/export/starexec/sandbox2/solver/bin/starexec_run_tc21-9.sh /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


YES
**************************************************
summary
**************************************************
SRS with 4 rules on 3 letters       DP
SRS with 6 strict rules and 4 weak rules on 6 letters       weights
SRS with 2 strict rules and 4 weak rules on 4 letters       EDG
SRS with 2 strict rules and 4 weak rules on 4 letters       tile all, by Config   { method = Overlap,width = 2,unlabel = True}
SRS with 8 strict rules and 80 weak rules on 21 letters       weights
SRS with 0 strict rules and 37 weak rules on 16 letters       no strict rules

**************************************************
proof
**************************************************
property Termination
has value Just True
for SRS
  [a] -> [] {- Input 0 -}
  [a, b] -> [c, a, a, c] {- Input 1 -}
  [b] -> [] {- Input 2 -}
  [c, c] -> [b, b] {- Input 3 -}
reason
  DP
   property Termination
has value Just True
for SRS
  [a] ->= [] {- DP Nontop (Input 0) -}
  [a, b] ->= [c, a, a, c] {- DP Nontop (Input 1) -}
  [b] ->= [] {- DP Nontop (Input 2) -}
  [c, c] ->= [b, b] {- DP Nontop (Input 3) -}
  [a#, b] |-> [a#, a, c] {- DP (Top 1) (Input 1) -}
  [a#, b] |-> [a#, c] {- DP (Top 2) (Input 1) -}
  [a#, b] |-> [c#] {- DP (Top 3) (Input 1) -}
  [a#, b] |-> [c#, a, a, c] {- DP (Top 0) (Input 1) -}
  [c#, c] |-> [b#] {- DP (Top 1) (Input 3) -}
  [c#, c] |-> [b#, b] {- DP (Top 0) (Input 3) -}
reason
  (a#, 3/1)
  (c#, 2/1)
   property Termination
has value Just True
for SRS
  [a] ->= [] {- DP Nontop (Input 0) -}
  [a, b] ->= [c, a, a, c] {- DP Nontop (Input 1) -}
  [b] ->= [] {- DP Nontop (Input 2) -}
  [c, c] ->= [b, b] {- DP Nontop (Input 3) -}
  [a#, b] |-> [a#, a, c] {- DP (Top 1) (Input 1) -}
  [a#, b] |-> [a#, c] {- DP (Top 2) (Input 1) -}
reason
  EDG
   property Termination
has value Just True
for SRS
  [a#, b] |-> [a#, a, c] {- DP (Top 1) (Input 1) -}
  [a#, b] |-> [a#, c] {- DP (Top 2) (Input 1) -}
  [a] ->= [] {- DP Nontop (Input 0) -}
  [a, b] ->= [c, a, a, c] {- DP Nontop (Input 1) -}
  [b] ->= [] {- DP Nontop (Input 2) -}
  [c, c] ->= [b, b] {- DP Nontop (Input 3) -}
reason
  Tiling   { method = Overlap, width = 2, state_type = Bit64, map_type = Enum, unlabel = True, print_completion_steps = False, print_tiles = False, max_num_tiles = Just 1000, max_num_rules = Just 100000, verbose = False, tracing = False}
  steps 2
  using 21 tiles
  tile all rules
  steps: 2
  
   property Termination
has value Just True
for SRS
  [[<, a#], [a#, b], [b, >]] |-> [ [<, a#] , [a#, a] , [a, c] , [ c , > ] ] {- Semlab 0 (Concon 0 (DP (Top 1) (Input 1))) -}
  [[<, a#], [a#, b], [b, a]] |-> [ [<, a#] , [a#, a] , [a, c] , [ c , a ] ] {- Semlab 0 (Concon 1 (DP (Top 1) (Input 1))) -}
  [[<, a#], [a#, b], [b, b]] |-> [ [<, a#] , [a#, a] , [a, c] , [ c , b ] ] {- Semlab 0 (Concon 2 (DP (Top 1) (Input 1))) -}
  [[<, a#], [a#, b], [b, c]] |-> [ [<, a#] , [a#, a] , [a, c] , [ c , c ] ] {- Semlab 0 (Concon 3 (DP (Top 1) (Input 1))) -}
  [[<, a#], [a#, b], [b, >]] |-> [ [<, a#] , [a#, c] , [ c , > ] ] {- Semlab 0 (Concon 0 (DP (Top 2) (Input 1))) -}
  [[<, a#], [a#, b], [b, a]] |-> [ [<, a#] , [a#, c] , [ c , a ] ] {- Semlab 0 (Concon 1 (DP (Top 2) (Input 1))) -}
  [[<, a#], [a#, b], [b, b]] |-> [ [<, a#] , [a#, c] , [ c , b ] ] {- Semlab 0 (Concon 2 (DP (Top 2) (Input 1))) -}
  [[<, a#], [a#, b], [b, c]] |-> [ [<, a#] , [a#, c] , [ c , c ] ] {- Semlab 0 (Concon 3 (DP (Top 2) (Input 1))) -}
  [[<, a], [a, >]] ->= [[<, >]] {- Semlab 0 (Concon 0 (DP Nontop (Input 0))) -}
  [[<, a], [a, a]] ->= [[<, a]] {- Semlab 0 (Concon 1 (DP Nontop (Input 0))) -}
  [[<, a], [a, b]] ->= [[<, b]] {- Semlab 0 (Concon 2 (DP Nontop (Input 0))) -}
  [[<, a], [a, c]] ->= [[<, c]] {- Semlab 0 (Concon 3 (DP Nontop (Input 0))) -}
  [[a, a], [a, >]] ->= [[a, >]] {- Semlab 1 (Concon 0 (DP Nontop (Input 0))) -}
  [[a, a], [a, a]] ->= [[a, a]] {- Semlab 1 (Concon 1 (DP Nontop (Input 0))) -}
  [[a, a], [a, b]] ->= [[a, b]] {- Semlab 1 (Concon 2 (DP Nontop (Input 0))) -}
  [[a, a], [a, c]] ->= [[a, c]] {- Semlab 1 (Concon 3 (DP Nontop (Input 0))) -}
  [[b, a], [a, >]] ->= [[b, >]] {- Semlab 2 (Concon 0 (DP Nontop (Input 0))) -}
  [[b, a], [a, a]] ->= [[b, a]] {- Semlab 2 (Concon 1 (DP Nontop (Input 0))) -}
  [[b, a], [a, b]] ->= [[b, b]] {- Semlab 2 (Concon 2 (DP Nontop (Input 0))) -}
  [[b, a], [a, c]] ->= [[b, c]] {- Semlab 2 (Concon 3 (DP Nontop (Input 0))) -}
  [[c, a], [a, >]] ->= [[c, >]] {- Semlab 3 (Concon 0 (DP Nontop (Input 0))) -}
  [[c, a], [a, a]] ->= [[c, a]] {- Semlab 3 (Concon 1 (DP Nontop (Input 0))) -}
  [[c, a], [a, b]] ->= [[c, b]] {- Semlab 3 (Concon 2 (DP Nontop (Input 0))) -}
  [[c, a], [a, c]] ->= [[c, c]] {- Semlab 3 (Concon 3 (DP Nontop (Input 0))) -}
  [[a#, a], [a, >]] ->= [[a#, >]] {- Semlab 4 (Concon 0 (DP Nontop (Input 0))) -}
  [[a#, a], [a, a]] ->= [[a#, a]] {- Semlab 4 (Concon 1 (DP Nontop (Input 0))) -}
  [[a#, a], [a, b]] ->= [[a#, b]] {- Semlab 4 (Concon 2 (DP Nontop (Input 0))) -}
  [[a#, a], [a, c]] ->= [[a#, c]] {- Semlab 4 (Concon 3 (DP Nontop (Input 0))) -}
  [[<, a], [a, b], [b, >]] ->= [ [<, c] , [c, a] , [a, a] , [a, c] , [ c , > ] ] {- Semlab 0 (Concon 0 (DP Nontop (Input 1))) -}
  [[<, a], [a, b], [b, a]] ->= [ [<, c] , [c, a] , [a, a] , [a, c] , [ c , a ] ] {- Semlab 0 (Concon 1 (DP Nontop (Input 1))) -}
  [[<, a], [a, b], [b, b]] ->= [ [<, c] , [c, a] , [a, a] , [a, c] , [ c , b ] ] {- Semlab 0 (Concon 2 (DP Nontop (Input 1))) -}
  [[<, a], [a, b], [b, c]] ->= [ [<, c] , [c, a] , [a, a] , [a, c] , [ c , c ] ] {- Semlab 0 (Concon 3 (DP Nontop (Input 1))) -}
  [[a, a], [a, b], [b, >]] ->= [ [a, c] , [c, a] , [a, a] , [a, c] , [ c , > ] ] {- Semlab 1 (Concon 0 (DP Nontop (Input 1))) -}
  [[a, a], [a, b], [b, a]] ->= [ [a, c] , [c, a] , [a, a] , [a, c] , [ c , a ] ] {- Semlab 1 (Concon 1 (DP Nontop (Input 1))) -}
  [[a, a], [a, b], [b, b]] ->= [ [a, c] , [c, a] , [a, a] , [a, c] , [ c , b ] ] {- Semlab 1 (Concon 2 (DP Nontop (Input 1))) -}
  [[a, a], [a, b], [b, c]] ->= [ [a, c] , [c, a] , [a, a] , [a, c] , [ c , c ] ] {- Semlab 1 (Concon 3 (DP Nontop (Input 1))) -}
  [[b, a], [a, b], [b, >]] ->= [ [b, c] , [c, a] , [a, a] , [a, c] , [ c , > ] ] {- Semlab 2 (Concon 0 (DP Nontop (Input 1))) -}
  [[b, a], [a, b], [b, a]] ->= [ [b, c] , [c, a] , [a, a] , [a, c] , [ c , a ] ] {- Semlab 2 (Concon 1 (DP Nontop (Input 1))) -}
  [[b, a], [a, b], [b, b]] ->= [ [b, c] , [c, a] , [a, a] , [a, c] , [ c , b ] ] {- Semlab 2 (Concon 2 (DP Nontop (Input 1))) -}
  [[b, a], [a, b], [b, c]] ->= [ [b, c] , [c, a] , [a, a] , [a, c] , [ c , c ] ] {- Semlab 2 (Concon 3 (DP Nontop (Input 1))) -}
  [[c, a], [a, b], [b, >]] ->= [ [c, c] , [c, a] , [a, a] , [a, c] , [ c , > ] ] {- Semlab 3 (Concon 0 (DP Nontop (Input 1))) -}
  [[c, a], [a, b], [b, a]] ->= [ [c, c] , [c, a] , [a, a] , [a, c] , [ c , a ] ] {- Semlab 3 (Concon 1 (DP Nontop (Input 1))) -}
  [[c, a], [a, b], [b, b]] ->= [ [c, c] , [c, a] , [a, a] , [a, c] , [ c , b ] ] {- Semlab 3 (Concon 2 (DP Nontop (Input 1))) -}
  [[c, a], [a, b], [b, c]] ->= [ [c, c] , [c, a] , [a, a] , [a, c] , [ c , c ] ] {- Semlab 3 (Concon 3 (DP Nontop (Input 1))) -}
  [[a#, a], [a, b], [b, >]] ->= [ [a#, c] , [c, a] , [a, a] , [a, c] , [ c , > ] ] {- Semlab 4 (Concon 0 (DP Nontop (Input 1))) -}
  [[a#, a], [a, b], [b, a]] ->= [ [a#, c] , [c, a] , [a, a] , [a, c] , [ c , a ] ] {- Semlab 4 (Concon 1 (DP Nontop (Input 1))) -}
  [[a#, a], [a, b], [b, b]] ->= [ [a#, c] , [c, a] , [a, a] , [a, c] , [ c , b ] ] {- Semlab 4 (Concon 2 (DP Nontop (Input 1))) -}
  [[a#, a], [a, b], [b, c]] ->= [ [a#, c] , [c, a] , [a, a] , [a, c] , [ c , c ] ] {- Semlab 4 (Concon 3 (DP Nontop (Input 1))) -}
  [[<, b], [b, >]] ->= [[<, >]] {- Semlab 0 (Concon 0 (DP Nontop (Input 2))) -}
  [[<, b], [b, a]] ->= [[<, a]] {- Semlab 0 (Concon 1 (DP Nontop (Input 2))) -}
  [[<, b], [b, b]] ->= [[<, b]] {- Semlab 0 (Concon 2 (DP Nontop (Input 2))) -}
  [[<, b], [b, c]] ->= [[<, c]] {- Semlab 0 (Concon 3 (DP Nontop (Input 2))) -}
  [[a, b], [b, >]] ->= [[a, >]] {- Semlab 1 (Concon 0 (DP Nontop (Input 2))) -}
  [[a, b], [b, a]] ->= [[a, a]] {- Semlab 1 (Concon 1 (DP Nontop (Input 2))) -}
  [[a, b], [b, b]] ->= [[a, b]] {- Semlab 1 (Concon 2 (DP Nontop (Input 2))) -}
  [[a, b], [b, c]] ->= [[a, c]] {- Semlab 1 (Concon 3 (DP Nontop (Input 2))) -}
  [[b, b], [b, >]] ->= [[b, >]] {- Semlab 2 (Concon 0 (DP Nontop (Input 2))) -}
  [[b, b], [b, a]] ->= [[b, a]] {- Semlab 2 (Concon 1 (DP Nontop (Input 2))) -}
  [[b, b], [b, b]] ->= [[b, b]] {- Semlab 2 (Concon 2 (DP Nontop (Input 2))) -}
  [[b, b], [b, c]] ->= [[b, c]] {- Semlab 2 (Concon 3 (DP Nontop (Input 2))) -}
  [[c, b], [b, >]] ->= [[c, >]] {- Semlab 3 (Concon 0 (DP Nontop (Input 2))) -}
  [[c, b], [b, a]] ->= [[c, a]] {- Semlab 3 (Concon 1 (DP Nontop (Input 2))) -}
  [[c, b], [b, b]] ->= [[c, b]] {- Semlab 3 (Concon 2 (DP Nontop (Input 2))) -}
  [[c, b], [b, c]] ->= [[c, c]] {- Semlab 3 (Concon 3 (DP Nontop (Input 2))) -}
  [[a#, b], [b, >]] ->= [[a#, >]] {- Semlab 4 (Concon 0 (DP Nontop (Input 2))) -}
  [[a#, b], [b, a]] ->= [[a#, a]] {- Semlab 4 (Concon 1 (DP Nontop (Input 2))) -}
  [[a#, b], [b, b]] ->= [[a#, b]] {- Semlab 4 (Concon 2 (DP Nontop (Input 2))) -}
  [[a#, b], [b, c]] ->= [[a#, c]] {- Semlab 4 (Concon 3 (DP Nontop (Input 2))) -}
  [[<, c], [c, c], [c, >]] ->= [ [<, b] , [b, b] , [ b , > ] ] {- Semlab 0 (Concon 0 (DP Nontop (Input 3))) -}
  [[<, c], [c, c], [c, a]] ->= [ [<, b] , [b, b] , [ b , a ] ] {- Semlab 0 (Concon 1 (DP Nontop (Input 3))) -}
  [[<, c], [c, c], [c, b]] ->= [ [<, b] , [b, b] , [ b , b ] ] {- Semlab 0 (Concon 2 (DP Nontop (Input 3))) -}
  [[<, c], [c, c], [c, c]] ->= [ [<, b] , [b, b] , [ b , c ] ] {- Semlab 0 (Concon 3 (DP Nontop (Input 3))) -}
  [[a, c], [c, c], [c, >]] ->= [ [a, b] , [b, b] , [ b , > ] ] {- Semlab 1 (Concon 0 (DP Nontop (Input 3))) -}
  [[a, c], [c, c], [c, a]] ->= [ [a, b] , [b, b] , [ b , a ] ] {- Semlab 1 (Concon 1 (DP Nontop (Input 3))) -}
  [[a, c], [c, c], [c, b]] ->= [ [a, b] , [b, b] , [ b , b ] ] {- Semlab 1 (Concon 2 (DP Nontop (Input 3))) -}
  [[a, c], [c, c], [c, c]] ->= [ [a, b] , [b, b] , [ b , c ] ] {- Semlab 1 (Concon 3 (DP Nontop (Input 3))) -}
  [[b, c], [c, c], [c, >]] ->= [ [b, b] , [b, b] , [ b , > ] ] {- Semlab 2 (Concon 0 (DP Nontop (Input 3))) -}
  [[b, c], [c, c], [c, a]] ->= [ [b, b] , [b, b] , [ b , a ] ] {- Semlab 2 (Concon 1 (DP Nontop (Input 3))) -}
  [[b, c], [c, c], [c, b]] ->= [ [b, b] , [b, b] , [ b , b ] ] {- Semlab 2 (Concon 2 (DP Nontop (Input 3))) -}
  [[b, c], [c, c], [c, c]] ->= [ [b, b] , [b, b] , [ b , c ] ] {- Semlab 2 (Concon 3 (DP Nontop (Input 3))) -}
  [[c, c], [c, c], [c, >]] ->= [ [c, b] , [b, b] , [ b , > ] ] {- Semlab 3 (Concon 0 (DP Nontop (Input 3))) -}
  [[c, c], [c, c], [c, a]] ->= [ [c, b] , [b, b] , [ b , a ] ] {- Semlab 3 (Concon 1 (DP Nontop (Input 3))) -}
  [[c, c], [c, c], [c, b]] ->= [ [c, b] , [b, b] , [ b , b ] ] {- Semlab 3 (Concon 2 (DP Nontop (Input 3))) -}
  [[c, c], [c, c], [c, c]] ->= [ [c, b] , [b, b] , [ b , c ] ] {- Semlab 3 (Concon 3 (DP Nontop (Input 3))) -}
  [[a#, c], [c, c], [c, >]] ->= [ [a#, b] , [b, b] , [ b , > ] ] {- Semlab 4 (Concon 0 (DP Nontop (Input 3))) -}
  [[a#, c], [c, c], [c, a]] ->= [ [a#, b] , [b, b] , [ b , a ] ] {- Semlab 4 (Concon 1 (DP Nontop (Input 3))) -}
  [[a#, c], [c, c], [c, b]] ->= [ [a#, b] , [b, b] , [ b , b ] ] {- Semlab 4 (Concon 2 (DP Nontop (Input 3))) -}
  [[a#, c], [c, c], [c, c]] ->= [ [a#, b] , [b, b] , [ b , c ] ] {- Semlab 4 (Concon 3 (DP Nontop (Input 3))) -}
reason
  ([a#, b], 39/1)
  ([b, >], 1/1)
  ([a#, a], 19/1)
  ([c, >], 20/1)
  ([c, a], 19/1)
  ([c, b], 19/1)
  ([c, c], 19/1)
  ([a#, c], 5/1)
  ([<, a], 5/1)
  ([a, >], 7/1)
  ([a, b], 38/1)
  ([<, b], 6/1)
   property Termination
has value Just True
for SRS
  [[<, a], [a, a]] ->= [[<, a]] {- Semlab 0 (Concon 1 (DP Nontop (Input 0))) -}
  [[a, a], [a, >]] ->= [[a, >]] {- Semlab 1 (Concon 0 (DP Nontop (Input 0))) -}
  [[a, a], [a, a]] ->= [[a, a]] {- Semlab 1 (Concon 1 (DP Nontop (Input 0))) -}
  [[a, a], [a, b]] ->= [[a, b]] {- Semlab 1 (Concon 2 (DP Nontop (Input 0))) -}
  [[a, a], [a, c]] ->= [[a, c]] {- Semlab 1 (Concon 3 (DP Nontop (Input 0))) -}
  [[b, a], [a, a]] ->= [[b, a]] {- Semlab 2 (Concon 1 (DP Nontop (Input 0))) -}
  [[b, a], [a, c]] ->= [[b, c]] {- Semlab 2 (Concon 3 (DP Nontop (Input 0))) -}
  [[c, a], [a, a]] ->= [[c, a]] {- Semlab 3 (Concon 1 (DP Nontop (Input 0))) -}
  [[c, a], [a, c]] ->= [[c, c]] {- Semlab 3 (Concon 3 (DP Nontop (Input 0))) -}
  [[a#, a], [a, a]] ->= [[a#, a]] {- Semlab 4 (Concon 1 (DP Nontop (Input 0))) -}
  [[a, a], [a, b], [b, >]] ->= [ [a, c] , [c, a] , [a, a] , [a, c] , [ c , > ] ] {- Semlab 1 (Concon 0 (DP Nontop (Input 1))) -}
  [[a, a], [a, b], [b, a]] ->= [ [a, c] , [c, a] , [a, a] , [a, c] , [ c , a ] ] {- Semlab 1 (Concon 1 (DP Nontop (Input 1))) -}
  [[a, a], [a, b], [b, b]] ->= [ [a, c] , [c, a] , [a, a] , [a, c] , [ c , b ] ] {- Semlab 1 (Concon 2 (DP Nontop (Input 1))) -}
  [[a, a], [a, b], [b, c]] ->= [ [a, c] , [c, a] , [a, a] , [a, c] , [ c , c ] ] {- Semlab 1 (Concon 3 (DP Nontop (Input 1))) -}
  [[b, a], [a, b], [b, >]] ->= [ [b, c] , [c, a] , [a, a] , [a, c] , [ c , > ] ] {- Semlab 2 (Concon 0 (DP Nontop (Input 1))) -}
  [[b, a], [a, b], [b, a]] ->= [ [b, c] , [c, a] , [a, a] , [a, c] , [ c , a ] ] {- Semlab 2 (Concon 1 (DP Nontop (Input 1))) -}
  [[b, a], [a, b], [b, b]] ->= [ [b, c] , [c, a] , [a, a] , [a, c] , [ c , b ] ] {- Semlab 2 (Concon 2 (DP Nontop (Input 1))) -}
  [[b, a], [a, b], [b, c]] ->= [ [b, c] , [c, a] , [a, a] , [a, c] , [ c , c ] ] {- Semlab 2 (Concon 3 (DP Nontop (Input 1))) -}
  [[c, a], [a, b], [b, >]] ->= [ [c, c] , [c, a] , [a, a] , [a, c] , [ c , > ] ] {- Semlab 3 (Concon 0 (DP Nontop (Input 1))) -}
  [[c, a], [a, b], [b, a]] ->= [ [c, c] , [c, a] , [a, a] , [a, c] , [ c , a ] ] {- Semlab 3 (Concon 1 (DP Nontop (Input 1))) -}
  [[c, a], [a, b], [b, b]] ->= [ [c, c] , [c, a] , [a, a] , [a, c] , [ c , b ] ] {- Semlab 3 (Concon 2 (DP Nontop (Input 1))) -}
  [[c, a], [a, b], [b, c]] ->= [ [c, c] , [c, a] , [a, a] , [a, c] , [ c , c ] ] {- Semlab 3 (Concon 3 (DP Nontop (Input 1))) -}
  [[<, b], [b, b]] ->= [[<, b]] {- Semlab 0 (Concon 2 (DP Nontop (Input 2))) -}
  [[a, b], [b, b]] ->= [[a, b]] {- Semlab 1 (Concon 2 (DP Nontop (Input 2))) -}
  [[b, b], [b, >]] ->= [[b, >]] {- Semlab 2 (Concon 0 (DP Nontop (Input 2))) -}
  [[b, b], [b, a]] ->= [[b, a]] {- Semlab 2 (Concon 1 (DP Nontop (Input 2))) -}
  [[b, b], [b, b]] ->= [[b, b]] {- Semlab 2 (Concon 2 (DP Nontop (Input 2))) -}
  [[b, b], [b, c]] ->= [[b, c]] {- Semlab 2 (Concon 3 (DP Nontop (Input 2))) -}
  [[c, b], [b, >]] ->= [[c, >]] {- Semlab 3 (Concon 0 (DP Nontop (Input 2))) -}
  [[c, b], [b, a]] ->= [[c, a]] {- Semlab 3 (Concon 1 (DP Nontop (Input 2))) -}
  [[c, b], [b, b]] ->= [[c, b]] {- Semlab 3 (Concon 2 (DP Nontop (Input 2))) -}
  [[c, b], [b, c]] ->= [[c, c]] {- Semlab 3 (Concon 3 (DP Nontop (Input 2))) -}
  [[a#, b], [b, b]] ->= [[a#, b]] {- Semlab 4 (Concon 2 (DP Nontop (Input 2))) -}
  [[a, c], [c, c], [c, >]] ->= [ [a, b] , [b, b] , [ b , > ] ] {- Semlab 1 (Concon 0 (DP Nontop (Input 3))) -}
  [[a, c], [c, c], [c, a]] ->= [ [a, b] , [b, b] , [ b , a ] ] {- Semlab 1 (Concon 1 (DP Nontop (Input 3))) -}
  [[a, c], [c, c], [c, b]] ->= [ [a, b] , [b, b] , [ b , b ] ] {- Semlab 1 (Concon 2 (DP Nontop (Input 3))) -}
  [[a, c], [c, c], [c, c]] ->= [ [a, b] , [b, b] , [ b , c ] ] {- Semlab 1 (Concon 3 (DP Nontop (Input 3))) -}
reason
  no strict rules

**************************************************
skeleton: (4,3)\Deepee(6/4,6)\Weight\EDG(2/4,4)\TileAllROC{2}(8/80,21)\Weight(0/37,16)[]
**************************************************
let {}
in let {trac ?= False;loop_cap = 1;match_cap = 2;tile_cap = 3;matrix_cap = 4;mo = Pre (Or_Else Count (IfSizeLeq 100000 (Simplex Sparse) Fail));wop = Or_Else (Worker (Weight {modus = mo})) Pass;weighted = \ m -> And_Then m wop;done = Worker No_Strict_Rules;dont = \ p -> Fail;tiling = \ m w -> On tile_cap (weighted (And_Then (Worker (Tiling {method = m,width = w,map_type = Enum,max_num_tiles = Just 1000,max_num_rules = Just 100000})) (Worker Remap)));tile_roc = Tree_Search_Preemptive 0 done let {ws = [ 2, 4, 8, 12]}in (for ws (\ w -> tiling Overlap w)) <> [ Worker Unlabel];mb = \ size -> On match_cap (Apply (Worker (Matchbound {method = RFC,max_size = Just size})) done);mbs = \ size -> First_Of [ mb size, Apply (Worker Mirror) (mb size)];tile_rfc = Tree_Search_Preemptive 0 done let {ws = [ 2, 4, 8, 12]}in (for ws (\ w -> tiling Forward w)) <> ((for ws (\ w -> tiling Backward w)) <> [ Worker Unlabel]);solver = Minisatapi;qpi = \ dim bits -> On matrix_cap (weighted (Worker (QPI {tracing = trac,dim = dim,bits = bits,solver = solver})));qpis = Seq [ Timeout 10 (qpi 2 3), Timeout 30 (qpi 4 3), Timeout 50 (qpi 6 3), qpi 8 3];kbo = \ b -> On matrix_cap (weighted (Worker (KBO {bits = b,solver = solver})));matrix = \ dom dim bits -> On matrix_cap (weighted (Worker (Matrix {monotone = Weak,domain = dom,dim = dim,bits = bits,encoding = Ersatz_Binary,tracing = trac,verbose = True,solver = solver})));arctics = Seq [ Timeout 10 (matrix Arctic 2 16), Timeout 30 (matrix Arctic 4 8), Timeout 50 (matrix Arctic 6 4), matrix Arctic 8 2];naturals = Seq [ Timeout 10 (matrix Natural 2 4), Timeout 30 (matrix Natural 4 3), Timeout 50 (matrix Natural 6 2), matrix Natural 8 1];remove = First_Of [ qpis, arctics, naturals, As_Transformer tile_roc];remove_wop = And_Then wop (Or_Else (As_Transformer (Worker No_Strict_Rules)) remove);deepee = Apply (And_Then (Worker DP) (Worker Remap)) (Apply wop (Branch (Worker (EDG {tracing = False,usable = True})) remove_wop));when_small = \ m -> Apply (Worker (SizeAtmost 1000)) m;yeah = First_Of [ when_small (First_Of [ deepee, Apply (Worker Mirror) deepee]), tile_rfc, mbs 100000];noh_for = \ side -> Worker (Simple (Config {closure = side,max_closure_width = Nothing,intermediates = All,priority = Linear [ ( 1, Log2 Steps), ( -1, Width_lhs), ( -2, Log2 Width_rhs)]}));noh = First_Of [ On loop_cap (noh_for Forward), On loop_cap (noh_for Backward), On loop_cap (Worker Transport)]}
  in Apply (Worker Remap) (Apply wop (Seq [ Worker KKST01, First_Of [ yeah, noh]]))
**************************************************
statistics on proof search (nodes types that (together) took more than 1.000000000000)
**************************************************
Success : Weight { modus = Pre (Or_Else Count (IfSizeLeq 100000 (Simplex Sparse) Fail)) , verbose = False , tracing = False}
  total number 5
  max duration 0.805411325000
  min duration 0.001828988000
  total durat. 1.447283620000
**************************************************