -> 0'
encode_p(x_1) -> p(encArg(x_1))
encode_false -> false
encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2))
encode_eq(x_1, x_2) -> eq(encArg(x_1), encArg(x_2))
encode_s(x_1) -> s(encArg(x_1))

Types:
cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
true :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
0' :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
false :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
and :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
eq :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
s :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encArg :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_eq :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
cons_and :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_true :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_0 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_false :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_and :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_eq :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
encode_s :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
hole_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and1_4 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and
gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4 :: Nat -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and


Lemmas:
gr(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(1, n4_4)), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(1, n4_4))) -> *3_4, rt in Omega(n4_4)
eq(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(1, n1350_4)), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(1, n1350_4))) -> *3_4, rt in Omega(n1350_4)
cond2(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(0), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(n3931_4), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(n3931_4)) -> *3_4, rt in Omega(n3931_4)


Generator Equations:
gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(0) <=> true
gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(x, 1)) <=> s(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(x))


The following defined symbols remain to be analysed:
cond1, encArg

They will be analysed ascendingly in the following order:
cond1 = cond2
cond1 < encArg
cond2 < encArg

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(31) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
encArg(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(n6742_4)) -> gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(n6742_4), rt in Omega(0)

Induction Base:
encArg(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(0)) ->_R^Omega(0)
true

Induction Step:
encArg(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(+(n6742_4, 1))) ->_R^Omega(0)
s(encArg(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(n6742_4))) ->_IH
s(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p:cons_eq:cons_and2_4(c6743_4))

We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0).
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(32)
BOUNDS(1, INF)