/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- NO After renaming modulo { b->0, c->1, a->2 }, it remains to prove termination of the 1-rule system { 0 1 1 2 2 2 2 2 2 -> 2 2 2 2 2 2 2 0 1 1 0 1 1 } Loop of length 64 starting with a string of length 45 using right expansion and the encoding { 0->a, 1->b, ... }: .abbcccccc.cccccccccccccccccccccccccccccccccccc rule abbcccccc-> cccccccabbabb at position 0 .cccccccabbabb.cccccccccccccccccccccccccccccccccccc rule abbcccccc-> cccccccabbabb at position 10 .cccccccabbcccccccabbabb.cccccccccccccccccccccccccccccc rule abbcccccc-> cccccccabbabb at position 20 .cccccccabbcccccccabbcccccccabbabb.cccccccccccccccccccccccc rule abbcccccc-> cccccccabbabb at position 17 .cccccccabbccccccccccccccabbabbcabbabb.cccccccccccccccccccccccc rule abbcccccc-> cccccccabbabb at position 34 .cccccccabbccccccccccccccabbabbcabbcccccccabbabb.cccccccccccccccccc rule abbcccccc-> cccccccabbabb at position 31 .cccccccabbccccccccccccccabbabbccccccccabbabbcabbabb.cccccccccccccccccc rule abbcccccc-> cccccccabbabb at position 27 .cccccccabbccccccccccccccabbcccccccabbabbccabbabbcabbabb.cccccccccccccccccc rule abbcccccc-> cccccccabbabb at position 24 .cccccccabbcccccccccccccccccccccabbabbcabbabbccabbabbcabbabb.cccccccccccccccccc rule abbcccccc-> cccccccabbabb at position 56 .cccccccabbcccccccccccccccccccccabbabbcabbabbccabbabbcabbcccccccabbabb.cccccccccccc rule abbcccccc-> cccccccabbabb at position 53 .cccccccabbcccccccccccccccccccccabbabbcabbabbccabbabbccccccccabbabbcabbabb.cccccccccccc rule abbcccccc-> cccccccabbabb at position 49 .cccccccabbcccccccccccccccccccccabbabbcabbabbccabbcccccccabbabbccabbabbcabbabb.cccccccccccc rule abbcccccc-> cccccccabbabb at position 46 .cccccccabbcccccccccccccccccccccabbabbcabbabbcccccccccabbabbcabbabbccabbabbcabbabb.cccccccccccc rule abbcccccc-> cccccccabbabb at position 41 .cccccccabbcccccccccccccccccccccabbabbcabbcccccccabbabbcccabbabbcabbabbccabbabbcabbabb.cccccccccccc rule abbcccccc-> cccccccabbabb at position 38 .cccccccabbcccccccccccccccccccccabbabbccccccccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb.cccccccccccc rule abbcccccc-> cccccccabbabb at position 34 .cccccccabbcccccccccccccccccccccabbcccccccabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb.cccccccccccc rule abbcccccc-> cccccccabbabb at position 31 .cccccccabbccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb.cccccccccccc rule abbcccccc-> cccccccabbabb at position 94 .cccccccabbccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbcccccccabbabb.cccccc rule abbcccccc-> cccccccabbabb at position 91 .cccccccabbccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbccccccccabbabbcabbabb.cccccc rule abbcccccc-> cccccccabbabb at position 87 .cccccccabbccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbcccccccabbabbccabbabbcabbabb.cccccc rule abbcccccc-> cccccccabbabb at position 84 .cccccccabbccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbcccccccccabbabbcabbabbccabbabbcabbabb.cccccc rule abbcccccc-> cccccccabbabb at position 79 .cccccccabbccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbcccccccabbabbcccabbabbcabbabbccabbabbcabbabb.cccccc rule abbcccccc-> cccccccabbabb at position 76 .cccccccabbccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbccccccccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb.cccccc rule abbcccccc-> cccccccabbabb at position 72 .cccccccabbccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbcccccccabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb.cccccc rule abbcccccc-> cccccccabbabb at position 69 .cccccccabbccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb.cccccc rule abbcccccc-> cccccccabbabb at position 63 .cccccccabbccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbcccccccabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb.cccccc rule abbcccccc-> cccccccabbabb at position 60 .cccccccabbccccccccccccccccccccccccccccabbabbcabbabbccabbabbccccccccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb.cccccc rule abbcccccc-> cccccccabbabb at position 56 .cccccccabbccccccccccccccccccccccccccccabbabbcabbabbccabbcccccccabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb.cccccc rule abbcccccc-> cccccccabbabb at position 53 .cccccccabbccccccccccccccccccccccccccccabbabbcabbabbcccccccccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb.cccccc rule abbcccccc-> cccccccabbabb at position 48 .cccccccabbccccccccccccccccccccccccccccabbabbcabbcccccccabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb.cccccc rule abbcccccc-> cccccccabbabb at position 45 .cccccccabbccccccccccccccccccccccccccccabbabbccccccccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb.cccccc rule abbcccccc-> cccccccabbabb at position 41 .cccccccabbccccccccccccccccccccccccccccabbcccccccabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb.cccccc rule abbcccccc-> cccccccabbabb at position 38 .cccccccabbcccccccccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb.cccccc rule abbcccccc-> cccccccabbabb at position 164 .cccccccabbcccccccccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbcccccccabbabb. rule abbcccccc-> cccccccabbabb at position 161 .cccccccabbcccccccccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbccccccccabbabbcabbabb. rule abbcccccc-> cccccccabbabb at position 157 .cccccccabbcccccccccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbcccccccabbabbccabbabbcabbabb. rule abbcccccc-> cccccccabbabb at position 154 .cccccccabbcccccccccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbcccccccccabbabbcabbabbccabbabbcabbabb. rule abbcccccc-> cccccccabbabb at position 149 .cccccccabbcccccccccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbcccccccabbabbcccabbabbcabbabbccabbabbcabbabb. rule abbcccccc-> cccccccabbabb at position 146 .cccccccabbcccccccccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbccccccccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb. rule abbcccccc-> cccccccabbabb at position 142 .cccccccabbcccccccccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbcccccccabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb. rule abbcccccc-> cccccccabbabb at position 139 .cccccccabbcccccccccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb. rule abbcccccc-> cccccccabbabb at position 133 .cccccccabbcccccccccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbcccccccabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb. rule abbcccccc-> cccccccabbabb at position 130 .cccccccabbcccccccccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbccccccccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb. rule abbcccccc-> cccccccabbabb at position 126 .cccccccabbcccccccccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbcccccccabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb. rule abbcccccc-> cccccccabbabb at position 123 .cccccccabbcccccccccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbcccccccccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb. rule abbcccccc-> cccccccabbabb at position 118 .cccccccabbcccccccccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbcccccccabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb. rule abbcccccc-> cccccccabbabb at position 115 .cccccccabbcccccccccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbccccccccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb. rule abbcccccc-> cccccccabbabb at position 111 .cccccccabbcccccccccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbcccccccabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb. rule abbcccccc-> cccccccabbabb at position 108 .cccccccabbcccccccccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbcccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb. rule abbcccccc-> cccccccabbabb at position 101 .cccccccabbcccccccccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbcccccccabbabbcccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb. rule abbcccccc-> cccccccabbabb at position 98 .cccccccabbcccccccccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbccccccccabbabbcabbabbcccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb. rule abbcccccc-> cccccccabbabb at position 94 .cccccccabbcccccccccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbcccccccabbabbccabbabbcabbabbcccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb. rule abbcccccc-> cccccccabbabb at position 91 .cccccccabbcccccccccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbcccccccccabbabbcabbabbccabbabbcabbabbcccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb. rule abbcccccc-> cccccccabbabb at position 86 .cccccccabbcccccccccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbcccccccabbabbcccabbabbcabbabbccabbabbcabbabbcccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb. rule abbcccccc-> cccccccabbabb at position 83 .cccccccabbcccccccccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbccccccccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbcccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb. rule abbcccccc-> cccccccabbabb at position 79 .cccccccabbcccccccccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbcccccccabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbcccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb. rule abbcccccc-> cccccccabbabb at position 76 .cccccccabbcccccccccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbcccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb. rule abbcccccc-> cccccccabbabb at position 70 .cccccccabbcccccccccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbcccccccabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbcccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb. rule abbcccccc-> cccccccabbabb at position 67 .cccccccabbcccccccccccccccccccccccccccccccccccabbabbcabbabbccabbabbccccccccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbcccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb. rule abbcccccc-> cccccccabbabb at position 63 .cccccccabbcccccccccccccccccccccccccccccccccccabbabbcabbabbccabbcccccccabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbcccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb. rule abbcccccc-> cccccccabbabb at position 60 .cccccccabbcccccccccccccccccccccccccccccccccccabbabbcabbabbcccccccccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbcccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb. rule abbcccccc-> cccccccabbabb at position 55 .cccccccabbcccccccccccccccccccccccccccccccccccabbabbcabbcccccccabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbcccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb. rule abbcccccc-> cccccccabbabb at position 52 .cccccccabbcccccccccccccccccccccccccccccccccccabbabbccccccccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbcccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb. rule abbcccccc-> cccccccabbabb at position 48 .cccccccabbcccccccccccccccccccccccccccccccccccabbcccccccabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbcccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb. rule abbcccccc-> cccccccabbabb at position 45 .cccccccabbccccccccccccccccccccccccccccccccccccccccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbcccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabbccccabbabbcabbabbccabbabbcabbabbcccabbabbcabbabbccabbabbcabbabb.