/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 2 rules on 2 letters tile all, by Config { method = Forward,width = 4,unlabel = True} SRS with 48 rules on 30 letters weights SRS with 18 rules on 16 letters remove some, by Config { method = Backward,width = 2,unlabel = True} SRS with 11 rules on 15 letters weights SRS with 4 rules on 10 letters remove some, by Config { method = Forward,width = 4,unlabel = True} SRS with 0 rules on 0 letters no strict rules ************************************************** proof ************************************************** property Termination has value Just True for SRS [b, a, b] -> [a, b, a] {- Input 0 -} [b, b, a] -> [b, b, b] {- Input 1 -} reason Tiling { method = Forward, width = 4, 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 3 using 29 tiles tile all rules steps: 3 property Termination has value Just True for SRS [ [<, <, <, b] , [<, <, b, a] , [<, b, a, b] , [b, a, b, a] , [a, b, a, >] , [b, a, >, >] ] -> [ [<, <, <, a] , [<, <, a, b] , [<, a, b, a] , [a, b, a, a] , [b, a, a, >] , [a, a, >, >] ] {- Semlab 0 (Concon 0 (Input 0)) -} [ [<, <, <, b] , [<, <, b, a] , [<, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, >] ] -> [ [<, <, <, a] , [<, <, a, b] , [<, a, b, a] , [a, b, a, a] , [b, a, a, a] , [a, a, a, >] ] {- Semlab 0 (Concon 1 (Input 0)) -} [ [<, <, <, b] , [<, <, b, a] , [<, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, b] ] -> [ [<, <, <, a] , [<, <, a, b] , [<, a, b, a] , [a, b, a, a] , [b, a, a, a] , [a, a, a, b] ] {- Semlab 0 (Concon 2 (Input 0)) -} [ [<, <, <, b] , [<, <, b, a] , [<, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, a] ] -> [ [<, <, <, a] , [<, <, a, b] , [<, a, b, a] , [a, b, a, a] , [b, a, a, a] , [a, a, a, a] ] {- Semlab 0 (Concon 3 (Input 0)) -} [ [<, <, b, b] , [<, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, >] , [b, a, >, >] ] -> [ [<, <, b, a] , [<, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, >] , [a, a, >, >] ] {- Semlab 1 (Concon 0 (Input 0)) -} [ [<, <, b, b] , [<, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, >] ] -> [ [<, <, b, a] , [<, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, a] , [a, a, a, >] ] {- Semlab 1 (Concon 1 (Input 0)) -} [ [<, <, b, b] , [<, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, b] ] -> [ [<, <, b, a] , [<, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, a] , [a, a, a, b] ] {- Semlab 1 (Concon 2 (Input 0)) -} [ [<, <, b, b] , [<, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, a] ] -> [ [<, <, b, a] , [<, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, a] , [a, a, a, a] ] {- Semlab 1 (Concon 3 (Input 0)) -} [ [<, b, b, b] , [b, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, >] , [b, a, >, >] ] -> [ [<, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, >] , [a, a, >, >] ] {- Semlab 2 (Concon 0 (Input 0)) -} [ [<, b, b, b] , [b, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, >] ] -> [ [<, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, a] , [a, a, a, >] ] {- Semlab 2 (Concon 1 (Input 0)) -} [ [<, b, b, b] , [b, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, b] ] -> [ [<, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, a] , [a, a, a, b] ] {- Semlab 2 (Concon 2 (Input 0)) -} [ [<, b, b, b] , [b, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, a] ] -> [ [<, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, a] , [a, a, a, a] ] {- Semlab 2 (Concon 3 (Input 0)) -} [ [b, b, b, b] , [b, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, >] , [b, a, >, >] ] -> [ [b, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, >] , [a, a, >, >] ] {- Semlab 3 (Concon 0 (Input 0)) -} [ [b, b, b, b] , [b, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, >] ] -> [ [b, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, a] , [a, a, a, >] ] {- Semlab 3 (Concon 1 (Input 0)) -} [ [b, b, b, b] , [b, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, b] ] -> [ [b, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, a] , [a, a, a, b] ] {- Semlab 3 (Concon 2 (Input 0)) -} [ [b, b, b, b] , [b, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, a] ] -> [ [b, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, a] , [a, a, a, a] ] {- Semlab 3 (Concon 3 (Input 0)) -} [ [<, <, <, b] , [<, <, b, b] , [<, b, b, a] , [b, b, a, >] , [b, a, >, >] , [a, >, >, >] ] -> [ [<, <, <, b] , [<, <, b, b] , [<, b, b, b] , [b, b, b, >] , [b, b, >, >] , [b, >, >, >] ] {- Semlab 0 (Concon 0 (Input 1)) -} [ [<, <, <, b] , [<, <, b, b] , [<, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, >] ] -> [ [<, <, <, b] , [<, <, b, b] , [<, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, >] ] {- Semlab 0 (Concon 1 (Input 1)) -} [ [<, <, <, b] , [<, <, b, b] , [<, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] ] -> [ [<, <, <, b] , [<, <, b, b] , [<, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] ] {- Semlab 0 (Concon 2 (Input 1)) -} [ [<, <, <, b] , [<, <, b, b] , [<, b, b, a] , [b, b, a, a] , [b, a, a, >] , [a, a, >, >] ] -> [ [<, <, <, b] , [<, <, b, b] , [<, b, b, b] , [b, b, b, a] , [b, b, a, >] , [b, a, >, >] ] {- Semlab 0 (Concon 3 (Input 1)) -} [ [<, <, <, b] , [<, <, b, b] , [<, b, b, a] , [b, b, a, a] , [b, a, a, b] , [a, a, b, a] ] -> [ [<, <, <, b] , [<, <, b, b] , [<, b, b, b] , [b, b, b, a] , [b, b, a, b] , [b, a, b, a] ] {- Semlab 0 (Concon 4 (Input 1)) -} [ [<, <, <, b] , [<, <, b, b] , [<, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, >] ] -> [ [<, <, <, b] , [<, <, b, b] , [<, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, >] ] {- Semlab 0 (Concon 5 (Input 1)) -} [ [<, <, <, b] , [<, <, b, b] , [<, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, b] ] -> [ [<, <, <, b] , [<, <, b, b] , [<, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, b] ] {- Semlab 0 (Concon 6 (Input 1)) -} [ [<, <, <, b] , [<, <, b, b] , [<, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, a] ] -> [ [<, <, <, b] , [<, <, b, b] , [<, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] ] {- Semlab 0 (Concon 7 (Input 1)) -} [ [<, <, b, b] , [<, b, b, b] , [b, b, b, a] , [b, b, a, >] , [b, a, >, >] , [a, >, >, >] ] -> [ [<, <, b, b] , [<, b, b, b] , [b, b, b, b] , [b, b, b, >] , [b, b, >, >] , [b, >, >, >] ] {- Semlab 1 (Concon 0 (Input 1)) -} [ [<, <, b, b] , [<, b, b, b] , [b, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, >] ] -> [ [<, <, b, b] , [<, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, >] ] {- Semlab 1 (Concon 1 (Input 1)) -} [ [<, <, b, b] , [<, b, b, b] , [b, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] ] -> [ [<, <, b, b] , [<, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] ] {- Semlab 1 (Concon 2 (Input 1)) -} [ [<, <, b, b] , [<, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, >] , [a, a, >, >] ] -> [ [<, <, b, b] , [<, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, >] , [b, a, >, >] ] {- Semlab 1 (Concon 3 (Input 1)) -} [ [<, <, b, b] , [<, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, b] , [a, a, b, a] ] -> [ [<, <, b, b] , [<, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, b] , [b, a, b, a] ] {- Semlab 1 (Concon 4 (Input 1)) -} [ [<, <, b, b] , [<, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, >] ] -> [ [<, <, b, b] , [<, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, >] ] {- Semlab 1 (Concon 5 (Input 1)) -} [ [<, <, b, b] , [<, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, b] ] -> [ [<, <, b, b] , [<, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, b] ] {- Semlab 1 (Concon 6 (Input 1)) -} [ [<, <, b, b] , [<, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, a] ] -> [ [<, <, b, b] , [<, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] ] {- Semlab 1 (Concon 7 (Input 1)) -} [ [<, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, >] , [b, a, >, >] , [a, >, >, >] ] -> [ [<, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, >] , [b, b, >, >] , [b, >, >, >] ] {- Semlab 2 (Concon 0 (Input 1)) -} [ [<, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, >] ] -> [ [<, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, >] ] {- Semlab 2 (Concon 1 (Input 1)) -} [ [<, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] ] -> [ [<, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] ] {- Semlab 2 (Concon 2 (Input 1)) -} [ [<, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, >] , [a, a, >, >] ] -> [ [<, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, >] , [b, a, >, >] ] {- Semlab 2 (Concon 3 (Input 1)) -} [ [<, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, b] , [a, a, b, a] ] -> [ [<, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, b] , [b, a, b, a] ] {- Semlab 2 (Concon 4 (Input 1)) -} [ [<, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, >] ] -> [ [<, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, >] ] {- Semlab 2 (Concon 5 (Input 1)) -} [ [<, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, b] ] -> [ [<, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, b] ] {- Semlab 2 (Concon 6 (Input 1)) -} [ [<, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, a] ] -> [ [<, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] ] {- Semlab 2 (Concon 7 (Input 1)) -} [ [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, >] , [b, a, >, >] , [a, >, >, >] ] -> [ [b, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, >] , [b, b, >, >] , [b, >, >, >] ] {- Semlab 3 (Concon 0 (Input 1)) -} [ [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, >] ] -> [ [b, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, >] ] {- Semlab 3 (Concon 1 (Input 1)) -} [ [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] ] -> [ [b, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] ] {- Semlab 3 (Concon 2 (Input 1)) -} [ [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, >] , [a, a, >, >] ] -> [ [b, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, >] , [b, a, >, >] ] {- Semlab 3 (Concon 3 (Input 1)) -} [ [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, b] , [a, a, b, a] ] -> [ [b, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, b] , [b, a, b, a] ] {- Semlab 3 (Concon 4 (Input 1)) -} [ [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, >] ] -> [ [b, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, >] ] {- Semlab 3 (Concon 5 (Input 1)) -} [ [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, b] ] -> [ [b, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, b] ] {- Semlab 3 (Concon 6 (Input 1)) -} [ [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, a] ] -> [ [b, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] ] {- Semlab 3 (Concon 7 (Input 1)) -} reason ([<, <, <, b], 10/1) ([b, a, b, a], 2/1) ([a, b, a, >], 15/1) ([a, b, a, a], 2/1) ([a, a, >, >], 2/1) ([<, <, b, b], 10/1) ([b, b, a, b], 2/1) ([a, >, >, >], 5/1) ([a, a, b, a], 5/1) property Termination has value Just True for SRS [ [<, b, b, b] , [b, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, >] ] -> [ [<, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, a] , [a, a, a, >] ] {- Semlab 2 (Concon 1 (Input 0)) -} [ [<, b, b, b] , [b, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, b] ] -> [ [<, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, a] , [a, a, a, b] ] {- Semlab 2 (Concon 2 (Input 0)) -} [ [<, b, b, b] , [b, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, a] ] -> [ [<, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, a] , [a, a, a, a] ] {- Semlab 2 (Concon 3 (Input 0)) -} [ [b, b, b, b] , [b, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, >] ] -> [ [b, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, a] , [a, a, a, >] ] {- Semlab 3 (Concon 1 (Input 0)) -} [ [b, b, b, b] , [b, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, b] ] -> [ [b, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, a] , [a, a, a, b] ] {- Semlab 3 (Concon 2 (Input 0)) -} [ [b, b, b, b] , [b, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, a] ] -> [ [b, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, a] , [a, a, a, a] ] {- Semlab 3 (Concon 3 (Input 0)) -} [ [<, <, <, b] , [<, <, b, b] , [<, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, >] ] -> [ [<, <, <, b] , [<, <, b, b] , [<, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, >] ] {- Semlab 0 (Concon 5 (Input 1)) -} [ [<, <, <, b] , [<, <, b, b] , [<, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, b] ] -> [ [<, <, <, b] , [<, <, b, b] , [<, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, b] ] {- Semlab 0 (Concon 6 (Input 1)) -} [ [<, <, <, b] , [<, <, b, b] , [<, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, a] ] -> [ [<, <, <, b] , [<, <, b, b] , [<, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] ] {- Semlab 0 (Concon 7 (Input 1)) -} [ [<, <, b, b] , [<, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, >] ] -> [ [<, <, b, b] , [<, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, >] ] {- Semlab 1 (Concon 5 (Input 1)) -} [ [<, <, b, b] , [<, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, b] ] -> [ [<, <, b, b] , [<, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, b] ] {- Semlab 1 (Concon 6 (Input 1)) -} [ [<, <, b, b] , [<, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, a] ] -> [ [<, <, b, b] , [<, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] ] {- Semlab 1 (Concon 7 (Input 1)) -} [ [<, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, >] ] -> [ [<, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, >] ] {- Semlab 2 (Concon 5 (Input 1)) -} [ [<, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, b] ] -> [ [<, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, b] ] {- Semlab 2 (Concon 6 (Input 1)) -} [ [<, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, a] ] -> [ [<, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] ] {- Semlab 2 (Concon 7 (Input 1)) -} [ [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, >] ] -> [ [b, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, >] ] {- Semlab 3 (Concon 5 (Input 1)) -} [ [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, b] ] -> [ [b, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, b] ] {- Semlab 3 (Concon 6 (Input 1)) -} [ [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, a] ] -> [ [b, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] ] {- Semlab 3 (Concon 7 (Input 1)) -} reason Tiling { method = Backward, 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 1 using 34 tiles remove some unmatched rules steps: 1 property Termination has value Just True for SRS [ [<, b, b, b] , [b, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, a] ] -> [ [<, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, a] , [a, a, a, a] ] {- Semlab 2 (Concon 3 (Input 0)) -} [ [b, b, b, b] , [b, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, a] ] -> [ [b, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, a] , [a, a, a, a] ] {- Semlab 3 (Concon 3 (Input 0)) -} [ [<, <, b, b] , [<, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, >] ] -> [ [<, <, b, b] , [<, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, >] ] {- Semlab 1 (Concon 5 (Input 1)) -} [ [<, <, b, b] , [<, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, b] ] -> [ [<, <, b, b] , [<, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, b] ] {- Semlab 1 (Concon 6 (Input 1)) -} [ [<, <, b, b] , [<, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, a] ] -> [ [<, <, b, b] , [<, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] ] {- Semlab 1 (Concon 7 (Input 1)) -} [ [<, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, >] ] -> [ [<, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, >] ] {- Semlab 2 (Concon 5 (Input 1)) -} [ [<, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, b] ] -> [ [<, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, b] ] {- Semlab 2 (Concon 6 (Input 1)) -} [ [<, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, a] ] -> [ [<, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] ] {- Semlab 2 (Concon 7 (Input 1)) -} [ [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, >] ] -> [ [b, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, >] ] {- Semlab 3 (Concon 5 (Input 1)) -} [ [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, b] ] -> [ [b, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, b] ] {- Semlab 3 (Concon 6 (Input 1)) -} [ [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, a] ] -> [ [b, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] ] {- Semlab 3 (Concon 7 (Input 1)) -} reason ([<, b, b, b], 1/1) ([b, b, b, a], 1/1) ([b, a, a, a], 2/1) ([a, a, a, >], 1/1) ([a, a, a, b], 1/1) property Termination has value Just True for SRS [ [b, b, b, b] , [b, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, a] ] -> [ [b, b, b, a] , [b, b, a, b] , [b, a, b, a] , [a, b, a, a] , [b, a, a, a] , [a, a, a, a] ] {- Semlab 3 (Concon 3 (Input 0)) -} [ [<, <, b, b] , [<, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, a] ] -> [ [<, <, b, b] , [<, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] ] {- Semlab 1 (Concon 7 (Input 1)) -} [ [<, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, a] ] -> [ [<, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] ] {- Semlab 2 (Concon 7 (Input 1)) -} [ [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] , [a, a, a, a] ] -> [ [b, b, b, b] , [b, b, b, b] , [b, b, b, b] , [b, b, b, a] , [b, b, a, a] , [b, a, a, a] ] {- Semlab 3 (Concon 7 (Input 1)) -} reason Tiling { method = Forward, width = 4, 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 1 using 26 tiles remove some unmatched rules steps: 1 property Termination has value Just True for SRS reason no strict rules ************************************************** skeleton: (2,2)\TileAllRFC{4}(48,30)\Weight(18,16)\TileRemoveRFCrev{2}(11,15)\Weight(4,10)\TileRemoveRFC{4}(0,0)[] ************************************************** 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) ************************************************** Except [ 'A' , 's' , 'y' , 'n' , 'c' , 'C' , 'a' , 'n' , 'c' , 'e' , 'l' , 'l' , 'e' , 'd' ] : Matchbound { method = RFC , max_size = Just 100000 , max_bound = Nothing , verbose = False , tracing = False} total number 2 max duration 1.675763031000 min duration 1.675761490000 total durat. 3.351524521000 Info { what = Matchbound { method = RFC , max_size = Just 100000 , max_bound = Nothing , verbose = False , tracing = False} , input_size = Size { num_rules = 2 , num_strict_rules = 2 , num_top_rules = 0 , num_weak_rules = 0 , alphabet_size = 2 , total_length = 12} , self = 100 , parent = Just 9 , duration = 1.675761490000 , status = Except [ 'A' , 's' , 'y' , 'n' , 'c' , 'C' , 'a' , 'n' , 'c' , 'e' , 'l' , 'l' , 'e' , 'd' ] , start = 2021-07-13 11:51:02.270533135 UTC , finish = 2021-07-13 11:51:03.946294625 UTC , thread_cap_info = ( [ 'T' , 'h' , 'r' , 'e' , 'a' , 'd' , 'I' , 'd' , ' ' , '4' , '9' ] , 2 , True )} Info { what = Matchbound { method = RFC , max_size = Just 100000 , max_bound = Nothing , verbose = False , tracing = False} , input_size = Size { num_rules = 2 , num_strict_rules = 2 , num_top_rules = 0 , num_weak_rules = 0 , alphabet_size = 2 , total_length = 12} , self = 99 , parent = Just 0 , duration = 1.675763031000 , status = Except [ 'A' , 's' , 'y' , 'n' , 'c' , 'C' , 'a' , 'n' , 'c' , 'e' , 'l' , 'l' , 'e' , 'd' ] , start = 2021-07-13 11:51:02.270495285 UTC , finish = 2021-07-13 11:51:03.946258316 UTC , thread_cap_info = ( [ 'T' , 'h' , 'r' , 'e' , 'a' , 'd' , 'I' , 'd' , ' ' , '4' , '6' ] , 2 , True )} Fail : Matrix { monotone = Weak , domain = Arctic , shape = Full , bits = 16 , encoding = Ersatz_Binary , dim = 2 , solver = Minisatapi , verbose = True , tracing = False} total number 1 max duration 1.213896096000 min duration 1.213896096000 total durat. 1.213896096000 Info { what = Matrix { monotone = Weak , domain = Arctic , shape = Full , bits = 16 , encoding = Ersatz_Binary , dim = 2 , solver = Minisatapi , verbose = True , tracing = False} , input_size = Size { num_rules = 3 , num_strict_rules = 1 , num_top_rules = 1 , num_weak_rules = 2 , alphabet_size = 3 , total_length = 18} , self = 77 , parent = Just 11 , duration = 1.213896096000 , status = Fail , start = 2021-07-13 11:51:02.271419061 UTC , finish = 2021-07-13 11:51:03.485315157 UTC , thread_cap_info = ( [ 'T' , 'h' , 'r' , 'e' , 'a' , 'd' , 'I' , 'd' , ' ' , '7' , '5' ] , 0 , True )} Fail : QPI { dim = 4, bits = 3, solver = Minisatapi, tracing = False, verbose = False} total number 1 max duration 1.188512718000 min duration 1.188512718000 total durat. 1.188512718000 Info { what = QPI { dim = 4 , bits = 3 , solver = Minisatapi , tracing = False , verbose = False} , input_size = Size { num_rules = 3 , num_strict_rules = 1 , num_top_rules = 1 , num_weak_rules = 2 , alphabet_size = 3 , total_length = 18} , self = 88 , parent = Just 11 , duration = 1.188512718000 , status = Fail , start = 2021-07-13 11:51:02.530363109 UTC , finish = 2021-07-13 11:51:03.718875827 UTC , thread_cap_info = ( [ 'T' , 'h' , 'r' , 'e' , 'a' , 'd' , 'I' , 'd' , ' ' , '2' , '0' , '5' ] , 0 , True )} Success : Tiling { method = Backward , width = 2 , state_type = Best , 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} total number 5 max duration 0.375619483000 min duration 0.037423309000 total durat. 1.201893414000 Success : Tiling { method = Backward , width = 4 , state_type = Best , 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} total number 1 max duration 1.294606517000 min duration 1.294606517000 total durat. 1.294606517000 Info { what = Tiling { method = Backward , width = 4 , state_type = Best , 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} , input_size = Size { num_rules = 2 , num_strict_rules = 2 , num_top_rules = 0 , num_weak_rules = 0 , alphabet_size = 2 , total_length = 12} , self = 82 , parent = Just 0 , duration = 1.294606517000 , status = Success , start = 2021-07-13 11:51:02.274798755 UTC , finish = 2021-07-13 11:51:03.569405272 UTC , thread_cap_info = ( [ 'T' , 'h' , 'r' , 'e' , 'a' , 'd' , 'I' , 'd' , ' ' , '1' , '3' , '9' ] , 3 , True )} Success : Tiling { method = Overlap , width = 2 , state_type = Best , 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} total number 3 max duration 1.186956883000 min duration 0.086444704000 total durat. 1.370843204000 Info { what = Tiling { method = Overlap , width = 2 , state_type = Best , 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} , input_size = Size { num_rules = 21 , num_strict_rules = 3 , num_top_rules = 3 , num_weak_rules = 18 , alphabet_size = 9 , total_length = 168} , self = 86 , parent = Just 41 , duration = 1.186956883000 , status = Success , start = 2021-07-13 11:51:02.438682807 UTC , finish = 2021-07-13 11:51:03.62563969 UTC , thread_cap_info = ( [ 'T' , 'h' , 'r' , 'e' , 'a' , 'd' , 'I' , 'd' , ' ' , '1' , '9' , '1' ] , 3 , True )} **************************************************