/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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WORST_CASE(Omega(n^1), O(n^2))
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) CpxTRS
(1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxWeightedTrs
    (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (4) CpxTypedWeightedTrs
    (5) CompletionProof [UPPER BOUND(ID), 0 ms]
    (6) CpxTypedWeightedCompleteTrs
    (7) NarrowingProof [BOTH BOUNDS(ID, ID), 3 ms]
    (8) CpxTypedWeightedCompleteTrs
    (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
    (10) CpxRNTS
    (11) InliningProof [UPPER BOUND(ID), 1564 ms]
    (12) CpxRNTS
    (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (14) CpxRNTS
    (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
    (16) CpxRNTS
    (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (18) CpxRNTS
    (19) IntTrsBoundProof [UPPER BOUND(ID), 262 ms]
    (20) CpxRNTS
    (21) IntTrsBoundProof [UPPER BOUND(ID), 78 ms]
    (22) CpxRNTS
    (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (24) CpxRNTS
    (25) IntTrsBoundProof [UPPER BOUND(ID), 131 ms]
    (26) CpxRNTS
    (27) IntTrsBoundProof [UPPER BOUND(ID), 0 ms]
    (28) CpxRNTS
    (29) ResultPropagationProof [UPPER BOUND(ID), 2 ms]
    (30) CpxRNTS
    (31) IntTrsBoundProof [UPPER BOUND(ID), 272 ms]
    (32) CpxRNTS
    (33) IntTrsBoundProof [UPPER BOUND(ID), 84 ms]
    (34) CpxRNTS
    (35) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (36) CpxRNTS
    (37) IntTrsBoundProof [UPPER BOUND(ID), 238 ms]
    (38) CpxRNTS
    (39) IntTrsBoundProof [UPPER BOUND(ID), 105 ms]
    (40) CpxRNTS
    (41) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (42) CpxRNTS
    (43) IntTrsBoundProof [UPPER BOUND(ID), 1555 ms]
    (44) CpxRNTS
    (45) IntTrsBoundProof [UPPER BOUND(ID), 1532 ms]
    (46) CpxRNTS
    (47) FinalProof [FINISHED, 0 ms]
    (48) BOUNDS(1, n^2)
(49) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(50) CpxTRS
    (51) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (52) typed CpxTrs
    (53) OrderProof [LOWER BOUND(ID), 0 ms]
    (54) typed CpxTrs
    (55) RewriteLemmaProof [LOWER BOUND(ID), 246 ms]
    (56) BEST
        (57) proven lower bound
            (58) LowerBoundPropagationProof [FINISHED, 0 ms]
            (59) BOUNDS(n^1, INF)
        (60) typed CpxTrs


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

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


The TRS R consists of the following rules:

   cond(true, x) -> cond(and(even(x), gr(x, 0)), p(x))
   and(x, false) -> false
   and(false, x) -> false
   and(true, true) -> true
   even(0) -> true
   even(s(0)) -> false
   even(s(s(x))) -> even(x)
   gr(0, x) -> false
   gr(s(x), 0) -> true
   gr(s(x), s(y)) -> gr(x, y)
   p(0) -> 0
   p(s(x)) -> x

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

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

(2)
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:

   cond(true, x) -> cond(and(even(x), gr(x, 0)), p(x)) [1]
   and(x, false) -> false [1]
   and(false, x) -> false [1]
   and(true, true) -> true [1]
   even(0) -> true [1]
   even(s(0)) -> false [1]
   even(s(s(x))) -> even(x) [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]

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

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

(4)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   cond(true, x) -> cond(and(even(x), gr(x, 0)), p(x)) [1]
   and(x, false) -> false [1]
   and(false, x) -> false [1]
   and(true, true) -> true [1]
   even(0) -> true [1]
   even(s(0)) -> false [1]
   even(s(s(x))) -> even(x) [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]

The TRS has the following type information:
cond :: true:false -> 0:s:y -> cond
true :: true:false
and :: true:false -> true:false -> true:false
even :: 0:s:y -> true:false
gr :: 0:s:y -> 0:s:y -> true:false
0 :: 0:s:y
p :: 0:s:y -> 0:s:y
false :: true:false
s :: 0:s:y -> 0:s:y
y :: 0:s:y

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

(5) CompletionProof (UPPER BOUND(ID))
The transformation into a RNTS is sound, since:

(a) The obligation is a constructor system where every type has a constant constructor,

(b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols:

   cond_2

(c) The following functions are completely defined:

   and_2
   even_1
   gr_2
   p_1

Due to the following rules being added:

   even(v0) -> null_even [0]
   gr(v0, v1) -> null_gr [0]
   p(v0) -> null_p [0]
   and(v0, v1) -> null_and [0]

And the following fresh constants:    null_even, null_gr, null_p, null_and, const

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

(6)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

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

   cond(true, x) -> cond(and(even(x), gr(x, 0)), p(x)) [1]
   and(x, false) -> false [1]
   and(false, x) -> false [1]
   and(true, true) -> true [1]
   even(0) -> true [1]
   even(s(0)) -> false [1]
   even(s(s(x))) -> even(x) [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]
   even(v0) -> null_even [0]
   gr(v0, v1) -> null_gr [0]
   p(v0) -> null_p [0]
   and(v0, v1) -> null_and [0]

The TRS has the following type information:
cond :: true:false:null_even:null_gr:null_and -> 0:s:y:null_p -> cond
true :: true:false:null_even:null_gr:null_and
and :: true:false:null_even:null_gr:null_and -> true:false:null_even:null_gr:null_and -> true:false:null_even:null_gr:null_and
even :: 0:s:y:null_p -> true:false:null_even:null_gr:null_and
gr :: 0:s:y:null_p -> 0:s:y:null_p -> true:false:null_even:null_gr:null_and
0 :: 0:s:y:null_p
p :: 0:s:y:null_p -> 0:s:y:null_p
false :: true:false:null_even:null_gr:null_and
s :: 0:s:y:null_p -> 0:s:y:null_p
y :: 0:s:y:null_p
null_even :: true:false:null_even:null_gr:null_and
null_gr :: true:false:null_even:null_gr:null_and
null_p :: 0:s:y:null_p
null_and :: true:false:null_even:null_gr:null_and
const :: cond

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

(7) NarrowingProof (BOTH BOUNDS(ID, ID))
Narrowed the inner basic terms of all right-hand sides by a single narrowing step.
----------------------------------------

(8)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

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

   cond(true, 0) -> cond(and(true, false), 0) [4]
   cond(true, 0) -> cond(and(true, false), null_p) [3]
   cond(true, 0) -> cond(and(true, null_gr), 0) [3]
   cond(true, 0) -> cond(and(true, null_gr), null_p) [2]
   cond(true, s(0)) -> cond(and(false, true), 0) [4]
   cond(true, s(0)) -> cond(and(false, true), null_p) [3]
   cond(true, s(0)) -> cond(and(false, null_gr), 0) [3]
   cond(true, s(0)) -> cond(and(false, null_gr), null_p) [2]
   cond(true, s(s(x'))) -> cond(and(even(x'), true), s(x')) [4]
   cond(true, s(s(x'))) -> cond(and(even(x'), true), null_p) [3]
   cond(true, s(s(x'))) -> cond(and(even(x'), null_gr), s(x')) [3]
   cond(true, s(s(x'))) -> cond(and(even(x'), null_gr), null_p) [2]
   cond(true, 0) -> cond(and(null_even, false), 0) [3]
   cond(true, 0) -> cond(and(null_even, false), null_p) [2]
   cond(true, s(x'')) -> cond(and(null_even, true), x'') [3]
   cond(true, s(x'')) -> cond(and(null_even, true), null_p) [2]
   cond(true, 0) -> cond(and(null_even, null_gr), 0) [2]
   cond(true, s(x1)) -> cond(and(null_even, null_gr), x1) [2]
   cond(true, x) -> cond(and(null_even, null_gr), null_p) [1]
   and(x, false) -> false [1]
   and(false, x) -> false [1]
   and(true, true) -> true [1]
   even(0) -> true [1]
   even(s(0)) -> false [1]
   even(s(s(x))) -> even(x) [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]
   even(v0) -> null_even [0]
   gr(v0, v1) -> null_gr [0]
   p(v0) -> null_p [0]
   and(v0, v1) -> null_and [0]

The TRS has the following type information:
cond :: true:false:null_even:null_gr:null_and -> 0:s:y:null_p -> cond
true :: true:false:null_even:null_gr:null_and
and :: true:false:null_even:null_gr:null_and -> true:false:null_even:null_gr:null_and -> true:false:null_even:null_gr:null_and
even :: 0:s:y:null_p -> true:false:null_even:null_gr:null_and
gr :: 0:s:y:null_p -> 0:s:y:null_p -> true:false:null_even:null_gr:null_and
0 :: 0:s:y:null_p
p :: 0:s:y:null_p -> 0:s:y:null_p
false :: true:false:null_even:null_gr:null_and
s :: 0:s:y:null_p -> 0:s:y:null_p
y :: 0:s:y:null_p
null_even :: true:false:null_even:null_gr:null_and
null_gr :: true:false:null_even:null_gr:null_and
null_p :: 0:s:y:null_p
null_and :: true:false:null_even:null_gr:null_and
const :: cond

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

(9) 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
   y => 1
   null_even => 0
   null_gr => 0
   null_p => 0
   null_and => 0
   const => 0

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

(10)
Obligation:
Complexity RNTS consisting of the following rules:

   and(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 1 }-> 1 :|: x >= 0, z' = 1, z = x
   and(z, z') -{ 1 }-> 1 :|: z' = x, z = 1, x >= 0
   and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   cond(z, z') -{ 3 }-> cond(and(even(x'), 2), 0) :|: z = 2, z' = 1 + (1 + x'), x' >= 0
   cond(z, z') -{ 4 }-> cond(and(even(x'), 2), 1 + x') :|: z = 2, z' = 1 + (1 + x'), x' >= 0
   cond(z, z') -{ 2 }-> cond(and(even(x'), 0), 0) :|: z = 2, z' = 1 + (1 + x'), x' >= 0
   cond(z, z') -{ 3 }-> cond(and(even(x'), 0), 1 + x') :|: z = 2, z' = 1 + (1 + x'), x' >= 0
   cond(z, z') -{ 4 }-> cond(and(2, 1), 0) :|: z = 2, z' = 0
   cond(z, z') -{ 3 }-> cond(and(2, 1), 0) :|: z = 2, z' = 0
   cond(z, z') -{ 3 }-> cond(and(2, 0), 0) :|: z = 2, z' = 0
   cond(z, z') -{ 2 }-> cond(and(2, 0), 0) :|: z = 2, z' = 0
   cond(z, z') -{ 4 }-> cond(and(1, 2), 0) :|: z = 2, z' = 1 + 0
   cond(z, z') -{ 3 }-> cond(and(1, 2), 0) :|: z = 2, z' = 1 + 0
   cond(z, z') -{ 3 }-> cond(and(1, 0), 0) :|: z = 2, z' = 1 + 0
   cond(z, z') -{ 2 }-> cond(and(1, 0), 0) :|: z = 2, z' = 1 + 0
   cond(z, z') -{ 3 }-> cond(and(0, 2), x'') :|: z = 2, z' = 1 + x'', x'' >= 0
   cond(z, z') -{ 2 }-> cond(and(0, 2), 0) :|: z = 2, z' = 1 + x'', x'' >= 0
   cond(z, z') -{ 3 }-> cond(and(0, 1), 0) :|: z = 2, z' = 0
   cond(z, z') -{ 2 }-> cond(and(0, 1), 0) :|: z = 2, z' = 0
   cond(z, z') -{ 2 }-> cond(and(0, 0), x1) :|: z = 2, x1 >= 0, z' = 1 + x1
   cond(z, z') -{ 2 }-> cond(and(0, 0), 0) :|: z = 2, z' = 0
   cond(z, z') -{ 1 }-> cond(and(0, 0), 0) :|: z = 2, z' = x, x >= 0
   even(z) -{ 1 }-> even(x) :|: x >= 0, z = 1 + (1 + x)
   even(z) -{ 1 }-> 2 :|: z = 0
   even(z) -{ 1 }-> 1 :|: z = 1 + 0
   even(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   gr(z, z') -{ 1 }-> gr(x, 1) :|: z' = 1 + 1, x >= 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


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

(11) InliningProof (UPPER BOUND(ID))
Inlined the following terminating rules on right-hand sides where appropriate:

   and(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 1 }-> 1 :|: x >= 0, z' = 1, z = x
   and(z, z') -{ 1 }-> 1 :|: z' = x, z = 1, x >= 0
   and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1

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

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

   and(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 1 }-> 1 :|: x >= 0, z' = 1, z = x
   and(z, z') -{ 1 }-> 1 :|: z' = x, z = 1, x >= 0
   and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   cond(z, z') -{ 3 }-> cond(and(even(x'), 2), 0) :|: z = 2, z' = 1 + (1 + x'), x' >= 0
   cond(z, z') -{ 4 }-> cond(and(even(x'), 2), 1 + x') :|: z = 2, z' = 1 + (1 + x'), x' >= 0
   cond(z, z') -{ 2 }-> cond(and(even(x'), 0), 0) :|: z = 2, z' = 1 + (1 + x'), x' >= 0
   cond(z, z') -{ 3 }-> cond(and(even(x'), 0), 1 + x') :|: z = 2, z' = 1 + (1 + x'), x' >= 0
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 3 }-> cond(0, x'') :|: z = 2, z' = 1 + x'', x'' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, x1) :|: z = 2, x1 >= 0, z' = 1 + x1, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 1 + x'', x'' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 1 }-> cond(0, 0) :|: z = 2, z' = x, x >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   even(z) -{ 1 }-> even(x) :|: x >= 0, z = 1 + (1 + x)
   even(z) -{ 1 }-> 2 :|: z = 0
   even(z) -{ 1 }-> 1 :|: z = 1 + 0
   even(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   gr(z, z') -{ 1 }-> gr(x, 1) :|: z' = 1 + 1, x >= 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


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

(13) SimplificationProof (BOTH BOUNDS(ID, ID))
Simplified the RNTS by moving equalities from the constraints into the right-hand sides.
----------------------------------------

(14)
Obligation:
Complexity RNTS consisting of the following rules:

   and(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   and(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cond(z, z') -{ 3 }-> cond(and(even(z' - 2), 2), 0) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 4 }-> cond(and(even(z' - 2), 2), 1 + (z' - 2)) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 2 }-> cond(and(even(z' - 2), 0), 0) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 3 }-> cond(and(even(z' - 2), 0), 1 + (z' - 2)) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 1 }-> cond(0, 0) :|: z = 2, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   even(z) -{ 1 }-> even(z - 2) :|: z - 2 >= 0
   even(z) -{ 1 }-> 2 :|: z = 0
   even(z) -{ 1 }-> 1 :|: z = 1 + 0
   even(z) -{ 0 }-> 0 :|: z >= 0
   gr(z, z') -{ 1 }-> gr(z - 1, 1) :|: z' = 1 + 1, z - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0


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

(15) CpxRntsAnalysisOrderProof (BOTH BOUNDS(ID, ID))
Found the following analysis order by SCC decomposition:

   { and }
   { p }
   { gr }
   { even }
   { cond }

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

(16)
Obligation:
Complexity RNTS consisting of the following rules:

   and(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   and(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cond(z, z') -{ 3 }-> cond(and(even(z' - 2), 2), 0) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 4 }-> cond(and(even(z' - 2), 2), 1 + (z' - 2)) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 2 }-> cond(and(even(z' - 2), 0), 0) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 3 }-> cond(and(even(z' - 2), 0), 1 + (z' - 2)) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 1 }-> cond(0, 0) :|: z = 2, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   even(z) -{ 1 }-> even(z - 2) :|: z - 2 >= 0
   even(z) -{ 1 }-> 2 :|: z = 0
   even(z) -{ 1 }-> 1 :|: z = 1 + 0
   even(z) -{ 0 }-> 0 :|: z >= 0
   gr(z, z') -{ 1 }-> gr(z - 1, 1) :|: z' = 1 + 1, z - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {and}, {p}, {gr}, {even}, {cond}

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

(17) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(18)
Obligation:
Complexity RNTS consisting of the following rules:

   and(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   and(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cond(z, z') -{ 3 }-> cond(and(even(z' - 2), 2), 0) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 4 }-> cond(and(even(z' - 2), 2), 1 + (z' - 2)) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 2 }-> cond(and(even(z' - 2), 0), 0) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 3 }-> cond(and(even(z' - 2), 0), 1 + (z' - 2)) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 1 }-> cond(0, 0) :|: z = 2, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   even(z) -{ 1 }-> even(z - 2) :|: z - 2 >= 0
   even(z) -{ 1 }-> 2 :|: z = 0
   even(z) -{ 1 }-> 1 :|: z = 1 + 0
   even(z) -{ 0 }-> 0 :|: z >= 0
   gr(z, z') -{ 1 }-> gr(z - 1, 1) :|: z' = 1 + 1, z - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {and}, {p}, {gr}, {even}, {cond}

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

(19) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: and
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 2

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

(20)
Obligation:
Complexity RNTS consisting of the following rules:

   and(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   and(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cond(z, z') -{ 3 }-> cond(and(even(z' - 2), 2), 0) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 4 }-> cond(and(even(z' - 2), 2), 1 + (z' - 2)) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 2 }-> cond(and(even(z' - 2), 0), 0) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 3 }-> cond(and(even(z' - 2), 0), 1 + (z' - 2)) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 1 }-> cond(0, 0) :|: z = 2, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   even(z) -{ 1 }-> even(z - 2) :|: z - 2 >= 0
   even(z) -{ 1 }-> 2 :|: z = 0
   even(z) -{ 1 }-> 1 :|: z = 1 + 0
   even(z) -{ 0 }-> 0 :|: z >= 0
   gr(z, z') -{ 1 }-> gr(z - 1, 1) :|: z' = 1 + 1, z - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {and}, {p}, {gr}, {even}, {cond}
Previous analysis results are:
  and: runtime: ?, size: O(1) [2]

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

(21) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: and
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

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

(22)
Obligation:
Complexity RNTS consisting of the following rules:

   and(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   and(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cond(z, z') -{ 3 }-> cond(and(even(z' - 2), 2), 0) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 4 }-> cond(and(even(z' - 2), 2), 1 + (z' - 2)) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 2 }-> cond(and(even(z' - 2), 0), 0) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 3 }-> cond(and(even(z' - 2), 0), 1 + (z' - 2)) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 1 }-> cond(0, 0) :|: z = 2, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   even(z) -{ 1 }-> even(z - 2) :|: z - 2 >= 0
   even(z) -{ 1 }-> 2 :|: z = 0
   even(z) -{ 1 }-> 1 :|: z = 1 + 0
   even(z) -{ 0 }-> 0 :|: z >= 0
   gr(z, z') -{ 1 }-> gr(z - 1, 1) :|: z' = 1 + 1, z - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {p}, {gr}, {even}, {cond}
Previous analysis results are:
  and: runtime: O(1) [1], size: O(1) [2]

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

(23) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(24)
Obligation:
Complexity RNTS consisting of the following rules:

   and(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   and(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cond(z, z') -{ 3 }-> cond(and(even(z' - 2), 2), 0) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 4 }-> cond(and(even(z' - 2), 2), 1 + (z' - 2)) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 2 }-> cond(and(even(z' - 2), 0), 0) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 3 }-> cond(and(even(z' - 2), 0), 1 + (z' - 2)) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 1 }-> cond(0, 0) :|: z = 2, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   even(z) -{ 1 }-> even(z - 2) :|: z - 2 >= 0
   even(z) -{ 1 }-> 2 :|: z = 0
   even(z) -{ 1 }-> 1 :|: z = 1 + 0
   even(z) -{ 0 }-> 0 :|: z >= 0
   gr(z, z') -{ 1 }-> gr(z - 1, 1) :|: z' = 1 + 1, z - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {p}, {gr}, {even}, {cond}
Previous analysis results are:
  and: runtime: O(1) [1], size: O(1) [2]

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

(25) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: p
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z

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

(26)
Obligation:
Complexity RNTS consisting of the following rules:

   and(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   and(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cond(z, z') -{ 3 }-> cond(and(even(z' - 2), 2), 0) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 4 }-> cond(and(even(z' - 2), 2), 1 + (z' - 2)) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 2 }-> cond(and(even(z' - 2), 0), 0) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 3 }-> cond(and(even(z' - 2), 0), 1 + (z' - 2)) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 1 }-> cond(0, 0) :|: z = 2, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   even(z) -{ 1 }-> even(z - 2) :|: z - 2 >= 0
   even(z) -{ 1 }-> 2 :|: z = 0
   even(z) -{ 1 }-> 1 :|: z = 1 + 0
   even(z) -{ 0 }-> 0 :|: z >= 0
   gr(z, z') -{ 1 }-> gr(z - 1, 1) :|: z' = 1 + 1, z - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {p}, {gr}, {even}, {cond}
Previous analysis results are:
  and: runtime: O(1) [1], size: O(1) [2]
  p: runtime: ?, size: O(n^1) [z]

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

(27) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: p
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

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

(28)
Obligation:
Complexity RNTS consisting of the following rules:

   and(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   and(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cond(z, z') -{ 3 }-> cond(and(even(z' - 2), 2), 0) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 4 }-> cond(and(even(z' - 2), 2), 1 + (z' - 2)) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 2 }-> cond(and(even(z' - 2), 0), 0) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 3 }-> cond(and(even(z' - 2), 0), 1 + (z' - 2)) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 1 }-> cond(0, 0) :|: z = 2, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   even(z) -{ 1 }-> even(z - 2) :|: z - 2 >= 0
   even(z) -{ 1 }-> 2 :|: z = 0
   even(z) -{ 1 }-> 1 :|: z = 1 + 0
   even(z) -{ 0 }-> 0 :|: z >= 0
   gr(z, z') -{ 1 }-> gr(z - 1, 1) :|: z' = 1 + 1, z - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {gr}, {even}, {cond}
Previous analysis results are:
  and: runtime: O(1) [1], size: O(1) [2]
  p: runtime: O(1) [1], size: O(n^1) [z]

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

(29) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(30)
Obligation:
Complexity RNTS consisting of the following rules:

   and(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   and(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cond(z, z') -{ 3 }-> cond(and(even(z' - 2), 2), 0) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 4 }-> cond(and(even(z' - 2), 2), 1 + (z' - 2)) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 2 }-> cond(and(even(z' - 2), 0), 0) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 3 }-> cond(and(even(z' - 2), 0), 1 + (z' - 2)) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 1 }-> cond(0, 0) :|: z = 2, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   even(z) -{ 1 }-> even(z - 2) :|: z - 2 >= 0
   even(z) -{ 1 }-> 2 :|: z = 0
   even(z) -{ 1 }-> 1 :|: z = 1 + 0
   even(z) -{ 0 }-> 0 :|: z >= 0
   gr(z, z') -{ 1 }-> gr(z - 1, 1) :|: z' = 1 + 1, z - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {gr}, {even}, {cond}
Previous analysis results are:
  and: runtime: O(1) [1], size: O(1) [2]
  p: runtime: O(1) [1], size: O(n^1) [z]

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

(31) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: gr
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 2

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

(32)
Obligation:
Complexity RNTS consisting of the following rules:

   and(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   and(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cond(z, z') -{ 3 }-> cond(and(even(z' - 2), 2), 0) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 4 }-> cond(and(even(z' - 2), 2), 1 + (z' - 2)) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 2 }-> cond(and(even(z' - 2), 0), 0) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 3 }-> cond(and(even(z' - 2), 0), 1 + (z' - 2)) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 1 }-> cond(0, 0) :|: z = 2, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   even(z) -{ 1 }-> even(z - 2) :|: z - 2 >= 0
   even(z) -{ 1 }-> 2 :|: z = 0
   even(z) -{ 1 }-> 1 :|: z = 1 + 0
   even(z) -{ 0 }-> 0 :|: z >= 0
   gr(z, z') -{ 1 }-> gr(z - 1, 1) :|: z' = 1 + 1, z - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {gr}, {even}, {cond}
Previous analysis results are:
  and: runtime: O(1) [1], size: O(1) [2]
  p: runtime: O(1) [1], size: O(n^1) [z]
  gr: runtime: ?, size: O(1) [2]

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

(33) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: gr
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 2

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

(34)
Obligation:
Complexity RNTS consisting of the following rules:

   and(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   and(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cond(z, z') -{ 3 }-> cond(and(even(z' - 2), 2), 0) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 4 }-> cond(and(even(z' - 2), 2), 1 + (z' - 2)) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 2 }-> cond(and(even(z' - 2), 0), 0) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 3 }-> cond(and(even(z' - 2), 0), 1 + (z' - 2)) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 1 }-> cond(0, 0) :|: z = 2, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   even(z) -{ 1 }-> even(z - 2) :|: z - 2 >= 0
   even(z) -{ 1 }-> 2 :|: z = 0
   even(z) -{ 1 }-> 1 :|: z = 1 + 0
   even(z) -{ 0 }-> 0 :|: z >= 0
   gr(z, z') -{ 1 }-> gr(z - 1, 1) :|: z' = 1 + 1, z - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {even}, {cond}
Previous analysis results are:
  and: runtime: O(1) [1], size: O(1) [2]
  p: runtime: O(1) [1], size: O(n^1) [z]
  gr: runtime: O(1) [2], size: O(1) [2]

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

(35) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(36)
Obligation:
Complexity RNTS consisting of the following rules:

   and(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   and(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cond(z, z') -{ 3 }-> cond(and(even(z' - 2), 2), 0) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 4 }-> cond(and(even(z' - 2), 2), 1 + (z' - 2)) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 2 }-> cond(and(even(z' - 2), 0), 0) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 3 }-> cond(and(even(z' - 2), 0), 1 + (z' - 2)) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 1 }-> cond(0, 0) :|: z = 2, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   even(z) -{ 1 }-> even(z - 2) :|: z - 2 >= 0
   even(z) -{ 1 }-> 2 :|: z = 0
   even(z) -{ 1 }-> 1 :|: z = 1 + 0
   even(z) -{ 0 }-> 0 :|: z >= 0
   gr(z, z') -{ 3 }-> s :|: s >= 0, s <= 2, z' = 1 + 1, z - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {even}, {cond}
Previous analysis results are:
  and: runtime: O(1) [1], size: O(1) [2]
  p: runtime: O(1) [1], size: O(n^1) [z]
  gr: runtime: O(1) [2], size: O(1) [2]

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

(37) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: even
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 2

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

(38)
Obligation:
Complexity RNTS consisting of the following rules:

   and(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   and(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cond(z, z') -{ 3 }-> cond(and(even(z' - 2), 2), 0) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 4 }-> cond(and(even(z' - 2), 2), 1 + (z' - 2)) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 2 }-> cond(and(even(z' - 2), 0), 0) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 3 }-> cond(and(even(z' - 2), 0), 1 + (z' - 2)) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 1 }-> cond(0, 0) :|: z = 2, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   even(z) -{ 1 }-> even(z - 2) :|: z - 2 >= 0
   even(z) -{ 1 }-> 2 :|: z = 0
   even(z) -{ 1 }-> 1 :|: z = 1 + 0
   even(z) -{ 0 }-> 0 :|: z >= 0
   gr(z, z') -{ 3 }-> s :|: s >= 0, s <= 2, z' = 1 + 1, z - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {even}, {cond}
Previous analysis results are:
  and: runtime: O(1) [1], size: O(1) [2]
  p: runtime: O(1) [1], size: O(n^1) [z]
  gr: runtime: O(1) [2], size: O(1) [2]
  even: runtime: ?, size: O(1) [2]

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

(39) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: even
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 2 + z

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

(40)
Obligation:
Complexity RNTS consisting of the following rules:

   and(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   and(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cond(z, z') -{ 3 }-> cond(and(even(z' - 2), 2), 0) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 4 }-> cond(and(even(z' - 2), 2), 1 + (z' - 2)) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 2 }-> cond(and(even(z' - 2), 0), 0) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 3 }-> cond(and(even(z' - 2), 0), 1 + (z' - 2)) :|: z = 2, z' - 2 >= 0
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 1 }-> cond(0, 0) :|: z = 2, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   even(z) -{ 1 }-> even(z - 2) :|: z - 2 >= 0
   even(z) -{ 1 }-> 2 :|: z = 0
   even(z) -{ 1 }-> 1 :|: z = 1 + 0
   even(z) -{ 0 }-> 0 :|: z >= 0
   gr(z, z') -{ 3 }-> s :|: s >= 0, s <= 2, z' = 1 + 1, z - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {cond}
Previous analysis results are:
  and: runtime: O(1) [1], size: O(1) [2]
  p: runtime: O(1) [1], size: O(n^1) [z]
  gr: runtime: O(1) [2], size: O(1) [2]
  even: runtime: O(n^1) [2 + z], size: O(1) [2]

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

(41) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(42)
Obligation:
Complexity RNTS consisting of the following rules:

   and(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   and(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cond(z, z') -{ 5 + z' }-> cond(s1, 1 + (z' - 2)) :|: s'' >= 0, s'' <= 2, s1 >= 0, s1 <= 2, z = 2, z' - 2 >= 0
   cond(z, z') -{ 4 + z' }-> cond(s3, 0) :|: s2 >= 0, s2 <= 2, s3 >= 0, s3 <= 2, z = 2, z' - 2 >= 0
   cond(z, z') -{ 4 + z' }-> cond(s5, 1 + (z' - 2)) :|: s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, z = 2, z' - 2 >= 0
   cond(z, z') -{ 3 + z' }-> cond(s7, 0) :|: s6 >= 0, s6 <= 2, s7 >= 0, s7 <= 2, z = 2, z' - 2 >= 0
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 1 }-> cond(0, 0) :|: z = 2, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   even(z) -{ 1 + z }-> s' :|: s' >= 0, s' <= 2, z - 2 >= 0
   even(z) -{ 1 }-> 2 :|: z = 0
   even(z) -{ 1 }-> 1 :|: z = 1 + 0
   even(z) -{ 0 }-> 0 :|: z >= 0
   gr(z, z') -{ 3 }-> s :|: s >= 0, s <= 2, z' = 1 + 1, z - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {cond}
Previous analysis results are:
  and: runtime: O(1) [1], size: O(1) [2]
  p: runtime: O(1) [1], size: O(n^1) [z]
  gr: runtime: O(1) [2], size: O(1) [2]
  even: runtime: O(n^1) [2 + z], size: O(1) [2]

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

(43) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: cond
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

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

(44)
Obligation:
Complexity RNTS consisting of the following rules:

   and(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   and(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cond(z, z') -{ 5 + z' }-> cond(s1, 1 + (z' - 2)) :|: s'' >= 0, s'' <= 2, s1 >= 0, s1 <= 2, z = 2, z' - 2 >= 0
   cond(z, z') -{ 4 + z' }-> cond(s3, 0) :|: s2 >= 0, s2 <= 2, s3 >= 0, s3 <= 2, z = 2, z' - 2 >= 0
   cond(z, z') -{ 4 + z' }-> cond(s5, 1 + (z' - 2)) :|: s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, z = 2, z' - 2 >= 0
   cond(z, z') -{ 3 + z' }-> cond(s7, 0) :|: s6 >= 0, s6 <= 2, s7 >= 0, s7 <= 2, z = 2, z' - 2 >= 0
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 1 }-> cond(0, 0) :|: z = 2, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   even(z) -{ 1 + z }-> s' :|: s' >= 0, s' <= 2, z - 2 >= 0
   even(z) -{ 1 }-> 2 :|: z = 0
   even(z) -{ 1 }-> 1 :|: z = 1 + 0
   even(z) -{ 0 }-> 0 :|: z >= 0
   gr(z, z') -{ 3 }-> s :|: s >= 0, s <= 2, z' = 1 + 1, z - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {cond}
Previous analysis results are:
  and: runtime: O(1) [1], size: O(1) [2]
  p: runtime: O(1) [1], size: O(n^1) [z]
  gr: runtime: O(1) [2], size: O(1) [2]
  even: runtime: O(n^1) [2 + z], size: O(1) [2]
  cond: runtime: ?, size: O(1) [0]

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

(45) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: cond
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 25 + 9*z' + z'^2

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

(46)
Obligation:
Complexity RNTS consisting of the following rules:

   and(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   and(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   cond(z, z') -{ 5 + z' }-> cond(s1, 1 + (z' - 2)) :|: s'' >= 0, s'' <= 2, s1 >= 0, s1 <= 2, z = 2, z' - 2 >= 0
   cond(z, z') -{ 4 + z' }-> cond(s3, 0) :|: s2 >= 0, s2 <= 2, s3 >= 0, s3 <= 2, z = 2, z' - 2 >= 0
   cond(z, z') -{ 4 + z' }-> cond(s5, 1 + (z' - 2)) :|: s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, z = 2, z' - 2 >= 0
   cond(z, z') -{ 3 + z' }-> cond(s7, 0) :|: s6 >= 0, s6 <= 2, s7 >= 0, s7 <= 2, z = 2, z' - 2 >= 0
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 2 = x
   cond(z, z') -{ 5 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 2 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 1 + 0, 0 = x, 1 = 1, x >= 0
   cond(z, z') -{ 4 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 3 }-> cond(1, 0) :|: z = 2, z' = 0, x >= 0, 1 = 1, 0 = x
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 2 = v0, 0 = v1
   cond(z, z') -{ 4 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 1 + 0, v0 >= 0, v1 >= 0, 1 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, 0) :|: z = 2, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 1 }-> cond(0, 0) :|: z = 2, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   cond(z, z') -{ 3 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 2 = v1
   cond(z, z') -{ 2 }-> cond(0, z' - 1) :|: z = 2, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   even(z) -{ 1 + z }-> s' :|: s' >= 0, s' <= 2, z - 2 >= 0
   even(z) -{ 1 }-> 2 :|: z = 0
   even(z) -{ 1 }-> 1 :|: z = 1 + 0
   even(z) -{ 0 }-> 0 :|: z >= 0
   gr(z, z') -{ 3 }-> s :|: s >= 0, s <= 2, z' = 1 + 1, z - 1 >= 0
   gr(z, z') -{ 1 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 1 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 1 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: 
Previous analysis results are:
  and: runtime: O(1) [1], size: O(1) [2]
  p: runtime: O(1) [1], size: O(n^1) [z]
  gr: runtime: O(1) [2], size: O(1) [2]
  even: runtime: O(n^1) [2 + z], size: O(1) [2]
  cond: runtime: O(n^2) [25 + 9*z' + z'^2], size: O(1) [0]

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

(47) FinalProof (FINISHED)
Computed overall runtime complexity
----------------------------------------

(48)
BOUNDS(1, n^2)

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

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

(50)
Obligation:
The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).


The TRS R consists of the following rules:

   cond(true, x) -> cond(and(even(x), gr(x, 0')), p(x))
   and(x, false) -> false
   and(false, x) -> false
   and(true, true) -> true
   even(0') -> true
   even(s(0')) -> false
   even(s(s(x))) -> even(x)
   gr(0', x) -> false
   gr(s(x), 0') -> true
   gr(s(x), s(y)) -> gr(x, y)
   p(0') -> 0'
   p(s(x)) -> x

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

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

(52)
Obligation:
Innermost TRS:
Rules:
cond(true, x) -> cond(and(even(x), gr(x, 0')), p(x))
and(x, false) -> false
and(false, x) -> false
and(true, true) -> true
even(0') -> true
even(s(0')) -> false
even(s(s(x))) -> even(x)
gr(0', x) -> false
gr(s(x), 0') -> true
gr(s(x), s(y)) -> gr(x, y)
p(0') -> 0'
p(s(x)) -> x

Types:
cond :: true:false -> 0':s:y -> cond
true :: true:false
and :: true:false -> true:false -> true:false
even :: 0':s:y -> true:false
gr :: 0':s:y -> 0':s:y -> true:false
0' :: 0':s:y
p :: 0':s:y -> 0':s:y
false :: true:false
s :: 0':s:y -> 0':s:y
y :: 0':s:y
hole_cond1_0 :: cond
hole_true:false2_0 :: true:false
hole_0':s:y3_0 :: 0':s:y
gen_0':s:y4_0 :: Nat -> 0':s:y

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

(53) OrderProof (LOWER BOUND(ID))
Heuristically decided to analyse the following defined symbols:
cond, even, gr

They will be analysed ascendingly in the following order:
even < cond
gr < cond

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

(54)
Obligation:
Innermost TRS:
Rules:
cond(true, x) -> cond(and(even(x), gr(x, 0')), p(x))
and(x, false) -> false
and(false, x) -> false
and(true, true) -> true
even(0') -> true
even(s(0')) -> false
even(s(s(x))) -> even(x)
gr(0', x) -> false
gr(s(x), 0') -> true
gr(s(x), s(y)) -> gr(x, y)
p(0') -> 0'
p(s(x)) -> x

Types:
cond :: true:false -> 0':s:y -> cond
true :: true:false
and :: true:false -> true:false -> true:false
even :: 0':s:y -> true:false
gr :: 0':s:y -> 0':s:y -> true:false
0' :: 0':s:y
p :: 0':s:y -> 0':s:y
false :: true:false
s :: 0':s:y -> 0':s:y
y :: 0':s:y
hole_cond1_0 :: cond
hole_true:false2_0 :: true:false
hole_0':s:y3_0 :: 0':s:y
gen_0':s:y4_0 :: Nat -> 0':s:y


Generator Equations:
gen_0':s:y4_0(0) <=> 0'
gen_0':s:y4_0(+(x, 1)) <=> s(gen_0':s:y4_0(x))


The following defined symbols remain to be analysed:
even, cond, gr

They will be analysed ascendingly in the following order:
even < cond
gr < cond

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(55) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
even(gen_0':s:y4_0(*(2, n6_0))) -> true, rt in Omega(1 + n6_0)

Induction Base:
even(gen_0':s:y4_0(*(2, 0))) ->_R^Omega(1)
true

Induction Step:
even(gen_0':s:y4_0(*(2, +(n6_0, 1)))) ->_R^Omega(1)
even(gen_0':s:y4_0(*(2, n6_0))) ->_IH
true

We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n).
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(56)
Complex Obligation (BEST)

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(57)
Obligation:
Proved the lower bound n^1 for the following obligation:

Innermost TRS:
Rules:
cond(true, x) -> cond(and(even(x), gr(x, 0')), p(x))
and(x, false) -> false
and(false, x) -> false
and(true, true) -> true
even(0') -> true
even(s(0')) -> false
even(s(s(x))) -> even(x)
gr(0', x) -> false
gr(s(x), 0') -> true
gr(s(x), s(y)) -> gr(x, y)
p(0') -> 0'
p(s(x)) -> x

Types:
cond :: true:false -> 0':s:y -> cond
true :: true:false
and :: true:false -> true:false -> true:false
even :: 0':s:y -> true:false
gr :: 0':s:y -> 0':s:y -> true:false
0' :: 0':s:y
p :: 0':s:y -> 0':s:y
false :: true:false
s :: 0':s:y -> 0':s:y
y :: 0':s:y
hole_cond1_0 :: cond
hole_true:false2_0 :: true:false
hole_0':s:y3_0 :: 0':s:y
gen_0':s:y4_0 :: Nat -> 0':s:y


Generator Equations:
gen_0':s:y4_0(0) <=> 0'
gen_0':s:y4_0(+(x, 1)) <=> s(gen_0':s:y4_0(x))


The following defined symbols remain to be analysed:
even, cond, gr

They will be analysed ascendingly in the following order:
even < cond
gr < cond

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(58) LowerBoundPropagationProof (FINISHED)
Propagated lower bound.
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(59)
BOUNDS(n^1, INF)

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(60)
Obligation:
Innermost TRS:
Rules:
cond(true, x) -> cond(and(even(x), gr(x, 0')), p(x))
and(x, false) -> false
and(false, x) -> false
and(true, true) -> true
even(0') -> true
even(s(0')) -> false
even(s(s(x))) -> even(x)
gr(0', x) -> false
gr(s(x), 0') -> true
gr(s(x), s(y)) -> gr(x, y)
p(0') -> 0'
p(s(x)) -> x

Types:
cond :: true:false -> 0':s:y -> cond
true :: true:false
and :: true:false -> true:false -> true:false
even :: 0':s:y -> true:false
gr :: 0':s:y -> 0':s:y -> true:false
0' :: 0':s:y
p :: 0':s:y -> 0':s:y
false :: true:false
s :: 0':s:y -> 0':s:y
y :: 0':s:y
hole_cond1_0 :: cond
hole_true:false2_0 :: true:false
hole_0':s:y3_0 :: 0':s:y
gen_0':s:y4_0 :: Nat -> 0':s:y


Lemmas:
even(gen_0':s:y4_0(*(2, n6_0))) -> true, rt in Omega(1 + n6_0)


Generator Equations:
gen_0':s:y4_0(0) <=> 0'
gen_0':s:y4_0(+(x, 1)) <=> s(gen_0':s:y4_0(x))


The following defined symbols remain to be analysed:
gr, cond

They will be analysed ascendingly in the following order:
gr < cond