WORST_CASE(?,O(1))
* Step 1: RestrictVarsProcessor WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f11(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) -> f14(A,0,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) [9 >= A] (?,1)
1. f33(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) -> f36(A,B,C,0,E,F,G,H,I,J,K,L,M,N,O,P,Q) [9 >= C] (?,1)
2. f36(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) -> f36(A,B,C,1 + D,E + S,1 + F,G,H,I,J,K,L,M,N,O,P,Q) [9 >= D && 0 >= 1 + R] (?,1)
3. f36(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) -> f36(A,B,C,1 + D,E,F,G + S,1 + H,I,J,K,L,M,N,O,P,Q) [9 >= D] (?,1)
4. f36(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) -> f33(A,B,1 + C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) [D >= 10] (?,1)
5. f33(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) -> f58(A,B,C,D,E,F,G,H,E,F,G,H,1500,S,O,P,Q) [C >= 10] (?,1)
6. f14(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) -> f14(A,1 + B,C,D,E,F,G,H,I,J,K,L,M,N,S,S,Q) [9 >= B] (?,1)
7. f14(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) -> f11(1 + A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) [B >= 10] (?,1)
8. f11(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) -> f33(A,B,0,D,0,0,0,0,I,J,K,L,M,N,O,P,1000) [A >= 10] (?,1)
9. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) -> f11(0,B,C,D,E,F,G,H,I,J,K,L,M,N,0,P,Q) True (1,1)
Signature:
{(f0,17);(f11,17);(f14,17);(f33,17);(f36,17);(f58,17)}
Flow Graph:
[0->{6,7},1->{2,3,4},2->{2,3,4},3->{2,3,4},4->{1,5},5->{},6->{6,7},7->{0,8},8->{1,5},9->{0,8}]
+ Applied Processor:
RestrictVarsProcessor
+ Details:
We removed the arguments [I,J,K,L,M,N,O,P,Q] .
* Step 2: LocalSizeboundsProc WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f11(A,B,C,D,E,F,G,H) -> f14(A,0,C,D,E,F,G,H) [9 >= A] (?,1)
1. f33(A,B,C,D,E,F,G,H) -> f36(A,B,C,0,E,F,G,H) [9 >= C] (?,1)
2. f36(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E + S,1 + F,G,H) [9 >= D && 0 >= 1 + R] (?,1)
3. f36(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E,F,G + S,1 + H) [9 >= D] (?,1)
4. f36(A,B,C,D,E,F,G,H) -> f33(A,B,1 + C,D,E,F,G,H) [D >= 10] (?,1)
5. f33(A,B,C,D,E,F,G,H) -> f58(A,B,C,D,E,F,G,H) [C >= 10] (?,1)
6. f14(A,B,C,D,E,F,G,H) -> f14(A,1 + B,C,D,E,F,G,H) [9 >= B] (?,1)
7. f14(A,B,C,D,E,F,G,H) -> f11(1 + A,B,C,D,E,F,G,H) [B >= 10] (?,1)
8. f11(A,B,C,D,E,F,G,H) -> f33(A,B,0,D,0,0,0,0) [A >= 10] (?,1)
9. f0(A,B,C,D,E,F,G,H) -> f11(0,B,C,D,E,F,G,H) True (1,1)
Signature:
{(f0,8);(f11,8);(f14,8);(f33,8);(f36,8);(f58,8)}
Flow Graph:
[0->{6,7},1->{2,3,4},2->{2,3,4},3->{2,3,4},4->{1,5},5->{},6->{6,7},7->{0,8},8->{1,5},9->{0,8}]
+ Applied Processor:
LocalSizeboundsProc
+ Details:
LocalSizebounds generated; rvgraph
(<0,0,A>, A, .= 0) (<0,0,B>, 0, .= 0) (<0,0,C>, C, .= 0) (<0,0,D>, D, .= 0) (<0,0,E>, E, .= 0) (<0,0,F>, F, .= 0) (<0,0,G>, G, .= 0) (<0,0,H>, H, .= 0)
(<1,0,A>, A, .= 0) (<1,0,B>, B, .= 0) (<1,0,C>, C, .= 0) (<1,0,D>, 0, .= 0) (<1,0,E>, E, .= 0) (<1,0,F>, F, .= 0) (<1,0,G>, G, .= 0) (<1,0,H>, H, .= 0)
(<2,0,A>, A, .= 0) (<2,0,B>, B, .= 0) (<2,0,C>, C, .= 0) (<2,0,D>, 1 + D, .+ 1) (<2,0,E>, ?, .?) (<2,0,F>, 1 + F, .+ 1) (<2,0,G>, G, .= 0) (<2,0,H>, H, .= 0)
(<3,0,A>, A, .= 0) (<3,0,B>, B, .= 0) (<3,0,C>, C, .= 0) (<3,0,D>, 1 + D, .+ 1) (<3,0,E>, E, .= 0) (<3,0,F>, F, .= 0) (<3,0,G>, ?, .?) (<3,0,H>, 1 + H, .+ 1)
(<4,0,A>, A, .= 0) (<4,0,B>, B, .= 0) (<4,0,C>, 1 + C, .+ 1) (<4,0,D>, D, .= 0) (<4,0,E>, E, .= 0) (<4,0,F>, F, .= 0) (<4,0,G>, G, .= 0) (<4,0,H>, H, .= 0)
(<5,0,A>, A, .= 0) (<5,0,B>, B, .= 0) (<5,0,C>, C, .= 0) (<5,0,D>, D, .= 0) (<5,0,E>, E, .= 0) (<5,0,F>, F, .= 0) (<5,0,G>, G, .= 0) (<5,0,H>, H, .= 0)
(<6,0,A>, A, .= 0) (<6,0,B>, 1 + B, .+ 1) (<6,0,C>, C, .= 0) (<6,0,D>, D, .= 0) (<6,0,E>, E, .= 0) (<6,0,F>, F, .= 0) (<6,0,G>, G, .= 0) (<6,0,H>, H, .= 0)
(<7,0,A>, 1 + A, .+ 1) (<7,0,B>, B, .= 0) (<7,0,C>, C, .= 0) (<7,0,D>, D, .= 0) (<7,0,E>, E, .= 0) (<7,0,F>, F, .= 0) (<7,0,G>, G, .= 0) (<7,0,H>, H, .= 0)
(<8,0,A>, A, .= 0) (<8,0,B>, B, .= 0) (<8,0,C>, 0, .= 0) (<8,0,D>, D, .= 0) (<8,0,E>, 0, .= 0) (<8,0,F>, 0, .= 0) (<8,0,G>, 0, .= 0) (<8,0,H>, 0, .= 0)
(<9,0,A>, 0, .= 0) (<9,0,B>, B, .= 0) (<9,0,C>, C, .= 0) (<9,0,D>, D, .= 0) (<9,0,E>, E, .= 0) (<9,0,F>, F, .= 0) (<9,0,G>, G, .= 0) (<9,0,H>, H, .= 0)
* Step 3: SizeboundsProc WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f11(A,B,C,D,E,F,G,H) -> f14(A,0,C,D,E,F,G,H) [9 >= A] (?,1)
1. f33(A,B,C,D,E,F,G,H) -> f36(A,B,C,0,E,F,G,H) [9 >= C] (?,1)
2. f36(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E + S,1 + F,G,H) [9 >= D && 0 >= 1 + R] (?,1)
3. f36(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E,F,G + S,1 + H) [9 >= D] (?,1)
4. f36(A,B,C,D,E,F,G,H) -> f33(A,B,1 + C,D,E,F,G,H) [D >= 10] (?,1)
5. f33(A,B,C,D,E,F,G,H) -> f58(A,B,C,D,E,F,G,H) [C >= 10] (?,1)
6. f14(A,B,C,D,E,F,G,H) -> f14(A,1 + B,C,D,E,F,G,H) [9 >= B] (?,1)
7. f14(A,B,C,D,E,F,G,H) -> f11(1 + A,B,C,D,E,F,G,H) [B >= 10] (?,1)
8. f11(A,B,C,D,E,F,G,H) -> f33(A,B,0,D,0,0,0,0) [A >= 10] (?,1)
9. f0(A,B,C,D,E,F,G,H) -> f11(0,B,C,D,E,F,G,H) True (1,1)
Signature:
{(f0,8);(f11,8);(f14,8);(f33,8);(f36,8);(f58,8)}
Flow Graph:
[0->{6,7},1->{2,3,4},2->{2,3,4},3->{2,3,4},4->{1,5},5->{},6->{6,7},7->{0,8},8->{1,5},9->{0,8}]
Sizebounds:
(<0,0,A>, ?) (<0,0,B>, ?) (<0,0,C>, ?) (<0,0,D>, ?) (<0,0,E>, ?) (<0,0,F>, ?) (<0,0,G>, ?) (<0,0,H>, ?)
(<1,0,A>, ?) (<1,0,B>, ?) (<1,0,C>, ?) (<1,0,D>, ?) (<1,0,E>, ?) (<1,0,F>, ?) (<1,0,G>, ?) (<1,0,H>, ?)
(<2,0,A>, ?) (<2,0,B>, ?) (<2,0,C>, ?) (<2,0,D>, ?) (<2,0,E>, ?) (<2,0,F>, ?) (<2,0,G>, ?) (<2,0,H>, ?)
(<3,0,A>, ?) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, ?) (<3,0,E>, ?) (<3,0,F>, ?) (<3,0,G>, ?) (<3,0,H>, ?)
(<4,0,A>, ?) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, ?) (<4,0,E>, ?) (<4,0,F>, ?) (<4,0,G>, ?) (<4,0,H>, ?)
(<5,0,A>, ?) (<5,0,B>, ?) (<5,0,C>, ?) (<5,0,D>, ?) (<5,0,E>, ?) (<5,0,F>, ?) (<5,0,G>, ?) (<5,0,H>, ?)
(<6,0,A>, ?) (<6,0,B>, ?) (<6,0,C>, ?) (<6,0,D>, ?) (<6,0,E>, ?) (<6,0,F>, ?) (<6,0,G>, ?) (<6,0,H>, ?)
(<7,0,A>, ?) (<7,0,B>, ?) (<7,0,C>, ?) (<7,0,D>, ?) (<7,0,E>, ?) (<7,0,F>, ?) (<7,0,G>, ?) (<7,0,H>, ?)
(<8,0,A>, ?) (<8,0,B>, ?) (<8,0,C>, ?) (<8,0,D>, ?) (<8,0,E>, ?) (<8,0,F>, ?) (<8,0,G>, ?) (<8,0,H>, ?)
(<9,0,A>, ?) (<9,0,B>, ?) (<9,0,C>, ?) (<9,0,D>, ?) (<9,0,E>, ?) (<9,0,F>, ?) (<9,0,G>, ?) (<9,0,H>, ?)
+ Applied Processor:
SizeboundsProc
+ Details:
Sizebounds computed:
(<0,0,A>, 9) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<0,0,F>, F) (<0,0,G>, G) (<0,0,H>, H)
(<1,0,A>, ?) (<1,0,B>, ?) (<1,0,C>, 9) (<1,0,D>, 0) (<1,0,E>, ?) (<1,0,F>, ?) (<1,0,G>, ?) (<1,0,H>, ?)
(<2,0,A>, ?) (<2,0,B>, ?) (<2,0,C>, ?) (<2,0,D>, 10) (<2,0,E>, ?) (<2,0,F>, ?) (<2,0,G>, ?) (<2,0,H>, ?)
(<3,0,A>, ?) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 10) (<3,0,E>, ?) (<3,0,F>, ?) (<3,0,G>, ?) (<3,0,H>, ?)
(<4,0,A>, ?) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, 10) (<4,0,E>, ?) (<4,0,F>, ?) (<4,0,G>, ?) (<4,0,H>, ?)
(<5,0,A>, ?) (<5,0,B>, ?) (<5,0,C>, ?) (<5,0,D>, 10 + D) (<5,0,E>, ?) (<5,0,F>, ?) (<5,0,G>, ?) (<5,0,H>, ?)
(<6,0,A>, 9) (<6,0,B>, 10) (<6,0,C>, C) (<6,0,D>, D) (<6,0,E>, E) (<6,0,F>, F) (<6,0,G>, G) (<6,0,H>, H)
(<7,0,A>, 9) (<7,0,B>, 10) (<7,0,C>, C) (<7,0,D>, D) (<7,0,E>, E) (<7,0,F>, F) (<7,0,G>, G) (<7,0,H>, H)
(<8,0,A>, 9) (<8,0,B>, 10 + B) (<8,0,C>, 0) (<8,0,D>, D) (<8,0,E>, 0) (<8,0,F>, 0) (<8,0,G>, 0) (<8,0,H>, 0)
(<9,0,A>, 0) (<9,0,B>, B) (<9,0,C>, C) (<9,0,D>, D) (<9,0,E>, E) (<9,0,F>, F) (<9,0,G>, G) (<9,0,H>, H)
* Step 4: UnsatPaths WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f11(A,B,C,D,E,F,G,H) -> f14(A,0,C,D,E,F,G,H) [9 >= A] (?,1)
1. f33(A,B,C,D,E,F,G,H) -> f36(A,B,C,0,E,F,G,H) [9 >= C] (?,1)
2. f36(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E + S,1 + F,G,H) [9 >= D && 0 >= 1 + R] (?,1)
3. f36(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E,F,G + S,1 + H) [9 >= D] (?,1)
4. f36(A,B,C,D,E,F,G,H) -> f33(A,B,1 + C,D,E,F,G,H) [D >= 10] (?,1)
5. f33(A,B,C,D,E,F,G,H) -> f58(A,B,C,D,E,F,G,H) [C >= 10] (?,1)
6. f14(A,B,C,D,E,F,G,H) -> f14(A,1 + B,C,D,E,F,G,H) [9 >= B] (?,1)
7. f14(A,B,C,D,E,F,G,H) -> f11(1 + A,B,C,D,E,F,G,H) [B >= 10] (?,1)
8. f11(A,B,C,D,E,F,G,H) -> f33(A,B,0,D,0,0,0,0) [A >= 10] (?,1)
9. f0(A,B,C,D,E,F,G,H) -> f11(0,B,C,D,E,F,G,H) True (1,1)
Signature:
{(f0,8);(f11,8);(f14,8);(f33,8);(f36,8);(f58,8)}
Flow Graph:
[0->{6,7},1->{2,3,4},2->{2,3,4},3->{2,3,4},4->{1,5},5->{},6->{6,7},7->{0,8},8->{1,5},9->{0,8}]
Sizebounds:
(<0,0,A>, 9) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<0,0,F>, F) (<0,0,G>, G) (<0,0,H>, H)
(<1,0,A>, ?) (<1,0,B>, ?) (<1,0,C>, 9) (<1,0,D>, 0) (<1,0,E>, ?) (<1,0,F>, ?) (<1,0,G>, ?) (<1,0,H>, ?)
(<2,0,A>, ?) (<2,0,B>, ?) (<2,0,C>, ?) (<2,0,D>, 10) (<2,0,E>, ?) (<2,0,F>, ?) (<2,0,G>, ?) (<2,0,H>, ?)
(<3,0,A>, ?) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 10) (<3,0,E>, ?) (<3,0,F>, ?) (<3,0,G>, ?) (<3,0,H>, ?)
(<4,0,A>, ?) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, 10) (<4,0,E>, ?) (<4,0,F>, ?) (<4,0,G>, ?) (<4,0,H>, ?)
(<5,0,A>, ?) (<5,0,B>, ?) (<5,0,C>, ?) (<5,0,D>, 10 + D) (<5,0,E>, ?) (<5,0,F>, ?) (<5,0,G>, ?) (<5,0,H>, ?)
(<6,0,A>, 9) (<6,0,B>, 10) (<6,0,C>, C) (<6,0,D>, D) (<6,0,E>, E) (<6,0,F>, F) (<6,0,G>, G) (<6,0,H>, H)
(<7,0,A>, 9) (<7,0,B>, 10) (<7,0,C>, C) (<7,0,D>, D) (<7,0,E>, E) (<7,0,F>, F) (<7,0,G>, G) (<7,0,H>, H)
(<8,0,A>, 9) (<8,0,B>, 10 + B) (<8,0,C>, 0) (<8,0,D>, D) (<8,0,E>, 0) (<8,0,F>, 0) (<8,0,G>, 0) (<8,0,H>, 0)
(<9,0,A>, 0) (<9,0,B>, B) (<9,0,C>, C) (<9,0,D>, D) (<9,0,E>, E) (<9,0,F>, F) (<9,0,G>, G) (<9,0,H>, H)
+ Applied Processor:
UnsatPaths
+ Details:
We remove following edges from the transition graph: [(0,7),(1,4),(8,5),(9,8)]
* Step 5: LeafRules WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f11(A,B,C,D,E,F,G,H) -> f14(A,0,C,D,E,F,G,H) [9 >= A] (?,1)
1. f33(A,B,C,D,E,F,G,H) -> f36(A,B,C,0,E,F,G,H) [9 >= C] (?,1)
2. f36(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E + S,1 + F,G,H) [9 >= D && 0 >= 1 + R] (?,1)
3. f36(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E,F,G + S,1 + H) [9 >= D] (?,1)
4. f36(A,B,C,D,E,F,G,H) -> f33(A,B,1 + C,D,E,F,G,H) [D >= 10] (?,1)
5. f33(A,B,C,D,E,F,G,H) -> f58(A,B,C,D,E,F,G,H) [C >= 10] (?,1)
6. f14(A,B,C,D,E,F,G,H) -> f14(A,1 + B,C,D,E,F,G,H) [9 >= B] (?,1)
7. f14(A,B,C,D,E,F,G,H) -> f11(1 + A,B,C,D,E,F,G,H) [B >= 10] (?,1)
8. f11(A,B,C,D,E,F,G,H) -> f33(A,B,0,D,0,0,0,0) [A >= 10] (?,1)
9. f0(A,B,C,D,E,F,G,H) -> f11(0,B,C,D,E,F,G,H) True (1,1)
Signature:
{(f0,8);(f11,8);(f14,8);(f33,8);(f36,8);(f58,8)}
Flow Graph:
[0->{6},1->{2,3},2->{2,3,4},3->{2,3,4},4->{1,5},5->{},6->{6,7},7->{0,8},8->{1},9->{0}]
Sizebounds:
(<0,0,A>, 9) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<0,0,F>, F) (<0,0,G>, G) (<0,0,H>, H)
(<1,0,A>, ?) (<1,0,B>, ?) (<1,0,C>, 9) (<1,0,D>, 0) (<1,0,E>, ?) (<1,0,F>, ?) (<1,0,G>, ?) (<1,0,H>, ?)
(<2,0,A>, ?) (<2,0,B>, ?) (<2,0,C>, ?) (<2,0,D>, 10) (<2,0,E>, ?) (<2,0,F>, ?) (<2,0,G>, ?) (<2,0,H>, ?)
(<3,0,A>, ?) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 10) (<3,0,E>, ?) (<3,0,F>, ?) (<3,0,G>, ?) (<3,0,H>, ?)
(<4,0,A>, ?) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, 10) (<4,0,E>, ?) (<4,0,F>, ?) (<4,0,G>, ?) (<4,0,H>, ?)
(<5,0,A>, ?) (<5,0,B>, ?) (<5,0,C>, ?) (<5,0,D>, 10 + D) (<5,0,E>, ?) (<5,0,F>, ?) (<5,0,G>, ?) (<5,0,H>, ?)
(<6,0,A>, 9) (<6,0,B>, 10) (<6,0,C>, C) (<6,0,D>, D) (<6,0,E>, E) (<6,0,F>, F) (<6,0,G>, G) (<6,0,H>, H)
(<7,0,A>, 9) (<7,0,B>, 10) (<7,0,C>, C) (<7,0,D>, D) (<7,0,E>, E) (<7,0,F>, F) (<7,0,G>, G) (<7,0,H>, H)
(<8,0,A>, 9) (<8,0,B>, 10 + B) (<8,0,C>, 0) (<8,0,D>, D) (<8,0,E>, 0) (<8,0,F>, 0) (<8,0,G>, 0) (<8,0,H>, 0)
(<9,0,A>, 0) (<9,0,B>, B) (<9,0,C>, C) (<9,0,D>, D) (<9,0,E>, E) (<9,0,F>, F) (<9,0,G>, G) (<9,0,H>, H)
+ Applied Processor:
LeafRules
+ Details:
The following transitions are estimated by its predecessors and are removed [5]
* Step 6: PolyRank WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f11(A,B,C,D,E,F,G,H) -> f14(A,0,C,D,E,F,G,H) [9 >= A] (?,1)
1. f33(A,B,C,D,E,F,G,H) -> f36(A,B,C,0,E,F,G,H) [9 >= C] (?,1)
2. f36(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E + S,1 + F,G,H) [9 >= D && 0 >= 1 + R] (?,1)
3. f36(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E,F,G + S,1 + H) [9 >= D] (?,1)
4. f36(A,B,C,D,E,F,G,H) -> f33(A,B,1 + C,D,E,F,G,H) [D >= 10] (?,1)
6. f14(A,B,C,D,E,F,G,H) -> f14(A,1 + B,C,D,E,F,G,H) [9 >= B] (?,1)
7. f14(A,B,C,D,E,F,G,H) -> f11(1 + A,B,C,D,E,F,G,H) [B >= 10] (?,1)
8. f11(A,B,C,D,E,F,G,H) -> f33(A,B,0,D,0,0,0,0) [A >= 10] (?,1)
9. f0(A,B,C,D,E,F,G,H) -> f11(0,B,C,D,E,F,G,H) True (1,1)
Signature:
{(f0,8);(f11,8);(f14,8);(f33,8);(f36,8);(f58,8)}
Flow Graph:
[0->{6},1->{2,3},2->{2,3,4},3->{2,3,4},4->{1},6->{6,7},7->{0,8},8->{1},9->{0}]
Sizebounds:
(<0,0,A>, 9) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<0,0,F>, F) (<0,0,G>, G) (<0,0,H>, H)
(<1,0,A>, ?) (<1,0,B>, ?) (<1,0,C>, 9) (<1,0,D>, 0) (<1,0,E>, ?) (<1,0,F>, ?) (<1,0,G>, ?) (<1,0,H>, ?)
(<2,0,A>, ?) (<2,0,B>, ?) (<2,0,C>, ?) (<2,0,D>, 10) (<2,0,E>, ?) (<2,0,F>, ?) (<2,0,G>, ?) (<2,0,H>, ?)
(<3,0,A>, ?) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 10) (<3,0,E>, ?) (<3,0,F>, ?) (<3,0,G>, ?) (<3,0,H>, ?)
(<4,0,A>, ?) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, 10) (<4,0,E>, ?) (<4,0,F>, ?) (<4,0,G>, ?) (<4,0,H>, ?)
(<6,0,A>, 9) (<6,0,B>, 10) (<6,0,C>, C) (<6,0,D>, D) (<6,0,E>, E) (<6,0,F>, F) (<6,0,G>, G) (<6,0,H>, H)
(<7,0,A>, 9) (<7,0,B>, 10) (<7,0,C>, C) (<7,0,D>, D) (<7,0,E>, E) (<7,0,F>, F) (<7,0,G>, G) (<7,0,H>, H)
(<8,0,A>, 9) (<8,0,B>, 10 + B) (<8,0,C>, 0) (<8,0,D>, D) (<8,0,E>, 0) (<8,0,F>, 0) (<8,0,G>, 0) (<8,0,H>, 0)
(<9,0,A>, 0) (<9,0,B>, B) (<9,0,C>, C) (<9,0,D>, D) (<9,0,E>, E) (<9,0,F>, F) (<9,0,G>, G) (<9,0,H>, H)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f0) = 1
p(f11) = 1
p(f14) = 1
p(f33) = 0
p(f36) = 0
The following rules are strictly oriented:
[A >= 10] ==>
f11(A,B,C,D,E,F,G,H) = 1
> 0
= f33(A,B,0,D,0,0,0,0)
The following rules are weakly oriented:
[9 >= A] ==>
f11(A,B,C,D,E,F,G,H) = 1
>= 1
= f14(A,0,C,D,E,F,G,H)
[9 >= C] ==>
f33(A,B,C,D,E,F,G,H) = 0
>= 0
= f36(A,B,C,0,E,F,G,H)
[9 >= D && 0 >= 1 + R] ==>
f36(A,B,C,D,E,F,G,H) = 0
>= 0
= f36(A,B,C,1 + D,E + S,1 + F,G,H)
[9 >= D] ==>
f36(A,B,C,D,E,F,G,H) = 0
>= 0
= f36(A,B,C,1 + D,E,F,G + S,1 + H)
[D >= 10] ==>
f36(A,B,C,D,E,F,G,H) = 0
>= 0
= f33(A,B,1 + C,D,E,F,G,H)
[9 >= B] ==>
f14(A,B,C,D,E,F,G,H) = 1
>= 1
= f14(A,1 + B,C,D,E,F,G,H)
[B >= 10] ==>
f14(A,B,C,D,E,F,G,H) = 1
>= 1
= f11(1 + A,B,C,D,E,F,G,H)
True ==>
f0(A,B,C,D,E,F,G,H) = 1
>= 1
= f11(0,B,C,D,E,F,G,H)
* Step 7: PolyRank WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f11(A,B,C,D,E,F,G,H) -> f14(A,0,C,D,E,F,G,H) [9 >= A] (?,1)
1. f33(A,B,C,D,E,F,G,H) -> f36(A,B,C,0,E,F,G,H) [9 >= C] (?,1)
2. f36(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E + S,1 + F,G,H) [9 >= D && 0 >= 1 + R] (?,1)
3. f36(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E,F,G + S,1 + H) [9 >= D] (?,1)
4. f36(A,B,C,D,E,F,G,H) -> f33(A,B,1 + C,D,E,F,G,H) [D >= 10] (?,1)
6. f14(A,B,C,D,E,F,G,H) -> f14(A,1 + B,C,D,E,F,G,H) [9 >= B] (?,1)
7. f14(A,B,C,D,E,F,G,H) -> f11(1 + A,B,C,D,E,F,G,H) [B >= 10] (?,1)
8. f11(A,B,C,D,E,F,G,H) -> f33(A,B,0,D,0,0,0,0) [A >= 10] (1,1)
9. f0(A,B,C,D,E,F,G,H) -> f11(0,B,C,D,E,F,G,H) True (1,1)
Signature:
{(f0,8);(f11,8);(f14,8);(f33,8);(f36,8);(f58,8)}
Flow Graph:
[0->{6},1->{2,3},2->{2,3,4},3->{2,3,4},4->{1},6->{6,7},7->{0,8},8->{1},9->{0}]
Sizebounds:
(<0,0,A>, 9) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<0,0,F>, F) (<0,0,G>, G) (<0,0,H>, H)
(<1,0,A>, ?) (<1,0,B>, ?) (<1,0,C>, 9) (<1,0,D>, 0) (<1,0,E>, ?) (<1,0,F>, ?) (<1,0,G>, ?) (<1,0,H>, ?)
(<2,0,A>, ?) (<2,0,B>, ?) (<2,0,C>, ?) (<2,0,D>, 10) (<2,0,E>, ?) (<2,0,F>, ?) (<2,0,G>, ?) (<2,0,H>, ?)
(<3,0,A>, ?) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 10) (<3,0,E>, ?) (<3,0,F>, ?) (<3,0,G>, ?) (<3,0,H>, ?)
(<4,0,A>, ?) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, 10) (<4,0,E>, ?) (<4,0,F>, ?) (<4,0,G>, ?) (<4,0,H>, ?)
(<6,0,A>, 9) (<6,0,B>, 10) (<6,0,C>, C) (<6,0,D>, D) (<6,0,E>, E) (<6,0,F>, F) (<6,0,G>, G) (<6,0,H>, H)
(<7,0,A>, 9) (<7,0,B>, 10) (<7,0,C>, C) (<7,0,D>, D) (<7,0,E>, E) (<7,0,F>, F) (<7,0,G>, G) (<7,0,H>, H)
(<8,0,A>, 9) (<8,0,B>, 10 + B) (<8,0,C>, 0) (<8,0,D>, D) (<8,0,E>, 0) (<8,0,F>, 0) (<8,0,G>, 0) (<8,0,H>, 0)
(<9,0,A>, 0) (<9,0,B>, B) (<9,0,C>, C) (<9,0,D>, D) (<9,0,E>, E) (<9,0,F>, F) (<9,0,G>, G) (<9,0,H>, H)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f0) = 10
p(f11) = 10
p(f14) = 10
p(f33) = 10 + -1*x3
p(f36) = 9 + -1*x3
The following rules are strictly oriented:
[9 >= C] ==>
f33(A,B,C,D,E,F,G,H) = 10 + -1*C
> 9 + -1*C
= f36(A,B,C,0,E,F,G,H)
The following rules are weakly oriented:
[9 >= A] ==>
f11(A,B,C,D,E,F,G,H) = 10
>= 10
= f14(A,0,C,D,E,F,G,H)
[9 >= D && 0 >= 1 + R] ==>
f36(A,B,C,D,E,F,G,H) = 9 + -1*C
>= 9 + -1*C
= f36(A,B,C,1 + D,E + S,1 + F,G,H)
[9 >= D] ==>
f36(A,B,C,D,E,F,G,H) = 9 + -1*C
>= 9 + -1*C
= f36(A,B,C,1 + D,E,F,G + S,1 + H)
[D >= 10] ==>
f36(A,B,C,D,E,F,G,H) = 9 + -1*C
>= 9 + -1*C
= f33(A,B,1 + C,D,E,F,G,H)
[9 >= B] ==>
f14(A,B,C,D,E,F,G,H) = 10
>= 10
= f14(A,1 + B,C,D,E,F,G,H)
[B >= 10] ==>
f14(A,B,C,D,E,F,G,H) = 10
>= 10
= f11(1 + A,B,C,D,E,F,G,H)
[A >= 10] ==>
f11(A,B,C,D,E,F,G,H) = 10
>= 10
= f33(A,B,0,D,0,0,0,0)
True ==>
f0(A,B,C,D,E,F,G,H) = 10
>= 10
= f11(0,B,C,D,E,F,G,H)
* Step 8: PolyRank WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f11(A,B,C,D,E,F,G,H) -> f14(A,0,C,D,E,F,G,H) [9 >= A] (?,1)
1. f33(A,B,C,D,E,F,G,H) -> f36(A,B,C,0,E,F,G,H) [9 >= C] (10,1)
2. f36(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E + S,1 + F,G,H) [9 >= D && 0 >= 1 + R] (?,1)
3. f36(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E,F,G + S,1 + H) [9 >= D] (?,1)
4. f36(A,B,C,D,E,F,G,H) -> f33(A,B,1 + C,D,E,F,G,H) [D >= 10] (?,1)
6. f14(A,B,C,D,E,F,G,H) -> f14(A,1 + B,C,D,E,F,G,H) [9 >= B] (?,1)
7. f14(A,B,C,D,E,F,G,H) -> f11(1 + A,B,C,D,E,F,G,H) [B >= 10] (?,1)
8. f11(A,B,C,D,E,F,G,H) -> f33(A,B,0,D,0,0,0,0) [A >= 10] (1,1)
9. f0(A,B,C,D,E,F,G,H) -> f11(0,B,C,D,E,F,G,H) True (1,1)
Signature:
{(f0,8);(f11,8);(f14,8);(f33,8);(f36,8);(f58,8)}
Flow Graph:
[0->{6},1->{2,3},2->{2,3,4},3->{2,3,4},4->{1},6->{6,7},7->{0,8},8->{1},9->{0}]
Sizebounds:
(<0,0,A>, 9) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<0,0,F>, F) (<0,0,G>, G) (<0,0,H>, H)
(<1,0,A>, ?) (<1,0,B>, ?) (<1,0,C>, 9) (<1,0,D>, 0) (<1,0,E>, ?) (<1,0,F>, ?) (<1,0,G>, ?) (<1,0,H>, ?)
(<2,0,A>, ?) (<2,0,B>, ?) (<2,0,C>, ?) (<2,0,D>, 10) (<2,0,E>, ?) (<2,0,F>, ?) (<2,0,G>, ?) (<2,0,H>, ?)
(<3,0,A>, ?) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 10) (<3,0,E>, ?) (<3,0,F>, ?) (<3,0,G>, ?) (<3,0,H>, ?)
(<4,0,A>, ?) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, 10) (<4,0,E>, ?) (<4,0,F>, ?) (<4,0,G>, ?) (<4,0,H>, ?)
(<6,0,A>, 9) (<6,0,B>, 10) (<6,0,C>, C) (<6,0,D>, D) (<6,0,E>, E) (<6,0,F>, F) (<6,0,G>, G) (<6,0,H>, H)
(<7,0,A>, 9) (<7,0,B>, 10) (<7,0,C>, C) (<7,0,D>, D) (<7,0,E>, E) (<7,0,F>, F) (<7,0,G>, G) (<7,0,H>, H)
(<8,0,A>, 9) (<8,0,B>, 10 + B) (<8,0,C>, 0) (<8,0,D>, D) (<8,0,E>, 0) (<8,0,F>, 0) (<8,0,G>, 0) (<8,0,H>, 0)
(<9,0,A>, 0) (<9,0,B>, B) (<9,0,C>, C) (<9,0,D>, D) (<9,0,E>, E) (<9,0,F>, F) (<9,0,G>, G) (<9,0,H>, H)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f0) = 10
p(f11) = 10 + -1*x1
p(f14) = 9 + -1*x1
p(f33) = 10 + -1*x1
p(f36) = 10 + -1*x1
The following rules are strictly oriented:
[9 >= A] ==>
f11(A,B,C,D,E,F,G,H) = 10 + -1*A
> 9 + -1*A
= f14(A,0,C,D,E,F,G,H)
The following rules are weakly oriented:
[9 >= C] ==>
f33(A,B,C,D,E,F,G,H) = 10 + -1*A
>= 10 + -1*A
= f36(A,B,C,0,E,F,G,H)
[9 >= D && 0 >= 1 + R] ==>
f36(A,B,C,D,E,F,G,H) = 10 + -1*A
>= 10 + -1*A
= f36(A,B,C,1 + D,E + S,1 + F,G,H)
[9 >= D] ==>
f36(A,B,C,D,E,F,G,H) = 10 + -1*A
>= 10 + -1*A
= f36(A,B,C,1 + D,E,F,G + S,1 + H)
[D >= 10] ==>
f36(A,B,C,D,E,F,G,H) = 10 + -1*A
>= 10 + -1*A
= f33(A,B,1 + C,D,E,F,G,H)
[9 >= B] ==>
f14(A,B,C,D,E,F,G,H) = 9 + -1*A
>= 9 + -1*A
= f14(A,1 + B,C,D,E,F,G,H)
[B >= 10] ==>
f14(A,B,C,D,E,F,G,H) = 9 + -1*A
>= 9 + -1*A
= f11(1 + A,B,C,D,E,F,G,H)
[A >= 10] ==>
f11(A,B,C,D,E,F,G,H) = 10 + -1*A
>= 10 + -1*A
= f33(A,B,0,D,0,0,0,0)
True ==>
f0(A,B,C,D,E,F,G,H) = 10
>= 10
= f11(0,B,C,D,E,F,G,H)
* Step 9: PolyRank WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f11(A,B,C,D,E,F,G,H) -> f14(A,0,C,D,E,F,G,H) [9 >= A] (10,1)
1. f33(A,B,C,D,E,F,G,H) -> f36(A,B,C,0,E,F,G,H) [9 >= C] (10,1)
2. f36(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E + S,1 + F,G,H) [9 >= D && 0 >= 1 + R] (?,1)
3. f36(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E,F,G + S,1 + H) [9 >= D] (?,1)
4. f36(A,B,C,D,E,F,G,H) -> f33(A,B,1 + C,D,E,F,G,H) [D >= 10] (?,1)
6. f14(A,B,C,D,E,F,G,H) -> f14(A,1 + B,C,D,E,F,G,H) [9 >= B] (?,1)
7. f14(A,B,C,D,E,F,G,H) -> f11(1 + A,B,C,D,E,F,G,H) [B >= 10] (?,1)
8. f11(A,B,C,D,E,F,G,H) -> f33(A,B,0,D,0,0,0,0) [A >= 10] (1,1)
9. f0(A,B,C,D,E,F,G,H) -> f11(0,B,C,D,E,F,G,H) True (1,1)
Signature:
{(f0,8);(f11,8);(f14,8);(f33,8);(f36,8);(f58,8)}
Flow Graph:
[0->{6},1->{2,3},2->{2,3,4},3->{2,3,4},4->{1},6->{6,7},7->{0,8},8->{1},9->{0}]
Sizebounds:
(<0,0,A>, 9) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<0,0,F>, F) (<0,0,G>, G) (<0,0,H>, H)
(<1,0,A>, ?) (<1,0,B>, ?) (<1,0,C>, 9) (<1,0,D>, 0) (<1,0,E>, ?) (<1,0,F>, ?) (<1,0,G>, ?) (<1,0,H>, ?)
(<2,0,A>, ?) (<2,0,B>, ?) (<2,0,C>, ?) (<2,0,D>, 10) (<2,0,E>, ?) (<2,0,F>, ?) (<2,0,G>, ?) (<2,0,H>, ?)
(<3,0,A>, ?) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 10) (<3,0,E>, ?) (<3,0,F>, ?) (<3,0,G>, ?) (<3,0,H>, ?)
(<4,0,A>, ?) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, 10) (<4,0,E>, ?) (<4,0,F>, ?) (<4,0,G>, ?) (<4,0,H>, ?)
(<6,0,A>, 9) (<6,0,B>, 10) (<6,0,C>, C) (<6,0,D>, D) (<6,0,E>, E) (<6,0,F>, F) (<6,0,G>, G) (<6,0,H>, H)
(<7,0,A>, 9) (<7,0,B>, 10) (<7,0,C>, C) (<7,0,D>, D) (<7,0,E>, E) (<7,0,F>, F) (<7,0,G>, G) (<7,0,H>, H)
(<8,0,A>, 9) (<8,0,B>, 10 + B) (<8,0,C>, 0) (<8,0,D>, D) (<8,0,E>, 0) (<8,0,F>, 0) (<8,0,G>, 0) (<8,0,H>, 0)
(<9,0,A>, 0) (<9,0,B>, B) (<9,0,C>, C) (<9,0,D>, D) (<9,0,E>, E) (<9,0,F>, F) (<9,0,G>, G) (<9,0,H>, H)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [7,6], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f11) = 0
p(f14) = 1
The following rules are strictly oriented:
[B >= 10] ==>
f14(A,B,C,D,E,F,G,H) = 1
> 0
= f11(1 + A,B,C,D,E,F,G,H)
The following rules are weakly oriented:
[9 >= B] ==>
f14(A,B,C,D,E,F,G,H) = 1
>= 1
= f14(A,1 + B,C,D,E,F,G,H)
We use the following global sizebounds:
(<0,0,A>, 9) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<0,0,F>, F) (<0,0,G>, G) (<0,0,H>, H)
(<1,0,A>, ?) (<1,0,B>, ?) (<1,0,C>, 9) (<1,0,D>, 0) (<1,0,E>, ?) (<1,0,F>, ?) (<1,0,G>, ?) (<1,0,H>, ?)
(<2,0,A>, ?) (<2,0,B>, ?) (<2,0,C>, ?) (<2,0,D>, 10) (<2,0,E>, ?) (<2,0,F>, ?) (<2,0,G>, ?) (<2,0,H>, ?)
(<3,0,A>, ?) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 10) (<3,0,E>, ?) (<3,0,F>, ?) (<3,0,G>, ?) (<3,0,H>, ?)
(<4,0,A>, ?) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, 10) (<4,0,E>, ?) (<4,0,F>, ?) (<4,0,G>, ?) (<4,0,H>, ?)
(<6,0,A>, 9) (<6,0,B>, 10) (<6,0,C>, C) (<6,0,D>, D) (<6,0,E>, E) (<6,0,F>, F) (<6,0,G>, G) (<6,0,H>, H)
(<7,0,A>, 9) (<7,0,B>, 10) (<7,0,C>, C) (<7,0,D>, D) (<7,0,E>, E) (<7,0,F>, F) (<7,0,G>, G) (<7,0,H>, H)
(<8,0,A>, 9) (<8,0,B>, 10 + B) (<8,0,C>, 0) (<8,0,D>, D) (<8,0,E>, 0) (<8,0,F>, 0) (<8,0,G>, 0) (<8,0,H>, 0)
(<9,0,A>, 0) (<9,0,B>, B) (<9,0,C>, C) (<9,0,D>, D) (<9,0,E>, E) (<9,0,F>, F) (<9,0,G>, G) (<9,0,H>, H)
* Step 10: PolyRank WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f11(A,B,C,D,E,F,G,H) -> f14(A,0,C,D,E,F,G,H) [9 >= A] (10,1)
1. f33(A,B,C,D,E,F,G,H) -> f36(A,B,C,0,E,F,G,H) [9 >= C] (10,1)
2. f36(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E + S,1 + F,G,H) [9 >= D && 0 >= 1 + R] (?,1)
3. f36(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E,F,G + S,1 + H) [9 >= D] (?,1)
4. f36(A,B,C,D,E,F,G,H) -> f33(A,B,1 + C,D,E,F,G,H) [D >= 10] (?,1)
6. f14(A,B,C,D,E,F,G,H) -> f14(A,1 + B,C,D,E,F,G,H) [9 >= B] (?,1)
7. f14(A,B,C,D,E,F,G,H) -> f11(1 + A,B,C,D,E,F,G,H) [B >= 10] (10,1)
8. f11(A,B,C,D,E,F,G,H) -> f33(A,B,0,D,0,0,0,0) [A >= 10] (1,1)
9. f0(A,B,C,D,E,F,G,H) -> f11(0,B,C,D,E,F,G,H) True (1,1)
Signature:
{(f0,8);(f11,8);(f14,8);(f33,8);(f36,8);(f58,8)}
Flow Graph:
[0->{6},1->{2,3},2->{2,3,4},3->{2,3,4},4->{1},6->{6,7},7->{0,8},8->{1},9->{0}]
Sizebounds:
(<0,0,A>, 9) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<0,0,F>, F) (<0,0,G>, G) (<0,0,H>, H)
(<1,0,A>, ?) (<1,0,B>, ?) (<1,0,C>, 9) (<1,0,D>, 0) (<1,0,E>, ?) (<1,0,F>, ?) (<1,0,G>, ?) (<1,0,H>, ?)
(<2,0,A>, ?) (<2,0,B>, ?) (<2,0,C>, ?) (<2,0,D>, 10) (<2,0,E>, ?) (<2,0,F>, ?) (<2,0,G>, ?) (<2,0,H>, ?)
(<3,0,A>, ?) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 10) (<3,0,E>, ?) (<3,0,F>, ?) (<3,0,G>, ?) (<3,0,H>, ?)
(<4,0,A>, ?) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, 10) (<4,0,E>, ?) (<4,0,F>, ?) (<4,0,G>, ?) (<4,0,H>, ?)
(<6,0,A>, 9) (<6,0,B>, 10) (<6,0,C>, C) (<6,0,D>, D) (<6,0,E>, E) (<6,0,F>, F) (<6,0,G>, G) (<6,0,H>, H)
(<7,0,A>, 9) (<7,0,B>, 10) (<7,0,C>, C) (<7,0,D>, D) (<7,0,E>, E) (<7,0,F>, F) (<7,0,G>, G) (<7,0,H>, H)
(<8,0,A>, 9) (<8,0,B>, 10 + B) (<8,0,C>, 0) (<8,0,D>, D) (<8,0,E>, 0) (<8,0,F>, 0) (<8,0,G>, 0) (<8,0,H>, 0)
(<9,0,A>, 0) (<9,0,B>, B) (<9,0,C>, C) (<9,0,D>, D) (<9,0,E>, E) (<9,0,F>, F) (<9,0,G>, G) (<9,0,H>, H)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [6], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f14) = 10 + -1*x2
The following rules are strictly oriented:
[9 >= B] ==>
f14(A,B,C,D,E,F,G,H) = 10 + -1*B
> 9 + -1*B
= f14(A,1 + B,C,D,E,F,G,H)
The following rules are weakly oriented:
We use the following global sizebounds:
(<0,0,A>, 9) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<0,0,F>, F) (<0,0,G>, G) (<0,0,H>, H)
(<1,0,A>, ?) (<1,0,B>, ?) (<1,0,C>, 9) (<1,0,D>, 0) (<1,0,E>, ?) (<1,0,F>, ?) (<1,0,G>, ?) (<1,0,H>, ?)
(<2,0,A>, ?) (<2,0,B>, ?) (<2,0,C>, ?) (<2,0,D>, 10) (<2,0,E>, ?) (<2,0,F>, ?) (<2,0,G>, ?) (<2,0,H>, ?)
(<3,0,A>, ?) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 10) (<3,0,E>, ?) (<3,0,F>, ?) (<3,0,G>, ?) (<3,0,H>, ?)
(<4,0,A>, ?) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, 10) (<4,0,E>, ?) (<4,0,F>, ?) (<4,0,G>, ?) (<4,0,H>, ?)
(<6,0,A>, 9) (<6,0,B>, 10) (<6,0,C>, C) (<6,0,D>, D) (<6,0,E>, E) (<6,0,F>, F) (<6,0,G>, G) (<6,0,H>, H)
(<7,0,A>, 9) (<7,0,B>, 10) (<7,0,C>, C) (<7,0,D>, D) (<7,0,E>, E) (<7,0,F>, F) (<7,0,G>, G) (<7,0,H>, H)
(<8,0,A>, 9) (<8,0,B>, 10 + B) (<8,0,C>, 0) (<8,0,D>, D) (<8,0,E>, 0) (<8,0,F>, 0) (<8,0,G>, 0) (<8,0,H>, 0)
(<9,0,A>, 0) (<9,0,B>, B) (<9,0,C>, C) (<9,0,D>, D) (<9,0,E>, E) (<9,0,F>, F) (<9,0,G>, G) (<9,0,H>, H)
* Step 11: PolyRank WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f11(A,B,C,D,E,F,G,H) -> f14(A,0,C,D,E,F,G,H) [9 >= A] (10,1)
1. f33(A,B,C,D,E,F,G,H) -> f36(A,B,C,0,E,F,G,H) [9 >= C] (10,1)
2. f36(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E + S,1 + F,G,H) [9 >= D && 0 >= 1 + R] (?,1)
3. f36(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E,F,G + S,1 + H) [9 >= D] (?,1)
4. f36(A,B,C,D,E,F,G,H) -> f33(A,B,1 + C,D,E,F,G,H) [D >= 10] (?,1)
6. f14(A,B,C,D,E,F,G,H) -> f14(A,1 + B,C,D,E,F,G,H) [9 >= B] (100,1)
7. f14(A,B,C,D,E,F,G,H) -> f11(1 + A,B,C,D,E,F,G,H) [B >= 10] (10,1)
8. f11(A,B,C,D,E,F,G,H) -> f33(A,B,0,D,0,0,0,0) [A >= 10] (1,1)
9. f0(A,B,C,D,E,F,G,H) -> f11(0,B,C,D,E,F,G,H) True (1,1)
Signature:
{(f0,8);(f11,8);(f14,8);(f33,8);(f36,8);(f58,8)}
Flow Graph:
[0->{6},1->{2,3},2->{2,3,4},3->{2,3,4},4->{1},6->{6,7},7->{0,8},8->{1},9->{0}]
Sizebounds:
(<0,0,A>, 9) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<0,0,F>, F) (<0,0,G>, G) (<0,0,H>, H)
(<1,0,A>, ?) (<1,0,B>, ?) (<1,0,C>, 9) (<1,0,D>, 0) (<1,0,E>, ?) (<1,0,F>, ?) (<1,0,G>, ?) (<1,0,H>, ?)
(<2,0,A>, ?) (<2,0,B>, ?) (<2,0,C>, ?) (<2,0,D>, 10) (<2,0,E>, ?) (<2,0,F>, ?) (<2,0,G>, ?) (<2,0,H>, ?)
(<3,0,A>, ?) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 10) (<3,0,E>, ?) (<3,0,F>, ?) (<3,0,G>, ?) (<3,0,H>, ?)
(<4,0,A>, ?) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, 10) (<4,0,E>, ?) (<4,0,F>, ?) (<4,0,G>, ?) (<4,0,H>, ?)
(<6,0,A>, 9) (<6,0,B>, 10) (<6,0,C>, C) (<6,0,D>, D) (<6,0,E>, E) (<6,0,F>, F) (<6,0,G>, G) (<6,0,H>, H)
(<7,0,A>, 9) (<7,0,B>, 10) (<7,0,C>, C) (<7,0,D>, D) (<7,0,E>, E) (<7,0,F>, F) (<7,0,G>, G) (<7,0,H>, H)
(<8,0,A>, 9) (<8,0,B>, 10 + B) (<8,0,C>, 0) (<8,0,D>, D) (<8,0,E>, 0) (<8,0,F>, 0) (<8,0,G>, 0) (<8,0,H>, 0)
(<9,0,A>, 0) (<9,0,B>, B) (<9,0,C>, C) (<9,0,D>, D) (<9,0,E>, E) (<9,0,F>, F) (<9,0,G>, G) (<9,0,H>, H)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [4,2,3], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f33) = 0
p(f36) = 1
The following rules are strictly oriented:
[D >= 10] ==>
f36(A,B,C,D,E,F,G,H) = 1
> 0
= f33(A,B,1 + C,D,E,F,G,H)
The following rules are weakly oriented:
[9 >= D && 0 >= 1 + R] ==>
f36(A,B,C,D,E,F,G,H) = 1
>= 1
= f36(A,B,C,1 + D,E + S,1 + F,G,H)
[9 >= D] ==>
f36(A,B,C,D,E,F,G,H) = 1
>= 1
= f36(A,B,C,1 + D,E,F,G + S,1 + H)
We use the following global sizebounds:
(<0,0,A>, 9) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<0,0,F>, F) (<0,0,G>, G) (<0,0,H>, H)
(<1,0,A>, ?) (<1,0,B>, ?) (<1,0,C>, 9) (<1,0,D>, 0) (<1,0,E>, ?) (<1,0,F>, ?) (<1,0,G>, ?) (<1,0,H>, ?)
(<2,0,A>, ?) (<2,0,B>, ?) (<2,0,C>, ?) (<2,0,D>, 10) (<2,0,E>, ?) (<2,0,F>, ?) (<2,0,G>, ?) (<2,0,H>, ?)
(<3,0,A>, ?) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 10) (<3,0,E>, ?) (<3,0,F>, ?) (<3,0,G>, ?) (<3,0,H>, ?)
(<4,0,A>, ?) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, 10) (<4,0,E>, ?) (<4,0,F>, ?) (<4,0,G>, ?) (<4,0,H>, ?)
(<6,0,A>, 9) (<6,0,B>, 10) (<6,0,C>, C) (<6,0,D>, D) (<6,0,E>, E) (<6,0,F>, F) (<6,0,G>, G) (<6,0,H>, H)
(<7,0,A>, 9) (<7,0,B>, 10) (<7,0,C>, C) (<7,0,D>, D) (<7,0,E>, E) (<7,0,F>, F) (<7,0,G>, G) (<7,0,H>, H)
(<8,0,A>, 9) (<8,0,B>, 10 + B) (<8,0,C>, 0) (<8,0,D>, D) (<8,0,E>, 0) (<8,0,F>, 0) (<8,0,G>, 0) (<8,0,H>, 0)
(<9,0,A>, 0) (<9,0,B>, B) (<9,0,C>, C) (<9,0,D>, D) (<9,0,E>, E) (<9,0,F>, F) (<9,0,G>, G) (<9,0,H>, H)
* Step 12: PolyRank WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f11(A,B,C,D,E,F,G,H) -> f14(A,0,C,D,E,F,G,H) [9 >= A] (10,1)
1. f33(A,B,C,D,E,F,G,H) -> f36(A,B,C,0,E,F,G,H) [9 >= C] (10,1)
2. f36(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E + S,1 + F,G,H) [9 >= D && 0 >= 1 + R] (?,1)
3. f36(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E,F,G + S,1 + H) [9 >= D] (?,1)
4. f36(A,B,C,D,E,F,G,H) -> f33(A,B,1 + C,D,E,F,G,H) [D >= 10] (10,1)
6. f14(A,B,C,D,E,F,G,H) -> f14(A,1 + B,C,D,E,F,G,H) [9 >= B] (100,1)
7. f14(A,B,C,D,E,F,G,H) -> f11(1 + A,B,C,D,E,F,G,H) [B >= 10] (10,1)
8. f11(A,B,C,D,E,F,G,H) -> f33(A,B,0,D,0,0,0,0) [A >= 10] (1,1)
9. f0(A,B,C,D,E,F,G,H) -> f11(0,B,C,D,E,F,G,H) True (1,1)
Signature:
{(f0,8);(f11,8);(f14,8);(f33,8);(f36,8);(f58,8)}
Flow Graph:
[0->{6},1->{2,3},2->{2,3,4},3->{2,3,4},4->{1},6->{6,7},7->{0,8},8->{1},9->{0}]
Sizebounds:
(<0,0,A>, 9) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<0,0,F>, F) (<0,0,G>, G) (<0,0,H>, H)
(<1,0,A>, ?) (<1,0,B>, ?) (<1,0,C>, 9) (<1,0,D>, 0) (<1,0,E>, ?) (<1,0,F>, ?) (<1,0,G>, ?) (<1,0,H>, ?)
(<2,0,A>, ?) (<2,0,B>, ?) (<2,0,C>, ?) (<2,0,D>, 10) (<2,0,E>, ?) (<2,0,F>, ?) (<2,0,G>, ?) (<2,0,H>, ?)
(<3,0,A>, ?) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 10) (<3,0,E>, ?) (<3,0,F>, ?) (<3,0,G>, ?) (<3,0,H>, ?)
(<4,0,A>, ?) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, 10) (<4,0,E>, ?) (<4,0,F>, ?) (<4,0,G>, ?) (<4,0,H>, ?)
(<6,0,A>, 9) (<6,0,B>, 10) (<6,0,C>, C) (<6,0,D>, D) (<6,0,E>, E) (<6,0,F>, F) (<6,0,G>, G) (<6,0,H>, H)
(<7,0,A>, 9) (<7,0,B>, 10) (<7,0,C>, C) (<7,0,D>, D) (<7,0,E>, E) (<7,0,F>, F) (<7,0,G>, G) (<7,0,H>, H)
(<8,0,A>, 9) (<8,0,B>, 10 + B) (<8,0,C>, 0) (<8,0,D>, D) (<8,0,E>, 0) (<8,0,F>, 0) (<8,0,G>, 0) (<8,0,H>, 0)
(<9,0,A>, 0) (<9,0,B>, B) (<9,0,C>, C) (<9,0,D>, D) (<9,0,E>, E) (<9,0,F>, F) (<9,0,G>, G) (<9,0,H>, H)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [2,3], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f36) = 10 + -1*x4
The following rules are strictly oriented:
[9 >= D] ==>
f36(A,B,C,D,E,F,G,H) = 10 + -1*D
> 9 + -1*D
= f36(A,B,C,1 + D,E,F,G + S,1 + H)
The following rules are weakly oriented:
[9 >= D && 0 >= 1 + R] ==>
f36(A,B,C,D,E,F,G,H) = 10 + -1*D
>= 9 + -1*D
= f36(A,B,C,1 + D,E + S,1 + F,G,H)
We use the following global sizebounds:
(<0,0,A>, 9) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<0,0,F>, F) (<0,0,G>, G) (<0,0,H>, H)
(<1,0,A>, ?) (<1,0,B>, ?) (<1,0,C>, 9) (<1,0,D>, 0) (<1,0,E>, ?) (<1,0,F>, ?) (<1,0,G>, ?) (<1,0,H>, ?)
(<2,0,A>, ?) (<2,0,B>, ?) (<2,0,C>, ?) (<2,0,D>, 10) (<2,0,E>, ?) (<2,0,F>, ?) (<2,0,G>, ?) (<2,0,H>, ?)
(<3,0,A>, ?) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 10) (<3,0,E>, ?) (<3,0,F>, ?) (<3,0,G>, ?) (<3,0,H>, ?)
(<4,0,A>, ?) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, 10) (<4,0,E>, ?) (<4,0,F>, ?) (<4,0,G>, ?) (<4,0,H>, ?)
(<6,0,A>, 9) (<6,0,B>, 10) (<6,0,C>, C) (<6,0,D>, D) (<6,0,E>, E) (<6,0,F>, F) (<6,0,G>, G) (<6,0,H>, H)
(<7,0,A>, 9) (<7,0,B>, 10) (<7,0,C>, C) (<7,0,D>, D) (<7,0,E>, E) (<7,0,F>, F) (<7,0,G>, G) (<7,0,H>, H)
(<8,0,A>, 9) (<8,0,B>, 10 + B) (<8,0,C>, 0) (<8,0,D>, D) (<8,0,E>, 0) (<8,0,F>, 0) (<8,0,G>, 0) (<8,0,H>, 0)
(<9,0,A>, 0) (<9,0,B>, B) (<9,0,C>, C) (<9,0,D>, D) (<9,0,E>, E) (<9,0,F>, F) (<9,0,G>, G) (<9,0,H>, H)
* Step 13: PolyRank WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f11(A,B,C,D,E,F,G,H) -> f14(A,0,C,D,E,F,G,H) [9 >= A] (10,1)
1. f33(A,B,C,D,E,F,G,H) -> f36(A,B,C,0,E,F,G,H) [9 >= C] (10,1)
2. f36(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E + S,1 + F,G,H) [9 >= D && 0 >= 1 + R] (?,1)
3. f36(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E,F,G + S,1 + H) [9 >= D] (100,1)
4. f36(A,B,C,D,E,F,G,H) -> f33(A,B,1 + C,D,E,F,G,H) [D >= 10] (10,1)
6. f14(A,B,C,D,E,F,G,H) -> f14(A,1 + B,C,D,E,F,G,H) [9 >= B] (100,1)
7. f14(A,B,C,D,E,F,G,H) -> f11(1 + A,B,C,D,E,F,G,H) [B >= 10] (10,1)
8. f11(A,B,C,D,E,F,G,H) -> f33(A,B,0,D,0,0,0,0) [A >= 10] (1,1)
9. f0(A,B,C,D,E,F,G,H) -> f11(0,B,C,D,E,F,G,H) True (1,1)
Signature:
{(f0,8);(f11,8);(f14,8);(f33,8);(f36,8);(f58,8)}
Flow Graph:
[0->{6},1->{2,3},2->{2,3,4},3->{2,3,4},4->{1},6->{6,7},7->{0,8},8->{1},9->{0}]
Sizebounds:
(<0,0,A>, 9) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<0,0,F>, F) (<0,0,G>, G) (<0,0,H>, H)
(<1,0,A>, ?) (<1,0,B>, ?) (<1,0,C>, 9) (<1,0,D>, 0) (<1,0,E>, ?) (<1,0,F>, ?) (<1,0,G>, ?) (<1,0,H>, ?)
(<2,0,A>, ?) (<2,0,B>, ?) (<2,0,C>, ?) (<2,0,D>, 10) (<2,0,E>, ?) (<2,0,F>, ?) (<2,0,G>, ?) (<2,0,H>, ?)
(<3,0,A>, ?) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 10) (<3,0,E>, ?) (<3,0,F>, ?) (<3,0,G>, ?) (<3,0,H>, ?)
(<4,0,A>, ?) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, 10) (<4,0,E>, ?) (<4,0,F>, ?) (<4,0,G>, ?) (<4,0,H>, ?)
(<6,0,A>, 9) (<6,0,B>, 10) (<6,0,C>, C) (<6,0,D>, D) (<6,0,E>, E) (<6,0,F>, F) (<6,0,G>, G) (<6,0,H>, H)
(<7,0,A>, 9) (<7,0,B>, 10) (<7,0,C>, C) (<7,0,D>, D) (<7,0,E>, E) (<7,0,F>, F) (<7,0,G>, G) (<7,0,H>, H)
(<8,0,A>, 9) (<8,0,B>, 10 + B) (<8,0,C>, 0) (<8,0,D>, D) (<8,0,E>, 0) (<8,0,F>, 0) (<8,0,G>, 0) (<8,0,H>, 0)
(<9,0,A>, 0) (<9,0,B>, B) (<9,0,C>, C) (<9,0,D>, D) (<9,0,E>, E) (<9,0,F>, F) (<9,0,G>, G) (<9,0,H>, H)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [2,3], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f36) = 10 + -1*x4
The following rules are strictly oriented:
[9 >= D && 0 >= 1 + R] ==>
f36(A,B,C,D,E,F,G,H) = 10 + -1*D
> 9 + -1*D
= f36(A,B,C,1 + D,E + S,1 + F,G,H)
[9 >= D] ==>
f36(A,B,C,D,E,F,G,H) = 10 + -1*D
> 9 + -1*D
= f36(A,B,C,1 + D,E,F,G + S,1 + H)
The following rules are weakly oriented:
We use the following global sizebounds:
(<0,0,A>, 9) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<0,0,F>, F) (<0,0,G>, G) (<0,0,H>, H)
(<1,0,A>, ?) (<1,0,B>, ?) (<1,0,C>, 9) (<1,0,D>, 0) (<1,0,E>, ?) (<1,0,F>, ?) (<1,0,G>, ?) (<1,0,H>, ?)
(<2,0,A>, ?) (<2,0,B>, ?) (<2,0,C>, ?) (<2,0,D>, 10) (<2,0,E>, ?) (<2,0,F>, ?) (<2,0,G>, ?) (<2,0,H>, ?)
(<3,0,A>, ?) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 10) (<3,0,E>, ?) (<3,0,F>, ?) (<3,0,G>, ?) (<3,0,H>, ?)
(<4,0,A>, ?) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, 10) (<4,0,E>, ?) (<4,0,F>, ?) (<4,0,G>, ?) (<4,0,H>, ?)
(<6,0,A>, 9) (<6,0,B>, 10) (<6,0,C>, C) (<6,0,D>, D) (<6,0,E>, E) (<6,0,F>, F) (<6,0,G>, G) (<6,0,H>, H)
(<7,0,A>, 9) (<7,0,B>, 10) (<7,0,C>, C) (<7,0,D>, D) (<7,0,E>, E) (<7,0,F>, F) (<7,0,G>, G) (<7,0,H>, H)
(<8,0,A>, 9) (<8,0,B>, 10 + B) (<8,0,C>, 0) (<8,0,D>, D) (<8,0,E>, 0) (<8,0,F>, 0) (<8,0,G>, 0) (<8,0,H>, 0)
(<9,0,A>, 0) (<9,0,B>, B) (<9,0,C>, C) (<9,0,D>, D) (<9,0,E>, E) (<9,0,F>, F) (<9,0,G>, G) (<9,0,H>, H)
* Step 14: KnowledgePropagation WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f11(A,B,C,D,E,F,G,H) -> f14(A,0,C,D,E,F,G,H) [9 >= A] (10,1)
1. f33(A,B,C,D,E,F,G,H) -> f36(A,B,C,0,E,F,G,H) [9 >= C] (10,1)
2. f36(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E + S,1 + F,G,H) [9 >= D && 0 >= 1 + R] (100,1)
3. f36(A,B,C,D,E,F,G,H) -> f36(A,B,C,1 + D,E,F,G + S,1 + H) [9 >= D] (100,1)
4. f36(A,B,C,D,E,F,G,H) -> f33(A,B,1 + C,D,E,F,G,H) [D >= 10] (10,1)
6. f14(A,B,C,D,E,F,G,H) -> f14(A,1 + B,C,D,E,F,G,H) [9 >= B] (100,1)
7. f14(A,B,C,D,E,F,G,H) -> f11(1 + A,B,C,D,E,F,G,H) [B >= 10] (10,1)
8. f11(A,B,C,D,E,F,G,H) -> f33(A,B,0,D,0,0,0,0) [A >= 10] (1,1)
9. f0(A,B,C,D,E,F,G,H) -> f11(0,B,C,D,E,F,G,H) True (1,1)
Signature:
{(f0,8);(f11,8);(f14,8);(f33,8);(f36,8);(f58,8)}
Flow Graph:
[0->{6},1->{2,3},2->{2,3,4},3->{2,3,4},4->{1},6->{6,7},7->{0,8},8->{1},9->{0}]
Sizebounds:
(<0,0,A>, 9) (<0,0,B>, 0) (<0,0,C>, C) (<0,0,D>, D) (<0,0,E>, E) (<0,0,F>, F) (<0,0,G>, G) (<0,0,H>, H)
(<1,0,A>, ?) (<1,0,B>, ?) (<1,0,C>, 9) (<1,0,D>, 0) (<1,0,E>, ?) (<1,0,F>, ?) (<1,0,G>, ?) (<1,0,H>, ?)
(<2,0,A>, ?) (<2,0,B>, ?) (<2,0,C>, ?) (<2,0,D>, 10) (<2,0,E>, ?) (<2,0,F>, ?) (<2,0,G>, ?) (<2,0,H>, ?)
(<3,0,A>, ?) (<3,0,B>, ?) (<3,0,C>, ?) (<3,0,D>, 10) (<3,0,E>, ?) (<3,0,F>, ?) (<3,0,G>, ?) (<3,0,H>, ?)
(<4,0,A>, ?) (<4,0,B>, ?) (<4,0,C>, ?) (<4,0,D>, 10) (<4,0,E>, ?) (<4,0,F>, ?) (<4,0,G>, ?) (<4,0,H>, ?)
(<6,0,A>, 9) (<6,0,B>, 10) (<6,0,C>, C) (<6,0,D>, D) (<6,0,E>, E) (<6,0,F>, F) (<6,0,G>, G) (<6,0,H>, H)
(<7,0,A>, 9) (<7,0,B>, 10) (<7,0,C>, C) (<7,0,D>, D) (<7,0,E>, E) (<7,0,F>, F) (<7,0,G>, G) (<7,0,H>, H)
(<8,0,A>, 9) (<8,0,B>, 10 + B) (<8,0,C>, 0) (<8,0,D>, D) (<8,0,E>, 0) (<8,0,F>, 0) (<8,0,G>, 0) (<8,0,H>, 0)
(<9,0,A>, 0) (<9,0,B>, B) (<9,0,C>, C) (<9,0,D>, D) (<9,0,E>, E) (<9,0,F>, F) (<9,0,G>, G) (<9,0,H>, H)
+ Applied Processor:
KnowledgePropagation
+ Details:
The problem is already solved.
WORST_CASE(?,O(1))